{"id":793,"date":"2021-07-23T09:20:44","date_gmt":"2021-07-23T13:20:44","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/relative-strengths-of-acids-and-bases\/"},"modified":"2022-06-23T09:20:48","modified_gmt":"2022-06-23T13:20:48","slug":"relative-strengths-of-acids-and-bases","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/relative-strengths-of-acids-and-bases\/","title":{"raw":"14.3 Relative Strengths of Acids and Bases","rendered":"14.3 Relative Strengths of Acids and Bases"},"content":{"raw":"&nbsp;\r\n<div class=\"textbox textbox--learning-objectives\">\r\n<h3><strong>Learning Objectives<\/strong><\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Assess the relative strengths of acids and bases according to their ionization constants<\/li>\r\n \t<li>Rationalize trends in acid\u2013base strength in relation to molecular structure<\/li>\r\n \t<li>Carry out equilibrium calculations for weak acid\u2013base systems<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div id=\"fs-idm477446592\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Acid and Base Ionization Constants<\/strong><\/h3>\r\n<p id=\"fs-idm193375984\">The relative strength of an acid or base is the extent to which it ionizes when dissolved in water. If the ionization reaction is essentially complete, the acid or base is termed <em data-effect=\"italics\">strong<\/em>; if relatively little ionization occurs, the acid or base is weak. As will be evident throughout the remainder of this chapter, there are many more weak acids and bases than strong ones. The most common strong acids and bases are listed in <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_strong\">(Figure)<\/a>.<\/p>\r\n\r\n<div id=\"CNX_Chem_14_03_strong\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">Some of the common strong acids and bases are listed here.<\/div>\r\n<span id=\"fs-idp3283088\" data-type=\"media\" data-alt=\"This table has seven rows and two columns. The first row is a header row, and it labels each column, \u201c6 Strong Acids,\u201d and, \u201c6 Strong Bases.\u201d Under the \u201c6 Strong Acids\u201d column are the following: H C l O subscript 4 perchloric acid; H C l hydrochloric acid; H B r hydrobromic acid; H I hydroiodic acid; H N O subscript 3 nitric acid; H subscript 2 S O subscript 4 sulfuric acid. Under the \u201c6 Strong Bases\u201d column are the following: L i O H lithium hydroxide; N a O H sodium hydroxide; K O H potassium hydroxide; C a ( O H ) subscript 2 calcium hydroxide; S r ( O H ) subscript 2 strontium hydroxide; B a ( O H ) subscript 2 barium hydroxide.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_strong-1.jpg\" alt=\"This table has seven rows and two columns. The first row is a header row, and it labels each column, \u201c6 Strong Acids,\u201d and, \u201c6 Strong Bases.\u201d Under the \u201c6 Strong Acids\u201d column are the following: H C l O subscript 4 perchloric acid; H C l hydrochloric acid; H B r hydrobromic acid; H I hydroiodic acid; H N O subscript 3 nitric acid; H subscript 2 S O subscript 4 sulfuric acid. Under the \u201c6 Strong Bases\u201d column are the following: L i O H lithium hydroxide; N a O H sodium hydroxide; K O H potassium hydroxide; C a ( O H ) subscript 2 calcium hydroxide; S r ( O H ) subscript 2 strontium hydroxide; B a ( O H ) subscript 2 barium hydroxide.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idp107824512\">The relative strengths of acids may be quantified by measuring their equilibrium constants in aqueous solutions. In solutions of the same concentration, stronger acids ionize to a greater extent, and so yield higher concentrations of hydronium ions than do weaker acids. The equilibrium constant for an acid is called the <span data-type=\"term\">acid-ionization constant, <em data-effect=\"italics\">K<\/em><sub>a<\/sub><\/span>. For the reaction of an acid HA:<\/p>\r\n\r\n<div id=\"fs-idm122858592\" style=\"padding-left: 40px\" data-type=\"equation\">HA(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + A<sup>\u2212<\/sup>(<em>aq<\/em>),<\/div>\r\n<p id=\"fs-idp44134944\">the acid ionization constant is written<\/p>\r\n\r\n<div id=\"fs-idp97870288\" style=\"padding-left: 40px\" data-type=\"equation\">\u00a0<img class=\"alignnone wp-image-1853\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/143a-300x111.png\" alt=\"\" width=\"130\" height=\"48\" \/><\/div>\r\n<p id=\"fs-idp39416656\">where the concentrations are those at equilibrium. Although water is a reactant in the reaction, it is the solvent as well, so we do not include [H<sub>2<\/sub>O] in the equation. The larger the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> of an acid, the larger the concentration of H<sub>3<\/sub>O<sup>+<\/sup> and A<sup>\u2212<\/sup> relative to the concentration of the nonionized acid, HA, in an equilibrium mixture, and the stronger the acid. An acid is classified as \u201cstrong\u201d when it undergoes complete ionization, in which case the concentration of HA is zero and the acid ionization constant is immeasurably large (<em data-effect=\"italics\">K<\/em><sub>a<\/sub> \u2248 \u221e). Acids that are partially ionized are called \u201cweak,\u201d and their acid ionization constants may be experimentally measured. A table of ionization constants for weak acids is provided in Appendix H.<\/p>\r\n<p id=\"fs-idm220763536\">To illustrate this idea, three acid ionization equations and <em data-effect=\"italics\">K<\/em><sub>a<\/sub> values are shown below. The ionization constants increase from first to last of the listed equations, indicating the relative acid strength increases in the order CH<sub>3<\/sub>CO<sub>2<\/sub>H &lt; HNO<sub>2<\/sub> &lt; HSO<sub>4<\/sub><sup>\u2212<\/sup>:<\/p>\r\n\r\n<div id=\"fs-idp100550608\" style=\"padding-left: 40px\" data-type=\"equation\">CH<sub>3<\/sub>CO<sub>2<\/sub>H(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + CH<sub>3<\/sub>CO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>a<\/sub> = 1.8 \u00d7 10<sup>-5<\/sup><\/div>\r\n<div id=\"fs-idm57962960\" style=\"padding-left: 40px\" data-type=\"equation\">HNO<sub>2<\/sub>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + NO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>a<\/sub> = 4.6 \u00d7 10<sup>-4<\/sup><\/div>\r\n<div id=\"fs-idm223507040\" style=\"padding-left: 40px\" data-type=\"equation\">HSO<sub>4<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>aq<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + SO<sub>4<\/sub><sup>2-<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0K<sub>a<\/sub> = 1.2 \u00d7 10<sup>-2<\/sup><\/div>\r\n<p id=\"fs-idm115717600\">Another measure of the strength of an acid is its percent ionization. The <span data-type=\"term\">percent ionization<\/span> of a weak acid is defined in terms of the composition of an equilibrium mixture:<\/p>\r\n\r\n<div id=\"fs-idm149756192\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1854\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3b-300x64.png\" alt=\"\" width=\"268\" height=\"57\" \/><\/div>\r\n<p id=\"fs-idm163389088\">where the numerator is equivalent to the concentration of the acid's conjugate base (per stoichiometry, [A<sup>\u2212<\/sup>] = [H<sub>3<\/sub>O<sup>+<\/sup>]). Unlike the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> value, the percent ionization of a weak acid varies with the initial concentration of acid, typically decreasing as concentration increases. Equilibrium calculations of the sort described later in this chapter can be used to confirm this behavior.<\/p>\r\n\r\n<div id=\"fs-idm163336240\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp45762800\"><strong>Calculation of Percent Ionization from pH <\/strong><\/p>\r\nCalculate the percent ionization of a 0.125-<em data-effect=\"italics\">M<\/em> solution of nitrous acid (a weak acid), with a pH of 2.09.\r\n<p id=\"fs-idm95442560\"><strong>Solution:<\/strong><\/p>\r\n<p id=\"fs-idm68557120\">Converting the provided pH to hydronium ion molarity yields<\/p>\r\n\r\n<div id=\"fs-idm173125616\" style=\"padding-left: 40px\" data-type=\"equation\">[H<sub>3<\/sub>O<sup>+<\/sup>] = 10<sup>-2.09 <\/sup>= 0.0081 M<\/div>\r\n<div data-type=\"equation\">\r\n\r\nThe percent ionization for an acid is:\r\n<div id=\"fs-idm119459936\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1856\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3c-300x132.png\" alt=\"\" width=\"100\" height=\"44\" \/><\/div>\r\n<\/div>\r\n<p id=\"fs-idm213993776\">Substituting this value and the provided initial acid concentration into the percent ionization equation gives<\/p>\r\n\r\n<div id=\"fs-idm83770448\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1857\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3d-300x67.png\" alt=\"\" width=\"175\" height=\"39\" \/><\/div>\r\n<p id=\"fs-idp164624\">(Recall the provided pH value of 2.09 is logarithmic, and so it contains just two significant digits, limiting the certainty of the computed percent ionization.)<\/p>\r\n<p id=\"fs-idp51316352\"><strong>Check Your Learning:<\/strong><\/p>\r\nCalculate the percent ionization of a 0.10-<em data-effect=\"italics\">M<\/em> solution of acetic acid with a pH of 2.89.\r\n\r\n&nbsp;\r\n<div id=\"fs-idp9633456\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm119453808\">1.3% ionized<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp45486128\" class=\"chemistry link-to-learning\" data-type=\"note\">\r\n<p id=\"fs-idm98260672\">View the <a href=\"http:\/\/openstaxcollege.org\/l\/16AcidBase\">simulation<\/a> of strong and weak acids and bases at the molecular level.<\/p>\r\n\r\n<\/div>\r\n<p id=\"fs-idm98628800\">Just as for acids, the relative strength of a base is reflected in the magnitude of its <span data-type=\"term\">base-ionization constant (<em data-effect=\"italics\">K<\/em><sub>b<\/sub>)<\/span> in aqueous solutions. In solutions of the same concentration, stronger bases ionize to a greater extent, and so yield higher hydroxide ion concentrations than do weaker bases. A stronger base has a larger ionization constant than does a weaker base. For the reaction of a base, B:<\/p>\r\n\r\n<div id=\"fs-idm69456656\" style=\"padding-left: 40px\" data-type=\"equation\">B(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc HB<sup>+<\/sup>(<em>aq<\/em>)+ OH<sup>\u2212<\/sup>(<em>aq<\/em>),<\/div>\r\n<p id=\"fs-idp1182192\">the ionization constant is written as<\/p>\r\n\r\n<div id=\"fs-idm72726864\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1858\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3e-300x113.png\" alt=\"\" width=\"135\" height=\"51\" \/><\/div>\r\n<p id=\"fs-idp86117152\">Inspection of the data for three weak bases presented below shows the base strength increases in the order NO<sub>2<\/sub><sup>-<\/sup> &lt; CH<sub>3<\/sub>CO<sub>2<\/sub><sup>-<\/sup> &lt;NH<sub>3<\/sub>.<\/p>\r\n\r\n<div id=\"fs-idm168482736\" style=\"padding-left: 40px\" data-type=\"equation\">NO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc HNO<sub>2<\/sub>(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>b<\/sub> = 2.17 \u00d7 10<sup>-11<\/sup><\/div>\r\n<div style=\"padding-left: 40px\" data-type=\"equation\">CH<sub>3<\/sub>CO<sub>2<\/sub><sup>-<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc CH<sub>3<\/sub>CO<sub>2<\/sub>H(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>b<\/sub> = 5.6 \u00d7 10<sup>-10<\/sup><\/div>\r\n<div style=\"padding-left: 40px\" data-type=\"equation\">NH<sub>3<\/sub>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc NH<sub>4<\/sub><sup>+<\/sup>(<em>aq<\/em>)+ OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>b<\/sub>=\u00a0 1.8 \u00d7 10<sup>-5<\/sup><\/div>\r\n<p id=\"fs-idm69273568\">A table of ionization constants for weak bases appears in Appendix I. As for acids, the relative strength of a base is also reflected in its percent ionization, computed as<\/p>\r\n\r\n<div id=\"fs-idm208527632\" style=\"padding-left: 40px\" data-type=\"equation\">% ionization = [OH<sup>\u2212<\/sup>]<sub>eq<\/sub>\/[B]<sub>0 <\/sub>\u00d7100%<\/div>\r\n<p id=\"fs-idm475449120\">but will vary depending on the base ionization constant and the initial concentration of the solution.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm178559536\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Relative Strengths of Conjugate Acid-Base Pairs<\/strong><\/h3>\r\n<p id=\"fs-idm172520016\">Br\u00f8nsted-Lowry acid-base chemistry is the transfer of protons; thus, logic suggests a relation between the relative strengths of conjugate acid-base pairs. The strength of an acid or base is quantified in its ionization constant, <em data-effect=\"italics\">K<\/em><sub>a<\/sub> or <em data-effect=\"italics\">K<\/em><sub>b<\/sub>, which represents the extent of the acid or base ionization reaction. For the conjugate acid-base pair HA \/ A<sup>\u2212<\/sup>, ionization equilibrium equations and ionization constant expressions are<\/p>\r\n\r\n<div id=\"fs-idm157208576\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1859\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f-300x68.png\" alt=\"\" width=\"450\" height=\"102\" \/><\/div>\r\n<p id=\"fs-idm217883488\">Adding these two chemical equations yields the equation for the autoionization for water:<\/p>\r\n\r\n<div id=\"fs-idp71522608\" style=\"padding-left: 40px\" data-type=\"equation\"><del>HA(<em>aq<\/em>)<\/del> + H<sub>2<\/sub>O(<em>l<\/em>) + <del>A<sup>\u2212<\/sup>(<em>aq<\/em>)<\/del> + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + <del>A<sup>\u2212<\/sup>(<em>aq<\/em>)<\/del> + OH<sup>\u2212<\/sup>(<em>aq<\/em>) + <del>HA(<em>aq<\/em>)<\/del><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<div id=\"fs-idm122391632\" style=\"padding-left: 40px\" data-type=\"equation\">\u00a0H<sub>2<\/sub>O(<em>l<\/em>) \u00a0+ H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>)\u00a0+ OH<sup>\u2212<\/sup>(<em>aq<\/em>)<\/div>\r\n<p id=\"fs-idm160491872\">As discussed in another chapter on equilibrium, the equilibrium constant for a summed reaction is equal to the mathematical product of the equilibrium constants for the added reactions, and so<\/p>\r\n\r\n<div id=\"fs-idm141982832\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1861\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g-300x31.png\" alt=\"\" width=\"348\" height=\"36\" \/><\/div>\r\n<p id=\"fs-idm224463760\">This equation states the relation between ionization constants for any conjugate acid-base pair, namely, their mathematical product is equal to the ion product of water, <em data-effect=\"italics\">K<\/em><sub>w<\/sub>. By rearranging this equation, a reciprocal relation between the strengths of a conjugate acid-base pair becomes evident:<\/p>\r\n\r\n<div id=\"fs-idm223919584\" style=\"padding-left: 40px\" data-type=\"equation\">K<sub>a<\/sub> = K<sub>w<\/sub>\/K<sub>b<\/sub>\u00a0 or\u00a0 K<sub>b<\/sub> = K<sub>w<\/sub>\/K<sub>a<\/sub><\/div>\r\n<p id=\"fs-idm225241056\">The inverse proportional relation between <em data-effect=\"italics\">K<\/em><sub>a<\/sub> and <em data-effect=\"italics\">K<\/em><sub>b<\/sub> means <em data-effect=\"italics\">the stronger the acid or base, the weaker its conjugate partner<\/em>. <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_strengths\">(Figure)<\/a> illustrates this relation for several conjugate acid-base pairs.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_14_03_strengths\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">Relative strengths of several conjugate acid-base pairs are shown.<\/div>\r\n<span id=\"fs-idm162584688\" data-type=\"media\" data-alt=\"The diagram shows two horizontal bars. The first, labeled, \u201cRelative acid strength,\u201d at the top is red on the left and gradually changes to purple on the right. The red end at the left is labeled, \u201cStronger acids.\u201d The purple end at the right is labeled, \u201cWeaker acids.\u201d Just outside the bar to the lower left is the label, \u201cK subscript a.\u201d The bar is marked off in increments with a specific acid listed above each increment. The first mark is at 1.0 with H subscript 3 O superscript positive sign. The second is ten raised to the negative two with H C l O subscript 2. The third is ten raised to the negative 4 with H F. The fourth is ten raised to the negative 6 with H subscript 2 C O subscript 3. The fifth is ten raised to a negative 8 with C H subscript 3 C O O H. The sixth is ten raised to the negative ten with N H subscript 4 superscript positive sign. The seventh is ten raised to a negative 12 with H P O subscript 4 superscript 2 negative sign. The eighth is ten raised to the negative 14 with H subscript 2 O. Similarly the second bar, which is labeled \u201cRelative conjugate base strength,\u201d is purple at the left end and gradually becomes blue at the right end. Outside the bar to the left is the label, \u201cWeaker bases.\u201d Outside the bar to the right is the label, \u201cStronger bases.\u201d Below and to the left of the bar is the label, \u201cK subscript b.\u201d The bar is similarly marked at increments with bases listed above each increment. The first is at ten raised to the negative 14 with H subscript 2 O above it. The second is ten raised to the negative 12 C l O subscript 2 superscript negative sign. The third is ten raised to the negative ten with F superscript negative sign. The fourth is ten raised to a negative eight with H C O subscript 3 superscript negative sign. The fifth is ten raised to the negative 6 with C H subscript 3 C O O superscript negative sign. The sixth is ten raised to the negative 4 with N H subscript 3. The seventh is ten raised to the negative 2 with P O subscript 4 superscript three negative sign. The eighth is 1.0 with O H superscript negative sign.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_strengths-1.jpg\" alt=\"The diagram shows two horizontal bars. The first, labeled, \u201cRelative acid strength,\u201d at the top is red on the left and gradually changes to purple on the right. The red end at the left is labeled, \u201cStronger acids.\u201d The purple end at the right is labeled, \u201cWeaker acids.\u201d Just outside the bar to the lower left is the label, \u201cK subscript a.\u201d The bar is marked off in increments with a specific acid listed above each increment. The first mark is at 1.0 with H subscript 3 O superscript positive sign. The second is ten raised to the negative two with H C l O subscript 2. The third is ten raised to the negative 4 with H F. The fourth is ten raised to the negative 6 with H subscript 2 C O subscript 3. The fifth is ten raised to a negative 8 with C H subscript 3 C O O H. The sixth is ten raised to the negative ten with N H subscript 4 superscript positive sign. The seventh is ten raised to a negative 12 with H P O subscript 4 superscript 2 negative sign. The eighth is ten raised to the negative 14 with H subscript 2 O. Similarly the second bar, which is labeled \u201cRelative conjugate base strength,\u201d is purple at the left end and gradually becomes blue at the right end. Outside the bar to the left is the label, \u201cWeaker bases.\u201d Outside the bar to the right is the label, \u201cStronger bases.\u201d Below and to the left of the bar is the label, \u201cK subscript b.\u201d The bar is similarly marked at increments with bases listed above each increment. The first is at ten raised to the negative 14 with H subscript 2 O above it. The second is ten raised to the negative 12 C l O subscript 2 superscript negative sign. The third is ten raised to the negative ten with F superscript negative sign. The fourth is ten raised to a negative eight with H C O subscript 3 superscript negative sign. The fifth is ten raised to the negative 6 with C H subscript 3 C O O superscript negative sign. The sixth is ten raised to the negative 4 with N H subscript 3. The seventh is ten raised to the negative 2 with P O subscript 4 superscript three negative sign. The eighth is 1.0 with O H superscript negative sign.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"CNX_Chem_14_03_Corresp\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">This figure shows strengths of conjugate acid-base pairs relative to the strength of water as the reference substance.<\/div>\r\n<span id=\"fs-idm44354768\" data-type=\"media\" data-alt=\"This figure includes a table separated into a left half which is labeled \u201cAcids\u201d and a right half labeled \u201cBases.\u201d A red arrow points up the left side, which is labeled \u201cIncreasing acid strength.\u201d Similarly, a blue arrow points downward along the right side, which is labeled \u201cIncreasing base strength.\u201d Names of acids and bases are listed next to each arrow toward the center of the table, followed by chemical formulas. Acids listed top to bottom are sulfuric acid, H subscript 2 S O subscript 4, hydrogen iodide, H I, hydrogen bromide, H B r, hydrogen chloride, H C l, nitric acid, H N O subscript 3, hydronium ion ( in pink text) H subscript 3 O superscript plus, hydrogen sulfate ion, H S O subscript 4 superscript negative, phosphoric acid, H subscript 3 P O subscript 4, hydrogen fluoride, H F, nitrous acid, H N O subscript 2, acetic acid, C H subscript 3 C O subscript 2 H, carbonic acid H subscript 2 C O subscript 3, hydrogen sulfide, H subscript 2 S, ammonium ion, N H subscript 4 superscript +, hydrogen cyanide, H C N, hydrogen carbonate ion, H C O subscript 3 superscript negative, water (shaded in beige) H subscript 2 O, hydrogen sulfide ion, H S superscript negative, ethanol, C subscript 2 H subscript 5 O H, ammonia, N H subscript 3, hydrogen, H subscript 2, methane, and C H subscript 4. The acids at the top of the listing from sulfuric acid through nitric acid are grouped with a bracket to the right labeled \u201cUndergo complete acid ionization in water.\u201d Similarly, the acids at the bottom from hydrogen sulfide ion through methane are grouped with a bracket and labeled, \u201cDo not undergo acid ionization in water.\u201d The right half of the figure lists bases and formulas. From top to bottom the bases listed are hydrogen sulfate ion, H S O subscript 4 superscript negative, iodide ion, I superscript negative, bromide ion, B r superscript negative, chloride ion, C l superscript negative, nitrate ion, N O subscript 3 superscript negative, water (shaded in beige), H subscript 2 O, sulfate ion, S O subscript 4 superscript 2 negative, dihydrogen phosphate ion, H subscript 2 P O subscript 4 superscript negative, fluoride ion, F superscript negative, nitrite ion, N O subscript 2 superscript negative, acetate ion, C H subscript 3 C O subscript 2 superscript negative, hydrogen carbonate ion, H C O subscript 3 superscript negative, hydrogen sulfide ion, H S superscript negative, ammonia, N H subscript 3, cyanide ion, C N superscript negative, carbonate ion, C O subscript 3 superscript 2 negative, hydroxide ion (in blue), O H superscript negative, sulfide ion, S superscript 2 negative, ethoxide ion, C subscript 2 H subscript 5 O superscript negative, amide ion N H subscript 2 superscript negative, hydride ion, H superscript negative, and methide ion C H subscript 3 superscript negative. The bases at the top, from perchlorate ion through nitrate ion are group with a bracket which is labeled \u201cDo not undergo base ionization in water.\u201d Similarly, the lower 5 in the listing, from sulfide ion through methide ion are grouped and labeled \u201cUndergo complete base ionization in water.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_corresp-1.jpg\" alt=\"This figure includes a table separated into a left half which is labeled \u201cAcids\u201d and a right half labeled \u201cBases.\u201d A red arrow points up the left side, which is labeled \u201cIncreasing acid strength.\u201d Similarly, a blue arrow points downward along the right side, which is labeled \u201cIncreasing base strength.\u201d Names of acids and bases are listed next to each arrow toward the center of the table, followed by chemical formulas. Acids listed top to bottom are sulfuric acid, H subscript 2 S O subscript 4, hydrogen iodide, H I, hydrogen bromide, H B r, hydrogen chloride, H C l, nitric acid, H N O subscript 3, hydronium ion ( in pink text) H subscript 3 O superscript plus, hydrogen sulfate ion, H S O subscript 4 superscript negative, phosphoric acid, H subscript 3 P O subscript 4, hydrogen fluoride, H F, nitrous acid, H N O subscript 2, acetic acid, C H subscript 3 C O subscript 2 H, carbonic acid H subscript 2 C O subscript 3, hydrogen sulfide, H subscript 2 S, ammonium ion, N H subscript 4 superscript +, hydrogen cyanide, H C N, hydrogen carbonate ion, H C O subscript 3 superscript negative, water (shaded in beige) H subscript 2 O, hydrogen sulfide ion, H S superscript negative, ethanol, C subscript 2 H subscript 5 O H, ammonia, N H subscript 3, hydrogen, H subscript 2, methane, and C H subscript 4. The acids at the top of the listing from sulfuric acid through nitric acid are grouped with a bracket to the right labeled \u201cUndergo complete acid ionization in water.\u201d Similarly, the acids at the bottom from hydrogen sulfide ion through methane are grouped with a bracket and labeled, \u201cDo not undergo acid ionization in water.\u201d The right half of the figure lists bases and formulas. From top to bottom the bases listed are hydrogen sulfate ion, H S O subscript 4 superscript negative, iodide ion, I superscript negative, bromide ion, B r superscript negative, chloride ion, C l superscript negative, nitrate ion, N O subscript 3 superscript negative, water (shaded in beige), H subscript 2 O, sulfate ion, S O subscript 4 superscript 2 negative, dihydrogen phosphate ion, H subscript 2 P O subscript 4 superscript negative, fluoride ion, F superscript negative, nitrite ion, N O subscript 2 superscript negative, acetate ion, C H subscript 3 C O subscript 2 superscript negative, hydrogen carbonate ion, H C O subscript 3 superscript negative, hydrogen sulfide ion, H S superscript negative, ammonia, N H subscript 3, cyanide ion, C N superscript negative, carbonate ion, C O subscript 3 superscript 2 negative, hydroxide ion (in blue), O H superscript negative, sulfide ion, S superscript 2 negative, ethoxide ion, C subscript 2 H subscript 5 O superscript negative, amide ion N H subscript 2 superscript negative, hydride ion, H superscript negative, and methide ion C H subscript 3 superscript negative. The bases at the top, from perchlorate ion through nitrate ion are group with a bracket which is labeled \u201cDo not undergo base ionization in water.\u201d Similarly, the lower 5 in the listing, from sulfide ion through methide ion are grouped and labeled \u201cUndergo complete base ionization in water.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm225187616\">The listing of conjugate acid\u2013base pairs shown in <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_Corresp\">(Figure)<\/a> is arranged to show the relative strength of each species as compared with water, whose entries are highlighted in each of the table\u2019s columns. In the acid column, those species listed below water are weaker acids than water. These species do not undergo acid ionization in water; they are not Bronsted-Lowry acids. All the species listed above water are stronger acids, transferring protons to water to some extent when dissolved in an aqueous solution to generate hydronium ions. Species above water but below hydronium ion are <em data-effect=\"italics\">weak acids<\/em>, undergoing partial acid ionization, whereas those above hydronium ion are <em data-effect=\"italics\">strong acids<\/em> that are completely ionized in aqueous solution.<\/p>\r\n<p id=\"fs-idm213445440\">If all these strong acids are completely ionized in water, why does the column indicate they vary in strength, with nitric acid being the weakest and perchloric acid the strongest? Notice that the sole acid species present in an aqueous solution of any strong acid is H<sub>3<\/sub>O<sup>+<\/sup>(<em data-effect=\"italics\">aq<\/em>), meaning that hydronium ion is the strongest acid that may exist in water; any stronger acid will react completely with water to generate hydronium ions. This limit on the acid strength of solutes in a solution is called a <strong data-effect=\"bold\">leveling effect<\/strong>. To measure the differences in acid strength for \u201cstrong\u201d acids, the acids must be dissolved in a solvent that is <em data-effect=\"italics\">less basic<\/em> than water. In such solvents, the acids will be \u201cweak,\u201d and so any differences in the extent of their ionization can be determined. For example, the binary hydrogen halides HCl, HBr, and HI are strong acids in water but weak acids in ethanol (strength increasing HCl &lt; HBr &lt; HI).<\/p>\r\n<p id=\"fs-idm167383056\">The right column of <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_Corresp\">(Figure)<\/a> lists a number of substances in order of increasing base strength from top to bottom. Following the same logic as for the left column, species listed above water are weaker bases and so they don\u2019t undergo base ionization when dissolved in water. Species listed between water and its conjugate base, hydroxide ion, are weak bases that partially ionize. Species listed below hydroxide ion are strong bases that completely ionize in water to yield hydroxide ions (i.e., they are <em data-effect=\"italics\">leveled<\/em> to hydroxide). A comparison of the acid and base columns in this table supports the reciprocal relation between the strengths of conjugate acid-base pairs. For example, the conjugate bases of the strong acids (top of table) are all of negligible strength. A strong acid exhibits an immeasurably large <em data-effect=\"italics\">K<\/em><sub>a<\/sub>, and so its conjugate base will exhibit a <em data-effect=\"italics\">K<\/em><sub>b<\/sub> that is essentially zero:<\/p>\r\n<p id=\"fs-idm200218096\" style=\"padding-left: 40px\">strong acid:\u00a0 \u00a0 \u00a0K<sub>a<\/sub> \u2248 \u221e<\/p>\r\n<p style=\"padding-left: 40px\">conjugate base:\u00a0 \u00a0 \u00a0K<sub>b<\/sub> = K<sub>w<\/sub>\/K<sub>a<\/sub> = K<sub>w<\/sub>\/\u221e \u2248 0<\/p>\r\n<p id=\"fs-idm225937888\">A similar approach can be used to support the observation that conjugate acids of strong bases (<em data-effect=\"italics\">K<\/em><sub>b<\/sub> \u2248 \u221e) are of negligible strength (<em data-effect=\"italics\">K<\/em><sub>a<\/sub> \u2248 0).<\/p>\r\n\r\n<div id=\"fs-idp2197392\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm154506736\"><strong>Calculating Ionization Constants for Conjugate Acid-Base Pairs <\/strong><\/p>\r\nUse the <em data-effect=\"italics\">K<\/em><sub>b<\/sub> for the nitrite ion, NO<sub>2<\/sub><sup>\u2212<\/sup>, to calculate the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for its conjugate acid.\r\n<p id=\"fs-idm172466976\"><strong>Solution:<\/strong><\/p>\r\n<em data-effect=\"italics\">K<\/em><sub>b<\/sub> for NO<sub>2<\/sub><sup>\u2212<\/sup> is given in this section as 2.17 \u00d7 10<sup>\u221211<\/sup>. The conjugate acid of NO<sub>2<\/sub><sup>\u2212<\/sup> is HNO<sub>2<\/sub>; <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for HNO<sub>2<\/sub> can be calculated using the relationship:\r\n<div id=\"fs-idm197198576\" style=\"padding-left: 40px\" data-type=\"equation\">K<sub>a<\/sub> \u00d7 K<sub>b<\/sub> = 1.0 \u00d7 10<sup>-14 <\/sup>= K<sub>w<\/sub><\/div>\r\n<p id=\"fs-idm174350000\">Solving for <em data-effect=\"italics\">K<\/em><sub>a<\/sub> yields<\/p>\r\n\r\n<div id=\"fs-idp100620656\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1863\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3h-300x46.png\" alt=\"\" width=\"274\" height=\"42\" \/><\/div>\r\n<p id=\"fs-idm122128048\">This answer can be verified by finding the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for HNO<sub>2<\/sub> in Appendix H.<\/p>\r\n<p id=\"fs-idp28811616\"><strong>Check Your Learning:<\/strong><\/p>\r\nDetermine the relative acid strengths of NH<sub>4<\/sub><sup>+<\/sup> and HCN by comparing their ionization constants. The ionization constant of HCN is given in Appendix H as 4.9 \u00d7 10<sup>\u221210<\/sup>. The ionization constant of NH<sub>4<\/sub><sup>+<\/sup> is not listed, but the ionization constant of its conjugate base, NH<sub>3<\/sub>, is listed as 1.8 \u00d7 10<sup>\u22125<\/sup>.\r\n<div id=\"fs-idp12994032\" data-type=\"note\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm80300528\">NH<sub>4<\/sub><sup>+ <\/sup>is the slightly stronger acid (<em data-effect=\"italics\">K<\/em><sub>a<\/sub> for NH<sub>4<\/sub><sup>+ <\/sup>= 5.6 \u00d7 10<sup>\u221210<\/sup>).<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm160956208\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Acid-Base Equilibrium Calculations<\/strong><\/h3>\r\n<p id=\"fs-idm226989136\">The chapter on chemical equilibria introduced several types of equilibrium calculations and the various mathematical strategies that are helpful in performing them. These strategies are generally useful for equilibrium systems regardless of chemical reaction class, and so they may be effectively applied to acid-base equilibrium problems. This section presents several example exercises involving equilibrium calculations for acid-base systems.<\/p>\r\n<span id=\"fs-idp23785056\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This image shows two bottles containing clear colorless solutions. Each bottle contains a single p H indicator strip. The strip in the bottle on the left is red, and a similar red strip is placed on a filter paper circle in front of the bottle on surface on which the bottles are resting. Similarly, the second bottle on the right contains and orange strip and an orange strip is placed in front of it on a filter paper circle. Between the two bottles is a pack of p Hydrion papers with a p H color scale on its cover.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_acetate_img-1.jpg\" alt=\"This image shows two bottles containing clear colorless solutions. Each bottle contains a single p H indicator strip. The strip in the bottle on the left is red, and a similar red strip is placed on a filter paper circle in front of the bottle on surface on which the bottles are resting. Similarly, the second bottle on the right contains and orange strip and an orange strip is placed in front of it on a filter paper circle. Between the two bottles is a pack of p Hydrion papers with a p H color scale on its cover.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-idm134302736\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This photo shows two glass containers filled with a transparent liquid. In between the containers is a p H strip indicator guide. There are p H strips placed in front of each glass container. The liquid in the container on the left appears to have a p H of 10 or 11. The liquid in the container on the right appears to have a p H of about 13 or 14.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ammonia-1.jpg\" alt=\"This photo shows two glass containers filled with a transparent liquid. In between the containers is a p H strip indicator guide. There are p H strips placed in front of each glass container. The liquid in the container on the left appears to have a p H of 10 or 11. The liquid in the container on the right appears to have a p H of about 13 or 14.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<div id=\"fs-idm223269056\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm118702752\"><strong>Determination of <em data-effect=\"italics\">K<\/em><sub>a<\/sub> from Equilibrium Concentrations <\/strong><\/p>\r\nAcetic acid is the principal ingredient in vinegar (<a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_Vinegar\">(Figure)<\/a>) that provides its sour taste. At equilibrium, a solution contains [CH<sub>3<\/sub>CO<sub>2<\/sub>H] = 0.0787 <em data-effect=\"italics\">M<\/em> and [H<sub>3<\/sub>O<sup>+<\/sup>] = [CH<sub>3<\/sub>CO<sub>2<\/sub><sup>\u2212<\/sup>] = 0.00118 M. What is the value of <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for acetic acid?\r\n\r\n&nbsp;\r\n<div id=\"CNX_Chem_14_03_Vinegar\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">Vinegar contains acetic acid, a weak acid. (credit: modification of work by \u201cHomeSpot HQ\u201d\/Flickr)<\/div>\r\n<span id=\"fs-idm137777920\" data-type=\"media\" data-alt=\"An image shows the label of a bottle of distilled white vinegar. The label states that the contents have been reduced with water to 5 percent acidity.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_Vinegar-1.jpg\" alt=\"An image shows the label of a bottle of distilled white vinegar. The label states that the contents have been reduced with water to 5 percent acidity.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm119280448\"><strong>Solution: <\/strong><\/p>\r\nThe relevant equilibrium equation and its equilibrium constant expression are shown below. Substitution of the provided equilibrium concentrations permits a straightforward calculation of the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for acetic acid.\r\n<div id=\"fs-idp69048880\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1865\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i-300x63.png\" alt=\"\" width=\"400\" height=\"84\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm68555680\"><strong>Check Your Learning: <\/strong><\/p>\r\nThe HSO<sub>4<\/sub><sup>\u2212<\/sup> ion is a weak acid used in some household cleansers:\r\n<div id=\"fs-idm174702176\" style=\"padding-left: 40px\" data-type=\"equation\">HSO<sub>4<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + SO<sub>4<\/sub><sup>2-<\/sup>(<em>aq<\/em>)<\/div>\r\n<p id=\"fs-idm168960944\">What is the acid ionization constant for this weak acid if an equilibrium mixture has the following composition: [H<sub>3<\/sub>O<sup>+<\/sup>] = 0.027 <em data-effect=\"italics\">M<\/em>; [HSO<sub>4<\/sub><sup>\u2212<\/sup>] = 0.29 M; and [SO<sub>4<\/sub><sup>2-<\/sup>] = 0.13 M?<\/p>\r\n&nbsp;\r\n<div id=\"fs-idp348400\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp1308432\"><em data-effect=\"italics\">K<\/em><sub>a<\/sub> for HSO<sub>4<\/sub><sup>\u2212<\/sup> = 1.2 \u00d7 10<sup>\u22122<\/sup><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm154542240\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm1585392\"><strong>Determination of <em data-effect=\"italics\">K<\/em><sub>b<\/sub> from Equilibrium Concentrations <\/strong><\/p>\r\nCaffeine, C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub> is a weak base. What is the value of <em data-effect=\"italics\">K<\/em><sub>b<\/sub> for caffeine if a solution at equilibrium has [C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub>] = 0.050 <em data-effect=\"italics\">M<\/em>, [C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub>H<sup>+<\/sup>] = 5.0 \u00d7 10<sup>\u22123 <\/sup><em data-effect=\"italics\">M<\/em>, and [OH<sup>\u2212<\/sup>] = 2.5 \u00d7 10<sup>\u22123<\/sup><em data-effect=\"italics\">M<\/em>?\r\n<p id=\"fs-idm64959408\"><strong>Solution:<\/strong><\/p>\r\nThe relevant equilibrium equation and its equilibrium constant expression are shown below. Substitution of the provided equilibrium concentrations permits a straightforward calculation of the <em data-effect=\"italics\">K<\/em><sub>b<\/sub> for caffeine.\r\n<div id=\"fs-idp57095280\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1866\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j-300x54.png\" alt=\"\" width=\"438\" height=\"79\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm122074528\"><strong>Check Your Learning: <\/strong><\/p>\r\nWhat is the equilibrium constant for the ionization of the HPO<sub>4<\/sub><sup>2-<\/sup>\u00a0ion, a weak base\r\n<div id=\"fs-idm98055840\" style=\"padding-left: 40px\" data-type=\"equation\">HPO<sub>4<\/sub><sup>2-<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>2<\/sub>PO<sub>4<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(aq)<\/div>\r\n<p id=\"fs-idp31344880\">if the composition of an equilibrium mixture is as follows: [OH<sup>\u2212<\/sup>] = 1.3 \u00d7 10<sup>\u22126<\/sup><em data-effect=\"italics\">M<\/em>; [H<sub>2<\/sub>PO<sub>4<\/sub><sup>\u2212<\/sup>] = 0.042 M; and [HPO<sub>4<\/sub><sup>2-<\/sup>] = 0.341 M?<\/p>\r\n&nbsp;\r\n<div id=\"fs-idm157882608\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp68248832\"><em data-effect=\"italics\">K<\/em><sub>b<\/sub> for HPO<sub>4<\/sub><sup>2- <\/sup>= 1.6 \u00d7 10<sup>-7<\/sup><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm1433984\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm1433728\"><strong>Determination of <em data-effect=\"italics\">K<\/em><sub>a<\/sub> or <em data-effect=\"italics\">K<\/em><sub>b<\/sub> from pH <\/strong><\/p>\r\nThe pH of a 0.0516-<em data-effect=\"italics\">M<\/em> solution of nitrous acid, HNO<sub>2<\/sub>, is 2.34. What is its <em data-effect=\"italics\">K<\/em><sub>a<\/sub>?\r\n<div id=\"fs-idp31767264\" style=\"padding-left: 40px\" data-type=\"equation\">HNO<sub>2<\/sub>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + NO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm163708144\"><strong>Solution:<\/strong><\/p>\r\nThe nitrous acid concentration provided is a <em data-effect=\"italics\">formal<\/em> concentration, one that does not account for any chemical equilibria that may be established in solution. Such concentrations are treated as \u201cinitial\u201d values for equilibrium calculations using the ICE table approach. Notice the initial value of hydronium ion is listed as <em data-effect=\"italics\">approximately<\/em> zero because a small concentration of H<sub>3<\/sub>O<sup>+<\/sup> is present (1.0 \u00d7 10<sup>\u22127<\/sup><em data-effect=\"italics\">M<\/em>) due to the autoionization of water. In many cases, such as all the ones presented in this chapter, this concentration is much less than that generated by ionization of the acid (or base) in question and may be neglected.\r\n<p id=\"fs-idm204817712\">The pH provided is a logarithmic measure of the hydronium ion concentration resulting from the acid ionization of the nitrous acid, and so it represents an \u201cequilibrium\u201d value for the ICE table:<\/p>\r\n<p style=\"padding-left: 40px\">[H<sub>3<\/sub>O<sup>+<\/sup>] = 10<sup>-2.34 <\/sup>= 0.0046 M<\/p>\r\n<p id=\"fs-idm214144400\">The ICE table for this system is then<\/p>\r\n<span id=\"fs-idm79844096\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201cH N O subscript 2 plus sign H subscript 2 O equilibrium sign H subscript 3 O superscript positive sign plus sign N O subscript 2 superscript negative sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.0516, negative 0.0046, 0.0470. The second column is blank in all three rows. The third column has the following: approximately 0, positive 0.0046, 0.0046. The fourth column has the following: 0, positive 0.0046, 0.0046.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ICETable2_img-1.jpg\" alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201cH N O subscript 2 plus sign H subscript 2 O equilibrium sign H subscript 3 O superscript positive sign plus sign N O subscript 2 superscript negative sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.0516, negative 0.0046, 0.0470. The second column is blank in all three rows. The third column has the following: approximately 0, positive 0.0046, 0.0046. The fourth column has the following: 0, positive 0.0046, 0.0046.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-idm98416272\">Finally, calculate the value of the equilibrium constant using the data in the table:<\/p>\r\n\r\n<div id=\"fs-idm98415888\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1867\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3k-300x37.png\" alt=\"\" width=\"365\" height=\"45\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm166688304\"><strong>Check Your Learning: <\/strong><\/p>\r\nThe pH of a solution of household ammonia, a 0.950-<em data-effect=\"italics\">M<\/em> solution of NH<sub>3,<\/sub> is 11.612. What is <em data-effect=\"italics\">K<\/em><sub>b<\/sub> for NH<sub>3<\/sub>?\r\n\r\n&nbsp;\r\n<div id=\"fs-idm56490624\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm56489984\"><em data-effect=\"italics\">K<\/em><sub>b<\/sub> = 1.8\u00a0 \u00d7 10<sup>\u22125<\/sup><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm159829376\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm159829120\"><strong>Calculating Equilibrium Concentrations in a Weak Acid Solution <\/strong><\/p>\r\nFormic acid, HCO<sub>2<\/sub>H, is one irritant that causes the body\u2019s reaction to some ant bites and stings (<a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_AntSting\">(Figure)<\/a>).\r\n\r\n&nbsp;\r\n<div id=\"CNX_Chem_14_03_AntSting\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">The pain of some ant bites and stings is caused by formic acid. (credit: John Tann)<\/div>\r\n<span id=\"fs-idm94059808\" data-type=\"media\" data-alt=\"A photograph is shown of a large black ant on the end of a human finger.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_AntSting-1.jpg\" alt=\"A photograph is shown of a large black ant on the end of a human finger.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idm94058112\">What is the concentration of hydronium ion and the pH of a 0.534-<em data-effect=\"italics\">M<\/em> solution of formic acid?<\/p>\r\n\r\n<div id=\"fs-idm83702544\" style=\"padding-left: 40px\" data-type=\"equation\">HCO<sub>2<\/sub>H(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + HCO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0K<sub>a<\/sub> = 1.8 \u00d7 10<sup>-4<\/sup><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm42704112\"><strong>Solution:<\/strong><\/p>\r\n<p id=\"fs-idm475800144\">The ICE table for this system is<\/p>\r\n<span id=\"fs-idm3940608\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201cH C O subscript 2 H plus sign H subscript 2 O equilibrium arrow H subscript 3 O superscript positive sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.534, blank, 0.534 minus x. The second column is blank in all three rows. The third column has the following: approximately 0, positive x, x. The fourth column has the following: 0, positive x, x.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ICETable3_img-1.jpg\" alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201cH C O subscript 2 H plus sign H subscript 2 O equilibrium arrow H subscript 3 O superscript positive sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.534, blank, 0.534 minus x. The second column is blank in all three rows. The third column has the following: approximately 0, positive x, x. The fourth column has the following: 0, positive x, x.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-idm467257104\">Substituting the equilibrium concentration terms into the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> expression gives<span data-type=\"newline\">\r\n<\/span><\/p>\r\n\r\n<div id=\"fs-idm121323008\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1868\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3l-300x155.png\" alt=\"\" width=\"277\" height=\"143\" \/><\/div>\r\n<span data-type=\"newline\">\r\n<\/span> The relatively large initial concentration and small equilibrium constant permits the simplifying assumption; ie that <em data-effect=\"italics\">x<\/em> &lt; 5% of 0.534 M, which is 0.0267 M. The equation becomes<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idp29061504\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1869\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3m-300x70.png\" alt=\"\" width=\"201\" height=\"47\" \/><\/div>\r\n<span data-type=\"newline\">\r\n<\/span> Solving the equation for <em data-effect=\"italics\">x<\/em> yields<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idp107591296\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em><sup>2<\/sup> = 0.534 \u00d7 (1.8 \u00d7 10<sup>-4<\/sup>) = 9.6 \u00d7 10<sup>-5<\/sup><\/div>\r\n<span data-type=\"newline\">\u00a0<\/span>\r\n<div id=\"fs-idm94907344\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em> = <span style=\"font-size: 1em\">9.8 \u00d7 10<sup>-3<\/sup> M<\/span><\/div>\r\n<p id=\"fs-idp83161504\">Now check the 5% assumption:\u00a0 <span style=\"font-size: 1em\">9.8 \u00d7 10<sup>-3<\/sup> M &lt; 0.0267 M\u00a0 \u00a0 <\/span><\/p>\r\n<p id=\"fs-idp87107328\">Because <em data-effect=\"italics\">x<\/em> is less than 5% of the initial concentration, the assumption is valid.<\/p>\r\n<p id=\"fs-idm490302912\">As defined in the ICE table, <em data-effect=\"italics\">x<\/em> is equal to the equilibrium concentration of hydronium ion:<\/p>\r\n\r\n<div id=\"fs-idm212466048\" style=\"padding-left: 40px\" data-type=\"equation\">\u00a0 <em>x<\/em> = [H<sub>3<\/sub>O<sup>+<\/sup>] = 0.0098 M<\/div>\r\n<p id=\"fs-idm218699232\">Finally, the pH is calculated to be<\/p>\r\n\r\n<div id=\"fs-idm479799296\" style=\"padding-left: 40px\" data-type=\"equation\">pH = \u2212 log[H<sub>3<\/sub>O<sup>+<\/sup>] = \u2212 log(0.0098) = 2.01<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp80326224\"><strong>Check Your Learning <\/strong><\/p>\r\nOnly a small fraction of a weak acid ionizes in aqueous solution. What is the percent ionization of a 0.100-<em data-effect=\"italics\">M<\/em> solution of acetic acid, CH<sub>3<\/sub>CO<sub>2<\/sub>H?\r\n<div id=\"fs-idp80328288\" style=\"padding-left: 40px\" data-type=\"equation\">CH<sub>3<\/sub>CO<sub>2<\/sub>H(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + CH<sub>3<\/sub>CO<sub>2<\/sub><sup>\u2212<\/sup>(aq)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0K<sub>a<\/sub> = 1.8 \u00d7 10<sup>-5<\/sup><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<div id=\"fs-idp77192016\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp77192656\">percent ionization = 1.3%<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp77193872\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp77194128\"><strong>Calculating Equilibrium Concentrations in a Weak Base Solution <\/strong><\/p>\r\nFind the concentration of hydroxide ion, the pOH, and the pH of a 0.25-<em data-effect=\"italics\">M<\/em> solution of trimethylamine, a weak base:\r\n<div id=\"fs-idm75350896\" style=\"padding-left: 40px\" data-type=\"equation\">(CH<sub>3<\/sub>)<sub>3<\/sub>N(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc (CH<sub>3<\/sub>)<sub>3<\/sub>NH<sup>+<\/sup>(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0K<sub>b<\/sub> = 6.3 \u00d7 10<sup>-5<\/sup><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp38644736\"><strong>Solution: <\/strong><\/p>\r\nThe ICE table for this system is<span data-type=\"newline\">\r\n<\/span>\r\n\r\n<span id=\"fs-idm115891984\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201c( C H subscript 3 ) subscript 3 N plus sign H subscript 2 O equilibrium arrow ( C H subscript 3 ) subscript 3 N H superscript positive sign plus sign O H superscript positive sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.25, negative x, 0.25 plus sign negative x. The second column is blank in all three rows. The third column has the following: 0, x, 0 plus x. The fourth column has the following: approximately 0, x, and approximately 0 plus x.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ICETable4_img-1.jpg\" alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201c( C H subscript 3 ) subscript 3 N plus sign H subscript 2 O equilibrium arrow ( C H subscript 3 ) subscript 3 N H superscript positive sign plus sign O H superscript positive sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.25, negative x, 0.25 plus sign negative x. The second column is blank in all three rows. The third column has the following: 0, x, 0 plus x. The fourth column has the following: approximately 0, x, and approximately 0 plus x.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<span data-type=\"newline\">\r\n<\/span> Substituting the equilibrium concentration terms into the <em data-effect=\"italics\">K<\/em><sub>b<\/sub> expression gives<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idp121892160\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1871\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3n-300x34.png\" alt=\"\" width=\"379\" height=\"43\" \/><\/div>\r\n<span data-type=\"newline\">\r\n<\/span> Assuming <em data-effect=\"italics\">x<\/em> &lt; 5% of 0.25 M, which is 0.012 M, and solving for <em data-effect=\"italics\">x<\/em> yields<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idm1664928\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em> = 4.0 \u00d7 10<sup>-3<\/sup> M<\/div>\r\n<span data-type=\"newline\">\r\n<\/span> This value is less than 0.012 M, so the 5% assumption is valid.<span data-type=\"newline\">\r\n<\/span> As defined in the ICE table, <em data-effect=\"italics\">x<\/em> is equal to the equilibrium concentration of hydroxide ion:<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idm79961072\" style=\"padding-left: 40px\" data-type=\"equation\">[OH<sup>\u2212<\/sup>] = <em>x<\/em> = 4.0 \u00d7 10<sup>-3 <\/sup>M<\/div>\r\n<div id=\"fs-idp50312800\" data-type=\"equation\"><\/div>\r\nThe pOH is calculated to be<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idm73318512\" style=\"padding-left: 40px\" data-type=\"equation\">pOH = \u2212log(4.0 \u00d7 10<sup>-3<\/sup>) = 2.40<\/div>\r\n<span data-type=\"newline\">\r\n<\/span> Using the relation introduced in the previous section of this chapter:<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idp50335856\" style=\"padding-left: 40px\" data-type=\"equation\">pH + pOH = pK<sub>w<\/sub> = 14.00<\/div>\r\n<span data-type=\"newline\">\r\n<\/span> permits the computation of pH:<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idp50339184\" style=\"padding-left: 40px\" data-type=\"equation\">pH = 14.00 - pOH = 14.00-2.40 = 11.60<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm83886080\"><strong>Check Your Learning:<\/strong><\/p>\r\nCalculate the hydroxide ion concentration and the percent ionization of a 0.0325-<em data-effect=\"italics\">M<\/em> solution of ammonia, a weak base with a <em data-effect=\"italics\">K<\/em><sub>b<\/sub> of 1.76 \u00d7 10<sup>\u22125<\/sup>.\r\n\r\n&nbsp;\r\n<div id=\"fs-idp71571472\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp71572112\">7.56 \u00d7 10<sup>\u22124 <\/sup><em data-effect=\"italics\">M<\/em>, 2.33%<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-idm114523920\">In some cases, the strength of the weak acid or base and its formal (initial) concentration result in an appreciable ionization. Though the ICE strategy remains effective for these systems, the algebra is a bit more involved because the simplifying assumption that <em data-effect=\"italics\">x<\/em> is negligible can not be made. Calculations of this sort are demonstrated in <a class=\"autogenerated-content\" href=\"#fs-idm114522688\">(Figure)<\/a> below.<\/p>\r\n\r\n<div id=\"fs-idm114522688\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm114522432\"><strong>Calculating Equilibrium Concentrations without Simplifying Assumptions<\/strong><\/p>\r\nSodium hydrogen sulfate, NaHSO<sub>4<\/sub>, is used in some household cleansers as a source of the HSO<sub>4<\/sub><sup>\u2212<\/sup>\u00a0ion, a weak acid. What is the pH of a 0.50-<em data-effect=\"italics\">M<\/em> solution of HSO<sub>4<\/sub><sup>\u2212<\/sup>?\r\n<div id=\"fs-idm83628320\" style=\"padding-left: 40px\" data-type=\"equation\">HSO<sub>4<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + SO<sub>4<\/sub><sup>2-<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0K<sub>a<\/sub> = 1.2 \u00d7 10<sup>-2<\/sup><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp42421216\"><strong>Solution:<\/strong><\/p>\r\nThe ICE table for this system is<span data-type=\"newline\">\r\n<\/span>\r\n\r\n<span id=\"fs-idm4774976\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium ( M ). The second column has the header of \u201cH S O subscript 4 superscript negative sign plus sign H subscript 2 O equilibrium sign H subscript 3 O superscript positive sign plus sign S O subscript 4 superscript 2 superscript negative sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.50, negative x, 0.50 minus x. The second column is blank for all three rows. The third column has the following: approximately 0, positive x, x. The fourth column has the following: 0, positive x, x.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ICETable5_img-1.jpg\" alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium ( M ). The second column has the header of \u201cH S O subscript 4 superscript negative sign plus sign H subscript 2 O equilibrium sign H subscript 3 O superscript positive sign plus sign S O subscript 4 superscript 2 superscript negative sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.50, negative x, 0.50 minus x. The second column is blank for all three rows. The third column has the following: approximately 0, positive x, x. The fourth column has the following: 0, positive x, x.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<span data-type=\"newline\">\r\n<\/span><img class=\"alignnone wp-image-1873\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3o-300x43.png\" alt=\"\" width=\"349\" height=\"50\" \/>\r\n\r\n<span data-type=\"newline\">\r\n<\/span> If the 5% assumption \u00a0(<em>x<\/em> &lt; 0.05 \u00d7 0.50 M, or <em>x<\/em> &lt; 0.025 M) is made, simplifying and solving the above equation yields<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idm181668752\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em> = 0.077 M<\/div>\r\n<div id=\"fs-idp85327312\" data-type=\"equation\">\u00a0Because the simplifying assumption is not valid for this system, the equilibrium constant expression is solved as follows:<span data-type=\"newline\">\r\n<\/span><\/div>\r\n<div id=\"fs-idm14221120\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1874\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3p-300x72.png\" alt=\"\" width=\"225\" height=\"54\" \/><\/div>\r\n<span data-type=\"newline\">\r\n<\/span> Rearranging this equation yields<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idm55224560\" style=\"padding-left: 40px\" data-type=\"equation\">6.0 \u00d7 10<sup>-3 <\/sup>- 1.2 \u00d7 10<sup>-2<\/sup><em>x <\/em>= <em>x<\/em><sup>2<\/sup><\/div>\r\n<span data-type=\"newline\">\r\n<\/span> Writing the equation in quadratic form gives<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idm46125840\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em><sup>2 <\/sup>+ 1.2 \u00d7 10<sup>-2<\/sup><em>x <\/em>- 6.0 \u00d7 10<sup>-3 <\/sup>= 0<\/div>\r\n<span data-type=\"newline\">\r\n<\/span> Solving for the two roots of this quadratic equation results in a negative value that may be discarded as physically irrelevant and a positive value equal to <em data-effect=\"italics\">x<\/em>. As defined in the ICE table, <em data-effect=\"italics\">x<\/em> is equal to the hydronium concentration.<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"fs-idm217752528\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em> = [H<sub>3<\/sub>O<sup>+<\/sup>] = 0.072 M<\/div>\r\n<div style=\"padding-left: 40px\" data-type=\"equation\">pH = - log[H<sub>3<\/sub>O<sup>+<\/sup>] = -log(0.072 M) = 1.14<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm108532480\"><strong>Check Your Learning:<\/strong><\/p>\r\nCalculate the pH in a 0.010-<em data-effect=\"italics\">M<\/em> solution of caffeine, a weak base:\r\n<div id=\"fs-idm108529312\" style=\"padding-left: 40px\" data-type=\"equation\">C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub>H<sup>+<\/sup>(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>b<\/sub> = 2.5 \u00d7 10<sup>-4<\/sup><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<div id=\"fs-idm75099248\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm30698512\">pH 11.16<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm95688656\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Effect of Molecular Structure on Acid-Base Strength<\/strong><\/h3>\r\n<div id=\"fs-idm178147248\" class=\"bc-section section\" data-depth=\"2\">\r\n<h4 data-type=\"title\"><strong>Binary Acids and Bases<\/strong><\/h4>\r\n<p id=\"fs-idm95688016\">In the absence of any leveling effect, the acid strength of binary compounds of hydrogen with nonmetals (A) increases as the H-A bond strength decreases down a group in the periodic table. For group 17, the order of increasing acidity is HF &lt; HCl &lt; HBr &lt; HI. Likewise, for group 16, the order of increasing acid strength is H<sub>2<\/sub>O &lt; H<sub>2<\/sub>S &lt; H<sub>2<\/sub>Se &lt; H<sub>2<\/sub>Te.<\/p>\r\n<p id=\"fs-idp81297776\">Across a row in the periodic table, the acid strength of binary hydrogen compounds increases with increasing electronegativity of the nonmetal atom because the polarity of the H-A bond increases. Thus, the order of increasing acidity (for removal of one proton) across the second row is CH<sub>4<\/sub> &lt; NH<sub>3<\/sub> &lt; H<sub>2<\/sub>O &lt; HF; across the third row, it is SiH<sub>4<\/sub> &lt; PH<sub>3<\/sub> &lt; H<sub>2<\/sub>S &lt; HCl (see <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_AcidpH\">(Figure)<\/a>).<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_14_03_AcidpH\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">The figure shows trends in the strengths of binary acids and bases.<\/div>\r\n<span id=\"fs-idp81301760\" data-type=\"media\" data-alt=\"This diagram has two rows and four columns. Red arrows point left across the bottom of the figure and down at the right side and are labeled \u201cIncreasing acid strength.\u201d Blue arrows point left across the bottom and up at the right side of the figure and are labeled \u201cIncreasing base strength.\u201d The first column is labeled 14 at the top and two white squares are beneath it. The first has the number 6 in the upper left corner and the formula C H subscript 4 in the center along with designation Neither acid nor base. The second square contains the number 14 in the upper left corner, the formula C H subscript 4 at the center and the designation Neither acid nor base. The second column is labeled 15 at the top and two blue squares are beneath it. The first has the number 7 in the upper left corner and the formula N H subscript 3 in the center along with the designation Weak base and K subscript b equals 1.8 times 10 superscript negative 5. The second square contains the number 15 in the upper left corner, the formula P H subscript 3 at the center and the designation Very weak base and K subscript b equals 4 times 10 superscript negative 28. The third column is labeled 16 at the top and two squares are beneath it. The first is shaded tan and has the number 8 in the upper left corner and the formula H subscript 2 O in the center along with the designation neutral. The second square is shaded pink, contains the number 16 in the upper left corner, the formula H subscript 2 S at the center and the designation Weak acid and K subscript a equals 9.5 times 10 superscript negative 8. The fourth column is labeled 17 at the top and two squares are beneath it. The first is shaded pink, has the number 9 in the upper left corner and the formula H F in the center along with the designation Weak acid and K subscript a equals 6.8 times 10 superscript negative 4. The second square is shaded a deeper pink, contains the number 17 in the upper left corner, the formula H C l at the center, and the designation Strong acid.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_AcidpH-1.jpg\" alt=\"This diagram has two rows and four columns. Red arrows point left across the bottom of the figure and down at the right side and are labeled \u201cIncreasing acid strength.\u201d Blue arrows point left across the bottom and up at the right side of the figure and are labeled \u201cIncreasing base strength.\u201d The first column is labeled 14 at the top and two white squares are beneath it. The first has the number 6 in the upper left corner and the formula C H subscript 4 in the center along with designation Neither acid nor base. The second square contains the number 14 in the upper left corner, the formula C H subscript 4 at the center and the designation Neither acid nor base. The second column is labeled 15 at the top and two blue squares are beneath it. The first has the number 7 in the upper left corner and the formula N H subscript 3 in the center along with the designation Weak base and K subscript b equals 1.8 times 10 superscript negative 5. The second square contains the number 15 in the upper left corner, the formula P H subscript 3 at the center and the designation Very weak base and K subscript b equals 4 times 10 superscript negative 28. The third column is labeled 16 at the top and two squares are beneath it. The first is shaded tan and has the number 8 in the upper left corner and the formula H subscript 2 O in the center along with the designation neutral. The second square is shaded pink, contains the number 16 in the upper left corner, the formula H subscript 2 S at the center and the designation Weak acid and K subscript a equals 9.5 times 10 superscript negative 8. The fourth column is labeled 17 at the top and two squares are beneath it. The first is shaded pink, has the number 9 in the upper left corner and the formula H F in the center along with the designation Weak acid and K subscript a equals 6.8 times 10 superscript negative 4. The second square is shaded a deeper pink, contains the number 17 in the upper left corner, the formula H C l at the center, and the designation Strong acid.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm222426752\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Ternary Acids and Bases<\/strong><\/h3>\r\n<p id=\"fs-idm107875680\">Ternary compounds composed of hydrogen, oxygen, and some third element (\u201cE\u201d) may be structured as depicted in the image below. In these compounds, the central E atom is bonded to one or more O atoms, and at least one of the O atoms is also bonded to an H atom, corresponding to the general molecular formula O<sub>m<\/sub>E(OH)<sub>n<\/sub>. These compounds may be acidic, basic, or amphoteric depending on the properties of the central E atom. Examples of such compounds include sulfuric acid, O<sub>2<\/sub>S(OH)<sub>2<\/sub>, sulfurous acid, OS(OH)<sub>2<\/sub>, nitric acid, O<sub>2<\/sub>NOH, perchloric acid, O<sub>3<\/sub>ClOH, aluminum hydroxide, Al(OH)<sub>3<\/sub>, calcium hydroxide, Ca(OH)<sub>2<\/sub>, and potassium hydroxide, KOH:<\/p>\r\n<span id=\"fs-idm107871568\" class=\"scaled-down\" data-type=\"media\" data-alt=\"A diagram is shown that includes a central atom designated with the letter E. Single bonds extend above, below, left, and right of the E. An O atom is bonded to the right of the E, and an arrow points to the bond labeling it, \u201cBond a.\u201d An H atom is single bonded to the right of the O atom. An arrow pointing to this bond connects it to the label, \u201cBond b.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_OHbonds_img-1.jpg\" alt=\"A diagram is shown that includes a central atom designated with the letter E. Single bonds extend above, below, left, and right of the E. An O atom is bonded to the right of the E, and an arrow points to the bond labeling it, \u201cBond a.\u201d An H atom is single bonded to the right of the O atom. An arrow pointing to this bond connects it to the label, \u201cBond b.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-idm107870208\">If the central atom, E, has a low electronegativity, its attraction for electrons is low. Little tendency exists for the central atom to form a strong covalent bond with the oxygen atom, and bond <em data-effect=\"italics\">a<\/em> between the element and oxygen is more readily broken than bond <em data-effect=\"italics\">b<\/em> between oxygen and hydrogen. Hence bond <em data-effect=\"italics\">a<\/em> is ionic, hydroxide ions are released to the solution, and the material behaves as a base\u2014this is the case with Ca(OH)<sub>2<\/sub> and KOH. Lower electronegativity is characteristic of the more metallic elements; hence, the metallic elements form ionic hydroxides that are by definition basic compounds.<\/p>\r\n<p id=\"fs-idm78964544\">If, on the other hand, the atom E has a relatively high electronegativity, it strongly attracts the electrons it shares with the oxygen atom, making bond <em data-effect=\"italics\">a<\/em> relatively strongly covalent. The oxygen-hydrogen bond, bond <em data-effect=\"italics\">b<\/em>, is thereby weakened because electrons are displaced toward E. Bond <em data-effect=\"italics\">b<\/em> is polar and readily releases hydrogen ions to the solution, so the material behaves as an acid. High electronegativities are characteristic of the more nonmetallic elements. Thus, nonmetallic elements form covalent compounds containing acidic \u2212OH groups that are called<strong> oxyacids<\/strong>.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm223365360\" class=\"summary\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\r\n<p id=\"fs-idm223364480\">The relative strengths of acids and bases are reflected in the magnitudes of their ionization constants; the stronger the acid or base, the larger its ionization constant. A reciprocal relation exists between the strengths of a conjugate acid-base pair: the stronger the acid, the weaker its conjugate base. Water exerts a leveling effect on dissolved acids or bases, reacting completely to generate its characteristic hydronium and hydroxide ions (the strongest acid and base that may exist in water). The strengths of the binary acids increase from left to right across a period of the periodic table (CH<sub>4<\/sub> &lt; NH<sub>3<\/sub> &lt; H<sub>2<\/sub>O &lt; HF), and they increase down a group (HF &lt; HCl &lt; HBr &lt; HI).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idm94405216\" class=\"exercises\" data-depth=\"1\"><\/div>\r\n<div class=\"textbox shaded\" data-type=\"glossary\">\r\n<h3 data-type=\"glossary-title\"><\/h3>\r\n<dl id=\"fs-idp86058640\">\r\n \t<dt>acid ionization constant (<em data-effect=\"italics\">K<\/em><sub>a<\/sub>)<\/dt>\r\n \t<dd id=\"fs-idp86060160\">equilibrium constant for an acid ionization reaction<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp86060672\">\r\n \t<dt>base ionization constant (<em data-effect=\"italics\">K<\/em><sub>b<\/sub>)<\/dt>\r\n \t<dd id=\"fs-idm94081232\">equilibrium constant for a base ionization reaction<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idm94080720\">\r\n \t<dt>leveling effect<\/dt>\r\n \t<dd id=\"fs-idm94080080\">observation that acid-base strength of solutes in a given solvent is limited to that of the solvent\u2019s characteristic acid and base species (in water, hydronium and hydroxide ions, respectively)<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idm94074528\">\r\n \t<dt>oxyacid<\/dt>\r\n \t<dd id=\"fs-idm94073888\">ternary compound with acidic properties, molecules of which contain a central nonmetallic atom bonded to one or more O atoms, at least one of which is bonded to an ionizable H atom<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idm94073376\">\r\n \t<dt>percent ionization<\/dt>\r\n \t<dd id=\"fs-idm94072736\">ratio of the concentration of ionized acid to initial acid concentration expressed as a percentage<\/dd>\r\n<\/dl>\r\n<\/div>","rendered":"<p>&nbsp;<\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<h3><strong>Learning Objectives<\/strong><\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Assess the relative strengths of acids and bases according to their ionization constants<\/li>\n<li>Rationalize trends in acid\u2013base strength in relation to molecular structure<\/li>\n<li>Carry out equilibrium calculations for weak acid\u2013base systems<\/li>\n<\/ul>\n<\/div>\n<div id=\"fs-idm477446592\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Acid and Base Ionization Constants<\/strong><\/h3>\n<p id=\"fs-idm193375984\">The relative strength of an acid or base is the extent to which it ionizes when dissolved in water. If the ionization reaction is essentially complete, the acid or base is termed <em data-effect=\"italics\">strong<\/em>; if relatively little ionization occurs, the acid or base is weak. As will be evident throughout the remainder of this chapter, there are many more weak acids and bases than strong ones. The most common strong acids and bases are listed in <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_strong\">(Figure)<\/a>.<\/p>\n<div id=\"CNX_Chem_14_03_strong\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">Some of the common strong acids and bases are listed here.<\/div>\n<p><span id=\"fs-idp3283088\" data-type=\"media\" data-alt=\"This table has seven rows and two columns. The first row is a header row, and it labels each column, \u201c6 Strong Acids,\u201d and, \u201c6 Strong Bases.\u201d Under the \u201c6 Strong Acids\u201d column are the following: H C l O subscript 4 perchloric acid; H C l hydrochloric acid; H B r hydrobromic acid; H I hydroiodic acid; H N O subscript 3 nitric acid; H subscript 2 S O subscript 4 sulfuric acid. Under the \u201c6 Strong Bases\u201d column are the following: L i O H lithium hydroxide; N a O H sodium hydroxide; K O H potassium hydroxide; C a ( O H ) subscript 2 calcium hydroxide; S r ( O H ) subscript 2 strontium hydroxide; B a ( O H ) subscript 2 barium hydroxide.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_strong-1.jpg\" alt=\"This table has seven rows and two columns. The first row is a header row, and it labels each column, \u201c6 Strong Acids,\u201d and, \u201c6 Strong Bases.\u201d Under the \u201c6 Strong Acids\u201d column are the following: H C l O subscript 4 perchloric acid; H C l hydrochloric acid; H B r hydrobromic acid; H I hydroiodic acid; H N O subscript 3 nitric acid; H subscript 2 S O subscript 4 sulfuric acid. Under the \u201c6 Strong Bases\u201d column are the following: L i O H lithium hydroxide; N a O H sodium hydroxide; K O H potassium hydroxide; C a ( O H ) subscript 2 calcium hydroxide; S r ( O H ) subscript 2 strontium hydroxide; B a ( O H ) subscript 2 barium hydroxide.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idp107824512\">The relative strengths of acids may be quantified by measuring their equilibrium constants in aqueous solutions. In solutions of the same concentration, stronger acids ionize to a greater extent, and so yield higher concentrations of hydronium ions than do weaker acids. The equilibrium constant for an acid is called the <span data-type=\"term\">acid-ionization constant, <em data-effect=\"italics\">K<\/em><sub>a<\/sub><\/span>. For the reaction of an acid HA:<\/p>\n<div id=\"fs-idm122858592\" style=\"padding-left: 40px\" data-type=\"equation\">HA(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + A<sup>\u2212<\/sup>(<em>aq<\/em>),<\/div>\n<p id=\"fs-idp44134944\">the acid ionization constant is written<\/p>\n<div id=\"fs-idp97870288\" style=\"padding-left: 40px\" data-type=\"equation\">\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1853\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/143a-300x111.png\" alt=\"\" width=\"130\" height=\"48\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/143a-300x111.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/143a-65x24.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/143a-225x83.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/143a-350x130.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/143a.png 475w\" sizes=\"auto, (max-width: 130px) 100vw, 130px\" \/><\/div>\n<p id=\"fs-idp39416656\">where the concentrations are those at equilibrium. Although water is a reactant in the reaction, it is the solvent as well, so we do not include [H<sub>2<\/sub>O] in the equation. The larger the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> of an acid, the larger the concentration of H<sub>3<\/sub>O<sup>+<\/sup> and A<sup>\u2212<\/sup> relative to the concentration of the nonionized acid, HA, in an equilibrium mixture, and the stronger the acid. An acid is classified as \u201cstrong\u201d when it undergoes complete ionization, in which case the concentration of HA is zero and the acid ionization constant is immeasurably large (<em data-effect=\"italics\">K<\/em><sub>a<\/sub> \u2248 \u221e). Acids that are partially ionized are called \u201cweak,\u201d and their acid ionization constants may be experimentally measured. A table of ionization constants for weak acids is provided in Appendix H.<\/p>\n<p id=\"fs-idm220763536\">To illustrate this idea, three acid ionization equations and <em data-effect=\"italics\">K<\/em><sub>a<\/sub> values are shown below. The ionization constants increase from first to last of the listed equations, indicating the relative acid strength increases in the order CH<sub>3<\/sub>CO<sub>2<\/sub>H &lt; HNO<sub>2<\/sub> &lt; HSO<sub>4<\/sub><sup>\u2212<\/sup>:<\/p>\n<div id=\"fs-idp100550608\" style=\"padding-left: 40px\" data-type=\"equation\">CH<sub>3<\/sub>CO<sub>2<\/sub>H(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + CH<sub>3<\/sub>CO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>a<\/sub> = 1.8 \u00d7 10<sup>-5<\/sup><\/div>\n<div id=\"fs-idm57962960\" style=\"padding-left: 40px\" data-type=\"equation\">HNO<sub>2<\/sub>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + NO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>a<\/sub> = 4.6 \u00d7 10<sup>-4<\/sup><\/div>\n<div id=\"fs-idm223507040\" style=\"padding-left: 40px\" data-type=\"equation\">HSO<sub>4<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>aq<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + SO<sub>4<\/sub><sup>2-<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0K<sub>a<\/sub> = 1.2 \u00d7 10<sup>-2<\/sup><\/div>\n<p id=\"fs-idm115717600\">Another measure of the strength of an acid is its percent ionization. The <span data-type=\"term\">percent ionization<\/span> of a weak acid is defined in terms of the composition of an equilibrium mixture:<\/p>\n<div id=\"fs-idm149756192\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1854\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3b-300x64.png\" alt=\"\" width=\"268\" height=\"57\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3b-300x64.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3b-768x164.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3b-65x14.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3b-225x48.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3b-350x75.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3b.png 828w\" sizes=\"auto, (max-width: 268px) 100vw, 268px\" \/><\/div>\n<p id=\"fs-idm163389088\">where the numerator is equivalent to the concentration of the acid&#8217;s conjugate base (per stoichiometry, [A<sup>\u2212<\/sup>] = [H<sub>3<\/sub>O<sup>+<\/sup>]). Unlike the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> value, the percent ionization of a weak acid varies with the initial concentration of acid, typically decreasing as concentration increases. Equilibrium calculations of the sort described later in this chapter can be used to confirm this behavior.<\/p>\n<div id=\"fs-idm163336240\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp45762800\"><strong>Calculation of Percent Ionization from pH <\/strong><\/p>\n<p>Calculate the percent ionization of a 0.125-<em data-effect=\"italics\">M<\/em> solution of nitrous acid (a weak acid), with a pH of 2.09.<\/p>\n<p id=\"fs-idm95442560\"><strong>Solution:<\/strong><\/p>\n<p id=\"fs-idm68557120\">Converting the provided pH to hydronium ion molarity yields<\/p>\n<div id=\"fs-idm173125616\" style=\"padding-left: 40px\" data-type=\"equation\">[H<sub>3<\/sub>O<sup>+<\/sup>] = 10<sup>-2.09 <\/sup>= 0.0081 M<\/div>\n<div data-type=\"equation\">\n<p>The percent ionization for an acid is:<\/p>\n<div id=\"fs-idm119459936\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1856\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3c-300x132.png\" alt=\"\" width=\"100\" height=\"44\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3c-300x132.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3c-65x29.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3c-225x99.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3c-350x154.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3c.png 431w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/><\/div>\n<\/div>\n<p id=\"fs-idm213993776\">Substituting this value and the provided initial acid concentration into the percent ionization equation gives<\/p>\n<div id=\"fs-idm83770448\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1857\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3d-300x67.png\" alt=\"\" width=\"175\" height=\"39\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3d-300x67.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3d-65x14.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3d-225x50.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3d-350x78.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3d.png 702w\" sizes=\"auto, (max-width: 175px) 100vw, 175px\" \/><\/div>\n<p id=\"fs-idp164624\">(Recall the provided pH value of 2.09 is logarithmic, and so it contains just two significant digits, limiting the certainty of the computed percent ionization.)<\/p>\n<p id=\"fs-idp51316352\"><strong>Check Your Learning:<\/strong><\/p>\n<p>Calculate the percent ionization of a 0.10-<em data-effect=\"italics\">M<\/em> solution of acetic acid with a pH of 2.89.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp9633456\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm119453808\">1.3% ionized<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp45486128\" class=\"chemistry link-to-learning\" data-type=\"note\">\n<p id=\"fs-idm98260672\">View the <a href=\"http:\/\/openstaxcollege.org\/l\/16AcidBase\">simulation<\/a> of strong and weak acids and bases at the molecular level.<\/p>\n<\/div>\n<p id=\"fs-idm98628800\">Just as for acids, the relative strength of a base is reflected in the magnitude of its <span data-type=\"term\">base-ionization constant (<em data-effect=\"italics\">K<\/em><sub>b<\/sub>)<\/span> in aqueous solutions. In solutions of the same concentration, stronger bases ionize to a greater extent, and so yield higher hydroxide ion concentrations than do weaker bases. A stronger base has a larger ionization constant than does a weaker base. For the reaction of a base, B:<\/p>\n<div id=\"fs-idm69456656\" style=\"padding-left: 40px\" data-type=\"equation\">B(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc HB<sup>+<\/sup>(<em>aq<\/em>)+ OH<sup>\u2212<\/sup>(<em>aq<\/em>),<\/div>\n<p id=\"fs-idp1182192\">the ionization constant is written as<\/p>\n<div id=\"fs-idm72726864\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1858\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3e-300x113.png\" alt=\"\" width=\"135\" height=\"51\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3e-300x113.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3e-65x24.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3e-225x84.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3e-350x131.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3e.png 533w\" sizes=\"auto, (max-width: 135px) 100vw, 135px\" \/><\/div>\n<p id=\"fs-idp86117152\">Inspection of the data for three weak bases presented below shows the base strength increases in the order NO<sub>2<\/sub><sup>&#8211;<\/sup> &lt; CH<sub>3<\/sub>CO<sub>2<\/sub><sup>&#8211;<\/sup> &lt;NH<sub>3<\/sub>.<\/p>\n<div id=\"fs-idm168482736\" style=\"padding-left: 40px\" data-type=\"equation\">NO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc HNO<sub>2<\/sub>(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>b<\/sub> = 2.17 \u00d7 10<sup>-11<\/sup><\/div>\n<div style=\"padding-left: 40px\" data-type=\"equation\">CH<sub>3<\/sub>CO<sub>2<\/sub><sup>&#8211;<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc CH<sub>3<\/sub>CO<sub>2<\/sub>H(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>b<\/sub> = 5.6 \u00d7 10<sup>-10<\/sup><\/div>\n<div style=\"padding-left: 40px\" data-type=\"equation\">NH<sub>3<\/sub>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc NH<sub>4<\/sub><sup>+<\/sup>(<em>aq<\/em>)+ OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>b<\/sub>=\u00a0 1.8 \u00d7 10<sup>-5<\/sup><\/div>\n<p id=\"fs-idm69273568\">A table of ionization constants for weak bases appears in Appendix I. As for acids, the relative strength of a base is also reflected in its percent ionization, computed as<\/p>\n<div id=\"fs-idm208527632\" style=\"padding-left: 40px\" data-type=\"equation\">% ionization = [OH<sup>\u2212<\/sup>]<sub>eq<\/sub>\/[B]<sub>0 <\/sub>\u00d7100%<\/div>\n<p id=\"fs-idm475449120\">but will vary depending on the base ionization constant and the initial concentration of the solution.<\/p>\n<\/div>\n<div id=\"fs-idm178559536\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Relative Strengths of Conjugate Acid-Base Pairs<\/strong><\/h3>\n<p id=\"fs-idm172520016\">Br\u00f8nsted-Lowry acid-base chemistry is the transfer of protons; thus, logic suggests a relation between the relative strengths of conjugate acid-base pairs. The strength of an acid or base is quantified in its ionization constant, <em data-effect=\"italics\">K<\/em><sub>a<\/sub> or <em data-effect=\"italics\">K<\/em><sub>b<\/sub>, which represents the extent of the acid or base ionization reaction. For the conjugate acid-base pair HA \/ A<sup>\u2212<\/sup>, ionization equilibrium equations and ionization constant expressions are<\/p>\n<div id=\"fs-idm157208576\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1859\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f-300x68.png\" alt=\"\" width=\"450\" height=\"102\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f-300x68.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f-1024x231.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f-768x173.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f-1536x347.png 1536w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f-65x15.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f-225x51.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f-350x79.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3f.png 1830w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/div>\n<p id=\"fs-idm217883488\">Adding these two chemical equations yields the equation for the autoionization for water:<\/p>\n<div id=\"fs-idp71522608\" style=\"padding-left: 40px\" data-type=\"equation\"><del>HA(<em>aq<\/em>)<\/del> + H<sub>2<\/sub>O(<em>l<\/em>) + <del>A<sup>\u2212<\/sup>(<em>aq<\/em>)<\/del> + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + <del>A<sup>\u2212<\/sup>(<em>aq<\/em>)<\/del> + OH<sup>\u2212<\/sup>(<em>aq<\/em>) + <del>HA(<em>aq<\/em>)<\/del><\/div>\n<div data-type=\"equation\"><\/div>\n<div id=\"fs-idm122391632\" style=\"padding-left: 40px\" data-type=\"equation\">\u00a0H<sub>2<\/sub>O(<em>l<\/em>) \u00a0+ H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>)\u00a0+ OH<sup>\u2212<\/sup>(<em>aq<\/em>)<\/div>\n<p id=\"fs-idm160491872\">As discussed in another chapter on equilibrium, the equilibrium constant for a summed reaction is equal to the mathematical product of the equilibrium constants for the added reactions, and so<\/p>\n<div id=\"fs-idm141982832\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1861\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g-300x31.png\" alt=\"\" width=\"348\" height=\"36\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g-300x31.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g-1024x105.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g-768x79.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g-1536x157.png 1536w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g-65x7.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g-225x23.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g-350x36.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3g.png 1662w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><\/div>\n<p id=\"fs-idm224463760\">This equation states the relation between ionization constants for any conjugate acid-base pair, namely, their mathematical product is equal to the ion product of water, <em data-effect=\"italics\">K<\/em><sub>w<\/sub>. By rearranging this equation, a reciprocal relation between the strengths of a conjugate acid-base pair becomes evident:<\/p>\n<div id=\"fs-idm223919584\" style=\"padding-left: 40px\" data-type=\"equation\">K<sub>a<\/sub> = K<sub>w<\/sub>\/K<sub>b<\/sub>\u00a0 or\u00a0 K<sub>b<\/sub> = K<sub>w<\/sub>\/K<sub>a<\/sub><\/div>\n<p id=\"fs-idm225241056\">The inverse proportional relation between <em data-effect=\"italics\">K<\/em><sub>a<\/sub> and <em data-effect=\"italics\">K<\/em><sub>b<\/sub> means <em data-effect=\"italics\">the stronger the acid or base, the weaker its conjugate partner<\/em>. <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_strengths\">(Figure)<\/a> illustrates this relation for several conjugate acid-base pairs.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_14_03_strengths\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Relative strengths of several conjugate acid-base pairs are shown.<\/div>\n<p><span id=\"fs-idm162584688\" data-type=\"media\" data-alt=\"The diagram shows two horizontal bars. The first, labeled, \u201cRelative acid strength,\u201d at the top is red on the left and gradually changes to purple on the right. The red end at the left is labeled, \u201cStronger acids.\u201d The purple end at the right is labeled, \u201cWeaker acids.\u201d Just outside the bar to the lower left is the label, \u201cK subscript a.\u201d The bar is marked off in increments with a specific acid listed above each increment. The first mark is at 1.0 with H subscript 3 O superscript positive sign. The second is ten raised to the negative two with H C l O subscript 2. The third is ten raised to the negative 4 with H F. The fourth is ten raised to the negative 6 with H subscript 2 C O subscript 3. The fifth is ten raised to a negative 8 with C H subscript 3 C O O H. The sixth is ten raised to the negative ten with N H subscript 4 superscript positive sign. The seventh is ten raised to a negative 12 with H P O subscript 4 superscript 2 negative sign. The eighth is ten raised to the negative 14 with H subscript 2 O. Similarly the second bar, which is labeled \u201cRelative conjugate base strength,\u201d is purple at the left end and gradually becomes blue at the right end. Outside the bar to the left is the label, \u201cWeaker bases.\u201d Outside the bar to the right is the label, \u201cStronger bases.\u201d Below and to the left of the bar is the label, \u201cK subscript b.\u201d The bar is similarly marked at increments with bases listed above each increment. The first is at ten raised to the negative 14 with H subscript 2 O above it. The second is ten raised to the negative 12 C l O subscript 2 superscript negative sign. The third is ten raised to the negative ten with F superscript negative sign. The fourth is ten raised to a negative eight with H C O subscript 3 superscript negative sign. The fifth is ten raised to the negative 6 with C H subscript 3 C O O superscript negative sign. The sixth is ten raised to the negative 4 with N H subscript 3. The seventh is ten raised to the negative 2 with P O subscript 4 superscript three negative sign. The eighth is 1.0 with O H superscript negative sign.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_strengths-1.jpg\" alt=\"The diagram shows two horizontal bars. The first, labeled, \u201cRelative acid strength,\u201d at the top is red on the left and gradually changes to purple on the right. The red end at the left is labeled, \u201cStronger acids.\u201d The purple end at the right is labeled, \u201cWeaker acids.\u201d Just outside the bar to the lower left is the label, \u201cK subscript a.\u201d The bar is marked off in increments with a specific acid listed above each increment. The first mark is at 1.0 with H subscript 3 O superscript positive sign. The second is ten raised to the negative two with H C l O subscript 2. The third is ten raised to the negative 4 with H F. The fourth is ten raised to the negative 6 with H subscript 2 C O subscript 3. The fifth is ten raised to a negative 8 with C H subscript 3 C O O H. The sixth is ten raised to the negative ten with N H subscript 4 superscript positive sign. The seventh is ten raised to a negative 12 with H P O subscript 4 superscript 2 negative sign. The eighth is ten raised to the negative 14 with H subscript 2 O. Similarly the second bar, which is labeled \u201cRelative conjugate base strength,\u201d is purple at the left end and gradually becomes blue at the right end. Outside the bar to the left is the label, \u201cWeaker bases.\u201d Outside the bar to the right is the label, \u201cStronger bases.\u201d Below and to the left of the bar is the label, \u201cK subscript b.\u201d The bar is similarly marked at increments with bases listed above each increment. The first is at ten raised to the negative 14 with H subscript 2 O above it. The second is ten raised to the negative 12 C l O subscript 2 superscript negative sign. The third is ten raised to the negative ten with F superscript negative sign. The fourth is ten raised to a negative eight with H C O subscript 3 superscript negative sign. The fifth is ten raised to the negative 6 with C H subscript 3 C O O superscript negative sign. The sixth is ten raised to the negative 4 with N H subscript 3. The seventh is ten raised to the negative 2 with P O subscript 4 superscript three negative sign. The eighth is 1.0 with O H superscript negative sign.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"CNX_Chem_14_03_Corresp\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">This figure shows strengths of conjugate acid-base pairs relative to the strength of water as the reference substance.<\/div>\n<p><span id=\"fs-idm44354768\" data-type=\"media\" data-alt=\"This figure includes a table separated into a left half which is labeled \u201cAcids\u201d and a right half labeled \u201cBases.\u201d A red arrow points up the left side, which is labeled \u201cIncreasing acid strength.\u201d Similarly, a blue arrow points downward along the right side, which is labeled \u201cIncreasing base strength.\u201d Names of acids and bases are listed next to each arrow toward the center of the table, followed by chemical formulas. Acids listed top to bottom are sulfuric acid, H subscript 2 S O subscript 4, hydrogen iodide, H I, hydrogen bromide, H B r, hydrogen chloride, H C l, nitric acid, H N O subscript 3, hydronium ion ( in pink text) H subscript 3 O superscript plus, hydrogen sulfate ion, H S O subscript 4 superscript negative, phosphoric acid, H subscript 3 P O subscript 4, hydrogen fluoride, H F, nitrous acid, H N O subscript 2, acetic acid, C H subscript 3 C O subscript 2 H, carbonic acid H subscript 2 C O subscript 3, hydrogen sulfide, H subscript 2 S, ammonium ion, N H subscript 4 superscript +, hydrogen cyanide, H C N, hydrogen carbonate ion, H C O subscript 3 superscript negative, water (shaded in beige) H subscript 2 O, hydrogen sulfide ion, H S superscript negative, ethanol, C subscript 2 H subscript 5 O H, ammonia, N H subscript 3, hydrogen, H subscript 2, methane, and C H subscript 4. The acids at the top of the listing from sulfuric acid through nitric acid are grouped with a bracket to the right labeled \u201cUndergo complete acid ionization in water.\u201d Similarly, the acids at the bottom from hydrogen sulfide ion through methane are grouped with a bracket and labeled, \u201cDo not undergo acid ionization in water.\u201d The right half of the figure lists bases and formulas. From top to bottom the bases listed are hydrogen sulfate ion, H S O subscript 4 superscript negative, iodide ion, I superscript negative, bromide ion, B r superscript negative, chloride ion, C l superscript negative, nitrate ion, N O subscript 3 superscript negative, water (shaded in beige), H subscript 2 O, sulfate ion, S O subscript 4 superscript 2 negative, dihydrogen phosphate ion, H subscript 2 P O subscript 4 superscript negative, fluoride ion, F superscript negative, nitrite ion, N O subscript 2 superscript negative, acetate ion, C H subscript 3 C O subscript 2 superscript negative, hydrogen carbonate ion, H C O subscript 3 superscript negative, hydrogen sulfide ion, H S superscript negative, ammonia, N H subscript 3, cyanide ion, C N superscript negative, carbonate ion, C O subscript 3 superscript 2 negative, hydroxide ion (in blue), O H superscript negative, sulfide ion, S superscript 2 negative, ethoxide ion, C subscript 2 H subscript 5 O superscript negative, amide ion N H subscript 2 superscript negative, hydride ion, H superscript negative, and methide ion C H subscript 3 superscript negative. The bases at the top, from perchlorate ion through nitrate ion are group with a bracket which is labeled \u201cDo not undergo base ionization in water.\u201d Similarly, the lower 5 in the listing, from sulfide ion through methide ion are grouped and labeled \u201cUndergo complete base ionization in water.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_corresp-1.jpg\" alt=\"This figure includes a table separated into a left half which is labeled \u201cAcids\u201d and a right half labeled \u201cBases.\u201d A red arrow points up the left side, which is labeled \u201cIncreasing acid strength.\u201d Similarly, a blue arrow points downward along the right side, which is labeled \u201cIncreasing base strength.\u201d Names of acids and bases are listed next to each arrow toward the center of the table, followed by chemical formulas. Acids listed top to bottom are sulfuric acid, H subscript 2 S O subscript 4, hydrogen iodide, H I, hydrogen bromide, H B r, hydrogen chloride, H C l, nitric acid, H N O subscript 3, hydronium ion ( in pink text) H subscript 3 O superscript plus, hydrogen sulfate ion, H S O subscript 4 superscript negative, phosphoric acid, H subscript 3 P O subscript 4, hydrogen fluoride, H F, nitrous acid, H N O subscript 2, acetic acid, C H subscript 3 C O subscript 2 H, carbonic acid H subscript 2 C O subscript 3, hydrogen sulfide, H subscript 2 S, ammonium ion, N H subscript 4 superscript +, hydrogen cyanide, H C N, hydrogen carbonate ion, H C O subscript 3 superscript negative, water (shaded in beige) H subscript 2 O, hydrogen sulfide ion, H S superscript negative, ethanol, C subscript 2 H subscript 5 O H, ammonia, N H subscript 3, hydrogen, H subscript 2, methane, and C H subscript 4. The acids at the top of the listing from sulfuric acid through nitric acid are grouped with a bracket to the right labeled \u201cUndergo complete acid ionization in water.\u201d Similarly, the acids at the bottom from hydrogen sulfide ion through methane are grouped with a bracket and labeled, \u201cDo not undergo acid ionization in water.\u201d The right half of the figure lists bases and formulas. From top to bottom the bases listed are hydrogen sulfate ion, H S O subscript 4 superscript negative, iodide ion, I superscript negative, bromide ion, B r superscript negative, chloride ion, C l superscript negative, nitrate ion, N O subscript 3 superscript negative, water (shaded in beige), H subscript 2 O, sulfate ion, S O subscript 4 superscript 2 negative, dihydrogen phosphate ion, H subscript 2 P O subscript 4 superscript negative, fluoride ion, F superscript negative, nitrite ion, N O subscript 2 superscript negative, acetate ion, C H subscript 3 C O subscript 2 superscript negative, hydrogen carbonate ion, H C O subscript 3 superscript negative, hydrogen sulfide ion, H S superscript negative, ammonia, N H subscript 3, cyanide ion, C N superscript negative, carbonate ion, C O subscript 3 superscript 2 negative, hydroxide ion (in blue), O H superscript negative, sulfide ion, S superscript 2 negative, ethoxide ion, C subscript 2 H subscript 5 O superscript negative, amide ion N H subscript 2 superscript negative, hydride ion, H superscript negative, and methide ion C H subscript 3 superscript negative. The bases at the top, from perchlorate ion through nitrate ion are group with a bracket which is labeled \u201cDo not undergo base ionization in water.\u201d Similarly, the lower 5 in the listing, from sulfide ion through methide ion are grouped and labeled \u201cUndergo complete base ionization in water.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm225187616\">The listing of conjugate acid\u2013base pairs shown in <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_Corresp\">(Figure)<\/a> is arranged to show the relative strength of each species as compared with water, whose entries are highlighted in each of the table\u2019s columns. In the acid column, those species listed below water are weaker acids than water. These species do not undergo acid ionization in water; they are not Bronsted-Lowry acids. All the species listed above water are stronger acids, transferring protons to water to some extent when dissolved in an aqueous solution to generate hydronium ions. Species above water but below hydronium ion are <em data-effect=\"italics\">weak acids<\/em>, undergoing partial acid ionization, whereas those above hydronium ion are <em data-effect=\"italics\">strong acids<\/em> that are completely ionized in aqueous solution.<\/p>\n<p id=\"fs-idm213445440\">If all these strong acids are completely ionized in water, why does the column indicate they vary in strength, with nitric acid being the weakest and perchloric acid the strongest? Notice that the sole acid species present in an aqueous solution of any strong acid is H<sub>3<\/sub>O<sup>+<\/sup>(<em data-effect=\"italics\">aq<\/em>), meaning that hydronium ion is the strongest acid that may exist in water; any stronger acid will react completely with water to generate hydronium ions. This limit on the acid strength of solutes in a solution is called a <strong data-effect=\"bold\">leveling effect<\/strong>. To measure the differences in acid strength for \u201cstrong\u201d acids, the acids must be dissolved in a solvent that is <em data-effect=\"italics\">less basic<\/em> than water. In such solvents, the acids will be \u201cweak,\u201d and so any differences in the extent of their ionization can be determined. For example, the binary hydrogen halides HCl, HBr, and HI are strong acids in water but weak acids in ethanol (strength increasing HCl &lt; HBr &lt; HI).<\/p>\n<p id=\"fs-idm167383056\">The right column of <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_Corresp\">(Figure)<\/a> lists a number of substances in order of increasing base strength from top to bottom. Following the same logic as for the left column, species listed above water are weaker bases and so they don\u2019t undergo base ionization when dissolved in water. Species listed between water and its conjugate base, hydroxide ion, are weak bases that partially ionize. Species listed below hydroxide ion are strong bases that completely ionize in water to yield hydroxide ions (i.e., they are <em data-effect=\"italics\">leveled<\/em> to hydroxide). A comparison of the acid and base columns in this table supports the reciprocal relation between the strengths of conjugate acid-base pairs. For example, the conjugate bases of the strong acids (top of table) are all of negligible strength. A strong acid exhibits an immeasurably large <em data-effect=\"italics\">K<\/em><sub>a<\/sub>, and so its conjugate base will exhibit a <em data-effect=\"italics\">K<\/em><sub>b<\/sub> that is essentially zero:<\/p>\n<p id=\"fs-idm200218096\" style=\"padding-left: 40px\">strong acid:\u00a0 \u00a0 \u00a0K<sub>a<\/sub> \u2248 \u221e<\/p>\n<p style=\"padding-left: 40px\">conjugate base:\u00a0 \u00a0 \u00a0K<sub>b<\/sub> = K<sub>w<\/sub>\/K<sub>a<\/sub> = K<sub>w<\/sub>\/\u221e \u2248 0<\/p>\n<p id=\"fs-idm225937888\">A similar approach can be used to support the observation that conjugate acids of strong bases (<em data-effect=\"italics\">K<\/em><sub>b<\/sub> \u2248 \u221e) are of negligible strength (<em data-effect=\"italics\">K<\/em><sub>a<\/sub> \u2248 0).<\/p>\n<div id=\"fs-idp2197392\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm154506736\"><strong>Calculating Ionization Constants for Conjugate Acid-Base Pairs <\/strong><\/p>\n<p>Use the <em data-effect=\"italics\">K<\/em><sub>b<\/sub> for the nitrite ion, NO<sub>2<\/sub><sup>\u2212<\/sup>, to calculate the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for its conjugate acid.<\/p>\n<p id=\"fs-idm172466976\"><strong>Solution:<\/strong><\/p>\n<p><em data-effect=\"italics\">K<\/em><sub>b<\/sub> for NO<sub>2<\/sub><sup>\u2212<\/sup> is given in this section as 2.17 \u00d7 10<sup>\u221211<\/sup>. The conjugate acid of NO<sub>2<\/sub><sup>\u2212<\/sup> is HNO<sub>2<\/sub>; <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for HNO<sub>2<\/sub> can be calculated using the relationship:<\/p>\n<div id=\"fs-idm197198576\" style=\"padding-left: 40px\" data-type=\"equation\">K<sub>a<\/sub> \u00d7 K<sub>b<\/sub> = 1.0 \u00d7 10<sup>-14 <\/sup>= K<sub>w<\/sub><\/div>\n<p id=\"fs-idm174350000\">Solving for <em data-effect=\"italics\">K<\/em><sub>a<\/sub> yields<\/p>\n<div id=\"fs-idp100620656\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1863\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3h-300x46.png\" alt=\"\" width=\"274\" height=\"42\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3h-300x46.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3h-1024x157.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3h-768x118.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3h-65x10.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3h-225x35.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3h-350x54.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3h.png 1081w\" sizes=\"auto, (max-width: 274px) 100vw, 274px\" \/><\/div>\n<p id=\"fs-idm122128048\">This answer can be verified by finding the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for HNO<sub>2<\/sub> in Appendix H.<\/p>\n<p id=\"fs-idp28811616\"><strong>Check Your Learning:<\/strong><\/p>\n<p>Determine the relative acid strengths of NH<sub>4<\/sub><sup>+<\/sup> and HCN by comparing their ionization constants. The ionization constant of HCN is given in Appendix H as 4.9 \u00d7 10<sup>\u221210<\/sup>. The ionization constant of NH<sub>4<\/sub><sup>+<\/sup> is not listed, but the ionization constant of its conjugate base, NH<sub>3<\/sub>, is listed as 1.8 \u00d7 10<sup>\u22125<\/sup>.<\/p>\n<div id=\"fs-idp12994032\" data-type=\"note\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm80300528\">NH<sub>4<\/sub><sup>+ <\/sup>is the slightly stronger acid (<em data-effect=\"italics\">K<\/em><sub>a<\/sub> for NH<sub>4<\/sub><sup>+ <\/sup>= 5.6 \u00d7 10<sup>\u221210<\/sup>).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idm160956208\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Acid-Base Equilibrium Calculations<\/strong><\/h3>\n<p id=\"fs-idm226989136\">The chapter on chemical equilibria introduced several types of equilibrium calculations and the various mathematical strategies that are helpful in performing them. These strategies are generally useful for equilibrium systems regardless of chemical reaction class, and so they may be effectively applied to acid-base equilibrium problems. This section presents several example exercises involving equilibrium calculations for acid-base systems.<\/p>\n<p><span id=\"fs-idp23785056\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This image shows two bottles containing clear colorless solutions. Each bottle contains a single p H indicator strip. The strip in the bottle on the left is red, and a similar red strip is placed on a filter paper circle in front of the bottle on surface on which the bottles are resting. Similarly, the second bottle on the right contains and orange strip and an orange strip is placed in front of it on a filter paper circle. Between the two bottles is a pack of p Hydrion papers with a p H color scale on its cover.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_acetate_img-1.jpg\" alt=\"This image shows two bottles containing clear colorless solutions. Each bottle contains a single p H indicator strip. The strip in the bottle on the left is red, and a similar red strip is placed on a filter paper circle in front of the bottle on surface on which the bottles are resting. Similarly, the second bottle on the right contains and orange strip and an orange strip is placed in front of it on a filter paper circle. Between the two bottles is a pack of p Hydrion papers with a p H color scale on its cover.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-idm134302736\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This photo shows two glass containers filled with a transparent liquid. In between the containers is a p H strip indicator guide. There are p H strips placed in front of each glass container. The liquid in the container on the left appears to have a p H of 10 or 11. The liquid in the container on the right appears to have a p H of about 13 or 14.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ammonia-1.jpg\" alt=\"This photo shows two glass containers filled with a transparent liquid. In between the containers is a p H strip indicator guide. There are p H strips placed in front of each glass container. The liquid in the container on the left appears to have a p H of 10 or 11. The liquid in the container on the right appears to have a p H of about 13 or 14.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-idm223269056\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm118702752\"><strong>Determination of <em data-effect=\"italics\">K<\/em><sub>a<\/sub> from Equilibrium Concentrations <\/strong><\/p>\n<p>Acetic acid is the principal ingredient in vinegar (<a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_Vinegar\">(Figure)<\/a>) that provides its sour taste. At equilibrium, a solution contains [CH<sub>3<\/sub>CO<sub>2<\/sub>H] = 0.0787 <em data-effect=\"italics\">M<\/em> and [H<sub>3<\/sub>O<sup>+<\/sup>] = [CH<sub>3<\/sub>CO<sub>2<\/sub><sup>\u2212<\/sup>] = 0.00118 M. What is the value of <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for acetic acid?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_14_03_Vinegar\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">Vinegar contains acetic acid, a weak acid. (credit: modification of work by \u201cHomeSpot HQ\u201d\/Flickr)<\/div>\n<p><span id=\"fs-idm137777920\" data-type=\"media\" data-alt=\"An image shows the label of a bottle of distilled white vinegar. The label states that the contents have been reduced with water to 5 percent acidity.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_Vinegar-1.jpg\" alt=\"An image shows the label of a bottle of distilled white vinegar. The label states that the contents have been reduced with water to 5 percent acidity.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm119280448\"><strong>Solution: <\/strong><\/p>\n<p>The relevant equilibrium equation and its equilibrium constant expression are shown below. Substitution of the provided equilibrium concentrations permits a straightforward calculation of the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> for acetic acid.<\/p>\n<div id=\"fs-idp69048880\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1865\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i-300x63.png\" alt=\"\" width=\"400\" height=\"84\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i-300x63.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i-1024x216.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i-768x162.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i-1536x324.png 1536w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i-65x14.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i-225x47.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i-350x74.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3i.png 1657w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm68555680\"><strong>Check Your Learning: <\/strong><\/p>\n<p>The HSO<sub>4<\/sub><sup>\u2212<\/sup> ion is a weak acid used in some household cleansers:<\/p>\n<div id=\"fs-idm174702176\" style=\"padding-left: 40px\" data-type=\"equation\">HSO<sub>4<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + SO<sub>4<\/sub><sup>2-<\/sup>(<em>aq<\/em>)<\/div>\n<p id=\"fs-idm168960944\">What is the acid ionization constant for this weak acid if an equilibrium mixture has the following composition: [H<sub>3<\/sub>O<sup>+<\/sup>] = 0.027 <em data-effect=\"italics\">M<\/em>; [HSO<sub>4<\/sub><sup>\u2212<\/sup>] = 0.29 M; and [SO<sub>4<\/sub><sup>2-<\/sup>] = 0.13 M?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp348400\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp1308432\"><em data-effect=\"italics\">K<\/em><sub>a<\/sub> for HSO<sub>4<\/sub><sup>\u2212<\/sup> = 1.2 \u00d7 10<sup>\u22122<\/sup><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm154542240\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm1585392\"><strong>Determination of <em data-effect=\"italics\">K<\/em><sub>b<\/sub> from Equilibrium Concentrations <\/strong><\/p>\n<p>Caffeine, C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub> is a weak base. What is the value of <em data-effect=\"italics\">K<\/em><sub>b<\/sub> for caffeine if a solution at equilibrium has [C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub>] = 0.050 <em data-effect=\"italics\">M<\/em>, [C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub>H<sup>+<\/sup>] = 5.0 \u00d7 10<sup>\u22123 <\/sup><em data-effect=\"italics\">M<\/em>, and [OH<sup>\u2212<\/sup>] = 2.5 \u00d7 10<sup>\u22123<\/sup><em data-effect=\"italics\">M<\/em>?<\/p>\n<p id=\"fs-idm64959408\"><strong>Solution:<\/strong><\/p>\n<p>The relevant equilibrium equation and its equilibrium constant expression are shown below. Substitution of the provided equilibrium concentrations permits a straightforward calculation of the <em data-effect=\"italics\">K<\/em><sub>b<\/sub> for caffeine.<\/p>\n<div id=\"fs-idp57095280\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1866\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j-300x54.png\" alt=\"\" width=\"438\" height=\"79\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j-300x54.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j-1024x184.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j-768x138.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j-1536x277.png 1536w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j-65x12.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j-225x41.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j-350x63.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3j.png 1899w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm122074528\"><strong>Check Your Learning: <\/strong><\/p>\n<p>What is the equilibrium constant for the ionization of the HPO<sub>4<\/sub><sup>2-<\/sup>\u00a0ion, a weak base<\/p>\n<div id=\"fs-idm98055840\" style=\"padding-left: 40px\" data-type=\"equation\">HPO<sub>4<\/sub><sup>2-<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>2<\/sub>PO<sub>4<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(aq)<\/div>\n<p id=\"fs-idp31344880\">if the composition of an equilibrium mixture is as follows: [OH<sup>\u2212<\/sup>] = 1.3 \u00d7 10<sup>\u22126<\/sup><em data-effect=\"italics\">M<\/em>; [H<sub>2<\/sub>PO<sub>4<\/sub><sup>\u2212<\/sup>] = 0.042 M; and [HPO<sub>4<\/sub><sup>2-<\/sup>] = 0.341 M?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm157882608\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp68248832\"><em data-effect=\"italics\">K<\/em><sub>b<\/sub> for HPO<sub>4<\/sub><sup>2- <\/sup>= 1.6 \u00d7 10<sup>-7<\/sup><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm1433984\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm1433728\"><strong>Determination of <em data-effect=\"italics\">K<\/em><sub>a<\/sub> or <em data-effect=\"italics\">K<\/em><sub>b<\/sub> from pH <\/strong><\/p>\n<p>The pH of a 0.0516-<em data-effect=\"italics\">M<\/em> solution of nitrous acid, HNO<sub>2<\/sub>, is 2.34. What is its <em data-effect=\"italics\">K<\/em><sub>a<\/sub>?<\/p>\n<div id=\"fs-idp31767264\" style=\"padding-left: 40px\" data-type=\"equation\">HNO<sub>2<\/sub>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + NO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>)<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm163708144\"><strong>Solution:<\/strong><\/p>\n<p>The nitrous acid concentration provided is a <em data-effect=\"italics\">formal<\/em> concentration, one that does not account for any chemical equilibria that may be established in solution. Such concentrations are treated as \u201cinitial\u201d values for equilibrium calculations using the ICE table approach. Notice the initial value of hydronium ion is listed as <em data-effect=\"italics\">approximately<\/em> zero because a small concentration of H<sub>3<\/sub>O<sup>+<\/sup> is present (1.0 \u00d7 10<sup>\u22127<\/sup><em data-effect=\"italics\">M<\/em>) due to the autoionization of water. In many cases, such as all the ones presented in this chapter, this concentration is much less than that generated by ionization of the acid (or base) in question and may be neglected.<\/p>\n<p id=\"fs-idm204817712\">The pH provided is a logarithmic measure of the hydronium ion concentration resulting from the acid ionization of the nitrous acid, and so it represents an \u201cequilibrium\u201d value for the ICE table:<\/p>\n<p style=\"padding-left: 40px\">[H<sub>3<\/sub>O<sup>+<\/sup>] = 10<sup>-2.34 <\/sup>= 0.0046 M<\/p>\n<p id=\"fs-idm214144400\">The ICE table for this system is then<\/p>\n<p><span id=\"fs-idm79844096\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201cH N O subscript 2 plus sign H subscript 2 O equilibrium sign H subscript 3 O superscript positive sign plus sign N O subscript 2 superscript negative sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.0516, negative 0.0046, 0.0470. The second column is blank in all three rows. The third column has the following: approximately 0, positive 0.0046, 0.0046. The fourth column has the following: 0, positive 0.0046, 0.0046.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ICETable2_img-1.jpg\" alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201cH N O subscript 2 plus sign H subscript 2 O equilibrium sign H subscript 3 O superscript positive sign plus sign N O subscript 2 superscript negative sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.0516, negative 0.0046, 0.0470. The second column is blank in all three rows. The third column has the following: approximately 0, positive 0.0046, 0.0046. The fourth column has the following: 0, positive 0.0046, 0.0046.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-idm98416272\">Finally, calculate the value of the equilibrium constant using the data in the table:<\/p>\n<div id=\"fs-idm98415888\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1867\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3k-300x37.png\" alt=\"\" width=\"365\" height=\"45\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3k-300x37.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3k-1024x126.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3k-768x94.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3k-65x8.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3k-225x28.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3k-350x43.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3k.png 1452w\" sizes=\"auto, (max-width: 365px) 100vw, 365px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm166688304\"><strong>Check Your Learning: <\/strong><\/p>\n<p>The pH of a solution of household ammonia, a 0.950-<em data-effect=\"italics\">M<\/em> solution of NH<sub>3,<\/sub> is 11.612. What is <em data-effect=\"italics\">K<\/em><sub>b<\/sub> for NH<sub>3<\/sub>?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm56490624\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm56489984\"><em data-effect=\"italics\">K<\/em><sub>b<\/sub> = 1.8\u00a0 \u00d7 10<sup>\u22125<\/sup><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm159829376\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm159829120\"><strong>Calculating Equilibrium Concentrations in a Weak Acid Solution <\/strong><\/p>\n<p>Formic acid, HCO<sub>2<\/sub>H, is one irritant that causes the body\u2019s reaction to some ant bites and stings (<a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_AntSting\">(Figure)<\/a>).<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_14_03_AntSting\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">The pain of some ant bites and stings is caused by formic acid. (credit: John Tann)<\/div>\n<p><span id=\"fs-idm94059808\" data-type=\"media\" data-alt=\"A photograph is shown of a large black ant on the end of a human finger.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_AntSting-1.jpg\" alt=\"A photograph is shown of a large black ant on the end of a human finger.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idm94058112\">What is the concentration of hydronium ion and the pH of a 0.534-<em data-effect=\"italics\">M<\/em> solution of formic acid?<\/p>\n<div id=\"fs-idm83702544\" style=\"padding-left: 40px\" data-type=\"equation\">HCO<sub>2<\/sub>H(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + HCO<sub>2<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0K<sub>a<\/sub> = 1.8 \u00d7 10<sup>-4<\/sup><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm42704112\"><strong>Solution:<\/strong><\/p>\n<p id=\"fs-idm475800144\">The ICE table for this system is<\/p>\n<p><span id=\"fs-idm3940608\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201cH C O subscript 2 H plus sign H subscript 2 O equilibrium arrow H subscript 3 O superscript positive sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.534, blank, 0.534 minus x. The second column is blank in all three rows. The third column has the following: approximately 0, positive x, x. The fourth column has the following: 0, positive x, x.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ICETable3_img-1.jpg\" alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201cH C O subscript 2 H plus sign H subscript 2 O equilibrium arrow H subscript 3 O superscript positive sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.534, blank, 0.534 minus x. The second column is blank in all three rows. The third column has the following: approximately 0, positive x, x. The fourth column has the following: 0, positive x, x.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-idm467257104\">Substituting the equilibrium concentration terms into the <em data-effect=\"italics\">K<\/em><sub>a<\/sub> expression gives<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idm121323008\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1868\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3l-300x155.png\" alt=\"\" width=\"277\" height=\"143\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3l-300x155.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3l-768x396.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3l-65x33.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3l-225x116.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3l-350x180.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3l.png 984w\" sizes=\"auto, (max-width: 277px) 100vw, 277px\" \/><\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span> The relatively large initial concentration and small equilibrium constant permits the simplifying assumption; ie that <em data-effect=\"italics\">x<\/em> &lt; 5% of 0.534 M, which is 0.0267 M. The equation becomes<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idp29061504\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1869\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3m-300x70.png\" alt=\"\" width=\"201\" height=\"47\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3m-300x70.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3m-65x15.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3m-225x52.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3m-350x81.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3m.png 685w\" sizes=\"auto, (max-width: 201px) 100vw, 201px\" \/><\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span> Solving the equation for <em data-effect=\"italics\">x<\/em> yields<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idp107591296\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em><sup>2<\/sup> = 0.534 \u00d7 (1.8 \u00d7 10<sup>-4<\/sup>) = 9.6 \u00d7 10<sup>-5<\/sup><\/div>\n<p><span data-type=\"newline\">\u00a0<\/span><\/p>\n<div id=\"fs-idm94907344\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em> = <span style=\"font-size: 1em\">9.8 \u00d7 10<sup>-3<\/sup> M<\/span><\/div>\n<p id=\"fs-idp83161504\">Now check the 5% assumption:\u00a0 <span style=\"font-size: 1em\">9.8 \u00d7 10<sup>-3<\/sup> M &lt; 0.0267 M\u00a0 \u00a0 <\/span><\/p>\n<p id=\"fs-idp87107328\">Because <em data-effect=\"italics\">x<\/em> is less than 5% of the initial concentration, the assumption is valid.<\/p>\n<p id=\"fs-idm490302912\">As defined in the ICE table, <em data-effect=\"italics\">x<\/em> is equal to the equilibrium concentration of hydronium ion:<\/p>\n<div id=\"fs-idm212466048\" style=\"padding-left: 40px\" data-type=\"equation\">\u00a0 <em>x<\/em> = [H<sub>3<\/sub>O<sup>+<\/sup>] = 0.0098 M<\/div>\n<p id=\"fs-idm218699232\">Finally, the pH is calculated to be<\/p>\n<div id=\"fs-idm479799296\" style=\"padding-left: 40px\" data-type=\"equation\">pH = \u2212 log[H<sub>3<\/sub>O<sup>+<\/sup>] = \u2212 log(0.0098) = 2.01<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp80326224\"><strong>Check Your Learning <\/strong><\/p>\n<p>Only a small fraction of a weak acid ionizes in aqueous solution. What is the percent ionization of a 0.100-<em data-effect=\"italics\">M<\/em> solution of acetic acid, CH<sub>3<\/sub>CO<sub>2<\/sub>H?<\/p>\n<div id=\"fs-idp80328288\" style=\"padding-left: 40px\" data-type=\"equation\">CH<sub>3<\/sub>CO<sub>2<\/sub>H(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + CH<sub>3<\/sub>CO<sub>2<\/sub><sup>\u2212<\/sup>(aq)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0K<sub>a<\/sub> = 1.8 \u00d7 10<sup>-5<\/sup><\/div>\n<div data-type=\"equation\"><\/div>\n<div id=\"fs-idp77192016\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp77192656\">percent ionization = 1.3%<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp77193872\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp77194128\"><strong>Calculating Equilibrium Concentrations in a Weak Base Solution <\/strong><\/p>\n<p>Find the concentration of hydroxide ion, the pOH, and the pH of a 0.25-<em data-effect=\"italics\">M<\/em> solution of trimethylamine, a weak base:<\/p>\n<div id=\"fs-idm75350896\" style=\"padding-left: 40px\" data-type=\"equation\">(CH<sub>3<\/sub>)<sub>3<\/sub>N(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc (CH<sub>3<\/sub>)<sub>3<\/sub>NH<sup>+<\/sup>(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0K<sub>b<\/sub> = 6.3 \u00d7 10<sup>-5<\/sup><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp38644736\"><strong>Solution: <\/strong><\/p>\n<p>The ICE table for this system is<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-idm115891984\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201c( C H subscript 3 ) subscript 3 N plus sign H subscript 2 O equilibrium arrow ( C H subscript 3 ) subscript 3 N H superscript positive sign plus sign O H superscript positive sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.25, negative x, 0.25 plus sign negative x. The second column is blank in all three rows. The third column has the following: 0, x, 0 plus x. The fourth column has the following: approximately 0, x, and approximately 0 plus x.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ICETable4_img-1.jpg\" alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium concentration ( M ). The second column has the header of \u201c( C H subscript 3 ) subscript 3 N plus sign H subscript 2 O equilibrium arrow ( C H subscript 3 ) subscript 3 N H superscript positive sign plus sign O H superscript positive sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.25, negative x, 0.25 plus sign negative x. The second column is blank in all three rows. The third column has the following: 0, x, 0 plus x. The fourth column has the following: approximately 0, x, and approximately 0 plus x.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span data-type=\"newline\"><br \/>\n<\/span> Substituting the equilibrium concentration terms into the <em data-effect=\"italics\">K<\/em><sub>b<\/sub> expression gives<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idp121892160\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1871\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3n-300x34.png\" alt=\"\" width=\"379\" height=\"43\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3n-300x34.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3n-1024x115.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3n-768x86.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3n-65x7.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3n-225x25.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3n-350x39.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3n.png 1415w\" sizes=\"auto, (max-width: 379px) 100vw, 379px\" \/><\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span> Assuming <em data-effect=\"italics\">x<\/em> &lt; 5% of 0.25 M, which is 0.012 M, and solving for <em data-effect=\"italics\">x<\/em> yields<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idm1664928\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em> = 4.0 \u00d7 10<sup>-3<\/sup> M<\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span> This value is less than 0.012 M, so the 5% assumption is valid.<span data-type=\"newline\"><br \/>\n<\/span> As defined in the ICE table, <em data-effect=\"italics\">x<\/em> is equal to the equilibrium concentration of hydroxide ion:<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idm79961072\" style=\"padding-left: 40px\" data-type=\"equation\">[OH<sup>\u2212<\/sup>] = <em>x<\/em> = 4.0 \u00d7 10<sup>-3 <\/sup>M<\/div>\n<div id=\"fs-idp50312800\" data-type=\"equation\"><\/div>\n<p>The pOH is calculated to be<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idm73318512\" style=\"padding-left: 40px\" data-type=\"equation\">pOH = \u2212log(4.0 \u00d7 10<sup>-3<\/sup>) = 2.40<\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span> Using the relation introduced in the previous section of this chapter:<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idp50335856\" style=\"padding-left: 40px\" data-type=\"equation\">pH + pOH = pK<sub>w<\/sub> = 14.00<\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span> permits the computation of pH:<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idp50339184\" style=\"padding-left: 40px\" data-type=\"equation\">pH = 14.00 &#8211; pOH = 14.00-2.40 = 11.60<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm83886080\"><strong>Check Your Learning:<\/strong><\/p>\n<p>Calculate the hydroxide ion concentration and the percent ionization of a 0.0325-<em data-effect=\"italics\">M<\/em> solution of ammonia, a weak base with a <em data-effect=\"italics\">K<\/em><sub>b<\/sub> of 1.76 \u00d7 10<sup>\u22125<\/sup>.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp71571472\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp71572112\">7.56 \u00d7 10<sup>\u22124 <\/sup><em data-effect=\"italics\">M<\/em>, 2.33%<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-idm114523920\">In some cases, the strength of the weak acid or base and its formal (initial) concentration result in an appreciable ionization. Though the ICE strategy remains effective for these systems, the algebra is a bit more involved because the simplifying assumption that <em data-effect=\"italics\">x<\/em> is negligible can not be made. Calculations of this sort are demonstrated in <a class=\"autogenerated-content\" href=\"#fs-idm114522688\">(Figure)<\/a> below.<\/p>\n<div id=\"fs-idm114522688\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm114522432\"><strong>Calculating Equilibrium Concentrations without Simplifying Assumptions<\/strong><\/p>\n<p>Sodium hydrogen sulfate, NaHSO<sub>4<\/sub>, is used in some household cleansers as a source of the HSO<sub>4<\/sub><sup>\u2212<\/sup>\u00a0ion, a weak acid. What is the pH of a 0.50-<em data-effect=\"italics\">M<\/em> solution of HSO<sub>4<\/sub><sup>\u2212<\/sup>?<\/p>\n<div id=\"fs-idm83628320\" style=\"padding-left: 40px\" data-type=\"equation\">HSO<sub>4<\/sub><sup>\u2212<\/sup>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc H<sub>3<\/sub>O<sup>+<\/sup>(<em>aq<\/em>) + SO<sub>4<\/sub><sup>2-<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0K<sub>a<\/sub> = 1.2 \u00d7 10<sup>-2<\/sup><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp42421216\"><strong>Solution:<\/strong><\/p>\n<p>The ICE table for this system is<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-idm4774976\" class=\"scaled-down\" data-type=\"media\" data-alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium ( M ). The second column has the header of \u201cH S O subscript 4 superscript negative sign plus sign H subscript 2 O equilibrium sign H subscript 3 O superscript positive sign plus sign S O subscript 4 superscript 2 superscript negative sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.50, negative x, 0.50 minus x. The second column is blank for all three rows. The third column has the following: approximately 0, positive x, x. The fourth column has the following: 0, positive x, x.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_ICETable5_img-1.jpg\" alt=\"This table has two main columns and four rows. The first row for the first column does not have a heading and then has the following in the first column: Initial concentration ( M ), Change ( M ), Equilibrium ( M ). The second column has the header of \u201cH S O subscript 4 superscript negative sign plus sign H subscript 2 O equilibrium sign H subscript 3 O superscript positive sign plus sign S O subscript 4 superscript 2 superscript negative sign.\u201d Under the second column is a subgroup of four columns and three rows. The first column has the following: 0.50, negative x, 0.50 minus x. The second column is blank for all three rows. The third column has the following: approximately 0, positive x, x. The fourth column has the following: 0, positive x, x.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span data-type=\"newline\"><br \/>\n<\/span><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1873\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3o-300x43.png\" alt=\"\" width=\"349\" height=\"50\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3o-300x43.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3o-1024x145.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3o-768x109.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3o-65x9.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3o-225x32.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3o-350x50.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3o.png 1240w\" sizes=\"auto, (max-width: 349px) 100vw, 349px\" \/><\/p>\n<p><span data-type=\"newline\"><br \/>\n<\/span> If the 5% assumption \u00a0(<em>x<\/em> &lt; 0.05 \u00d7 0.50 M, or <em>x<\/em> &lt; 0.025 M) is made, simplifying and solving the above equation yields<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idm181668752\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em> = 0.077 M<\/div>\n<div id=\"fs-idp85327312\" data-type=\"equation\">\u00a0Because the simplifying assumption is not valid for this system, the equilibrium constant expression is solved as follows:<span data-type=\"newline\"><br \/>\n<\/span><\/div>\n<div id=\"fs-idm14221120\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1874\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3p-300x72.png\" alt=\"\" width=\"225\" height=\"54\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3p-300x72.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3p-65x16.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3p-225x54.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3p-350x84.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/14.3p.png 744w\" sizes=\"auto, (max-width: 225px) 100vw, 225px\" \/><\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span> Rearranging this equation yields<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idm55224560\" style=\"padding-left: 40px\" data-type=\"equation\">6.0 \u00d7 10<sup>-3 <\/sup>&#8211; 1.2 \u00d7 10<sup>-2<\/sup><em>x <\/em>= <em>x<\/em><sup>2<\/sup><\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span> Writing the equation in quadratic form gives<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idm46125840\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em><sup>2 <\/sup>+ 1.2 \u00d7 10<sup>-2<\/sup><em>x <\/em>&#8211; 6.0 \u00d7 10<sup>-3 <\/sup>= 0<\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span> Solving for the two roots of this quadratic equation results in a negative value that may be discarded as physically irrelevant and a positive value equal to <em data-effect=\"italics\">x<\/em>. As defined in the ICE table, <em data-effect=\"italics\">x<\/em> is equal to the hydronium concentration.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"fs-idm217752528\" style=\"padding-left: 40px\" data-type=\"equation\"><em>x<\/em> = [H<sub>3<\/sub>O<sup>+<\/sup>] = 0.072 M<\/div>\n<div style=\"padding-left: 40px\" data-type=\"equation\">pH = &#8211; log[H<sub>3<\/sub>O<sup>+<\/sup>] = -log(0.072 M) = 1.14<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm108532480\"><strong>Check Your Learning:<\/strong><\/p>\n<p>Calculate the pH in a 0.010-<em data-effect=\"italics\">M<\/em> solution of caffeine, a weak base:<\/p>\n<div id=\"fs-idm108529312\" style=\"padding-left: 40px\" data-type=\"equation\">C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub>(<em>aq<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>) \u21cc C<sub>8<\/sub>H<sub>10<\/sub>N<sub>4<\/sub>O<sub>2<\/sub>H<sup>+<\/sup>(<em>aq<\/em>) + OH<sup>\u2212<\/sup>(<em>aq<\/em>)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 K<sub>b<\/sub> = 2.5 \u00d7 10<sup>-4<\/sup><\/div>\n<div data-type=\"equation\"><\/div>\n<div id=\"fs-idm75099248\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm30698512\">pH 11.16<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idm95688656\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Effect of Molecular Structure on Acid-Base Strength<\/strong><\/h3>\n<div id=\"fs-idm178147248\" class=\"bc-section section\" data-depth=\"2\">\n<h4 data-type=\"title\"><strong>Binary Acids and Bases<\/strong><\/h4>\n<p id=\"fs-idm95688016\">In the absence of any leveling effect, the acid strength of binary compounds of hydrogen with nonmetals (A) increases as the H-A bond strength decreases down a group in the periodic table. For group 17, the order of increasing acidity is HF &lt; HCl &lt; HBr &lt; HI. Likewise, for group 16, the order of increasing acid strength is H<sub>2<\/sub>O &lt; H<sub>2<\/sub>S &lt; H<sub>2<\/sub>Se &lt; H<sub>2<\/sub>Te.<\/p>\n<p id=\"fs-idp81297776\">Across a row in the periodic table, the acid strength of binary hydrogen compounds increases with increasing electronegativity of the nonmetal atom because the polarity of the H-A bond increases. Thus, the order of increasing acidity (for removal of one proton) across the second row is CH<sub>4<\/sub> &lt; NH<sub>3<\/sub> &lt; H<sub>2<\/sub>O &lt; HF; across the third row, it is SiH<sub>4<\/sub> &lt; PH<sub>3<\/sub> &lt; H<sub>2<\/sub>S &lt; HCl (see <a class=\"autogenerated-content\" href=\"#CNX_Chem_14_03_AcidpH\">(Figure)<\/a>).<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_14_03_AcidpH\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">The figure shows trends in the strengths of binary acids and bases.<\/div>\n<p><span id=\"fs-idp81301760\" data-type=\"media\" data-alt=\"This diagram has two rows and four columns. Red arrows point left across the bottom of the figure and down at the right side and are labeled \u201cIncreasing acid strength.\u201d Blue arrows point left across the bottom and up at the right side of the figure and are labeled \u201cIncreasing base strength.\u201d The first column is labeled 14 at the top and two white squares are beneath it. The first has the number 6 in the upper left corner and the formula C H subscript 4 in the center along with designation Neither acid nor base. The second square contains the number 14 in the upper left corner, the formula C H subscript 4 at the center and the designation Neither acid nor base. The second column is labeled 15 at the top and two blue squares are beneath it. The first has the number 7 in the upper left corner and the formula N H subscript 3 in the center along with the designation Weak base and K subscript b equals 1.8 times 10 superscript negative 5. The second square contains the number 15 in the upper left corner, the formula P H subscript 3 at the center and the designation Very weak base and K subscript b equals 4 times 10 superscript negative 28. The third column is labeled 16 at the top and two squares are beneath it. The first is shaded tan and has the number 8 in the upper left corner and the formula H subscript 2 O in the center along with the designation neutral. The second square is shaded pink, contains the number 16 in the upper left corner, the formula H subscript 2 S at the center and the designation Weak acid and K subscript a equals 9.5 times 10 superscript negative 8. The fourth column is labeled 17 at the top and two squares are beneath it. The first is shaded pink, has the number 9 in the upper left corner and the formula H F in the center along with the designation Weak acid and K subscript a equals 6.8 times 10 superscript negative 4. The second square is shaded a deeper pink, contains the number 17 in the upper left corner, the formula H C l at the center, and the designation Strong acid.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_AcidpH-1.jpg\" alt=\"This diagram has two rows and four columns. Red arrows point left across the bottom of the figure and down at the right side and are labeled \u201cIncreasing acid strength.\u201d Blue arrows point left across the bottom and up at the right side of the figure and are labeled \u201cIncreasing base strength.\u201d The first column is labeled 14 at the top and two white squares are beneath it. The first has the number 6 in the upper left corner and the formula C H subscript 4 in the center along with designation Neither acid nor base. The second square contains the number 14 in the upper left corner, the formula C H subscript 4 at the center and the designation Neither acid nor base. The second column is labeled 15 at the top and two blue squares are beneath it. The first has the number 7 in the upper left corner and the formula N H subscript 3 in the center along with the designation Weak base and K subscript b equals 1.8 times 10 superscript negative 5. The second square contains the number 15 in the upper left corner, the formula P H subscript 3 at the center and the designation Very weak base and K subscript b equals 4 times 10 superscript negative 28. The third column is labeled 16 at the top and two squares are beneath it. The first is shaded tan and has the number 8 in the upper left corner and the formula H subscript 2 O in the center along with the designation neutral. The second square is shaded pink, contains the number 16 in the upper left corner, the formula H subscript 2 S at the center and the designation Weak acid and K subscript a equals 9.5 times 10 superscript negative 8. The fourth column is labeled 17 at the top and two squares are beneath it. The first is shaded pink, has the number 9 in the upper left corner and the formula H F in the center along with the designation Weak acid and K subscript a equals 6.8 times 10 superscript negative 4. The second square is shaded a deeper pink, contains the number 17 in the upper left corner, the formula H C l at the center, and the designation Strong acid.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idm222426752\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Ternary Acids and Bases<\/strong><\/h3>\n<p id=\"fs-idm107875680\">Ternary compounds composed of hydrogen, oxygen, and some third element (\u201cE\u201d) may be structured as depicted in the image below. In these compounds, the central E atom is bonded to one or more O atoms, and at least one of the O atoms is also bonded to an H atom, corresponding to the general molecular formula O<sub>m<\/sub>E(OH)<sub>n<\/sub>. These compounds may be acidic, basic, or amphoteric depending on the properties of the central E atom. Examples of such compounds include sulfuric acid, O<sub>2<\/sub>S(OH)<sub>2<\/sub>, sulfurous acid, OS(OH)<sub>2<\/sub>, nitric acid, O<sub>2<\/sub>NOH, perchloric acid, O<sub>3<\/sub>ClOH, aluminum hydroxide, Al(OH)<sub>3<\/sub>, calcium hydroxide, Ca(OH)<sub>2<\/sub>, and potassium hydroxide, KOH:<\/p>\n<p><span id=\"fs-idm107871568\" class=\"scaled-down\" data-type=\"media\" data-alt=\"A diagram is shown that includes a central atom designated with the letter E. Single bonds extend above, below, left, and right of the E. An O atom is bonded to the right of the E, and an arrow points to the bond labeling it, \u201cBond a.\u201d An H atom is single bonded to the right of the O atom. An arrow pointing to this bond connects it to the label, \u201cBond b.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_14_03_OHbonds_img-1.jpg\" alt=\"A diagram is shown that includes a central atom designated with the letter E. Single bonds extend above, below, left, and right of the E. An O atom is bonded to the right of the E, and an arrow points to the bond labeling it, \u201cBond a.\u201d An H atom is single bonded to the right of the O atom. An arrow pointing to this bond connects it to the label, \u201cBond b.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-idm107870208\">If the central atom, E, has a low electronegativity, its attraction for electrons is low. Little tendency exists for the central atom to form a strong covalent bond with the oxygen atom, and bond <em data-effect=\"italics\">a<\/em> between the element and oxygen is more readily broken than bond <em data-effect=\"italics\">b<\/em> between oxygen and hydrogen. Hence bond <em data-effect=\"italics\">a<\/em> is ionic, hydroxide ions are released to the solution, and the material behaves as a base\u2014this is the case with Ca(OH)<sub>2<\/sub> and KOH. Lower electronegativity is characteristic of the more metallic elements; hence, the metallic elements form ionic hydroxides that are by definition basic compounds.<\/p>\n<p id=\"fs-idm78964544\">If, on the other hand, the atom E has a relatively high electronegativity, it strongly attracts the electrons it shares with the oxygen atom, making bond <em data-effect=\"italics\">a<\/em> relatively strongly covalent. The oxygen-hydrogen bond, bond <em data-effect=\"italics\">b<\/em>, is thereby weakened because electrons are displaced toward E. Bond <em data-effect=\"italics\">b<\/em> is polar and readily releases hydrogen ions to the solution, so the material behaves as an acid. High electronegativities are characteristic of the more nonmetallic elements. Thus, nonmetallic elements form covalent compounds containing acidic \u2212OH groups that are called<strong> oxyacids<\/strong>.<\/p>\n<\/div>\n<div id=\"fs-idm223365360\" class=\"summary\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\n<p id=\"fs-idm223364480\">The relative strengths of acids and bases are reflected in the magnitudes of their ionization constants; the stronger the acid or base, the larger its ionization constant. A reciprocal relation exists between the strengths of a conjugate acid-base pair: the stronger the acid, the weaker its conjugate base. Water exerts a leveling effect on dissolved acids or bases, reacting completely to generate its characteristic hydronium and hydroxide ions (the strongest acid and base that may exist in water). The strengths of the binary acids increase from left to right across a period of the periodic table (CH<sub>4<\/sub> &lt; NH<sub>3<\/sub> &lt; H<sub>2<\/sub>O &lt; HF), and they increase down a group (HF &lt; HCl &lt; HBr &lt; HI).<\/p>\n<\/div>\n<div id=\"fs-idm94405216\" class=\"exercises\" data-depth=\"1\"><\/div>\n<div class=\"textbox shaded\" data-type=\"glossary\">\n<h3 data-type=\"glossary-title\"><\/h3>\n<dl id=\"fs-idp86058640\">\n<dt>acid ionization constant (<em data-effect=\"italics\">K<\/em><sub>a<\/sub>)<\/dt>\n<dd id=\"fs-idp86060160\">equilibrium constant for an acid ionization reaction<\/dd>\n<\/dl>\n<dl id=\"fs-idp86060672\">\n<dt>base ionization constant (<em data-effect=\"italics\">K<\/em><sub>b<\/sub>)<\/dt>\n<dd id=\"fs-idm94081232\">equilibrium constant for a base ionization reaction<\/dd>\n<\/dl>\n<dl id=\"fs-idm94080720\">\n<dt>leveling effect<\/dt>\n<dd id=\"fs-idm94080080\">observation that acid-base strength of solutes in a given solvent is limited to that of the solvent\u2019s characteristic acid and base species (in water, hydronium and hydroxide ions, respectively)<\/dd>\n<\/dl>\n<dl id=\"fs-idm94074528\">\n<dt>oxyacid<\/dt>\n<dd id=\"fs-idm94073888\">ternary compound with acidic properties, molecules of which contain a central nonmetallic atom bonded to one or more O atoms, at least one of which is bonded to an ionizable H atom<\/dd>\n<\/dl>\n<dl id=\"fs-idm94073376\">\n<dt>percent ionization<\/dt>\n<dd id=\"fs-idm94072736\">ratio of the concentration of ionized acid to initial acid concentration expressed as a percentage<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":1392,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-793","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":766,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/793","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/users\/1392"}],"version-history":[{"count":16,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/793\/revisions"}],"predecessor-version":[{"id":2172,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/793\/revisions\/2172"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/parts\/766"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/793\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/media?parent=793"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapter-type?post=793"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/contributor?post=793"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/license?post=793"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}