{"id":1753,"date":"2020-04-30T17:54:37","date_gmt":"2020-04-30T21:54:37","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/chapter\/strengths-of-ionic-and-covalent-bonds\/"},"modified":"2021-07-13T22:08:26","modified_gmt":"2021-07-14T02:08:26","slug":"strengths-of-ionic-and-covalent-bonds","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/chapter\/strengths-of-ionic-and-covalent-bonds\/","title":{"raw":"2.5 Strengths of Ionic and Covalent Bonds","rendered":"2.5 Strengths of Ionic and Covalent Bonds"},"content":{"raw":"[latexpage]\r\n<div>\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Describe the energetics of covalent and ionic bond formation and breakage<\/li>\r\n \t<li>Use the Born-Haber cycle to compute lattice energies for ionic compounds<\/li>\r\n \t<li>Use average covalent bond energies to estimate enthalpies of reaction<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-idp176876736\">A bond\u2019s strength describes how strongly each atom is joined to another atom, and therefore how much energy is required to break the bond between the two atoms. In this section, you will learn about the bond strength of covalent bonds, and then compare that to the strength of ionic bonds, which is related to the lattice energy of a compound.<\/p>\r\n\r\n<div id=\"fs-idp66065152\" class=\"bc-section section\" data-depth=\"1\">\r\n<h2 data-type=\"title\">Bond Strength: Covalent Bonds<\/h2>\r\n<p id=\"fs-idm12470240\">Stable molecules exist because covalent bonds hold the atoms together. We measure the strength of a covalent bond by the energy required to break it, that is, the energy necessary to separate the bonded atoms. Separating any pair of bonded atoms requires energy (see <a class=\"autogenerated-content\" href=\"#2.5.1\">(Figure 2.5.1)<\/a>). The stronger a bond, the greater the energy required to break it.<\/p>\r\n<p id=\"fs-idp84340368\">The energy required to break a specific covalent bond in one mole of gaseous molecules is called the bond energy or the bond dissociation energy. The bond energy for a diatomic molecule, D<sub>X\u2013Y<\/sub>, is defined as the standard enthalpy change for the endothermic reaction:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idm36464112\" data-type=\"equation\">\\(\\text{XY}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}\\text{X}\\left(g\\right)+\\text{Y}\\left(g\\right)\\phantom{\\rule{3em}{0ex}}{\\text{D}}_{\\text{X\u2212Y}}=\\text{$\\Delta$}H\\text{\u00b0}\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm12974112\">For example, the bond energy of the pure covalent H\u2013H bond, D<sub>H\u2013H<\/sub>, is 436 kJ per mole of H\u2013H bonds broken:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp119487888\" data-type=\"equation\">\\({\\text{H}}_{\\text{2}}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}2\\text{H}\\left(g\\right)\\phantom{\\rule{3em}{0ex}}{\\text{D}}_{\\text{H\u2212H}}=\\text{$\\Delta$}H\\text{\u00b0}=436\\phantom{\\rule{0.2em}{0ex}}\\text{kJ}\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp244347920\">Molecules with three or more atoms have two or more bonds. The sum of all bond energies in such a molecule is equal to the standard enthalpy change for the endothermic reaction that breaks all the bonds in the molecule.<\/p>\r\n&nbsp;\r\n<div id=\"2.5.1\" class=\"scaled-down\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"975\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_CH4bond_img-1.jpg\" alt=\"A reaction is shown with Lewis structures. The first structure shows a carbon atom single bonded to four hydrogen atoms with the symbol, \u201c( g )\u201d written next to it. A right-facing arrow points to the letter \u201cC\u201d and the symbol \u201c( g ),\u201d which is followed by a plus sign. Next is the number 4, the letter \u201cH\u201d and the symbol, \u201c( g ).\u201d To the right of this equation is another equation: capital delta H superscript degree symbol equals 1660 k J.\" width=\"975\" height=\"144\" data-media-type=\"image\/jpeg\" \/> <strong>Figure 2.5.1 - The sum of the four C\u2013H bond energies in CH4, 1660 kJ, is equal to the standard enthalpy change of the reaction<\/strong>[\/caption]\r\n<p id=\"fs-idp85707472\">The average C\u2013H bond energy, D<sub>C\u2013H<\/sub>, is 1660\/4 = 415 kJ\/mol because there are four moles of C\u2013H bonds broken per mole of the reaction. Although the four C\u2013H bonds are equivalent in the original molecule, they do not each require the same energy to break; once the first bond is broken (which requires 439 kJ\/mol), the remaining bonds are easier to break. The 415 kJ\/mol value is the average, not the exact value required to break any one bond.<\/p>\r\n<p id=\"fs-idp26225392\">The strength of a bond between two atoms increases as the number of electron pairs in the bond increases. Generally, as the bond strength increases, the bond length decreases. Thus, we find that triple bonds are stronger and shorter than double bonds between the same two atoms; likewise, double bonds are stronger and shorter than single bonds between the same two atoms. Average bond energies for some common bonds appear in <a class=\"autogenerated-content\" href=\"#fs-idp13638832\">(Table 2.5.1)<\/a>, and a comparison of bond lengths and bond strengths for some common bonds appears in <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>. When one atom bonds to various atoms in a group, the bond strength typically decreases as we move down the group. For example, C\u2013F is 439 kJ\/mol, C\u2013Cl is 330 kJ\/mol, and C\u2013Br is 275 kJ\/mol.<\/p>\r\n\r\n<table id=\"fs-idp13638832\" class=\"aligncenter\" style=\"height: 375px\" summary=\"This table has six columns and twenty-four rows. The first row is a header row that labels the columns: \u201cBond,\u201d \u201cBond Energy,\u201d \u201cBond,\u201d \u201cBond Energy,\u201d \u201cBond,\u201d and, \u201cBond Energy.\u201d Under the first \u201cBond\u201d column are the values: H bond to H with a single bond; H bonds to C with a single bond; H bonds to N with a single bond; H bonds to O with a single bond; H bonds to F with a single bond; H bonds to S i with a single bond; H bonds to P with a single bond; H bonds to S with a single bond; H bonds to C l with a single bond; H bonds to B r with a single bond; H bonds to I with a single bond; C bonds to C with a single bond; C bonds to C with a double bond; C bonds to C with a triple bond; C bonds to N with a single bond; C bonds to N with a double bond; C bonds to N with a triple bond; C bonds to O with a single bond; C bonds to O with a double bond; C bonds to O with a triple bond; C bonds to F with a single bond; C bonds to S i with a single bond; and C bonds to P with a single bond. Under the first \u201cBond Energy\u201d column are the values: 436; 415; 390; 464; 569; 395; 320; 340; 432; 370; 295; 345; 611; 837; 290; 615; 891; 350; 741; 1080; 439; 360; and 265. Under the second \u201cBond\u201d column are the values: C bonds to S with a single bond; C bonds to C l with a single bond; C bonds to B r with a single bond; C bonds to I with a single bond; N bonds to N with a single bond; N bonds to N with a double bond; N bonds to N with a triple bond; N bonds to O with a single bond; N bonds to F with a single bond; N bonds to P with a single bond; N bonds to C l with a single bond; N bonds to B r with a single bond; O bonds to O with a single bond; O bonds to O with a double bond; O bonds to F with a single bond; O bonds to S i with a single bond; O bonds to P with a single bond; O bonds to C l with a single bond; O bonds to I with a single bond; F bonds to F with a single bond; F bonds to S i with a single bond; F bonds to P with a single bond; and F bonds to S with a single bond. Under the second \u201cBond Energy\u201d column are the values: 260; 330; 275; 240; 160; 418; 946; 200; 270; 210; 200; 245; 140; 498; 160; 370; 350; 205; 200; 160; 540; 489; and 285. Under the third \u201cBond\u201d column are the values: F bonds to C l with a single bond; F bonds to B r with a single bond; S i bonds to S i with a single bond; S i bonds to P with a single bond; S i bonds to S with a single bond; S i bonds to C l with a single bond; S i bonds to B r with a single bond; S i bonds to I with a single bond; P bonds to P with a single bond; P bonds to S with a single bond; P bonds to C l with a single bond; P bonds to B r with a single bond; P bonds to I with a single bond; S bonds to S with a single bond; S bonds to C l with a single bond; S bonds to B r with a single bond; C l bonds to C l with a single bond; C l bonds to B r with a single bond; C l bonds to I with a single bond; B r bonds to B r with a single bond; B r bonds to I with a single bond; I bonds to I with a single bond; and the last cell in the column is empty. Under the third \u201cBond Energy\u201d column are the values: 255; 235; 230; 215; 225; 359; 290; 215; 215; 230; 330; 270; 215; 215; 250; 215; 243; 220; 210; 190; 180; 150; and the last cell in the column is empty.\"><caption><strong>Table 2.5.1 - <\/strong>Bond Energies (kJ\/mol)<\/caption>\r\n<thead>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<th style=\"height: 15px;width: 187.95px\" data-align=\"left\">Bond<\/th>\r\n<th style=\"height: 15px;width: 88.2333px\" data-align=\"left\">Bond Energy<\/th>\r\n<th style=\"height: 15px;width: 0.0166667px\" data-align=\"left\"><\/th>\r\n<th style=\"height: 15px;width: 189.15px\" data-align=\"left\">Bond<\/th>\r\n<th style=\"height: 15px;width: 88.2333px\" data-align=\"left\">Bond Energy<\/th>\r\n<th style=\"height: 15px;width: 0.0166667px\" data-align=\"left\"><\/th>\r\n<th style=\"height: 15px;width: 37.1667px\" data-align=\"left\">Bond<\/th>\r\n<th style=\"height: 15px;width: 88.2333px\" data-align=\"left\">Bond Energy<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013H<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">436<\/td>\r\n<td style=\"height: 345px;width: 1.13333px\" rowspan=\"23\" data-align=\"left\"><\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">C\u2013S<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">260<\/td>\r\n<td style=\"height: 345px;width: 1.13333px\" rowspan=\"23\" data-align=\"left\"><\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">F\u2013Cl<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">255<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013C<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">415<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">C\u2013Cl<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">330<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">F\u2013Br<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">235<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013N<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">390<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">C\u2013Br<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">275<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013Si<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">230<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013O<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">464<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">C\u2013I<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">240<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013P<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013F<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">569<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013N<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">160<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013S<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">225<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013Si<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">395<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">\\(\\text{N}=\\text{N}\\)<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">418<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013Cl<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">359<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013P<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">320<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">\\(\\text{N}\\equiv \\text{N}\\)<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">946<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013Br<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">290<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013S<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">340<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013O<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">200<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013I<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013Cl<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">432<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013F<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">270<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013P<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013Br<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">370<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013P<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">210<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013S<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">230<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013I<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">295<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013Cl<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">200<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013Cl<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">330<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013C<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">345<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013Br<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">245<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013Br<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">270<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">\\(\\text{C}=\\text{C}\\)<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">611<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013O<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">140<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013I<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\">\\(\\text{C}\\equiv \\text{C}\\)<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">837<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">\\(\\text{O}=\\text{O}\\)<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">498<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">S\u2013S<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013N<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">290<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013F<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">160<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">S\u2013Cl<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">250<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">\\(\\text{C}=\\text{N}\\)<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">615<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013Si<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">370<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">S\u2013Br<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">\\(\\text{C}\\equiv \\text{N}\\)<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">891<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013P<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">350<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Cl\u2013Cl<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">243<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013O<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">350<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013Cl<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">205<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Cl\u2013Br<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">220<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">\\(\\text{C}=\\text{O}\\)<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">741<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013I<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">200<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Cl\u2013I<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">210<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">\\(\\text{C}\\equiv \\text{O}\\)<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">1080<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">F\u2013F<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">160<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Br\u2013Br<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">190<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013F<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">439<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">F\u2013Si<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">540<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Br\u2013I<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">180<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013Si<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">360<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">F\u2013P<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">489<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">I\u2013I<\/td>\r\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">150<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013P<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">265<\/td>\r\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">F\u2013S<\/td>\r\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">285<\/td>\r\n<td style=\"height: 15px;width: 38.2833px\"><\/td>\r\n<td style=\"height: 15px;width: 88.2333px\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"fs-idm44464336\" class=\"aligncenter\" summary=\"This table has three columns and ten rows. The first row is a header row that labels the columns: \u201cBond,\u201d \u201cBond Length in angstroms,\u201d and, \u201cBond Energy in k J \/ mol.\u201d Under the column \u201cBond\u201d are the values: C bonds to C with a single bond; C bonds to C with a double bond; C bonds to C with a triple bond; C bonds to N with a single bond; C bonds to N with a double bond; C bonds to N with a triple bond; C bonds to O with a single bond; C bonds to O with a double bond; and C bonds to O with a triple bond. Under the column \u201cBond Length in angstroms\u201d are the values: 1.54; 1.34; 1.20; 1.43; 1.38; 1.16; 1.43; 1.23; and 1.13. Under the column \u201cBond Energy in k J \/ mol\u201d are the values: 345; 611; 837; 290; 615; 891; 350; 741; and 1080.\"><caption><strong>Table 2.5.2 - <\/strong>Average Bond Lengths and Bond Energies for Some Common Bonds<\/caption>\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"left\">Bond<\/th>\r\n<th data-align=\"left\">Bond Length (\u00c5)<\/th>\r\n<th data-align=\"left\">Bond Energy (kJ\/mol)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">C\u2013C<\/td>\r\n<td data-align=\"left\">1.54<\/td>\r\n<td data-align=\"left\">345<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(\\text{C}=\\text{C}\\)<\/td>\r\n<td data-align=\"left\">1.34<\/td>\r\n<td data-align=\"left\">611<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(\\text{C}\\equiv \\text{C}\\)<\/td>\r\n<td data-align=\"left\">1.20<\/td>\r\n<td data-align=\"left\">837<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">C\u2013N<\/td>\r\n<td data-align=\"left\">1.43<\/td>\r\n<td data-align=\"left\">290<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(\\text{C}=\\text{N}\\)<\/td>\r\n<td data-align=\"left\">1.38<\/td>\r\n<td data-align=\"left\">615<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(\\text{C}\\equiv \\text{N}\\)<\/td>\r\n<td data-align=\"left\">1.16<\/td>\r\n<td data-align=\"left\">891<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">C\u2013O<\/td>\r\n<td data-align=\"left\">1.43<\/td>\r\n<td data-align=\"left\">350<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(\\text{C}=\\text{O}\\)<\/td>\r\n<td data-align=\"left\">1.23<\/td>\r\n<td data-align=\"left\">741<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(\\text{C}\\equiv \\text{O}\\)<\/td>\r\n<td data-align=\"left\">1.13<\/td>\r\n<td data-align=\"left\">1080<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<p id=\"fs-idp29959728\">We can use bond energies to calculate approximate enthalpy changes for reactions where enthalpies of formation are not available. Calculations of this type will also tell us whether a reaction is exothermic or endothermic. An exothermic reaction ($\\Delta$<em data-effect=\"italics\">H<\/em> negative, heat produced) results when the bonds in the products are stronger than the bonds in the reactants. An endothermic reaction ($\\Delta$<em data-effect=\"italics\">H<\/em> positive, heat absorbed) results when the bonds in the products are weaker than those in the reactants.<\/p>\r\n<p id=\"fs-idp234028832\">The enthalpy change, $\\Delta$<em data-effect=\"italics\">H<\/em>, for a chemical reaction is approximately equal to the sum of the energy required to break all bonds in the reactants (energy \u201cin\u201d, positive sign) plus the energy released when all bonds are formed in the products (energy \u201cout,\u201d negative sign). This can be expressed mathematically in the following way:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idm40243760\" data-type=\"equation\">\\(\\text{$\\Delta$}H={\\text{\u01a9D}}_{\\text{bonds broken}}-{\\text{\u01a9D}}_{\\text{bonds formed}}\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp118053616\">In this expression, the symbol \u01a9 means \u201cthe sum of\u201d and D represents the bond energy in kilojoules per mole, which is always a positive number. The bond energy is obtained from a table (like <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>) and will depend on whether the particular bond is a single, double, or triple bond. Thus, in calculating enthalpies in this manner, it is important that we consider the bonding in all reactants and products. Because D values are typically averages for one type of bond in many different molecules, this calculation provides a rough estimate, not an exact value, for the enthalpy of reaction.<\/p>\r\n<p id=\"fs-idp17129504\">Consider the following reaction:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp51383312\" data-type=\"equation\">\\({\\text{H}}_{2}\\left(g\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}2\\text{HCl}\\left(g\\right)\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp77710320\">or<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp56299152\" data-type=\"equation\">\\(\\text{H\u2013H}\\left(g\\right)+\\text{Cl\u2013Cl}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}2\\text{H\u2013Cl}\\left(g\\right)\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp201091440\">To form two moles of HCl, one mole of H\u2013H bonds and one mole of Cl\u2013Cl bonds must be broken. The energy required to break these bonds is the sum of the bond energy of the H\u2013H bond (436 kJ\/mol) and the Cl\u2013Cl bond (243 kJ\/mol). During the reaction, two moles of H\u2013Cl bonds are formed (bond energy = 432 kJ\/mol), releasing 2 \\(\u00d7\\) 432 kJ; or 864 kJ. Because the bonds in the products are stronger than those in the reactants, the reaction releases more energy than it consumes:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp14860448\" data-type=\"equation\">\\(\\begin{array}{lll}\\hfill \\text{$\\Delta$}H&amp; =&amp; {\\text{\u01a9D}}_{\\text{bonds broken}}-{\\text{\u01a9D}}_{\\text{bonds formed}}\\hfill \\\\ \\hfill \\text{$\\Delta$}H&amp; =&amp; \\left[{\\text{D}}_{\\text{H\u2212H}}+{\\text{D}}_{\\text{Cl\u2212Cl}}\\right]\\phantom{\\rule{0.2em}{0ex}}-\\phantom{\\rule{0.2em}{0ex}}2{\\text{D}}_{\\text{H\u2212Cl}}\\hfill \\\\ &amp; =&amp; \\left[436+243\\right]-2\\left(432\\right)=-185\\phantom{\\rule{0.2em}{0ex}}\\text{kJ}\\hfill \\end{array}\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp29639024\">This excess energy is released as heat, so the reaction is exothermic. <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a> gives a value for the standard molar enthalpy of formation of HCl(g), \\(\\text{$\\Delta$}{H}_{\\text{f}}^{\u00b0},\\) of \u201392.307 kJ\/mol. Twice that value is \u2013184.6 kJ, which agrees well with the answer obtained earlier for the formation of two moles of HCl.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Activity 2.5.1 - Using Bond Energies to Calculate Approximate Enthalpy<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<span data-type=\"title\">Changes<\/span> Methanol, CH<sub>3<\/sub>OH, may be an excellent alternative fuel. The high-temperature reaction of steam and carbon produces a mixture of the gases carbon monoxide, CO, and hydrogen, H<sub>2<\/sub>, from which methanol can be produced. Using the bond energies in <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>, calculate the approximate enthalpy change, $\\Delta$<em data-effect=\"italics\">H<\/em>, for the reaction here:\r\n\r\n&nbsp;\r\n<div id=\"fs-idp93467344\" data-type=\"equation\">\\(\\text{CO}\\left(g\\right)+2{\\text{H}}_{\\text{2}}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}{\\text{CH}}_{3}\\text{OH}\\left(g\\right)\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<h2 id=\"fs-idp41458304\">Solution<\/h2>\r\nFirst, we need to write the Lewis structures of the reactants and the products:\r\n\r\n<span id=\"fs-idp525280\" class=\"scaled-down\" data-type=\"media\" data-alt=\"A set of Lewis diagrams show a chemical reaction. The first structure shows a carbon atom with a lone pair of electrons triple bonded to an oxygen with a lone pair of electrons. To the right of this structure is a plus sign, then the number 2 followed by a hydrogen atom single bonded to a hydrogen atom. To the right of this structure is a right-facing arrow followed by a hydrogen atom single bonded to a carbon atom that is single bonded to two hydrogen atoms and an oxygen atom with two lone pairs of electrons. The oxygen atom is also single bonded to a hydrogen atom.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_CH3OHLew_img-1-1.jpg\" alt=\"A set of Lewis diagrams show a chemical reaction. The first structure shows a carbon atom with a lone pair of electrons triple bonded to an oxygen with a lone pair of electrons. To the right of this structure is a plus sign, then the number 2 followed by a hydrogen atom single bonded to a hydrogen atom. To the right of this structure is a right-facing arrow followed by a hydrogen atom single bonded to a carbon atom that is single bonded to two hydrogen atoms and an oxygen atom with two lone pairs of electrons. The oxygen atom is also single bonded to a hydrogen atom.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-idp202067232\">From this, we see that \u0394<em data-effect=\"italics\">H<\/em> for this reaction involves the energy required to break a C\u2013O triple bond and two H\u2013H single bonds, as well as the energy produced by the formation of three C\u2013H single bonds, a C\u2013O single bond, and an O\u2013H single bond. We can express this as follows:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp76020096\" data-type=\"equation\">\\(\\begin{array}{lll}\\hfill \\text{$\\Delta$}H&amp; =&amp; {\\text{\u01a9D}}_{\\text{bonds broken}}-{\\text{\u01a9D}}_{\\text{bonds formed}}\\hfill \\\\ \\hfill \\text{$\\Delta$}H&amp; =&amp; \\left[{\\text{D}}_{\\text{C}\\equiv \\text{O}}+2\\left({\\text{D}}_{\\text{H\u2212H}}\\right)\\right]\\phantom{\\rule{0.2em}{0ex}}-\\left[3\\left({\\text{D}}_{\\text{C\u2212H}}\\right)+{\\text{D}}_{\\text{C\u2212O}}+{\\text{D}}_{\\text{O\u2212H}}\\right]\\hfill \\end{array}\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n&nbsp;\r\n<p id=\"fs-idp53734416\">Using the bond energy values in <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>, we obtain:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idm103164880\" data-type=\"equation\">\\(\\begin{array}{ll}\\hfill \\text{$\\Delta$}H&amp; =\\left[1080+2\\left(436\\right)\\right]\\phantom{\\rule{0.2em}{0ex}}-\\phantom{\\rule{0.2em}{0ex}}\\left[3\\left(415\\right)+350+464\\right]\\\\ &amp; =-107\\phantom{\\rule{0.2em}{0ex}}\\text{kJ}\\end{array}\\)<\/div>\r\n<div data-type=\"equation\"><em>\u00a0<\/em><\/div>\r\n&nbsp;\r\n<p id=\"fs-idp126256512\">We can compare this value to the value calculated based on \\(\\text{$\\Delta$}{H}_{\\text{f}}^{\u00b0}\\) data from Appendix G:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp158903840\" data-type=\"equation\">\\(\\begin{array}{ll}\\hfill \\text{$\\Delta$}H&amp; =\\left[\\text{$\\Delta$}{H}_{\\text{f}}^{$\\degree$}{\\left(\\text{CH}}_{3}\\text{OH}\\left(g\\right)\\right)\\right]\\phantom{\\rule{0.2em}{0ex}}-\\phantom{\\rule{0.2em}{0ex}}\\left[\\text{$\\Delta$}{H}_{\\text{f}}^{\u00b0}\\left(\\text{CO}\\left(g\\right)\\right)+2\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\text{$\\Delta$}{H}_{\\text{f}}^{\u00b0}{\\text{H}}_{2}\\right]\\\\ &amp; =\\left[-201.0\\right]\\phantom{\\rule{0.2em}{0ex}}-\\phantom{\\rule{0.2em}{0ex}}\\left[-110.52+2\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}0\\right]\\\\ &amp; =-90.5\\phantom{\\rule{0.2em}{0ex}}\\text{kJ}\\end{array}\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n&nbsp;\r\n<p id=\"fs-idp56832128\">Note that there is a fairly significant gap between the values calculated using the two different methods. This occurs because D values are the <em data-effect=\"italics\">average<\/em> of different bond strengths; therefore, they often give only rough agreement with other data.<\/p>\r\n\r\n\r\n<hr \/>\r\n\r\n<h2 id=\"fs-idp36454672\"><span data-type=\"title\">Check Your Learning<\/span><\/h2>\r\nEthyl alcohol, CH<sub>3<\/sub>CH<sub>2<\/sub>OH, was one of the first organic chemicals deliberately synthesized by humans. It has many uses in industry, and it is the alcohol contained in alcoholic beverages. It can be obtained by the fermentation of sugar or synthesized by the hydration of ethylene in the following reaction:\r\n\r\n<span id=\"fs-idp144672\" class=\"scaled-down\" data-type=\"media\" data-alt=\"A set of Lewis structures show a chemical reaction. The first structure shows two carbon atoms that are double bonded together and are each single bonded to two hydrogen atoms. This structure is followed by a plus sign, then an oxygen atom with two lone pairs of electrons single bonded to two hydrogen atoms. A right-facing arrow leads to a carbon atom single bonded to three hydrogen atoms and a second carbon atom. The second carbon atom is single bonded to two hydrogen atoms and an oxygen atom with two lone pairs of electrons. The oxygen atom is single bonded to a hydrogen atom as well.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_Ethanol_img-1-1.jpg\" alt=\"A set of Lewis structures show a chemical reaction. The first structure shows two carbon atoms that are double bonded together and are each single bonded to two hydrogen atoms. This structure is followed by a plus sign, then an oxygen atom with two lone pairs of electrons single bonded to two hydrogen atoms. A right-facing arrow leads to a carbon atom single bonded to three hydrogen atoms and a second carbon atom. The second carbon atom is single bonded to two hydrogen atoms and an oxygen atom with two lone pairs of electrons. The oxygen atom is single bonded to a hydrogen atom as well.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-idp27645248\">Using the bond energies in <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>, calculate an approximate enthalpy change, \u0394<em data-effect=\"italics\">H<\/em>, for this reaction.<\/p>\r\n\r\n<div id=\"fs-idp88406224\" data-type=\"note\">\r\n<h3 style=\"text-align: right\" data-type=\"title\">Answer<\/h3>\r\n<p id=\"fs-idp24314032\" style=\"text-align: right\">\u201335 kJ<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm34679504\" class=\"bc-section section\" data-depth=\"1\">\r\n<h2 data-type=\"title\">Ionic Bond Strength and Lattice Energy<\/h2>\r\n<p id=\"fs-idm57606496\">An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The <span data-type=\"term\">lattice energy (\u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub>)<\/span> of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid MX, the lattice energy is the enthalpy change of the process:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp69066736\" data-type=\"equation\">\\(\\text{MX}\\left(s\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}{\\text{M}}^{n\\text{+}}\\left(g\\right)+{\\text{X}}^{n-\\text{\u2212}}\\left(g\\right)\\phantom{\\rule{3em}{0ex}}\\text{$\\Delta$}{H}_{\\text{lattice}}\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm45000976\">Note that we are using the convention where the ionic solid is separated into ions, so our lattice energies will be <em data-effect=\"italics\">endothermic<\/em> (positive values). Some texts use the equivalent but opposite convention, defining lattice energy as the energy released when separate ions combine to form a lattice and giving negative (exothermic) values. Thus, if you are looking up lattice energies in another reference, be certain to check which definition is being used. In both cases, a larger magnitude for lattice energy indicates a more stable ionic compound. For sodium chloride, \u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub> = 769 kJ. Thus, it requires 769 kJ to separate one mole of solid NaCl into gaseous Na<sup>+<\/sup> and Cl<sup>\u2013<\/sup> ions. When one mole, each of gaseous Na<sup>+<\/sup> and Cl<sup>\u2013<\/sup> ions form solid NaCl, 769 kJ of heat is released.<\/p>\r\n<p id=\"fs-idp17453088\">The lattice energy \u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub> of an ionic crystal can be expressed by the following equation (derived from Coulomb\u2019s law, governing the forces between electric charges):<\/p>\r\n&nbsp;\r\n<div id=\"fs-idm6917696\" data-type=\"equation\">\\(\\text{$\\Delta$}{H}_{\\text{lattice}}=\\phantom{\\rule{0.2em}{0ex}}\\frac{\\text{C}\\left({\\text{Z}}^{\\text{+}}\\right)\\left({\\text{Z}}^{-\\text{\u2212}}\\right)}{{\\text{R}}_{\\text{o}}}\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp14812032\">in which C is a constant that depends on the type of crystal structure; Z<sup>+<\/sup> and Z<sup>\u2013<\/sup> are the charges on the ions; and R<sub>o<\/sub> is the interionic distance (the sum of the radii of the positive and negative ions). Thus, the lattice energy of an ionic crystal increases rapidly as the charges of the ions increase and the sizes of the ions decrease. When all other parameters are kept constant, doubling the charge of both the cation and anion quadruples the lattice energy. For example, the lattice energy of LiF (Z<sup>+<\/sup> and Z<sup>\u2013<\/sup> = 1) is 1023 kJ\/mol, whereas that of MgO (Z<sup>+<\/sup> and Z<sup>\u2013<\/sup> = 2) is 3900 kJ\/mol (R<sub>o<\/sub> is nearly the same\u2014about 200 pm for both compounds).<\/p>\r\n<p id=\"fs-idp119064064\">Different interatomic distances produce different lattice energies. For example, we can compare the lattice energy of MgF<sub>2<\/sub> (2957 kJ\/mol) to that of MgI<sub>2<\/sub> (2327 kJ\/mol) to observe the effect on lattice energy of the smaller ionic size of F<sup>\u2013<\/sup> as compared to I<sup>\u2013<\/sup>.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Activity 2.5.2 - Lattice Energy Comparisons<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nThe precious gem ruby is aluminum oxide, Al<sub>2<\/sub>O<sub>3<\/sub>, containing traces of Cr<sup>3+<\/sup>. The compound Al<sub>2<\/sub>Se<sub>3<\/sub> is used in the fabrication of some semiconductor devices. Which has the larger lattice energy, Al<sub>2<\/sub>O<sub>3<\/sub> or Al<sub>2<\/sub>Se<sub>3<\/sub>?\r\n<h2 id=\"fs-idm3251216\">Solution<\/h2>\r\nIn these two ionic compounds, the charges Z<sup>+<\/sup> and Z<sup>\u2013<\/sup> are the same, so the difference in lattice energy will depend upon R<sub>o<\/sub>. The O<sup>2\u2013<\/sup> ion is smaller than the Se<sup>2\u2013<\/sup> ion. Thus, Al<sub>2<\/sub>O<sub>3<\/sub> would have a shorter interionic distance than Al<sub>2<\/sub>Se<sub>3<\/sub>, and Al<sub>2<\/sub>O<sub>3<\/sub> would have the larger lattice energy.\r\n\r\n<hr \/>\r\n\r\n<h2 id=\"fs-idp49595360\"><span data-type=\"title\">Check Your Learning<\/span><\/h2>\r\nZinc oxide, ZnO, is a very effective sunscreen. How would the lattice energy of ZnO compare to that of NaCl?\r\n<div id=\"fs-idp176836208\" data-type=\"note\">\r\n<h3 style=\"text-align: right\" data-type=\"title\">Answer<\/h3>\r\n<p id=\"fs-idp821600\" style=\"text-align: right\">ZnO would have the larger lattice energy because the Z values of both the cation and the anion in ZnO are greater, and the interionic distance of ZnO is smaller than that of NaCl.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp112167568\" class=\"bc-section section\" data-depth=\"1\">\r\n<h2 data-type=\"title\">The Born-Haber Cycle<\/h2>\r\n<p id=\"fs-idp51725632\">It is not possible to measure lattice energies directly. However, the lattice energy can be calculated using the equation given in the previous section or by using a thermochemical cycle. The <span data-type=\"term\">Born-Haber cycle<\/span> is an application of Hess\u2019s law that breaks down the formation of an ionic solid into a series of individual steps:<\/p>\r\n\r\n<ul id=\"fs-idp77725760\" data-bullet-style=\"bullet\">\r\n \t<li>\\(\\text{$\\Delta$}{H}_{\\text{f}}^{\\circ},\\) the standard enthalpy of formation of the compound<\/li>\r\n \t<li><em data-effect=\"italics\">IE<\/em>, the ionization energy of the metal<\/li>\r\n \t<li><em data-effect=\"italics\">EA<\/em>, the electron affinity of the nonmetal<\/li>\r\n \t<li>\\(\\text{$\\Delta$}{H}_{s}^{\\circ},\\) the enthalpy of sublimation of the metal<\/li>\r\n \t<li><em data-effect=\"italics\">D<\/em>, the bond dissociation energy of the nonmetal<\/li>\r\n \t<li>\u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub>, the lattice energy of the compound<\/li>\r\n<\/ul>\r\n<p id=\"fs-idm6705632\"><a class=\"autogenerated-content\" href=\"#CNX_Chem_07_05_BornHaber\">(Figure 2.5.2)<\/a> diagrams the Born-Haber cycle for the formation of solid cesium fluoride.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_07_05_BornHaber\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\"><\/div>\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"975\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_BornHaber-1-1.jpg\" alt=\"A diagram is shown. An upward facing arrow is drawn to the far left of the chart and is labeled \u201cH increasing.\u201d A horizontal line is drawn at the bottom of the chart. A downward-facing, vertical arrow to the left side of this line is labeled, \u201cOverall change.\u201d Beside this arrow is another label, \u201ccapital delta H subscript f, equals negative 553.5 k J per mol, ( Enthalpy of formation ).\u201d Three horizontal lines, one above the other, and all above the bottom line, are labeled, from bottom to top, as: \u201cC s ( s ), plus sign, one half F subscript 2, ( g ),\u201d \u201cC s ( g ), plus sign, one half F subscript 2, ( g ),\u201d and \u201cC s, superscript positive sign, ( g ), plus sign, one half F subscript 2, ( g ).\u201d Each of these lines is connected by an upward-facing vertical arrow. Each arrow is labeled, \u201ccapital delta H subscript 1, equals 76.5 k J per mol, ( Enthalpy of sublimation ),\u201d \u201ccapital delta H subscript 2, equals 375.7 k J per mol, ( ionization energy ),\u201d and \u201ccapital delta H subscript 3 equals 79.4 k J \/ mol ( one half dissociation energy ).\u201d Another horizontal line is drawn in the center top portion of the diagram and is labeled \u201cC s, superscript positive sign, ( g ), plus sign, F, ( g ).\u201d There is one more horizontal line drawn to the right of the overall diagram and located halfway down the image. An arrow connects the top line to this line and is labeled, \u201ccapital delta H equals negative 328.2 k J \/ mol ( electron affinity ).\u201d The line is labeled, \u201cC s superscript positive sign ( g ) plus F superscript negative sign ( g ).\u201d The arrow connecting this line to the bottom line is labeled, \u201cnegative capital delta H subscript lattice equals negative 756.9 k J \/ mol.\u201d The arrow points to a label on the bottom line which reads, \u201cC s F ( s ).\u201d\" width=\"975\" height=\"528\" data-media-type=\"image\/jpeg\" \/> <strong>Figure 2.5.2 - The Born-Haber cycle shows the relative energies of each step involved in the formation of an ionic solid from the necessary elements in their reference states.<\/strong>[\/caption]\r\n\r\n<\/div>\r\n<p id=\"fs-idp53345328\">We begin with the elements in their most common states, Cs(<em data-effect=\"italics\">s<\/em>) and F<sub>2<\/sub>(<em data-effect=\"italics\">g<\/em>). The \\(\\text{\u0394}{H}_{s}^{\u00b0}\\) represents the conversion of solid cesium into a gas, and then the ionization energy converts the gaseous cesium atoms into cations. In the next step, we account for the energy required to break the F\u2013F bond to produce fluorine atoms. Converting one mole of fluorine atoms into fluoride ions is an exothermic process, so this step gives off energy (the electron affinity) and is shown as decreasing along the <em data-effect=\"italics\">y<\/em>-axis. We now have one mole of Cs cations and one mole of F anions. These ions combine to produce solid cesium fluoride. The enthalpy change in this step is the negative of the lattice energy, so it is also an exothermic quantity. The total energy involved in this conversion is equal to the experimentally determined enthalpy of formation, \\(\\text{\u0394}{H}_{\\text{f}}^{\u00b0},\\) of the compound from its elements. In this case, the overall change is exothermic.<\/p>\r\n<p id=\"fs-idm23453808\">Hess\u2019s law can also be used to show the relationship between the enthalpies of the individual steps and the enthalpy of formation. <a class=\"autogenerated-content\" href=\"#fs-idm33829552\">(Table 2.5.3)<\/a> shows this for cesium fluoride, CsF.<\/p>\r\n\r\n<table id=\"fs-idm33829552\" class=\"aligncenter\" summary=\"This table has two columns and six rows. The first row is labeled, \u201cEnthalpy of sublimation of C s ( s )\u201d and the enthalpy reaction is C s ( s ) yields C s ( g ). Beside this equation is capital delta H which equals capital delta H subscript s superscript degree symbol which also equals 76.5 k J. The second row is labeled, \u201cOne-half of the bond energy of C l subscript 2.\u201d The equation for this is one half C l subscript 2 ( g ) yields C l ( g ). Beside this equation is capital delta H equals one half D which also equals 122 k J. The third row is labeled, \u201cIonization Energy of N a ( g ).\u201d The equation for the ionization energy of N a ( g ) is N a ( g ) yields N a superscript positive sign ( g ) plus lower case e superscript negative sign. Beside this equation is capital delta H equals I E which also equals 496 k J. The fourth row is labeled, \u201cNegative of the electron affinity of C l.\u201d The equation for this is C l ( g ) plus lowercase e superscript negative sign yields C l superscript negative sign ( g ). Beside this equation is capital delta H equals negative E A which also equals negative 368 k J. The fifth row is labeled \u201cNegative of the lattice energy of N a C l ( s ).\u201d The equation for this is N a superscript positive sign ( g ) plus C l superscript negative sign ( g ) yields N a C l ( s ). Beside this equation is capital delta H equals negative capital delta H subscript lattice which also equals unknown. The sixth and final row is labeled, \u201cEnthalpy of formation of N a C l ( s ), add steps 1 - 5.\u201d The equation for this is capital delta H equals capital delta H subscript f superscript degree symbol which also equals capital delta H subscript s superscript degree symbol plus one-half D plus I E plus negative E A plus negative capital delta H subscript lattice. Underneath that equation, is another which is N a ( s ) plus one-half C l subscript 2 ( g ) yields N a C l ( s ) which equals negative 411 k J.\" data-label=\"\"><caption><strong>Table 2.5.3 - The enthalpies of the individual steps of the formation of CsF<\/strong><\/caption>\r\n<tbody>\r\n<tr valign=\"middle\">\r\n<td data-align=\"left\">Enthalpy of sublimation of Cs(<em data-effect=\"italics\">s<\/em>)<\/td>\r\n<td data-align=\"left\">\\(\\text{Cs}\\left(s\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}\\text{Cs}\\left(g\\right)\\)<\/td>\r\n<td data-align=\"left\">\\(\\Delta{H}=\\Delta{H}_{s}^{\\circ}=76.5\\text{kJ\/mol}\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"middle\">\r\n<td data-align=\"left\">One-half of the bond energy of F<sub>2<\/sub><\/td>\r\n<td data-align=\"left\">\\(\\frac{1}{2}\\phantom{\\rule{0.2em}{0ex}}{\\text{F}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}\\text{F}\\left(g\\right)\\)<\/td>\r\n<td data-align=\"left\">\\(\\Delta{H}=\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\phantom{\\rule{0.2em}{0ex}}D=79.4\\text{kJ\/mol}\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"middle\">\r\n<td data-align=\"left\">Ionization energy of Cs(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td data-align=\"left\">\\(\\text{Cs}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}{\\text{Cs}}^{\\text{+}}\\left(g\\right)+{\\text{e}^-}^{\\text{\u2212}}\\)<\/td>\r\n<td data-align=\"left\">\\(\\Delta{H}=IE=375.7\\text{kJ\/mol}\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"middle\">\r\n<td data-align=\"left\">Negative of the electron affinity of F<\/td>\r\n<td data-align=\"left\">\\(\\text{F}\\left(g\\right)+{\\text{e}^-}^{\\text{\u2212}}\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}{\\text{F}^-}^{\\text{\u2212}}\\left(g\\right)\\)<\/td>\r\n<td data-align=\"left\">\\(\\Delta{H}=\\text{\u2212}-EA=-328.2\\text{kJ\/mol}\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"middle\">\r\n<td data-align=\"left\">Negative of the lattice energy of CsF(<em data-effect=\"italics\">s<\/em>)<\/td>\r\n<td data-align=\"left\">\\({\\text{Cs}}^{\\text{+}}\\left(g\\right)+{\\text{F}^-}^{\\text{\u2212}}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}\\text{CsF}\\left(s\\right)\\)<\/td>\r\n<td data-align=\"left\">\\(\\Delta{H}=-\\Delta{H}_{\\text{lattice}}=?\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"middle\">\r\n<td data-align=\"left\">Enthalpy of formation of CsF(<em data-effect=\"italics\">s<\/em>), add steps 1\u20135<\/td>\r\n<td data-align=\"left\">\\(\\begin{array}{l}\\Delta{H}=\\Delta{H}_{f}^{\\circ}=\\Delta{H}_{s}^{\\circ}+\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\phantom{\\rule{0.2em}{0ex}}D+IE+\\left(-EA\\right)+\\left(-\\Delta{H}_{\\text{lattice}}\\right)\\\\ \\text{Cs}\\left(s\\right)+\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\phantom{\\rule{0.2em}{0ex}}{\\text{F}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}\\text{CsF}\\left(s\\right)\\end{array}\\)<\/td>\r\n<td data-align=\"left\">\\(\\Delta{H}=-553.5\\text{kJ\/mol}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div id=\"fs-idp112167568\" class=\"bc-section section\" data-depth=\"1\">\r\n<p id=\"fs-idp28364752\">Thus, the lattice energy can be calculated from other values. For cesium fluoride, using this data, the lattice energy is:<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp37818096\" data-type=\"equation\">\\(\\Delta{H}_{\\text{lattice}}=\\left(553.5+76.5+79.4+375.7+328.2\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{kJ\/mol}=1413.3\\phantom{\\rule{0.2em}{0ex}}\\text{kJ\/mol}\\)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm78151632\">The Born-Haber cycle may also be used to calculate any one of the other quantities in the equation for lattice energy, provided that the remainder is known. For example, if the relevant enthalpy of sublimation \\(\\Delta{H}_{s}^{\\circ},\\) ionization energy (IE), bond dissociation enthalpy (D), lattice energy \u0394<em data-effect=\"italics\">H<\/em><sub>lattice,<\/sub> and standard enthalpy of formation \\(\\Delta{H}_{\\text{f}}^{\\circ}\\) are known, the Born-Haber cycle can be used to determine the electron affinity of an atom.<\/p>\r\n<p id=\"fs-idm10039728\">Lattice energies calculated for ionic compounds are typically much higher than bond dissociation energies measured for covalent bonds. Whereas lattice energies typically fall in the range of 600\u20134000 kJ\/mol (some even higher), covalent bond dissociation energies are typically between 150\u2013400 kJ\/mol for single bonds. Keep in mind, however, that these are not directly comparable values. For ionic compounds, lattice energies are associated with many interactions, as cations and anions pack together in an extended lattice. For covalent bonds, the bond dissociation energy is associated with the interaction of just two atoms.<\/p>\r\n\r\n<\/div>\r\n<h1>Key Concepts and Summary<\/h1>\r\nThe strength of a covalent bond is measured by its bond dissociation energy, that is, the amount of energy required to break that particular bond in a mole of molecules. Multiple bonds are stronger than single bonds between the same atoms. The enthalpy of a reaction can be estimated based on the energy input required to break bonds and the energy released when new bonds are formed. For ionic bonds, the lattice energy is the energy required to separate one mole of a compound into its gas phase ions. Lattice energy increases for ions with higher charges and shorter distances between ions. Lattice energies are often calculated using the Born-Haber cycle, a thermochemical cycle including all of the energetic steps involved in converting elements into an ionic compound.\r\n<h2 data-type=\"title\">Key Equations<\/h2>\r\n<ul id=\"fs-idp25406976\" data-bullet-style=\"bullet\">\r\n \t<li>Bond energy for a diatomic molecule: \\(\\text{XY}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}\\text{X}\\left(g\\right)+\\text{Y}\\left(g\\right)\\phantom{\\rule{3em}{0ex}}{\\text{D}}_{\\text{X\u2013Y}}=\\Delta{H}\\text{\\circ}\\)<\/li>\r\n \t<li>Enthalpy change: \u0394<em data-effect=\"italics\">H<\/em> = \u01a9D<sub>bonds broken<\/sub> \u2013 \u01a9D<sub>bonds formed<\/sub><\/li>\r\n \t<li>Lattice energy for a solid MX: \\(\\text{MX}\\left(s\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}{\\text{M}}^{n\\text{+}}\\left(g\\right)+{\\text{X}^{n-}}\\left(g\\right)\\phantom{\\rule{3em}{0ex}}\\Delta{H}_{\\text{lattice}}\\)<\/li>\r\n \t<li>Lattice energy for an ionic crystal: \\(\\Delta{H}_{\\text{lattice}}=\\phantom{\\rule{0.2em}{0ex}}\\frac{\\text{C}\\left({\\text{Z}}^{\\text{+}}\\right)\\left({\\text{Z}^-}^{\\text{\u2212}}\\right)}{{\\text{R}}_{\\text{o}}}\\)<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">End of Chapter Exercises<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-idp18527664\" data-type=\"exercise\">\r\n<div id=\"fs-idm31250240\" data-type=\"problem\">\r\n<p id=\"fs-idp75695024\">Which bond in each of the following pairs of bonds is the strongest?<\/p>\r\n<p id=\"fs-idp174181168\">(1a) C\u2013C or \\(\\text{C}=\\text{C}\\)<\/p>\r\n<p id=\"fs-idp191457408\">(1b) C\u2013N or \\(\\text{C}\\equiv \\text{N}\\)<\/p>\r\n<p id=\"fs-idm37995600\">(1c)\\(\\text{C}\\equiv \\text{O}\\) or \\(\\text{C}=\\text{O}\\)<\/p>\r\n<p id=\"fs-idp19512320\">(1d) H\u2013F or H\u2013Cl<\/p>\r\n<p id=\"fs-idm2333776\">(1e) C\u2013H or O\u2013H<\/p>\r\n<p id=\"fs-idp120232048\">(1f) C\u2013N or C\u2013O<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp16780032\" data-type=\"exercise\">\r\n<div id=\"fs-idp37241056\" data-type=\"problem\">\r\n<p id=\"fs-idm20426752\">Using the bond energies in <a class=\"autogenerated-content\" href=\"#fs-idp13638832\">(Table 2.5.1)<\/a>, determine the approximate enthalpy change for each of the following reactions:<\/p>\r\n<p id=\"fs-idp13624240\">(2a) \\({\\text{H}}_{2}\\left(g\\right)+{\\text{Br}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}2\\text{HBr}\\left(g\\right)\\)<\/p>\r\n<p id=\"fs-idm48592992\">(2b) \\({\\text{CH}}_{4}\\left(g\\right)+{\\text{I}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}{\\text{CH}}_{3}\\text{I}\\left(g\\right)+\\text{HI}\\left(g\\right)\\)<\/p>\r\n<p id=\"fs-idm27033728\">(2c) \\({\\text{C}}_{2}{\\text{H}}_{4}\\left(g\\right)+3{\\text{O}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}2{\\text{CO}}_{2}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\)<\/p>\r\n&nbsp;\r\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\r\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">(a) \u2212114 kJ; (b) 30 kJ; (c) \u22121055 kJ<\/span><\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idp55504208\" style=\"padding-left: 40px\" data-type=\"solution\">\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp57429280\" data-type=\"exercise\">\r\n<div id=\"fs-idp48795376\" data-type=\"problem\">\r\n<p id=\"fs-idp240397744\">Using the bond energies in <a class=\"autogenerated-content\" href=\"#fs-idp13638832\">(Table 2.5.1)<\/a>, determine the approximate enthalpy change for each of the following reactions:<\/p>\r\n<p id=\"fs-idp188770912\">(3a) \\({\\text{Cl}}_{2}\\left(g\\right)+3{\\text{F}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}2{\\text{ClF}}_{3}\\left(g\\right)\\)<\/p>\r\n<p id=\"fs-idp123909120\">(3b) \\({\\text{H}}_{2}\\text{C}={\\text{CH}}_{2}\\left(g\\right)+{\\text{H}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}{\\text{H}}_{3}{\\text{CCH}}_{3}\\left(g\\right)\\)<\/p>\r\n<p id=\"fs-idp30139536\">(3c) \\(2{\\text{C}}_{2}{\\text{H}}_{6}\\left(g\\right)+7{\\text{O}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}4{\\text{CO}}_{2}\\left(g\\right)+6{\\text{H}}_{2}\\text{O}\\left(g\\right)\\)<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp28520976\" data-type=\"exercise\">\r\n<div id=\"fs-idp28294656\" data-type=\"problem\">\r\n<p id=\"fs-idp220216256\">(4) When a molecule can form two different structures, the structure with the stronger bonds is usually the more stable form. Use bond energies to predict the correct structure of the hydroxylamine molecule:<\/p>\r\n<span id=\"fs-idm6604832\" data-type=\"media\" data-alt=\"Two Lewis structures are shows with the word \u201cor\u201d written in between them. The left structure shows a nitrogen atom with one lone pair of electrons single bonded to two hydrogen atoms. It is also bonded to an oxygen atom with two lone pairs of electrons. The oxygen atom is bonded to a hydrogen atom. The right structure shows a nitrogen atom single bonded to three hydrogen atoms and an oxygen atom with three lone pairs of electrons.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_Hydroxya_img-1-1.jpg\" alt=\"Two Lewis structures are shows with the word \u201cor\u201d written in between them. The left structure shows a nitrogen atom with one lone pair of electrons single bonded to two hydrogen atoms. It is also bonded to an oxygen atom with two lone pairs of electrons. The oxygen atom is bonded to a hydrogen atom. The right structure shows a nitrogen atom single bonded to three hydrogen atoms and an oxygen atom with three lone pairs of electrons.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n&nbsp;\r\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\r\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">The greater bond energy is in the figure on the left. It is the more stable form.<\/span><\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idp16844192\" style=\"padding-left: 40px\" data-type=\"solution\">\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp20766256\" data-type=\"exercise\">\r\n<div id=\"fs-idm6034544\" data-type=\"problem\">\r\n<p id=\"fs-idm22015856\">(5) How does the bond energy of HCl(<em data-effect=\"italics\">g<\/em>) differ from the standard enthalpy of formation of HCl(<em data-effect=\"italics\">g<\/em>)?<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp19159472\" data-type=\"exercise\">\r\n<div id=\"fs-idm7424064\" data-type=\"problem\">\r\n<p id=\"fs-idp16480976\">(6) Using the standard enthalpy of formation data in <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a>, show how the standard enthalpy of formation of HCl(<em data-effect=\"italics\">g<\/em>) can be used to determine the bond energy.<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"fs-idp65612672\" data-type=\"solution\">\r\n\r\n(7) Using the standard enthalpy of formation data in <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a>, calculate the bond energy of the carbon-sulfur double bond in CS<sub>2<\/sub>.\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp65498352\" data-type=\"exercise\">\r\n<div id=\"fs-idp23041056\" data-type=\"problem\">\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp19660960\" data-type=\"exercise\">\r\n<div id=\"fs-idp16871040\" data-type=\"problem\">\r\n<p id=\"fs-idp16871296\">(8) Using the standard enthalpy of formation data in <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a>, determine which bond is stronger: the S\u2013F bond in SF<sub>4<\/sub>(<em data-effect=\"italics\">g<\/em>) or in SF<sub>6<\/sub>(<em data-effect=\"italics\">g<\/em>)?<\/p>\r\n&nbsp;\r\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\r\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">The S\u2013F bond in SF<\/span><sub style=\"text-align: initial\">4<\/sub><span style=\"text-align: initial;font-size: 1em\"> is stronger.<\/span><\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idp19698336\" style=\"padding-left: 40px\" data-type=\"solution\">\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm2894352\" data-type=\"exercise\">\r\n<div id=\"fs-idm2894096\" data-type=\"problem\">\r\n<p id=\"fs-idp88452992\">(9) Using the standard enthalpy of formation data in <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a>, determine which bond is stronger: the P\u2013Cl bond in PCl<sub>3<\/sub>(<em data-effect=\"italics\">g<\/em>) or in PCl<sub>5<\/sub>(<em data-effect=\"italics\">g<\/em>)?<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm22310960\" data-type=\"exercise\">\r\n<div id=\"fs-idp16666336\" data-type=\"problem\">\r\n<p id=\"fs-idp16666592\">(10) Complete the following Lewis structure by adding bonds (not atoms), and then indicate the longest bond:<\/p>\r\n&nbsp;\r\n\r\n<span id=\"fs-idp123644096\" data-type=\"media\" data-alt=\"A Lewis structure is shown that is missing its bonds. It shows a horizontal row of six carbon atoms, equally spaced. Three hydrogen atoms are drawn around the first carbon, two around the second, one above the fifth, and two by the sixth.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_C6H8Lew_img-1-1.jpg\" alt=\"A Lewis structure is shown that is missing its bonds. It shows a horizontal row of six carbon atoms, equally spaced. Three hydrogen atoms are drawn around the first carbon, two around the second, one above the fifth, and two by the sixth.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<div id=\"fs-idp44310208\" data-type=\"solution\">\r\n<p id=\"fs-idp46735152\"><span data-type=\"newline\">\u00a0<\/span><\/p>\r\n<span id=\"fs-idp57448112\" data-type=\"media\" data-alt=\"A Lewis structure is shown. A carbon atom that is single bonded to three hydrogen atoms is bonded to a second carbon atom. The second carbon atom is single bonded to two hydrogen atoms. The second carbon atom is single bonded to a third carbon atom that is triple bonded to a fourth carbon atom and single bonded to a fifth carbon atom. The fifth carbon atom is single bonded to a hydrogen atom and double bonded to a sixth carbon atom that is single bonded to two hydrogen atoms.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_C6H8ans_img-1-1.jpg\" alt=\"A Lewis structure is shown. A carbon atom that is single bonded to three hydrogen atoms is bonded to a second carbon atom. The second carbon atom is single bonded to two hydrogen atoms. The second carbon atom is single bonded to a third carbon atom that is triple bonded to a fourth carbon atom and single bonded to a fifth carbon atom. The fifth carbon atom is single bonded to a hydrogen atom and double bonded to a sixth carbon atom that is single bonded to two hydrogen atoms.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n&nbsp;\r\n<p style=\"padding-left: 40px\"><span data-type=\"newline\"><em>Solution<\/em><\/span><\/p>\r\n<p style=\"padding-left: 40px\"><span data-type=\"newline\">\r\n<\/span> The C\u2013C single bonds are longest.<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp57420000\" data-type=\"exercise\">\r\n<div id=\"fs-idp78457408\" data-type=\"problem\">\r\n<p id=\"fs-idp78457664\">(11) Use the bond energy to calculate an approximate value of \u0394<em data-effect=\"italics\">H<\/em> for the following reaction. Which is the more stable form of FNO<sub>2<\/sub>?<\/p>\r\n<span id=\"fs-idp40889632\" data-type=\"media\" data-alt=\"Two Lewis structures are shown with a right-facing arrow in between. The left structure shows a nitrogen atom double bonded to an oxygen atom with two lone pairs of electrons. It is also bonded to a fluorine atom and another oxygen atom, each with three lone pairs of electrons. The right structure shows an oxygen atom with two lone pairs of electrons double bonded to a nitrogen atom with one lone pair of electrons. This nitrogen atom is single bonded to an oxygen with two lone pairs of electrons. The oxygen atom is single bonded to a fluorine atom with three lone pairs of electrons.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_FNO2_img-1-1.jpg\" alt=\"Two Lewis structures are shown with a right-facing arrow in between. The left structure shows a nitrogen atom double bonded to an oxygen atom with two lone pairs of electrons. It is also bonded to a fluorine atom and another oxygen atom, each with three lone pairs of electrons. The right structure shows an oxygen atom with two lone pairs of electrons double bonded to a nitrogen atom with one lone pair of electrons. This nitrogen atom is single bonded to an oxygen with two lone pairs of electrons. The oxygen atom is single bonded to a fluorine atom with three lone pairs of electrons.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp12625232\" data-type=\"exercise\">\r\n<div id=\"fs-idp15947632\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<div id=\"fs-idp46666496\" data-type=\"exercise\">\r\n<div id=\"fs-idp46666752\" data-type=\"problem\">\r\n<p id=\"fs-idp794240\">(12) The lattice energy of LiF is 1023 kJ\/mol, and the Li\u2013F distance is 200.8 pm. NaF crystallizes in the same structure as LiF but with a Na\u2013F distance of 231 pm. Which of the following values most closely approximates the lattice energy of NaF: 510, 890, 1023, 1175, or 4090 kJ\/mol? Explain your choice.<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp236067168\" data-type=\"exercise\">\r\n<div id=\"fs-idp236067424\" data-type=\"problem\">\r\n<p id=\"fs-idp236067680\">For which of the following substances is the least energy required to convert one mole of the solid into separate ions?<\/p>\r\n<p id=\"fs-idp211527872\">(13a) MgO<\/p>\r\n<p id=\"fs-idp90299856\">(13b) SrO<\/p>\r\n<p id=\"fs-idp90300240\">(13c) KF<\/p>\r\n<p id=\"fs-idp174354464\">(13d) CsF<\/p>\r\n<p id=\"fs-idp174354848\">(13e) MgF<sub>2<\/sub><\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"fs-idm39061296\" data-type=\"exercise\">\r\n<div id=\"fs-idm39061040\" data-type=\"problem\">\r\n<p id=\"fs-idm39060784\">(14) The reaction of a metal, M, with a halogen, X<sub>2<\/sub>, proceeds by an exothermic reaction as indicated by this equation: \\(\\text{M}\\left(s\\right)+{\\text{X}}_{2}\\left(g\\right)\\phantom{\\rule{0.2em}{0ex}}$\\rightarrow$\\phantom{\\rule{0.2em}{0ex}}{\\text{MX}}_{2}\\left(s\\right).\\) For each of the following, indicate which option will make the reaction more exothermic. Explain your answers.<\/p>\r\n<p id=\"fs-idp48865984\">(14a) a large radius vs. a small radius for M<sup>+2<\/sup><\/p>\r\n<p id=\"fs-idm52945984\">(14b) a high ionization energy vs. a low ionization energy for M<\/p>\r\n<p id=\"fs-idm37748736\">(14c) an increasing bond energy for the halogen<\/p>\r\n<p id=\"fs-idm37748352\">(14d) a decreasing electron affinity for the halogen<\/p>\r\n<p id=\"fs-idm38878512\">(14e) an increasing size of the anion formed by the halogen<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp55219680\" data-type=\"exercise\">\r\n<div id=\"fs-idp10681296\" data-type=\"problem\">\r\n<p id=\"fs-idp10681552\">(15) The lattice energy of LiF is 1023 kJ\/mol, and the Li\u2013F distance is 201 pm. MgO crystallizes in the same structure as LiF but with a Mg\u2013O distance of 205 pm. Which of the following values most closely approximates the lattice energy of MgO: 256 kJ\/mol, 512 kJ\/mol, 1023 kJ\/mol, 2046 kJ\/mol, or 4008 kJ\/mol? Explain your choice.<\/p>\r\n&nbsp;\r\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\r\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">4008 kJ\/mol; both ions in MgO have twice the charge of the ions in LiF; the bond length is very similar and both have the same structure; a quadrupling of the energy is expected based on the equation for lattice energy<\/span><\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm27862768\" style=\"padding-left: 40px\" data-type=\"solution\">\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm27862256\" data-type=\"exercise\">\r\n<div id=\"fs-idp23005264\" data-type=\"problem\">\r\n<p id=\"fs-idp23005520\">Which compound in each of the following pairs has the larger lattice energy? Note: Mg<sup>2+<\/sup> and Li<sup>+<\/sup> have similar radii; O<sup>2\u2013<\/sup> and F<sup>\u2013<\/sup> have similar radii. Explain your choices.<\/p>\r\n<p id=\"fs-idm42318048\">(16a) MgO or MgSe<\/p>\r\n<p id=\"fs-idp14229536\">(16b) LiF or MgO<\/p>\r\n<p id=\"fs-idp14229920\">(16c) Li<sub>2<\/sub>O or LiCl<\/p>\r\n<p id=\"fs-idm39601280\">(16d) Li<sub>2<\/sub>Se or MgO<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp29388832\" data-type=\"exercise\">\r\n<div id=\"fs-idp19286528\" data-type=\"problem\">\r\n<p id=\"fs-idp19286784\">Which compound in each of the following pairs has the larger lattice energy? Note: Ba<sup>2+<\/sup> and<\/p>\r\n<p id=\"fs-idp1147008\">K<sup>+<\/sup> have similar radii; S<sup>2\u2013<\/sup> and Cl<sup>\u2013<\/sup> have similar radii. Explain your choices.<\/p>\r\n<p id=\"fs-idp26686336\">(17a) K<sub>2<\/sub>O or Na<sub>2<\/sub>O<\/p>\r\n<p id=\"fs-idp81635552\">(17b) K<sub>2<\/sub>S or BaS<\/p>\r\n<p id=\"fs-idp55153232\">(17c) KCl or BaS<\/p>\r\n<p id=\"fs-idp55110752\">(17d) BaS or BaCl<sub>2<\/sub><\/p>\r\n&nbsp;\r\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\r\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">(a) Na<\/span><sub style=\"text-align: initial\">2<\/sub><span style=\"text-align: initial;font-size: 1em\">O; Na<\/span><sup style=\"text-align: initial\">+<\/sup><span style=\"text-align: initial;font-size: 1em\"> has a smaller radius than K<\/span><sup style=\"text-align: initial\">+<\/sup><span style=\"text-align: initial;font-size: 1em\">; (b) BaS; Ba has a larger charge than K; (c) BaS; Ba and S have larger charges; (d) BaS; S has a larger charge<\/span><\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm42840528\" style=\"padding-left: 40px\" data-type=\"solution\">\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp51586816\" data-type=\"exercise\">\r\n<div id=\"fs-idp51587072\" data-type=\"problem\">\r\n<p id=\"fs-idp51587328\">Which of the following compounds requires the most energy to convert one mole of the solid into separate ions?<\/p>\r\n<p id=\"fs-idm8325008\">(18a) MgO<\/p>\r\n<p id=\"fs-idm8324624\">(18b) SrO<\/p>\r\n<p id=\"fs-idm2086432\">(18c) KF<\/p>\r\n<p id=\"fs-idm2086048\">(18d) CsF<\/p>\r\n<p id=\"fs-idp185408896\">(18e) MgF<sub>2<\/sub><\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp56209472\" data-type=\"exercise\">\r\n<div id=\"fs-idp56209728\" data-type=\"problem\">\r\n<p id=\"fs-idp16978800\">Which of the following compounds requires the most energy to convert one mole of the solid into separate ions?<\/p>\r\n<p id=\"fs-idp16979312\">(19a) K<sub>2<\/sub>S<\/p>\r\n<p id=\"fs-idp58281056\">(19b) K<sub>2<\/sub>O<\/p>\r\n<p id=\"fs-idp48854512\">(19c) CaS<\/p>\r\n<p id=\"fs-idp123580176\">(19d) Cs<sub>2<\/sub>S<\/p>\r\n<p id=\"fs-idp110456432\">(19e) CaO<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"fs-idp15208208\" data-type=\"exercise\">\r\n<div id=\"fs-idp15208464\" data-type=\"problem\">\r\n<p id=\"fs-idp15208720\">(20) The lattice energy of KF is 794 kJ\/mol, and the interionic distance is 269 pm. The Na\u2013F distance in NaF, which has the same structure as KF, is 231 pm. Which of the following values is the closest approximation of the lattice energy of NaF: 682 kJ\/mol, 794 kJ\/mol, 924 kJ\/mol, 1588 kJ\/mol, or 3175 kJ\/mol? Explain your answer.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox shaded\" data-type=\"glossary\">\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-idp10319376\">[pb_glossary id=\"2956\"]bond energy[\/pb_glossary]\r\n \t<dd id=\"fs-idm69489984\">(also, bond dissociation energy) energy required to break a covalent bond in a gaseous substance<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp39711472\">\r\n \t<dt>[pb_glossary id=\"2957\"]Born-Haber cycle[\/pb_glossary]<\/dt>\r\n \t<dd id=\"fs-idp39712112\">thermochemical cycle relating the various energetic steps involved in the formation of an ionic solid from the relevant elements<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp29295648\">\r\n \t<dt>[pb_glossary id=\"2959\"]lattice energy[\/pb_glossary] (\u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub>)<\/dt>\r\n \t<dd id=\"fs-idm7620624\">energy required to separate one mole of an ionic solid into its component gaseous ions<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<\/div>","rendered":"<div>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Describe the energetics of covalent and ionic bond formation and breakage<\/li>\n<li>Use the Born-Haber cycle to compute lattice energies for ionic compounds<\/li>\n<li>Use average covalent bond energies to estimate enthalpies of reaction<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-idp176876736\">A bond\u2019s strength describes how strongly each atom is joined to another atom, and therefore how much energy is required to break the bond between the two atoms. In this section, you will learn about the bond strength of covalent bonds, and then compare that to the strength of ionic bonds, which is related to the lattice energy of a compound.<\/p>\n<div id=\"fs-idp66065152\" class=\"bc-section section\" data-depth=\"1\">\n<h2 data-type=\"title\">Bond Strength: Covalent Bonds<\/h2>\n<p id=\"fs-idm12470240\">Stable molecules exist because covalent bonds hold the atoms together. We measure the strength of a covalent bond by the energy required to break it, that is, the energy necessary to separate the bonded atoms. Separating any pair of bonded atoms requires energy (see <a class=\"autogenerated-content\" href=\"#2.5.1\">(Figure 2.5.1)<\/a>). The stronger a bond, the greater the energy required to break it.<\/p>\n<p id=\"fs-idp84340368\">The energy required to break a specific covalent bond in one mole of gaseous molecules is called the bond energy or the bond dissociation energy. The bond energy for a diatomic molecule, D<sub>X\u2013Y<\/sub>, is defined as the standard enthalpy change for the endothermic reaction:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm36464112\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-cdc5b557165bb1b38132b885de662e82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#89;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#8722;&#89;&#125;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#72;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"323\" style=\"vertical-align: -5px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm12974112\">For example, the bond energy of the pure covalent H\u2013H bond, D<sub>H\u2013H<\/sub>, is 436 kJ per mole of H\u2013H bonds broken:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp119487888\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-c827837e3ac69c1a1d0498a003f61dc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#8722;&#72;&#125;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#72;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#61;&#52;&#51;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"337\" style=\"vertical-align: -5px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp244347920\">Molecules with three or more atoms have two or more bonds. The sum of all bond energies in such a molecule is equal to the standard enthalpy change for the endothermic reaction that breaks all the bonds in the molecule.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"2.5.1\" class=\"scaled-down\">\n<figure style=\"width: 975px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_CH4bond_img-1.jpg\" alt=\"A reaction is shown with Lewis structures. The first structure shows a carbon atom single bonded to four hydrogen atoms with the symbol, \u201c( g )\u201d written next to it. A right-facing arrow points to the letter \u201cC\u201d and the symbol \u201c( g ),\u201d which is followed by a plus sign. Next is the number 4, the letter \u201cH\u201d and the symbol, \u201c( g ).\u201d To the right of this equation is another equation: capital delta H superscript degree symbol equals 1660 k J.\" width=\"975\" height=\"144\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 2.5.1 &#8211; The sum of the four C\u2013H bond energies in CH4, 1660 kJ, is equal to the standard enthalpy change of the reaction<\/strong><\/figcaption><\/figure>\n<p id=\"fs-idp85707472\">The average C\u2013H bond energy, D<sub>C\u2013H<\/sub>, is 1660\/4 = 415 kJ\/mol because there are four moles of C\u2013H bonds broken per mole of the reaction. Although the four C\u2013H bonds are equivalent in the original molecule, they do not each require the same energy to break; once the first bond is broken (which requires 439 kJ\/mol), the remaining bonds are easier to break. The 415 kJ\/mol value is the average, not the exact value required to break any one bond.<\/p>\n<p id=\"fs-idp26225392\">The strength of a bond between two atoms increases as the number of electron pairs in the bond increases. Generally, as the bond strength increases, the bond length decreases. Thus, we find that triple bonds are stronger and shorter than double bonds between the same two atoms; likewise, double bonds are stronger and shorter than single bonds between the same two atoms. Average bond energies for some common bonds appear in <a class=\"autogenerated-content\" href=\"#fs-idp13638832\">(Table 2.5.1)<\/a>, and a comparison of bond lengths and bond strengths for some common bonds appears in <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>. When one atom bonds to various atoms in a group, the bond strength typically decreases as we move down the group. For example, C\u2013F is 439 kJ\/mol, C\u2013Cl is 330 kJ\/mol, and C\u2013Br is 275 kJ\/mol.<\/p>\n<table id=\"fs-idp13638832\" class=\"aligncenter\" style=\"height: 375px\" summary=\"This table has six columns and twenty-four rows. The first row is a header row that labels the columns: \u201cBond,\u201d \u201cBond Energy,\u201d \u201cBond,\u201d \u201cBond Energy,\u201d \u201cBond,\u201d and, \u201cBond Energy.\u201d Under the first \u201cBond\u201d column are the values: H bond to H with a single bond; H bonds to C with a single bond; H bonds to N with a single bond; H bonds to O with a single bond; H bonds to F with a single bond; H bonds to S i with a single bond; H bonds to P with a single bond; H bonds to S with a single bond; H bonds to C l with a single bond; H bonds to B r with a single bond; H bonds to I with a single bond; C bonds to C with a single bond; C bonds to C with a double bond; C bonds to C with a triple bond; C bonds to N with a single bond; C bonds to N with a double bond; C bonds to N with a triple bond; C bonds to O with a single bond; C bonds to O with a double bond; C bonds to O with a triple bond; C bonds to F with a single bond; C bonds to S i with a single bond; and C bonds to P with a single bond. Under the first \u201cBond Energy\u201d column are the values: 436; 415; 390; 464; 569; 395; 320; 340; 432; 370; 295; 345; 611; 837; 290; 615; 891; 350; 741; 1080; 439; 360; and 265. Under the second \u201cBond\u201d column are the values: C bonds to S with a single bond; C bonds to C l with a single bond; C bonds to B r with a single bond; C bonds to I with a single bond; N bonds to N with a single bond; N bonds to N with a double bond; N bonds to N with a triple bond; N bonds to O with a single bond; N bonds to F with a single bond; N bonds to P with a single bond; N bonds to C l with a single bond; N bonds to B r with a single bond; O bonds to O with a single bond; O bonds to O with a double bond; O bonds to F with a single bond; O bonds to S i with a single bond; O bonds to P with a single bond; O bonds to C l with a single bond; O bonds to I with a single bond; F bonds to F with a single bond; F bonds to S i with a single bond; F bonds to P with a single bond; and F bonds to S with a single bond. Under the second \u201cBond Energy\u201d column are the values: 260; 330; 275; 240; 160; 418; 946; 200; 270; 210; 200; 245; 140; 498; 160; 370; 350; 205; 200; 160; 540; 489; and 285. Under the third \u201cBond\u201d column are the values: F bonds to C l with a single bond; F bonds to B r with a single bond; S i bonds to S i with a single bond; S i bonds to P with a single bond; S i bonds to S with a single bond; S i bonds to C l with a single bond; S i bonds to B r with a single bond; S i bonds to I with a single bond; P bonds to P with a single bond; P bonds to S with a single bond; P bonds to C l with a single bond; P bonds to B r with a single bond; P bonds to I with a single bond; S bonds to S with a single bond; S bonds to C l with a single bond; S bonds to B r with a single bond; C l bonds to C l with a single bond; C l bonds to B r with a single bond; C l bonds to I with a single bond; B r bonds to B r with a single bond; B r bonds to I with a single bond; I bonds to I with a single bond; and the last cell in the column is empty. Under the third \u201cBond Energy\u201d column are the values: 255; 235; 230; 215; 225; 359; 290; 215; 215; 230; 330; 270; 215; 215; 250; 215; 243; 220; 210; 190; 180; 150; and the last cell in the column is empty.\">\n<caption><strong>Table 2.5.1 &#8211; <\/strong>Bond Energies (kJ\/mol)<\/caption>\n<thead>\n<tr style=\"height: 15px\" valign=\"top\">\n<th style=\"height: 15px;width: 187.95px\" data-align=\"left\">Bond<\/th>\n<th style=\"height: 15px;width: 88.2333px\" data-align=\"left\">Bond Energy<\/th>\n<th style=\"height: 15px;width: 0.0166667px\" data-align=\"left\"><\/th>\n<th style=\"height: 15px;width: 189.15px\" data-align=\"left\">Bond<\/th>\n<th style=\"height: 15px;width: 88.2333px\" data-align=\"left\">Bond Energy<\/th>\n<th style=\"height: 15px;width: 0.0166667px\" data-align=\"left\"><\/th>\n<th style=\"height: 15px;width: 37.1667px\" data-align=\"left\">Bond<\/th>\n<th style=\"height: 15px;width: 88.2333px\" data-align=\"left\">Bond Energy<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013H<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">436<\/td>\n<td style=\"height: 345px;width: 1.13333px\" rowspan=\"23\" data-align=\"left\"><\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">C\u2013S<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">260<\/td>\n<td style=\"height: 345px;width: 1.13333px\" rowspan=\"23\" data-align=\"left\"><\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">F\u2013Cl<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">255<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013C<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">415<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">C\u2013Cl<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">330<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">F\u2013Br<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">235<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013N<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">390<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">C\u2013Br<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">275<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013Si<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">230<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013O<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">464<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">C\u2013I<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">240<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013P<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013F<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">569<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013N<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">160<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013S<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">225<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013Si<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">395<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-9a3e7031c3bb020f9b4d19e4af72b7ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">418<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013Cl<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">359<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013P<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">320<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-f4d2e40bcd153c8d52655460c82fdb57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">946<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013Br<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">290<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013S<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">340<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013O<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">200<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Si\u2013I<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013Cl<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">432<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013F<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">270<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013P<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013Br<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">370<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013P<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">210<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013S<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">230<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">H\u2013I<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">295<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013Cl<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">200<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013Cl<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">330<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013C<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">345<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">N\u2013Br<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">245<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013Br<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">270<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-551c7343192e9bf18bd2458a5b9f2dbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">611<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013O<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">140<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">P\u2013I<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-28b33e1efd5588c3cc51ee761d2fc0b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">837<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-8e9db83c004e17cde078e8f08cd909e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">498<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">S\u2013S<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013N<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">290<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013F<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">160<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">S\u2013Cl<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">250<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-fd802aedad19e54c7fc4c4f1f0b84227_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">615<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013Si<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">370<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">S\u2013Br<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">215<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-f529ffe544b78b7c0dcced50cc4db154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">891<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013P<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">350<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Cl\u2013Cl<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">243<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013O<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">350<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013Cl<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">205<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Cl\u2013Br<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">220<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-c25395cd76461950ad5d76092a507742_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">741<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">O\u2013I<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">200<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Cl\u2013I<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">210<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-40632c15e57b05aa1d24920b873736c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">1080<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">F\u2013F<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">160<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Br\u2013Br<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">190<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013F<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">439<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">F\u2013Si<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">540<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">Br\u2013I<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">180<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013Si<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">360<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">F\u2013P<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">489<\/td>\n<td style=\"height: 15px;width: 38.2833px\" data-align=\"left\">I\u2013I<\/td>\n<td style=\"height: 15px;width: 88.2333px\" data-align=\"left\">150<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 189.067px\" data-align=\"left\">C\u2013P<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">265<\/td>\n<td style=\"height: 15px;width: 190.267px\" data-align=\"left\">F\u2013S<\/td>\n<td style=\"height: 15px;width: 89.35px\" data-align=\"left\">285<\/td>\n<td style=\"height: 15px;width: 38.2833px\"><\/td>\n<td style=\"height: 15px;width: 88.2333px\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"fs-idm44464336\" class=\"aligncenter\" summary=\"This table has three columns and ten rows. The first row is a header row that labels the columns: \u201cBond,\u201d \u201cBond Length in angstroms,\u201d and, \u201cBond Energy in k J \/ mol.\u201d Under the column \u201cBond\u201d are the values: C bonds to C with a single bond; C bonds to C with a double bond; C bonds to C with a triple bond; C bonds to N with a single bond; C bonds to N with a double bond; C bonds to N with a triple bond; C bonds to O with a single bond; C bonds to O with a double bond; and C bonds to O with a triple bond. Under the column \u201cBond Length in angstroms\u201d are the values: 1.54; 1.34; 1.20; 1.43; 1.38; 1.16; 1.43; 1.23; and 1.13. Under the column \u201cBond Energy in k J \/ mol\u201d are the values: 345; 611; 837; 290; 615; 891; 350; 741; and 1080.\">\n<caption><strong>Table 2.5.2 &#8211; <\/strong>Average Bond Lengths and Bond Energies for Some Common Bonds<\/caption>\n<thead>\n<tr valign=\"top\">\n<th data-align=\"left\">Bond<\/th>\n<th data-align=\"left\">Bond Length (\u00c5)<\/th>\n<th data-align=\"left\">Bond Energy (kJ\/mol)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">C\u2013C<\/td>\n<td data-align=\"left\">1.54<\/td>\n<td data-align=\"left\">345<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-551c7343192e9bf18bd2458a5b9f2dbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">1.34<\/td>\n<td data-align=\"left\">611<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-28b33e1efd5588c3cc51ee761d2fc0b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">1.20<\/td>\n<td data-align=\"left\">837<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">C\u2013N<\/td>\n<td data-align=\"left\">1.43<\/td>\n<td data-align=\"left\">290<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-fd802aedad19e54c7fc4c4f1f0b84227_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">1.38<\/td>\n<td data-align=\"left\">615<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-f529ffe544b78b7c0dcced50cc4db154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">1.16<\/td>\n<td data-align=\"left\">891<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">C\u2013O<\/td>\n<td data-align=\"left\">1.43<\/td>\n<td data-align=\"left\">350<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-c25395cd76461950ad5d76092a507742_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">1.23<\/td>\n<td data-align=\"left\">741<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-40632c15e57b05aa1d24920b873736c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">1.13<\/td>\n<td data-align=\"left\">1080<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p id=\"fs-idp29959728\">We can use bond energies to calculate approximate enthalpy changes for reactions where enthalpies of formation are not available. Calculations of this type will also tell us whether a reaction is exothermic or endothermic. An exothermic reaction (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-60a3042519bbff12247a1ac81bcd611e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/><em data-effect=\"italics\">H<\/em> negative, heat produced) results when the bonds in the products are stronger than the bonds in the reactants. An endothermic reaction (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-60a3042519bbff12247a1ac81bcd611e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/><em data-effect=\"italics\">H<\/em> positive, heat absorbed) results when the bonds in the products are weaker than those in the reactants.<\/p>\n<p id=\"fs-idp234028832\">The enthalpy change, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-60a3042519bbff12247a1ac81bcd611e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/><em data-effect=\"italics\">H<\/em>, for a chemical reaction is approximately equal to the sum of the energy required to break all bonds in the reactants (energy \u201cin\u201d, positive sign) plus the energy released when all bonds are formed in the products (energy \u201cout,\u201d negative sign). This can be expressed mathematically in the following way:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm40243760\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-8f3d1c5564f08e1d834723b514288015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#72;&#61;&#123;&#92;&#116;&#101;&#120;&#116;&#123;\u01a9&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#110;&#100;&#115;&#32;&#98;&#114;&#111;&#107;&#101;&#110;&#125;&#125;&#45;&#123;&#92;&#116;&#101;&#120;&#116;&#123;\u01a9&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#110;&#100;&#115;&#32;&#102;&#111;&#114;&#109;&#101;&#100;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"266\" style=\"vertical-align: -3px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp118053616\">In this expression, the symbol \u01a9 means \u201cthe sum of\u201d and D represents the bond energy in kilojoules per mole, which is always a positive number. The bond energy is obtained from a table (like <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>) and will depend on whether the particular bond is a single, double, or triple bond. Thus, in calculating enthalpies in this manner, it is important that we consider the bonding in all reactants and products. Because D values are typically averages for one type of bond in many different molecules, this calculation provides a rough estimate, not an exact value, for the enthalpy of reaction.<\/p>\n<p id=\"fs-idp17129504\">Consider the following reaction:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp51383312\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-35523131b2b55638a7da63ecf27b03ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#108;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#67;&#108;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -5px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp77710320\">or<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp56299152\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-d10aa1246cff23d5070f6d5f6efea8ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#45;&#72;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#108;&#45;&#67;&#108;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#45;&#67;&#108;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"243\" style=\"vertical-align: -5px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp201091440\">To form two moles of HCl, one mole of H\u2013H bonds and one mole of Cl\u2013Cl bonds must be broken. The energy required to break these bonds is the sum of the bond energy of the H\u2013H bond (436 kJ\/mol) and the Cl\u2013Cl bond (243 kJ\/mol). During the reaction, two moles of H\u2013Cl bonds are formed (bond energy = 432 kJ\/mol), releasing 2 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-c9448d0c3ab42155fc705b58fe04b3b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&times;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/> 432 kJ; or 864 kJ. Because the bonds in the products are stronger than those in the reactants, the reaction releases more energy than it consumes:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp14860448\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-60c7a196603f087487efbdbf382334a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#108;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#72;&#38;&#32;&#61;&#38;&#32;&#123;&#92;&#116;&#101;&#120;&#116;&#123;\u01a9&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#110;&#100;&#115;&#32;&#98;&#114;&#111;&#107;&#101;&#110;&#125;&#125;&#45;&#123;&#92;&#116;&#101;&#120;&#116;&#123;\u01a9&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#110;&#100;&#115;&#32;&#102;&#111;&#114;&#109;&#101;&#100;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#72;&#38;&#32;&#61;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#091;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#8722;&#72;&#125;&#125;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#108;&#8722;&#67;&#108;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#8722;&#67;&#108;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#61;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#091;&#52;&#51;&#54;&#43;&#50;&#52;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#51;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#56;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"321\" style=\"vertical-align: -27px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp29639024\">This excess energy is released as heat, so the reaction is exothermic. <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a> gives a value for the standard molar enthalpy of formation of HCl(g), <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-e79b9ccae671f511ed9806ea66ee3b68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#125;&#125;&#94;&#123;&deg;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -5px;\" \/> of \u201392.307 kJ\/mol. Twice that value is \u2013184.6 kJ, which agrees well with the answer obtained earlier for the formation of two moles of HCl.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Activity 2.5.1 &#8211; Using Bond Energies to Calculate Approximate Enthalpy<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><span data-type=\"title\">Changes<\/span> Methanol, CH<sub>3<\/sub>OH, may be an excellent alternative fuel. The high-temperature reaction of steam and carbon produces a mixture of the gases carbon monoxide, CO, and hydrogen, H<sub>2<\/sub>, from which methanol can be produced. Using the bond energies in <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>, calculate the approximate enthalpy change, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-60a3042519bbff12247a1ac81bcd611e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/><em data-effect=\"italics\">H<\/em>, for the reaction here:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp93467344\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-687ef22d2473877b0d04c1ac1c68081d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#79;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#72;&#125;&#125;&#95;&#123;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#72;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"243\" style=\"vertical-align: -5px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<div data-type=\"equation\"><\/div>\n<h2 id=\"fs-idp41458304\">Solution<\/h2>\n<p>First, we need to write the Lewis structures of the reactants and the products:<\/p>\n<p><span id=\"fs-idp525280\" class=\"scaled-down\" data-type=\"media\" data-alt=\"A set of Lewis diagrams show a chemical reaction. The first structure shows a carbon atom with a lone pair of electrons triple bonded to an oxygen with a lone pair of electrons. To the right of this structure is a plus sign, then the number 2 followed by a hydrogen atom single bonded to a hydrogen atom. To the right of this structure is a right-facing arrow followed by a hydrogen atom single bonded to a carbon atom that is single bonded to two hydrogen atoms and an oxygen atom with two lone pairs of electrons. The oxygen atom is also single bonded to a hydrogen atom.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_CH3OHLew_img-1-1.jpg\" alt=\"A set of Lewis diagrams show a chemical reaction. The first structure shows a carbon atom with a lone pair of electrons triple bonded to an oxygen with a lone pair of electrons. To the right of this structure is a plus sign, then the number 2 followed by a hydrogen atom single bonded to a hydrogen atom. To the right of this structure is a right-facing arrow followed by a hydrogen atom single bonded to a carbon atom that is single bonded to two hydrogen atoms and an oxygen atom with two lone pairs of electrons. The oxygen atom is also single bonded to a hydrogen atom.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-idp202067232\">From this, we see that \u0394<em data-effect=\"italics\">H<\/em> for this reaction involves the energy required to break a C\u2013O triple bond and two H\u2013H single bonds, as well as the energy produced by the formation of three C\u2013H single bonds, a C\u2013O single bond, and an O\u2013H single bond. We can express this as follows:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp76020096\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-e912cd6ccba7531b867fcb79631d00a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#108;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#72;&#38;&#32;&#61;&#38;&#32;&#123;&#92;&#116;&#101;&#120;&#116;&#123;\u01a9&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#110;&#100;&#115;&#32;&#98;&#114;&#111;&#107;&#101;&#110;&#125;&#125;&#45;&#123;&#92;&#116;&#101;&#120;&#116;&#123;\u01a9&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#110;&#100;&#115;&#32;&#102;&#111;&#114;&#109;&#101;&#100;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#72;&#38;&#32;&#61;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#091;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;&#125;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#8722;&#72;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#091;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#8722;&#72;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#8722;&#79;&#125;&#125;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#8722;&#72;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"425\" style=\"vertical-align: -16px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p>&nbsp;<\/p>\n<p id=\"fs-idp53734416\">Using the bond energy values in <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>, we obtain:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm103164880\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-c42556f76c7c677e61193adcf139523e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#72;&#38;&#32;&#61;&#92;&#108;&#101;&#102;&#116;&#091;&#49;&#48;&#56;&#48;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#51;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#091;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#53;&#48;&#43;&#52;&#54;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#92;&#32;&#38;&#32;&#61;&#45;&#49;&#48;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"377\" style=\"vertical-align: -11px;\" \/><\/div>\n<div data-type=\"equation\"><em>\u00a0<\/em><\/div>\n<p>&nbsp;<\/p>\n<p id=\"fs-idp126256512\">We can compare this value to the value calculated based on <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-bf8f16fcc53d42947fcdf2d73b636639_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#125;&#125;&#94;&#123;&deg;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -5px;\" \/> data from Appendix G:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp158903840\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-f04b954078f28385a78f3e4ec977302f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#72;&#38;&#32;&#61;&#92;&#108;&#101;&#102;&#116;&#091;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#125;&#125;&#94;&#123;&#36;&#92;&#100;&#101;&#103;&#114;&#101;&#101;&#36;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#72;&#125;&#125;&#95;&#123;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#72;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#091;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#125;&#125;&#94;&#123;&deg;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#79;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&times;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#125;&#125;&#94;&#123;&deg;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#92;&#32;&#38;&#32;&#61;&#92;&#108;&#101;&#102;&#116;&#091;&#45;&#50;&#48;&#49;&#46;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#091;&#45;&#49;&#49;&#48;&#46;&#53;&#50;&#43;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&times;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#92;&#32;&#38;&#32;&#61;&#45;&#57;&#48;&#46;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"444\" style=\"vertical-align: -22px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p>&nbsp;<\/p>\n<p id=\"fs-idp56832128\">Note that there is a fairly significant gap between the values calculated using the two different methods. This occurs because D values are the <em data-effect=\"italics\">average<\/em> of different bond strengths; therefore, they often give only rough agreement with other data.<\/p>\n<hr \/>\n<h2 id=\"fs-idp36454672\"><span data-type=\"title\">Check Your Learning<\/span><\/h2>\n<p>Ethyl alcohol, CH<sub>3<\/sub>CH<sub>2<\/sub>OH, was one of the first organic chemicals deliberately synthesized by humans. It has many uses in industry, and it is the alcohol contained in alcoholic beverages. It can be obtained by the fermentation of sugar or synthesized by the hydration of ethylene in the following reaction:<\/p>\n<p><span id=\"fs-idp144672\" class=\"scaled-down\" data-type=\"media\" data-alt=\"A set of Lewis structures show a chemical reaction. The first structure shows two carbon atoms that are double bonded together and are each single bonded to two hydrogen atoms. This structure is followed by a plus sign, then an oxygen atom with two lone pairs of electrons single bonded to two hydrogen atoms. A right-facing arrow leads to a carbon atom single bonded to three hydrogen atoms and a second carbon atom. The second carbon atom is single bonded to two hydrogen atoms and an oxygen atom with two lone pairs of electrons. The oxygen atom is single bonded to a hydrogen atom as well.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_Ethanol_img-1-1.jpg\" alt=\"A set of Lewis structures show a chemical reaction. The first structure shows two carbon atoms that are double bonded together and are each single bonded to two hydrogen atoms. This structure is followed by a plus sign, then an oxygen atom with two lone pairs of electrons single bonded to two hydrogen atoms. A right-facing arrow leads to a carbon atom single bonded to three hydrogen atoms and a second carbon atom. The second carbon atom is single bonded to two hydrogen atoms and an oxygen atom with two lone pairs of electrons. The oxygen atom is single bonded to a hydrogen atom as well.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-idp27645248\">Using the bond energies in <a class=\"autogenerated-content\" href=\"#fs-idm44464336\">(Table 2.5.2)<\/a>, calculate an approximate enthalpy change, \u0394<em data-effect=\"italics\">H<\/em>, for this reaction.<\/p>\n<div id=\"fs-idp88406224\" data-type=\"note\">\n<h3 style=\"text-align: right\" data-type=\"title\">Answer<\/h3>\n<p id=\"fs-idp24314032\" style=\"text-align: right\">\u201335 kJ<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idm34679504\" class=\"bc-section section\" data-depth=\"1\">\n<h2 data-type=\"title\">Ionic Bond Strength and Lattice Energy<\/h2>\n<p id=\"fs-idm57606496\">An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The <span data-type=\"term\">lattice energy (\u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub>)<\/span> of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid MX, the lattice energy is the enthalpy change of the process:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp69066736\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-70113b4c807155efff9b515b0ff0847d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#88;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#125;&#125;&#94;&#123;&#110;&#92;&#116;&#101;&#120;&#116;&#123;&#43;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#94;&#123;&#110;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#97;&#116;&#116;&#105;&#99;&#101;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"348\" style=\"vertical-align: -5px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm45000976\">Note that we are using the convention where the ionic solid is separated into ions, so our lattice energies will be <em data-effect=\"italics\">endothermic<\/em> (positive values). Some texts use the equivalent but opposite convention, defining lattice energy as the energy released when separate ions combine to form a lattice and giving negative (exothermic) values. Thus, if you are looking up lattice energies in another reference, be certain to check which definition is being used. In both cases, a larger magnitude for lattice energy indicates a more stable ionic compound. For sodium chloride, \u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub> = 769 kJ. Thus, it requires 769 kJ to separate one mole of solid NaCl into gaseous Na<sup>+<\/sup> and Cl<sup>\u2013<\/sup> ions. When one mole, each of gaseous Na<sup>+<\/sup> and Cl<sup>\u2013<\/sup> ions form solid NaCl, 769 kJ of heat is released.<\/p>\n<p id=\"fs-idp17453088\">The lattice energy \u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub> of an ionic crystal can be expressed by the following equation (derived from Coulomb\u2019s law, governing the forces between electric charges):<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm6917696\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-98fb146b38177ac0e494b646c269574a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#97;&#116;&#116;&#105;&#99;&#101;&#125;&#125;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#90;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#43;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#90;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"172\" style=\"vertical-align: -8px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp14812032\">in which C is a constant that depends on the type of crystal structure; Z<sup>+<\/sup> and Z<sup>\u2013<\/sup> are the charges on the ions; and R<sub>o<\/sub> is the interionic distance (the sum of the radii of the positive and negative ions). Thus, the lattice energy of an ionic crystal increases rapidly as the charges of the ions increase and the sizes of the ions decrease. When all other parameters are kept constant, doubling the charge of both the cation and anion quadruples the lattice energy. For example, the lattice energy of LiF (Z<sup>+<\/sup> and Z<sup>\u2013<\/sup> = 1) is 1023 kJ\/mol, whereas that of MgO (Z<sup>+<\/sup> and Z<sup>\u2013<\/sup> = 2) is 3900 kJ\/mol (R<sub>o<\/sub> is nearly the same\u2014about 200 pm for both compounds).<\/p>\n<p id=\"fs-idp119064064\">Different interatomic distances produce different lattice energies. For example, we can compare the lattice energy of MgF<sub>2<\/sub> (2957 kJ\/mol) to that of MgI<sub>2<\/sub> (2327 kJ\/mol) to observe the effect on lattice energy of the smaller ionic size of F<sup>\u2013<\/sup> as compared to I<sup>\u2013<\/sup>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Activity 2.5.2 &#8211; Lattice Energy Comparisons<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The precious gem ruby is aluminum oxide, Al<sub>2<\/sub>O<sub>3<\/sub>, containing traces of Cr<sup>3+<\/sup>. The compound Al<sub>2<\/sub>Se<sub>3<\/sub> is used in the fabrication of some semiconductor devices. Which has the larger lattice energy, Al<sub>2<\/sub>O<sub>3<\/sub> or Al<sub>2<\/sub>Se<sub>3<\/sub>?<\/p>\n<h2 id=\"fs-idm3251216\">Solution<\/h2>\n<p>In these two ionic compounds, the charges Z<sup>+<\/sup> and Z<sup>\u2013<\/sup> are the same, so the difference in lattice energy will depend upon R<sub>o<\/sub>. The O<sup>2\u2013<\/sup> ion is smaller than the Se<sup>2\u2013<\/sup> ion. Thus, Al<sub>2<\/sub>O<sub>3<\/sub> would have a shorter interionic distance than Al<sub>2<\/sub>Se<sub>3<\/sub>, and Al<sub>2<\/sub>O<sub>3<\/sub> would have the larger lattice energy.<\/p>\n<hr \/>\n<h2 id=\"fs-idp49595360\"><span data-type=\"title\">Check Your Learning<\/span><\/h2>\n<p>Zinc oxide, ZnO, is a very effective sunscreen. How would the lattice energy of ZnO compare to that of NaCl?<\/p>\n<div id=\"fs-idp176836208\" data-type=\"note\">\n<h3 style=\"text-align: right\" data-type=\"title\">Answer<\/h3>\n<p id=\"fs-idp821600\" style=\"text-align: right\">ZnO would have the larger lattice energy because the Z values of both the cation and the anion in ZnO are greater, and the interionic distance of ZnO is smaller than that of NaCl.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idp112167568\" class=\"bc-section section\" data-depth=\"1\">\n<h2 data-type=\"title\">The Born-Haber Cycle<\/h2>\n<p id=\"fs-idp51725632\">It is not possible to measure lattice energies directly. However, the lattice energy can be calculated using the equation given in the previous section or by using a thermochemical cycle. The <span data-type=\"term\">Born-Haber cycle<\/span> is an application of Hess\u2019s law that breaks down the formation of an ionic solid into a series of individual steps:<\/p>\n<ul id=\"fs-idp77725760\" data-bullet-style=\"bullet\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-8c8e9c9f1808af83ca132c286a192c25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#125;&#125;&#94;&#123;&#92;&#99;&#105;&#114;&#99;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -5px;\" \/> the standard enthalpy of formation of the compound<\/li>\n<li><em data-effect=\"italics\">IE<\/em>, the ionization energy of the metal<\/li>\n<li><em data-effect=\"italics\">EA<\/em>, the electron affinity of the nonmetal<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-bad69b87c4cb72389d2def77964fc93b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#36;&#92;&#68;&#101;&#108;&#116;&#97;&#36;&#125;&#123;&#72;&#125;&#95;&#123;&#115;&#125;&#94;&#123;&#92;&#99;&#105;&#114;&#99;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"43\" style=\"vertical-align: -4px;\" \/> the enthalpy of sublimation of the metal<\/li>\n<li><em data-effect=\"italics\">D<\/em>, the bond dissociation energy of the nonmetal<\/li>\n<li>\u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub>, the lattice energy of the compound<\/li>\n<\/ul>\n<p id=\"fs-idm6705632\"><a class=\"autogenerated-content\" href=\"#CNX_Chem_07_05_BornHaber\">(Figure 2.5.2)<\/a> diagrams the Born-Haber cycle for the formation of solid cesium fluoride.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_07_05_BornHaber\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\"><\/div>\n<figure style=\"width: 975px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_BornHaber-1-1.jpg\" alt=\"A diagram is shown. An upward facing arrow is drawn to the far left of the chart and is labeled \u201cH increasing.\u201d A horizontal line is drawn at the bottom of the chart. A downward-facing, vertical arrow to the left side of this line is labeled, \u201cOverall change.\u201d Beside this arrow is another label, \u201ccapital delta H subscript f, equals negative 553.5 k J per mol, ( Enthalpy of formation ).\u201d Three horizontal lines, one above the other, and all above the bottom line, are labeled, from bottom to top, as: \u201cC s ( s ), plus sign, one half F subscript 2, ( g ),\u201d \u201cC s ( g ), plus sign, one half F subscript 2, ( g ),\u201d and \u201cC s, superscript positive sign, ( g ), plus sign, one half F subscript 2, ( g ).\u201d Each of these lines is connected by an upward-facing vertical arrow. Each arrow is labeled, \u201ccapital delta H subscript 1, equals 76.5 k J per mol, ( Enthalpy of sublimation ),\u201d \u201ccapital delta H subscript 2, equals 375.7 k J per mol, ( ionization energy ),\u201d and \u201ccapital delta H subscript 3 equals 79.4 k J \/ mol ( one half dissociation energy ).\u201d Another horizontal line is drawn in the center top portion of the diagram and is labeled \u201cC s, superscript positive sign, ( g ), plus sign, F, ( g ).\u201d There is one more horizontal line drawn to the right of the overall diagram and located halfway down the image. An arrow connects the top line to this line and is labeled, \u201ccapital delta H equals negative 328.2 k J \/ mol ( electron affinity ).\u201d The line is labeled, \u201cC s superscript positive sign ( g ) plus F superscript negative sign ( g ).\u201d The arrow connecting this line to the bottom line is labeled, \u201cnegative capital delta H subscript lattice equals negative 756.9 k J \/ mol.\u201d The arrow points to a label on the bottom line which reads, \u201cC s F ( s ).\u201d\" width=\"975\" height=\"528\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 2.5.2 &#8211; The Born-Haber cycle shows the relative energies of each step involved in the formation of an ionic solid from the necessary elements in their reference states.<\/strong><\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-idp53345328\">We begin with the elements in their most common states, Cs(<em data-effect=\"italics\">s<\/em>) and F<sub>2<\/sub>(<em data-effect=\"italics\">g<\/em>). The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-8f7e9038ee2e555c291d56d73e686773_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&Delta;&#125;&#123;&#72;&#125;&#95;&#123;&#115;&#125;&#94;&#123;&deg;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> represents the conversion of solid cesium into a gas, and then the ionization energy converts the gaseous cesium atoms into cations. In the next step, we account for the energy required to break the F\u2013F bond to produce fluorine atoms. Converting one mole of fluorine atoms into fluoride ions is an exothermic process, so this step gives off energy (the electron affinity) and is shown as decreasing along the <em data-effect=\"italics\">y<\/em>-axis. We now have one mole of Cs cations and one mole of F anions. These ions combine to produce solid cesium fluoride. The enthalpy change in this step is the negative of the lattice energy, so it is also an exothermic quantity. The total energy involved in this conversion is equal to the experimentally determined enthalpy of formation, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-7d6e7a1b151cb249a0f634a913b8e85f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&Delta;&#125;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#125;&#125;&#94;&#123;&deg;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"24\" style=\"vertical-align: -6px;\" \/> of the compound from its elements. In this case, the overall change is exothermic.<\/p>\n<p id=\"fs-idm23453808\">Hess\u2019s law can also be used to show the relationship between the enthalpies of the individual steps and the enthalpy of formation. <a class=\"autogenerated-content\" href=\"#fs-idm33829552\">(Table 2.5.3)<\/a> shows this for cesium fluoride, CsF.<\/p>\n<table id=\"fs-idm33829552\" class=\"aligncenter\" summary=\"This table has two columns and six rows. The first row is labeled, \u201cEnthalpy of sublimation of C s ( s )\u201d and the enthalpy reaction is C s ( s ) yields C s ( g ). Beside this equation is capital delta H which equals capital delta H subscript s superscript degree symbol which also equals 76.5 k J. The second row is labeled, \u201cOne-half of the bond energy of C l subscript 2.\u201d The equation for this is one half C l subscript 2 ( g ) yields C l ( g ). Beside this equation is capital delta H equals one half D which also equals 122 k J. The third row is labeled, \u201cIonization Energy of N a ( g ).\u201d The equation for the ionization energy of N a ( g ) is N a ( g ) yields N a superscript positive sign ( g ) plus lower case e superscript negative sign. Beside this equation is capital delta H equals I E which also equals 496 k J. The fourth row is labeled, \u201cNegative of the electron affinity of C l.\u201d The equation for this is C l ( g ) plus lowercase e superscript negative sign yields C l superscript negative sign ( g ). Beside this equation is capital delta H equals negative E A which also equals negative 368 k J. The fifth row is labeled \u201cNegative of the lattice energy of N a C l ( s ).\u201d The equation for this is N a superscript positive sign ( g ) plus C l superscript negative sign ( g ) yields N a C l ( s ). Beside this equation is capital delta H equals negative capital delta H subscript lattice which also equals unknown. The sixth and final row is labeled, \u201cEnthalpy of formation of N a C l ( s ), add steps 1 - 5.\u201d The equation for this is capital delta H equals capital delta H subscript f superscript degree symbol which also equals capital delta H subscript s superscript degree symbol plus one-half D plus I E plus negative E A plus negative capital delta H subscript lattice. Underneath that equation, is another which is N a ( s ) plus one-half C l subscript 2 ( g ) yields N a C l ( s ) which equals negative 411 k J.\" data-label=\"\">\n<caption><strong>Table 2.5.3 &#8211; The enthalpies of the individual steps of the formation of CsF<\/strong><\/caption>\n<tbody>\n<tr valign=\"middle\">\n<td data-align=\"left\">Enthalpy of sublimation of Cs(<em data-effect=\"italics\">s<\/em>)<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-59ad04bbb582d10a1e898765da6a81d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#115;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#115;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -5px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-a64a922e4d3de5c0cfefa1e9fc56bc7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#61;&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#115;&#125;&#94;&#123;&#92;&#99;&#105;&#114;&#99;&#125;&#61;&#55;&#54;&#46;&#53;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#47;&#109;&#111;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"205\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"middle\">\n<td data-align=\"left\">One-half of the bond energy of F<sub>2<\/sub><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-53352b8a6d2f8e5c9cbab6a7f7d6f5fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"119\" style=\"vertical-align: -6px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-6c88331357e6efea349a36a7efe2f17e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#68;&#61;&#55;&#57;&#46;&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#47;&#109;&#111;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"199\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr valign=\"middle\">\n<td data-align=\"left\">Ionization energy of Cs(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-522f173f97b6b058a7c8ce6c4634ed25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#115;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#115;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#43;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#125;&#94;&#45;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"170\" style=\"vertical-align: -5px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-a66a421c8958cb12d0a9e08d0da7860a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#61;&#73;&#69;&#61;&#51;&#55;&#53;&#46;&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#47;&#109;&#111;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"199\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"middle\">\n<td data-align=\"left\">Negative of the electron affinity of F<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-079a4f25eb4cc014c26b49a093a07597_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#125;&#94;&#45;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#125;&#94;&#45;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -5px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-217ab24b4d4c147902d1e8a6ec924298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#45;&#69;&#65;&#61;&#45;&#51;&#50;&#56;&#46;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#47;&#109;&#111;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"238\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"middle\">\n<td data-align=\"left\">Negative of the lattice energy of CsF(<em data-effect=\"italics\">s<\/em>)<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-764daa826ba0e49523de582a23bd2f21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#115;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#43;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#125;&#94;&#45;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#115;&#70;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"209\" style=\"vertical-align: -5px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-18e239a9eb32d517a81e9610d40d7ba8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#61;&#45;&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#97;&#116;&#116;&#105;&#99;&#101;&#125;&#125;&#61;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"163\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr valign=\"middle\">\n<td data-align=\"left\">Enthalpy of formation of CsF(<em data-effect=\"italics\">s<\/em>), add steps 1\u20135<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-3a7d606f940613b79967694a04cf1d6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#61;&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#102;&#125;&#94;&#123;&#92;&#99;&#105;&#114;&#99;&#125;&#61;&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#115;&#125;&#94;&#123;&#92;&#99;&#105;&#114;&#99;&#125;&#43;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#68;&#43;&#73;&#69;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#69;&#65;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#97;&#116;&#116;&#105;&#99;&#101;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#115;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#115;&#70;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"448\" style=\"vertical-align: -18px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-07ea5ba3f668d0f7e772e0f2026eb49d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#61;&#45;&#53;&#53;&#51;&#46;&#53;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#47;&#109;&#111;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"166\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-idp112167568\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-idp28364752\">Thus, the lattice energy can be calculated from other values. For cesium fluoride, using this data, the lattice energy is:<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp37818096\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-0d683d8a8e9aacd3505b7235011f4421_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#97;&#116;&#116;&#105;&#99;&#101;&#125;&#125;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#53;&#51;&#46;&#53;&#43;&#55;&#54;&#46;&#53;&#43;&#55;&#57;&#46;&#52;&#43;&#51;&#55;&#53;&#46;&#55;&#43;&#51;&#50;&#56;&#46;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#47;&#109;&#111;&#108;&#125;&#61;&#49;&#52;&#49;&#51;&#46;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#74;&#47;&#109;&#111;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"571\" style=\"vertical-align: -5px;\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm78151632\">The Born-Haber cycle may also be used to calculate any one of the other quantities in the equation for lattice energy, provided that the remainder is known. For example, if the relevant enthalpy of sublimation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-f67d5a5205d45c3998870a5111a72903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#115;&#125;&#94;&#123;&#92;&#99;&#105;&#114;&#99;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"43\" style=\"vertical-align: -4px;\" \/> ionization energy (IE), bond dissociation enthalpy (D), lattice energy \u0394<em data-effect=\"italics\">H<\/em><sub>lattice,<\/sub> and standard enthalpy of formation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-0c7cfd2941363e502f45d86b2607f3f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#125;&#125;&#94;&#123;&#92;&#99;&#105;&#114;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -5px;\" \/> are known, the Born-Haber cycle can be used to determine the electron affinity of an atom.<\/p>\n<p id=\"fs-idm10039728\">Lattice energies calculated for ionic compounds are typically much higher than bond dissociation energies measured for covalent bonds. Whereas lattice energies typically fall in the range of 600\u20134000 kJ\/mol (some even higher), covalent bond dissociation energies are typically between 150\u2013400 kJ\/mol for single bonds. Keep in mind, however, that these are not directly comparable values. For ionic compounds, lattice energies are associated with many interactions, as cations and anions pack together in an extended lattice. For covalent bonds, the bond dissociation energy is associated with the interaction of just two atoms.<\/p>\n<\/div>\n<h1>Key Concepts and Summary<\/h1>\n<p>The strength of a covalent bond is measured by its bond dissociation energy, that is, the amount of energy required to break that particular bond in a mole of molecules. Multiple bonds are stronger than single bonds between the same atoms. The enthalpy of a reaction can be estimated based on the energy input required to break bonds and the energy released when new bonds are formed. For ionic bonds, the lattice energy is the energy required to separate one mole of a compound into its gas phase ions. Lattice energy increases for ions with higher charges and shorter distances between ions. Lattice energies are often calculated using the Born-Haber cycle, a thermochemical cycle including all of the energetic steps involved in converting elements into an ionic compound.<\/p>\n<h2 data-type=\"title\">Key Equations<\/h2>\n<ul id=\"fs-idp25406976\" data-bullet-style=\"bullet\">\n<li>Bond energy for a diatomic molecule: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-89bf551fe9cabd90c6b9a3c95c4ae392_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#89;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#45;&#89;&#125;&#125;&#61;&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#99;&#105;&#114;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"328\" style=\"vertical-align: -5px;\" \/><\/li>\n<li>Enthalpy change: \u0394<em data-effect=\"italics\">H<\/em> = \u01a9D<sub>bonds broken<\/sub> \u2013 \u01a9D<sub>bonds formed<\/sub><\/li>\n<li>Lattice energy for a solid MX: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-0df38e5a1bed47d4cfbe11c507795f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#88;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#125;&#125;&#94;&#123;&#110;&#92;&#116;&#101;&#120;&#116;&#123;&#43;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#94;&#123;&#110;&#45;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#97;&#116;&#116;&#105;&#99;&#101;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"348\" style=\"vertical-align: -5px;\" \/><\/li>\n<li>Lattice energy for an ionic crystal: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-ba8ac94bf57d8af040e9cd320f9888ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#123;&#72;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#97;&#116;&#116;&#105;&#99;&#101;&#125;&#125;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#90;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#43;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#90;&#125;&#94;&#45;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"173\" style=\"vertical-align: -8px;\" \/><\/li>\n<\/ul>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">End of Chapter Exercises<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-idp18527664\" data-type=\"exercise\">\n<div id=\"fs-idm31250240\" data-type=\"problem\">\n<p id=\"fs-idp75695024\">Which bond in each of the following pairs of bonds is the strongest?<\/p>\n<p id=\"fs-idp174181168\">(1a) C\u2013C or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-551c7343192e9bf18bd2458a5b9f2dbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-idp191457408\">(1b) C\u2013N or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-f529ffe544b78b7c0dcced50cc4db154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-idm37995600\">(1c)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-40632c15e57b05aa1d24920b873736c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-c25395cd76461950ad5d76092a507742_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-idp19512320\">(1d) H\u2013F or H\u2013Cl<\/p>\n<p id=\"fs-idm2333776\">(1e) C\u2013H or O\u2013H<\/p>\n<p id=\"fs-idp120232048\">(1f) C\u2013N or C\u2013O<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp16780032\" data-type=\"exercise\">\n<div id=\"fs-idp37241056\" data-type=\"problem\">\n<p id=\"fs-idm20426752\">Using the bond energies in <a class=\"autogenerated-content\" href=\"#fs-idp13638832\">(Table 2.5.1)<\/a>, determine the approximate enthalpy change for each of the following reactions:<\/p>\n<p id=\"fs-idp13624240\">(2a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-98a42b3690853f3993d9e760fae1a9b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#114;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#66;&#114;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"213\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"fs-idm48592992\">(2b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-28456116a6ac0bbaa56edcf1b889b545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#72;&#125;&#125;&#95;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#72;&#125;&#125;&#95;&#123;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#73;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"281\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"fs-idm27033728\">(2c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-92c0d3b7aa967c58120b1b288653b4af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#125;&#95;&#123;&#50;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#79;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"332\" style=\"vertical-align: -5px;\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">(a) \u2212114 kJ; (b) 30 kJ; (c) \u22121055 kJ<\/span><\/p>\n<\/div>\n<div id=\"fs-idp55504208\" style=\"padding-left: 40px\" data-type=\"solution\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp57429280\" data-type=\"exercise\">\n<div id=\"fs-idp48795376\" data-type=\"problem\">\n<p id=\"fs-idp240397744\">Using the bond energies in <a class=\"autogenerated-content\" href=\"#fs-idp13638832\">(Table 2.5.1)<\/a>, determine the approximate enthalpy change for each of the following reactions:<\/p>\n<p id=\"fs-idp188770912\">(3a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-9728368438745c4ab1dafbde48e01862_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#108;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#108;&#70;&#125;&#125;&#95;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"225\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"fs-idp123909120\">(3b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-952b89d980a6beaa78567e5a10e42874_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#61;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#72;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#51;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#67;&#72;&#125;&#125;&#95;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"306\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"fs-idp30139536\">(3c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-454d05d3e354d63b365928a324a41c1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#125;&#95;&#123;&#50;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#54;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#55;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#79;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#54;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"341\" style=\"vertical-align: -5px;\" \/><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp28520976\" data-type=\"exercise\">\n<div id=\"fs-idp28294656\" data-type=\"problem\">\n<p id=\"fs-idp220216256\">(4) When a molecule can form two different structures, the structure with the stronger bonds is usually the more stable form. Use bond energies to predict the correct structure of the hydroxylamine molecule:<\/p>\n<p><span id=\"fs-idm6604832\" data-type=\"media\" data-alt=\"Two Lewis structures are shows with the word \u201cor\u201d written in between them. The left structure shows a nitrogen atom with one lone pair of electrons single bonded to two hydrogen atoms. It is also bonded to an oxygen atom with two lone pairs of electrons. The oxygen atom is bonded to a hydrogen atom. The right structure shows a nitrogen atom single bonded to three hydrogen atoms and an oxygen atom with three lone pairs of electrons.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_Hydroxya_img-1-1.jpg\" alt=\"Two Lewis structures are shows with the word \u201cor\u201d written in between them. The left structure shows a nitrogen atom with one lone pair of electrons single bonded to two hydrogen atoms. It is also bonded to an oxygen atom with two lone pairs of electrons. The oxygen atom is bonded to a hydrogen atom. The right structure shows a nitrogen atom single bonded to three hydrogen atoms and an oxygen atom with three lone pairs of electrons.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">The greater bond energy is in the figure on the left. It is the more stable form.<\/span><\/p>\n<\/div>\n<div id=\"fs-idp16844192\" style=\"padding-left: 40px\" data-type=\"solution\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp20766256\" data-type=\"exercise\">\n<div id=\"fs-idm6034544\" data-type=\"problem\">\n<p id=\"fs-idm22015856\">(5) How does the bond energy of HCl(<em data-effect=\"italics\">g<\/em>) differ from the standard enthalpy of formation of HCl(<em data-effect=\"italics\">g<\/em>)?<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp19159472\" data-type=\"exercise\">\n<div id=\"fs-idm7424064\" data-type=\"problem\">\n<p id=\"fs-idp16480976\">(6) Using the standard enthalpy of formation data in <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a>, show how the standard enthalpy of formation of HCl(<em data-effect=\"italics\">g<\/em>) can be used to determine the bond energy.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"fs-idp65612672\" data-type=\"solution\">\n<p>(7) Using the standard enthalpy of formation data in <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a>, calculate the bond energy of the carbon-sulfur double bond in CS<sub>2<\/sub>.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp65498352\" data-type=\"exercise\">\n<div id=\"fs-idp23041056\" data-type=\"problem\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp19660960\" data-type=\"exercise\">\n<div id=\"fs-idp16871040\" data-type=\"problem\">\n<p id=\"fs-idp16871296\">(8) Using the standard enthalpy of formation data in <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a>, determine which bond is stronger: the S\u2013F bond in SF<sub>4<\/sub>(<em data-effect=\"italics\">g<\/em>) or in SF<sub>6<\/sub>(<em data-effect=\"italics\">g<\/em>)?<\/p>\n<p>&nbsp;<\/p>\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">The S\u2013F bond in SF<\/span><sub style=\"text-align: initial\">4<\/sub><span style=\"text-align: initial;font-size: 1em\"> is stronger.<\/span><\/p>\n<\/div>\n<div id=\"fs-idp19698336\" style=\"padding-left: 40px\" data-type=\"solution\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm2894352\" data-type=\"exercise\">\n<div id=\"fs-idm2894096\" data-type=\"problem\">\n<p id=\"fs-idp88452992\">(9) Using the standard enthalpy of formation data in <a class=\"target-chapter\" href=\"\/contents\/667adccf-f900-4d86-a13d-409c014086ea\">Appendix G<\/a>, determine which bond is stronger: the P\u2013Cl bond in PCl<sub>3<\/sub>(<em data-effect=\"italics\">g<\/em>) or in PCl<sub>5<\/sub>(<em data-effect=\"italics\">g<\/em>)?<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm22310960\" data-type=\"exercise\">\n<div id=\"fs-idp16666336\" data-type=\"problem\">\n<p id=\"fs-idp16666592\">(10) Complete the following Lewis structure by adding bonds (not atoms), and then indicate the longest bond:<\/p>\n<p>&nbsp;<\/p>\n<p><span id=\"fs-idp123644096\" data-type=\"media\" data-alt=\"A Lewis structure is shown that is missing its bonds. It shows a horizontal row of six carbon atoms, equally spaced. Three hydrogen atoms are drawn around the first carbon, two around the second, one above the fifth, and two by the sixth.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_C6H8Lew_img-1-1.jpg\" alt=\"A Lewis structure is shown that is missing its bonds. It shows a horizontal row of six carbon atoms, equally spaced. Three hydrogen atoms are drawn around the first carbon, two around the second, one above the fifth, and two by the sixth.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-idp44310208\" data-type=\"solution\">\n<p id=\"fs-idp46735152\"><span data-type=\"newline\">\u00a0<\/span><\/p>\n<p><span id=\"fs-idp57448112\" data-type=\"media\" data-alt=\"A Lewis structure is shown. A carbon atom that is single bonded to three hydrogen atoms is bonded to a second carbon atom. The second carbon atom is single bonded to two hydrogen atoms. The second carbon atom is single bonded to a third carbon atom that is triple bonded to a fourth carbon atom and single bonded to a fifth carbon atom. The fifth carbon atom is single bonded to a hydrogen atom and double bonded to a sixth carbon atom that is single bonded to two hydrogen atoms.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_C6H8ans_img-1-1.jpg\" alt=\"A Lewis structure is shown. A carbon atom that is single bonded to three hydrogen atoms is bonded to a second carbon atom. The second carbon atom is single bonded to two hydrogen atoms. The second carbon atom is single bonded to a third carbon atom that is triple bonded to a fourth carbon atom and single bonded to a fifth carbon atom. The fifth carbon atom is single bonded to a hydrogen atom and double bonded to a sixth carbon atom that is single bonded to two hydrogen atoms.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"padding-left: 40px\"><span data-type=\"newline\"><em>Solution<\/em><\/span><\/p>\n<p style=\"padding-left: 40px\"><span data-type=\"newline\"><br \/>\n<\/span> The C\u2013C single bonds are longest.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp57420000\" data-type=\"exercise\">\n<div id=\"fs-idp78457408\" data-type=\"problem\">\n<p id=\"fs-idp78457664\">(11) Use the bond energy to calculate an approximate value of \u0394<em data-effect=\"italics\">H<\/em> for the following reaction. Which is the more stable form of FNO<sub>2<\/sub>?<\/p>\n<p><span id=\"fs-idp40889632\" data-type=\"media\" data-alt=\"Two Lewis structures are shown with a right-facing arrow in between. The left structure shows a nitrogen atom double bonded to an oxygen atom with two lone pairs of electrons. It is also bonded to a fluorine atom and another oxygen atom, each with three lone pairs of electrons. The right structure shows an oxygen atom with two lone pairs of electrons double bonded to a nitrogen atom with one lone pair of electrons. This nitrogen atom is single bonded to an oxygen with two lone pairs of electrons. The oxygen atom is single bonded to a fluorine atom with three lone pairs of electrons.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/uploads\/sites\/989\/2020\/04\/CNX_Chem_07_05_FNO2_img-1-1.jpg\" alt=\"Two Lewis structures are shown with a right-facing arrow in between. The left structure shows a nitrogen atom double bonded to an oxygen atom with two lone pairs of electrons. It is also bonded to a fluorine atom and another oxygen atom, each with three lone pairs of electrons. The right structure shows an oxygen atom with two lone pairs of electrons double bonded to a nitrogen atom with one lone pair of electrons. This nitrogen atom is single bonded to an oxygen with two lone pairs of electrons. The oxygen atom is single bonded to a fluorine atom with three lone pairs of electrons.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp12625232\" data-type=\"exercise\">\n<div id=\"fs-idp15947632\" data-type=\"problem\"><\/div>\n<\/div>\n<div id=\"fs-idp46666496\" data-type=\"exercise\">\n<div id=\"fs-idp46666752\" data-type=\"problem\">\n<p id=\"fs-idp794240\">(12) The lattice energy of LiF is 1023 kJ\/mol, and the Li\u2013F distance is 200.8 pm. NaF crystallizes in the same structure as LiF but with a Na\u2013F distance of 231 pm. Which of the following values most closely approximates the lattice energy of NaF: 510, 890, 1023, 1175, or 4090 kJ\/mol? Explain your choice.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp236067168\" data-type=\"exercise\">\n<div id=\"fs-idp236067424\" data-type=\"problem\">\n<p id=\"fs-idp236067680\">For which of the following substances is the least energy required to convert one mole of the solid into separate ions?<\/p>\n<p id=\"fs-idp211527872\">(13a) MgO<\/p>\n<p id=\"fs-idp90299856\">(13b) SrO<\/p>\n<p id=\"fs-idp90300240\">(13c) KF<\/p>\n<p id=\"fs-idp174354464\">(13d) CsF<\/p>\n<p id=\"fs-idp174354848\">(13e) MgF<sub>2<\/sub><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"fs-idm39061296\" data-type=\"exercise\">\n<div id=\"fs-idm39061040\" data-type=\"problem\">\n<p id=\"fs-idm39060784\">(14) The reaction of a metal, M, with a halogen, X<sub>2<\/sub>, proceeds by an exothermic reaction as indicated by this equation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-content\/ql-cache\/quicklatex.com-cc9efc6aafb452f1394bf3bb59daed4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#36;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#36;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#88;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"207\" style=\"vertical-align: -5px;\" \/> For each of the following, indicate which option will make the reaction more exothermic. Explain your answers.<\/p>\n<p id=\"fs-idp48865984\">(14a) a large radius vs. a small radius for M<sup>+2<\/sup><\/p>\n<p id=\"fs-idm52945984\">(14b) a high ionization energy vs. a low ionization energy for M<\/p>\n<p id=\"fs-idm37748736\">(14c) an increasing bond energy for the halogen<\/p>\n<p id=\"fs-idm37748352\">(14d) a decreasing electron affinity for the halogen<\/p>\n<p id=\"fs-idm38878512\">(14e) an increasing size of the anion formed by the halogen<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp55219680\" data-type=\"exercise\">\n<div id=\"fs-idp10681296\" data-type=\"problem\">\n<p id=\"fs-idp10681552\">(15) The lattice energy of LiF is 1023 kJ\/mol, and the Li\u2013F distance is 201 pm. MgO crystallizes in the same structure as LiF but with a Mg\u2013O distance of 205 pm. Which of the following values most closely approximates the lattice energy of MgO: 256 kJ\/mol, 512 kJ\/mol, 1023 kJ\/mol, 2046 kJ\/mol, or 4008 kJ\/mol? Explain your choice.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">4008 kJ\/mol; both ions in MgO have twice the charge of the ions in LiF; the bond length is very similar and both have the same structure; a quadrupling of the energy is expected based on the equation for lattice energy<\/span><\/p>\n<\/div>\n<div id=\"fs-idm27862768\" style=\"padding-left: 40px\" data-type=\"solution\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm27862256\" data-type=\"exercise\">\n<div id=\"fs-idp23005264\" data-type=\"problem\">\n<p id=\"fs-idp23005520\">Which compound in each of the following pairs has the larger lattice energy? Note: Mg<sup>2+<\/sup> and Li<sup>+<\/sup> have similar radii; O<sup>2\u2013<\/sup> and F<sup>\u2013<\/sup> have similar radii. Explain your choices.<\/p>\n<p id=\"fs-idm42318048\">(16a) MgO or MgSe<\/p>\n<p id=\"fs-idp14229536\">(16b) LiF or MgO<\/p>\n<p id=\"fs-idp14229920\">(16c) Li<sub>2<\/sub>O or LiCl<\/p>\n<p id=\"fs-idm39601280\">(16d) Li<sub>2<\/sub>Se or MgO<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp29388832\" data-type=\"exercise\">\n<div id=\"fs-idp19286528\" data-type=\"problem\">\n<p id=\"fs-idp19286784\">Which compound in each of the following pairs has the larger lattice energy? Note: Ba<sup>2+<\/sup> and<\/p>\n<p id=\"fs-idp1147008\">K<sup>+<\/sup> have similar radii; S<sup>2\u2013<\/sup> and Cl<sup>\u2013<\/sup> have similar radii. Explain your choices.<\/p>\n<p id=\"fs-idp26686336\">(17a) K<sub>2<\/sub>O or Na<sub>2<\/sub>O<\/p>\n<p id=\"fs-idp81635552\">(17b) K<sub>2<\/sub>S or BaS<\/p>\n<p id=\"fs-idp55153232\">(17c) KCl or BaS<\/p>\n<p id=\"fs-idp55110752\">(17d) BaS or BaCl<sub>2<\/sub><\/p>\n<p>&nbsp;<\/p>\n<p style=\"padding-left: 40px\"><em>Solution<\/em><\/p>\n<p style=\"padding-left: 40px\"><span style=\"text-align: initial;font-size: 1em\">(a) Na<\/span><sub style=\"text-align: initial\">2<\/sub><span style=\"text-align: initial;font-size: 1em\">O; Na<\/span><sup style=\"text-align: initial\">+<\/sup><span style=\"text-align: initial;font-size: 1em\"> has a smaller radius than K<\/span><sup style=\"text-align: initial\">+<\/sup><span style=\"text-align: initial;font-size: 1em\">; (b) BaS; Ba has a larger charge than K; (c) BaS; Ba and S have larger charges; (d) BaS; S has a larger charge<\/span><\/p>\n<\/div>\n<div id=\"fs-idm42840528\" style=\"padding-left: 40px\" data-type=\"solution\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp51586816\" data-type=\"exercise\">\n<div id=\"fs-idp51587072\" data-type=\"problem\">\n<p id=\"fs-idp51587328\">Which of the following compounds requires the most energy to convert one mole of the solid into separate ions?<\/p>\n<p id=\"fs-idm8325008\">(18a) MgO<\/p>\n<p id=\"fs-idm8324624\">(18b) SrO<\/p>\n<p id=\"fs-idm2086432\">(18c) KF<\/p>\n<p id=\"fs-idm2086048\">(18d) CsF<\/p>\n<p id=\"fs-idp185408896\">(18e) MgF<sub>2<\/sub><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp56209472\" data-type=\"exercise\">\n<div id=\"fs-idp56209728\" data-type=\"problem\">\n<p id=\"fs-idp16978800\">Which of the following compounds requires the most energy to convert one mole of the solid into separate ions?<\/p>\n<p id=\"fs-idp16979312\">(19a) K<sub>2<\/sub>S<\/p>\n<p id=\"fs-idp58281056\">(19b) K<sub>2<\/sub>O<\/p>\n<p id=\"fs-idp48854512\">(19c) CaS<\/p>\n<p id=\"fs-idp123580176\">(19d) Cs<sub>2<\/sub>S<\/p>\n<p id=\"fs-idp110456432\">(19e) CaO<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"fs-idp15208208\" data-type=\"exercise\">\n<div id=\"fs-idp15208464\" data-type=\"problem\">\n<p id=\"fs-idp15208720\">(20) The lattice energy of KF is 794 kJ\/mol, and the interionic distance is 269 pm. The Na\u2013F distance in NaF, which has the same structure as KF, is 231 pm. Which of the following values is the closest approximation of the lattice energy of NaF: 682 kJ\/mol, 794 kJ\/mol, 924 kJ\/mol, 1588 kJ\/mol, or 3175 kJ\/mol? Explain your answer.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\" data-type=\"glossary\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-idp10319376\">\n<dd id=\"fs-idm69489984\">(also, bond dissociation energy) energy required to break a covalent bond in a gaseous substance<\/dd>\n<\/dl>\n<dl id=\"fs-idp39711472\">\n<dt><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1753_2957\">Born-Haber cycle<\/a><\/dt>\n<dd id=\"fs-idp39712112\">thermochemical cycle relating the various energetic steps involved in the formation of an ionic solid from the relevant elements<\/dd>\n<\/dl>\n<dl id=\"fs-idp29295648\">\n<dt><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1753_2959\">lattice energy<\/a> (\u0394<em data-effect=\"italics\">H<\/em><sub>lattice<\/sub>)<\/dt>\n<dd id=\"fs-idm7620624\">energy required to separate one mole of an ionic solid into its component gaseous ions<\/dd>\n<\/dl>\n<\/div>\n<\/div>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_1753_2957\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1753_2957\"><div tabindex=\"-1\"><p>thermochemical cycle relating the various energetic steps involved in the formation of an ionic solid from the relevant elements<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_1753_2959\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1753_2959\"><div tabindex=\"-1\"><p>energy require<a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1753_2957\">Born-Haber cycle<\/a>d to separate one mole of an ionic solid into its component gaseous ions<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":801,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1753","chapter","type-chapter","status-publish","hentry"],"part":1620,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/pressbooks\/v2\/chapters\/1753","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/wp\/v2\/users\/801"}],"version-history":[{"count":16,"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/pressbooks\/v2\/chapters\/1753\/revisions"}],"predecessor-version":[{"id":3592,"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/pressbooks\/v2\/chapters\/1753\/revisions\/3592"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/pressbooks\/v2\/parts\/1620"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/pressbooks\/v2\/chapters\/1753\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/wp\/v2\/media?parent=1753"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/pressbooks\/v2\/chapter-type?post=1753"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/wp\/v2\/contributor?post=1753"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/inorganicchemistrychem250\/wp-json\/wp\/v2\/license?post=1753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}