{"id":864,"date":"2021-07-23T09:20:56","date_gmt":"2021-07-23T13:20:56","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/the-second-and-third-laws-of-thermodynamics\/"},"modified":"2022-06-23T09:23:45","modified_gmt":"2022-06-23T13:23:45","slug":"the-second-and-third-laws-of-thermodynamics","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/the-second-and-third-laws-of-thermodynamics\/","title":{"raw":"16.3 The Second and Third Laws of Thermodynamics","rendered":"16.3 The Second and Third Laws of Thermodynamics"},"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>State and explain the second and third laws of thermodynamics<\/li>\r\n \t<li>Calculate entropy changes for phase transitions and chemical reactions under standard conditions<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div id=\"fs-idm4119136\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>The Second Law of Thermodynamics<\/strong><\/h3>\r\n<p id=\"fs-idp3609760\">In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy <em data-effect=\"italics\">of the system<\/em> (\u0394<em data-effect=\"italics\">S<\/em> &gt; 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include <em data-effect=\"italics\">the surroundings<\/em>, we may reach a significant conclusion regarding the relation between this property and spontaneity. In thermodynamic models, the system and surroundings comprise everything, that is, the universe, and so the following is true:<\/p>\r\n\r\n<div id=\"fs-idm7595760\" style=\"padding-left: 40px\" data-type=\"equation\">\u0394<em>S<\/em><sub>univ<\/sub> = \u0394<em>S<\/em><sub>sys<\/sub> + \u0394<em>S<\/em><sub>surr<\/sub><\/div>\r\n<p id=\"fs-idp115428960\">To illustrate this relation, consider again the process of heat flow between two objects, one identified as the system and the other as the surroundings. There are three possibilities for such a process:<\/p>\r\n\r\n<ol id=\"fs-idm90348816\" type=\"1\">\r\n \t<li>The objects are at different temperatures, and heat flows from the hotter to the cooler object. <em data-effect=\"italics\">This is always observed to occur spontaneously.<\/em> Designating the hotter object as the system and invoking the definition of entropy yields the following:\r\n<div id=\"fs-idp67516128\" data-type=\"equation\"><img class=\"alignnone wp-image-1983\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3a-300x44.png\" alt=\"\" width=\"328\" height=\"48\" \/><\/div>\r\nThe magnitudes of \u2212<em data-effect=\"italics\">q<\/em><sub>rev<\/sub> and <em data-effect=\"italics\">q<\/em><sub>rev<\/sub> are equal, their opposite arithmetic signs denoting loss of heat by the system and gain of heat by the surroundings. Since <em data-effect=\"italics\">T<\/em><sub>sys<\/sub> &gt; <em data-effect=\"italics\">T<\/em><sub>surr<\/sub> in this scenario, the entropy <em data-effect=\"italics\">decrease<\/em> of the system will be less than the entropy <em data-effect=\"italics\">increase<\/em> of the surroundings, and so <em data-effect=\"italics\">the entropy of the universe will increase<\/em>:\r\n<div id=\"fs-idm241116384\" data-type=\"equation\"><img class=\"alignnone wp-image-1984\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3b-300x77.png\" alt=\"\" width=\"226\" height=\"58\" \/><\/div><\/li>\r\n \t<li>The objects are at different temperatures, and heat flows from the cooler to the hotter object. <em data-effect=\"italics\">This is never observed to occur spontaneously.<\/em> Again designating the hotter object as the system and invoking the definition of entropy yields the following:\r\n<div id=\"fs-idp14273600\" data-type=\"equation\"><img class=\"alignnone wp-image-1985\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3c-300x37.png\" alt=\"\" width=\"308\" height=\"38\" \/><\/div>\r\nThe arithmetic signs of <em data-effect=\"italics\">q<\/em><sub>rev<\/sub> denote the gain of heat by the system and the loss of heat by the surroundings. The magnitude of the entropy change for the surroundings will again be greater than that for the system, but in this case, the signs of the heat changes (that is, <em data-effect=\"italics\">the direction of the heat flow<\/em>) will yield a negative value for \u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub>. <em data-effect=\"italics\">This process involves a decrease in the entropy of the universe.<\/em><\/li>\r\n \t<li>The objects are at essentially the same temperature, <em data-effect=\"italics\">T<\/em><sub>sys<\/sub> \u2248 <em data-effect=\"italics\">T<\/em><sub>surr<\/sub>, and so the magnitudes of the entropy changes are essentially the same for both the system and the surroundings. In this case, the entropy change of the universe is zero, and the system is <em data-effect=\"italics\">at equilibrium<\/em>.\r\n<div id=\"fs-idm250691808\" data-type=\"equation\"><img class=\"alignnone wp-image-1986\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3d-300x69.png\" alt=\"\" width=\"244\" height=\"56\" \/><\/div><\/li>\r\n<\/ol>\r\n<p id=\"fs-idp26583536\">These results lead to a profound statement regarding the relation between entropy and spontaneity known as the <strong>second law of thermodynamics<\/strong>: <em data-effect=\"italics\">all spontaneous changes cause an increase in the entropy of the universe.<\/em> A summary of these three relations is provided in <a class=\"autogenerated-content\" href=\"#fs-idp41455824\">(Figure)<\/a>.<\/p>\r\n\r\n<table id=\"fs-idp41455824\" class=\"top-titled\" summary=\"This table contains two columns and three rows. The first column has the following: \u201ccapital delta S subscript univ is greater than 0,\u201d \u201ccapital delta S subscript univ is less than 0,\u201d and, \u201ccapital delta S subscript univ equals 0.\u201d The second column contains the following: \u201cSpontaneous,\u201d \u201cnonspontaneous ( spontaneous in opposite direction ),\u201d and, \u201creversible ( system is at equilibrium ).\u201d\">\r\n<thead>\r\n<tr>\r\n<th colspan=\"2\" data-align=\"center\">The Second Law of Thermodynamics<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>\u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &gt; 0<\/td>\r\n<td>spontaneous<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>\u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &lt; 0<\/td>\r\n<td>nonspontaneous (spontaneous in opposite direction)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>\u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> = 0<\/td>\r\n<td>at equilibrium<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-idp172517200\">For many realistic applications, the surroundings are vast in comparison to the system. In such cases, the heat gained or lost by the surroundings as a result of some process represents a very small, nearly infinitesimal, fraction of its total thermal energy. For example, combustion of a fuel in air involves transfer of heat from a system (the fuel and oxygen molecules undergoing reaction) to surroundings that are infinitely more massive (the earth\u2019s atmosphere). As a result, <em data-effect=\"italics\">q<\/em><sub>surr<\/sub> is a good approximation of <em data-effect=\"italics\">q<\/em><sub>rev<\/sub>, and the second law may be stated as the following:<\/p>\r\n\r\n<div id=\"fs-idp179481536\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1987\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-300x39.png\" alt=\"\" width=\"338\" height=\"44\" \/><\/div>\r\n<p id=\"fs-idp5341920\">We may use this equation to predict the spontaneity of a process as illustrated in <a class=\"autogenerated-content\" href=\"#fs-idp33042160\">(Figure)<\/a>.<\/p>\r\n\r\n<div id=\"fs-idp33042160\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp271291696\"><strong>Will Ice Spontaneously Melt? <\/strong><\/p>\r\nThe entropy change for the process\r\n<div id=\"fs-idp179791152\" style=\"padding-left: 40px\" data-type=\"equation\">H<sub>2<\/sub>O(<em>s<\/em>) \u27f6 H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\r\n<p id=\"fs-idp175389120\">is 22.1 J\/K and requires that the surroundings transfer 6.00 kJ of heat to the system. Is the process spontaneous at \u221210.00 \u00b0C? Is it spontaneous at +10.00 \u00b0C?<\/p>\r\n<p id=\"fs-idp54282352\"><strong>Solution:<\/strong><\/p>\r\nWe can assess the spontaneity of the process by calculating the entropy change of the universe. If \u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> is positive, then the process is spontaneous. At both temperatures, \u0394<em data-effect=\"italics\">S<\/em><sub>sys<\/sub> = 22.1 J\/K and <em data-effect=\"italics\">q<\/em><sub>surr<\/sub> = \u22126.00 kJ.\r\n<p id=\"fs-idp9805936\">At \u221210.00 \u00b0C (263.15 K), the following is true:<\/p>\r\n\r\n<div id=\"fs-idp170559696\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1988\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3f-300x49.png\" alt=\"\" width=\"355\" height=\"58\" \/><\/div>\r\n<p id=\"fs-idp43894736\"><em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &lt; 0, so melting is nonspontaneous (<em data-effect=\"italics\">not<\/em> spontaneous) at \u221210.0 \u00b0C.<\/p>\r\n<p id=\"fs-idp156182416\">At 10.00 \u00b0C (283.15 K), the following is true:<\/p>\r\n\r\n<div id=\"fs-idm42720272\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1989\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3g-300x88.png\" alt=\"\" width=\"294\" height=\"86\" \/><\/div>\r\n<p id=\"fs-idp34700864\"><em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &gt; 0, so melting <em data-effect=\"italics\">is<\/em> spontaneous at 10.00 \u00b0C.<\/p>\r\n<p id=\"fs-idp54808912\"><strong>Check Your Learning:<\/strong><\/p>\r\nUsing this information, determine if liquid water will spontaneously freeze at the same temperatures. What can you say about the values of <em data-effect=\"italics\">S<\/em><sub>univ<\/sub>?\r\n\r\n&nbsp;\r\n<div id=\"fs-idp106254880\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp105321744\">Entropy is a state function, so \u0394<em data-effect=\"italics\">S<\/em><sub>freezing<\/sub> = \u2212\u0394<em data-effect=\"italics\">S<\/em><sub>melting<\/sub> = \u221222.1 J\/K and <em data-effect=\"italics\">q<\/em><sub>surr<\/sub> = +6.00 kJ. At \u221210.00 \u00b0C spontaneous, +0.7 J\/K; at +10.00 \u00b0C nonspontaneous, \u22120.9 J\/K.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp45100816\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>The Third Law of Thermodynamics<\/strong><\/h3>\r\n<p id=\"fs-idm3499504\">The previous section described the various contributions of matter and energy dispersal that contribute to the entropy of a system. With these contributions in mind, consider the entropy of a pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K). This system may be described by a single microstate, as its purity, perfect crystallinity and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (<em data-effect=\"italics\">W<\/em> = 1). According to the Boltzmann equation, the entropy of this system is zero.<\/p>\r\n\r\n<div id=\"fs-idp179521936\" style=\"padding-left: 40px\" data-type=\"equation\"><em>S<\/em> = <em>k<\/em> ln <em>W<\/em>= <em>k<\/em> ln <span style=\"font-size: 1em\">(1) =0\u00a0<\/span><\/div>\r\n<p id=\"fs-idm15206896\">This limiting condition for a system\u2019s entropy represents the <strong>third law of thermodynamics<\/strong>: <em data-effect=\"italics\">the entropy of a pure, perfect crystalline substance at 0 K is zero.<\/em><\/p>\r\n<p id=\"fs-idp12220368\">Careful calorimetric measurements can be made to determine the temperature dependence of a substance\u2019s entropy and to derive absolute entropy values under specific conditions. <span data-type=\"term\"><strong>Standard entropies<\/strong> (<em data-effect=\"italics\">S<\/em>\u00b0)<\/span> are for one mole of substance under standard conditions (a pressure of 1 bar and a temperature of 298.15 K; see details regarding standard conditions in the thermochemistry chapter of this text). The <span data-type=\"term\"><strong>standard entropy change<\/strong> (\u0394<em data-effect=\"italics\">S<\/em>\u00b0)<\/span> for a reaction may be computed using standard entropies as shown below:<\/p>\r\n\r\n<div id=\"fs-idp35409536\" style=\"padding-left: 40px\" data-type=\"equation\"><img class=\"alignnone wp-image-1990\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-300x31.png\" alt=\"\" width=\"348\" height=\"36\" \/><\/div>\r\n<p id=\"fs-idm44012816\">where \u03bd represents stoichiometric coefficients in the balanced equation representing the process. For example, \u0394<em data-effect=\"italics\">S<\/em>\u00b0 for the following reaction at room temperature<\/p>\r\n\r\n<div id=\"fs-idm48571920\" style=\"padding-left: 40px\" data-type=\"equation\"><em>m<\/em>A + <em>n<\/em>B \u27f6 <em>x<\/em>C + <em>y<\/em>D,<\/div>\r\n<p id=\"fs-idp156085024\">is computed as:<\/p>\r\n\r\n<div id=\"fs-idp34261696\" style=\"padding-left: 40px\" data-type=\"equation\">\u0394<em data-effect=\"italics\">S<\/em>\u00b0 = [<em>xS<\/em>\u00b0(C) + <em>yS<\/em>\u00b0(D)] - [<em>mS<\/em>\u00b0(A) + <em>nS<\/em>\u00b0(B)]<\/div>\r\n<p id=\"fs-idp43524064\">A partial listing of standard entropies is provided in <a class=\"autogenerated-content\" href=\"#fs-idm78597984\">(Figure)<\/a>, and additional values are provided in Appendix G. The example exercises that follow demonstrate the use of <em data-effect=\"italics\">S<\/em>\u00b0 values in calculating standard entropy changes for physical and chemical processes.<\/p>\r\n\r\n<table id=\"fs-idm78597984\" style=\"height: 300px;width: 406px\" summary=\"The table has two columns and twenty rows. The first row is a header row and it labels the columns, \u201cSubstance,\u201d and \u201cS subscript 298 superscript degree symbol ( J mol superscript negative 1 K superscript negative 1 ).\u201d The second row spans both columns and contains the word, \u201cCarbon.\u201d Under the \u201cSubstance\u201d column for carbon are the following: C ( s, graphite ), C ( s, diamond ), C O ( g ), C O subscript 2 ( g ), C H subscript 4 ( g ), C subscript 2 H subscript 4 ( g ), C subscript 2 H subscript 6 ( g ), C H subscript 3 O H ( l ), and C subscript 2 H subscript 5 O H ( l ). Under the \u201cS subscript 298 superscript degree symbol ( J mol superscript negative 1 K superscript negative 1 )\u201d column for carbon are the following: 5.740, 2.38, 197.7, 213.8, 186.3, 219.5, 229.5, 126.8, and 160.7. The twelfth row spans both columns and contains the word, \u201cHydrogen.\u201d Under the \u201cSubstance\u201d column for hydrogen are the following: H subscript 2 ( g ), H ( g ), H subscript 2 O ( g ), H subscript 2 O ( l ), H C I ( g ), and H subscript 2 S ( g ). Under the \u201cS subscript 298 superscript degree symbol ( J mol superscript negative 1 K superscript negative 1 )\u201d column for hydrogen are the following: 130.57, 114.6, 188.71, 69.91, 186.8, and 205.7. The nineteenth row spans both columns and contains the word, \u201cOxygen.\u201d Under the \u201cSubstance\u201d column for oxygen is O subscript 2 ( g ). Under the \u201cS subscript 298 superscript degree symbol ( J mol superscript negative 1 K superscript negative 1 )\u201d column for oxygen is 205.03.\"><caption>Standard entropies for selected substances measured at 1 atm and 298.15 K. (Values are approximately equal to those measured at 1 bar, the currently accepted standard state pressure.)<\/caption>\r\n<tbody>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\"><strong data-effect=\"bold\">Substance<\/strong><\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"left\"><strong data-effect=\"bold\">S\u00b0(J mol<sup>\u22121<\/sup> K<sup>\u22121<\/sup>)<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 391.042px\" colspan=\"2\"><strong>carbon<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C(<em data-effect=\"italics\">s<\/em>, graphite)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">5.740<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C(<em data-effect=\"italics\">s<\/em>, diamond)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">2.38<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">CO(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">197.7<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">CO<sub>2<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">213.8<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">CH<sub>4<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">186.3<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C<sub>2<\/sub>H<sub>4<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">219.5<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C<sub>2<\/sub>H<sub>6<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">229.5<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">CH<sub>3<\/sub>OH(<em data-effect=\"italics\">l<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">126.8<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C<sub>2<\/sub>H<sub>5<\/sub>OH(<em data-effect=\"italics\">l<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">160.7<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 391.042px\" colspan=\"2\" data-align=\"left\"><strong>hydrogen<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H<sub>2<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">130.57<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">114.6<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H<sub>2<\/sub>O(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">188.71<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H<sub>2<\/sub>O(<em data-effect=\"italics\">l<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">69.91<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">HCI(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">186.8<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H<sub>2<\/sub>S(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">205.7<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 391.042px\" colspan=\"2\" data-align=\"left\"><strong>oxygen<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">O<sub>2<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\r\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">205.03<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-idp173892208\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp155406304\"><strong>Determination of \u0394<em data-effect=\"italics\">S<\/em>\u00b0 <\/strong><\/p>\r\nCalculate the standard entropy change for the following process:\r\n<div id=\"fs-idp582800\" style=\"padding-left: 40px\" data-type=\"equation\">H<sub>2<\/sub>O(<em>g<\/em>) \u27f6 H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp180269712\"><strong>Solution: <\/strong><\/p>\r\nCalculate the entropy change using standard entropies as shown above:\r\n<div id=\"fs-idm7244112\" style=\"padding-left: 40px\" data-type=\"equation\">\u0394S\u00b0 = (1 mol)(70.0 Jmol<sup>\u22121<\/sup>K<sup>\u22121<\/sup>) - (1 mol)(188.8 Jmol<sup>\u22121<\/sup>K<sup>\u22121<\/sup>) = \u2212118.8 J\/K<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm47317216\">The value for \u0394<em data-effect=\"italics\">S<\/em>\u00b0 is negative, as expected for this phase transition (condensation), which the previous section discussed.<\/p>\r\n<p id=\"fs-idp319200\"><strong>Check Your Learning:<\/strong><\/p>\r\nCalculate the standard entropy change for the following process:\r\n<div id=\"fs-idp43728512\" style=\"padding-left: 40px\" data-type=\"equation\">H<sub>2<\/sub>(<em>g<\/em>) + C<sub>2<\/sub>H<sub>4<\/sub>(<em>g<\/em>) \u27f6 C<sub>2<\/sub>H<sub>6<\/sub>(<em>g<\/em>)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<div id=\"fs-idp34672944\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm48282704\">\u2212120.6 J\/K<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp34274768\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idp44594448\"><strong>Determination of \u0394<em data-effect=\"italics\">S<\/em>\u00b0 <\/strong><\/p>\r\nCalculate the standard entropy change for the combustion of methanol, CH<sub>3<\/sub>OH:\r\n<div id=\"fs-idp22586368\" style=\"padding-left: 40px\" data-type=\"equation\">2CH<sub>3<\/sub>OH(<em>l<\/em>) + 3O<sub>2<\/sub>(<em>g<\/em>) \u27f6 2CO<sub>2<\/sub>(<em>g<\/em>) + 4H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idp118976224\"><strong>Solution:<\/strong><\/p>\r\nCalculate the entropy change using standard entropies as shown above:\r\n<div id=\"fs-idp26460064\" style=\"padding-left: 40px\" data-type=\"equation\"><span style=\"font-size: 1em\"><img class=\"alignnone wp-image-1990\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-300x31.png\" alt=\"\" width=\"367\" height=\"38\" \/><\/span><\/div>\r\n<div style=\"padding-left: 40px\" data-type=\"equation\"><span style=\"font-size: 1em\">[(2 mol)(<em>S\u00b0<\/em>(CO<sub>2<\/sub>(<em>g<\/em>)) + (4 mol)<em>S\u00b0<\/em>(H<sub>2<\/sub>O(<em>l<\/em>))] -[(2 mol)(<em>S\u00b0<\/em>(CH<sub>3<\/sub>OH(<em>l<\/em>)) + (3 mol)(<em>S\u00b0<\/em>(O<sub>2<\/sub>(<em>g<\/em>))] = [2(213.8 J\/K) + 4(70.0 J\/K)] - [2(126.8 J\/K) + 3(205.03 J\/K)] = -161.1 J\/K\u00a0<\/span><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm27377968\"><strong>Check Your Learning:<\/strong><\/p>\r\nCalculate the standard entropy change for the following reaction:\r\n<div id=\"fs-idp53679664\" style=\"padding-left: 40px\" data-type=\"equation\">Ca(OH)<sub>2<\/sub>(<em>s<\/em>) \u27f6CaO(<em>s<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<div id=\"fs-idp174350576\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idp170733152\">24.7 J\/K<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp139289936\" class=\"summary\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\r\n<p id=\"fs-idp116042384\">The second law of thermodynamics states that a spontaneous process increases the entropy of the universe, <em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &gt; 0. If \u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &lt; 0, the process is nonspontaneous, and if \u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> = 0, the system is at equilibrium. The third law of thermodynamics establishes the zero for entropy as that of a perfect, pure crystalline solid at 0 K. With only one possible microstate, the entropy is zero. We may compute the standard entropy change for a process by using standard entropy values for the reactants and products involved in the process.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idp50875552\" class=\"key-equations\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Key Equations<\/strong><\/h3>\r\n<ul id=\"fs-idp170583392\" data-bullet-style=\"bullet\">\r\n \t<li><span style=\"font-size: 1em\"><img class=\"alignnone wp-image-1990\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-300x31.png\" alt=\"\" width=\"367\" height=\"38\" \/><\/span><\/li>\r\n \t<li>\u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> = \u0394<em data-effect=\"italics\">S<\/em><sub>sys<\/sub> + \u0394<em data-effect=\"italics\">S<\/em><sub>surr<\/sub><\/li>\r\n \t<li><img class=\"alignnone wp-image-1987\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-300x39.png\" alt=\"\" width=\"338\" height=\"44\" \/><\/li>\r\n<\/ul>\r\n<\/div>\r\n<div id=\"fs-idm53180608\" class=\"exercises\" data-depth=\"1\">\r\n<div id=\"fs-idp127896592\" data-type=\"exercise\">\r\n<div id=\"fs-idp209528688\" data-type=\"solution\">\r\n<p id=\"fs-idp209528944\"><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox shaded\" data-type=\"glossary\">\r\n<h3 data-type=\"glossary-title\"><strong>Glossary<\/strong><\/h3>\r\n<dl id=\"fs-idp194754048\">\r\n \t<dt>second law of thermodynamics<\/dt>\r\n \t<dd id=\"fs-idp194754688\">all spontaneous processes involve an increase in the entropy of the universe<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp170415152\">\r\n \t<dt>standard entropy (<em data-effect=\"italics\">S<\/em>\u00b0)<\/dt>\r\n \t<dd id=\"fs-idp170416304\">entropy for one mole of a substance at 1 bar pressure; tabulated values are usually determined at 298.15 K<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp85418944\">\r\n \t<dt>standard entropy change (\u0394<em data-effect=\"italics\">S<\/em>\u00b0)<\/dt>\r\n \t<dd id=\"fs-idp85420096\">change in entropy for a reaction calculated using the standard entropies<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp90512720\">\r\n \t<dt>third law of thermodynamics<\/dt>\r\n \t<dd id=\"fs-idp90513360\">entropy of a perfect crystal at absolute zero (0 K) is zero<\/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>State and explain the second and third laws of thermodynamics<\/li>\n<li>Calculate entropy changes for phase transitions and chemical reactions under standard conditions<\/li>\n<\/ul>\n<\/div>\n<div id=\"fs-idm4119136\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>The Second Law of Thermodynamics<\/strong><\/h3>\n<p id=\"fs-idp3609760\">In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy <em data-effect=\"italics\">of the system<\/em> (\u0394<em data-effect=\"italics\">S<\/em> &gt; 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include <em data-effect=\"italics\">the surroundings<\/em>, we may reach a significant conclusion regarding the relation between this property and spontaneity. In thermodynamic models, the system and surroundings comprise everything, that is, the universe, and so the following is true:<\/p>\n<div id=\"fs-idm7595760\" style=\"padding-left: 40px\" data-type=\"equation\">\u0394<em>S<\/em><sub>univ<\/sub> = \u0394<em>S<\/em><sub>sys<\/sub> + \u0394<em>S<\/em><sub>surr<\/sub><\/div>\n<p id=\"fs-idp115428960\">To illustrate this relation, consider again the process of heat flow between two objects, one identified as the system and the other as the surroundings. There are three possibilities for such a process:<\/p>\n<ol id=\"fs-idm90348816\" type=\"1\">\n<li>The objects are at different temperatures, and heat flows from the hotter to the cooler object. <em data-effect=\"italics\">This is always observed to occur spontaneously.<\/em> Designating the hotter object as the system and invoking the definition of entropy yields the following:\n<div id=\"fs-idp67516128\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1983\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3a-300x44.png\" alt=\"\" width=\"328\" height=\"48\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3a-300x44.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3a-1024x149.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3a-768x112.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3a-65x9.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3a-225x33.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3a-350x51.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3a.png 1078w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/div>\n<p>The magnitudes of \u2212<em data-effect=\"italics\">q<\/em><sub>rev<\/sub> and <em data-effect=\"italics\">q<\/em><sub>rev<\/sub> are equal, their opposite arithmetic signs denoting loss of heat by the system and gain of heat by the surroundings. Since <em data-effect=\"italics\">T<\/em><sub>sys<\/sub> &gt; <em data-effect=\"italics\">T<\/em><sub>surr<\/sub> in this scenario, the entropy <em data-effect=\"italics\">decrease<\/em> of the system will be less than the entropy <em data-effect=\"italics\">increase<\/em> of the surroundings, and so <em data-effect=\"italics\">the entropy of the universe will increase<\/em>:<\/p>\n<div id=\"fs-idm241116384\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1984\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3b-300x77.png\" alt=\"\" width=\"226\" height=\"58\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3b-300x77.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3b-65x17.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3b-225x58.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3b-350x90.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3b.png 739w\" sizes=\"auto, (max-width: 226px) 100vw, 226px\" \/><\/div>\n<\/li>\n<li>The objects are at different temperatures, and heat flows from the cooler to the hotter object. <em data-effect=\"italics\">This is never observed to occur spontaneously.<\/em> Again designating the hotter object as the system and invoking the definition of entropy yields the following:\n<div id=\"fs-idp14273600\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1985\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3c-300x37.png\" alt=\"\" width=\"308\" height=\"38\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3c-300x37.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3c-1024x127.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3c-768x95.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3c-65x8.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3c-225x28.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3c-350x43.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3c.png 1072w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/div>\n<p>The arithmetic signs of <em data-effect=\"italics\">q<\/em><sub>rev<\/sub> denote the gain of heat by the system and the loss of heat by the surroundings. The magnitude of the entropy change for the surroundings will again be greater than that for the system, but in this case, the signs of the heat changes (that is, <em data-effect=\"italics\">the direction of the heat flow<\/em>) will yield a negative value for \u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub>. <em data-effect=\"italics\">This process involves a decrease in the entropy of the universe.<\/em><\/li>\n<li>The objects are at essentially the same temperature, <em data-effect=\"italics\">T<\/em><sub>sys<\/sub> \u2248 <em data-effect=\"italics\">T<\/em><sub>surr<\/sub>, and so the magnitudes of the entropy changes are essentially the same for both the system and the surroundings. In this case, the entropy change of the universe is zero, and the system is <em data-effect=\"italics\">at equilibrium<\/em>.\n<div id=\"fs-idm250691808\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1986\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3d-300x69.png\" alt=\"\" width=\"244\" height=\"56\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3d-300x69.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3d-65x15.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3d-225x52.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3d-350x81.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3d.png 753w\" sizes=\"auto, (max-width: 244px) 100vw, 244px\" \/><\/div>\n<\/li>\n<\/ol>\n<p id=\"fs-idp26583536\">These results lead to a profound statement regarding the relation between entropy and spontaneity known as the <strong>second law of thermodynamics<\/strong>: <em data-effect=\"italics\">all spontaneous changes cause an increase in the entropy of the universe.<\/em> A summary of these three relations is provided in <a class=\"autogenerated-content\" href=\"#fs-idp41455824\">(Figure)<\/a>.<\/p>\n<table id=\"fs-idp41455824\" class=\"top-titled\" summary=\"This table contains two columns and three rows. The first column has the following: \u201ccapital delta S subscript univ is greater than 0,\u201d \u201ccapital delta S subscript univ is less than 0,\u201d and, \u201ccapital delta S subscript univ equals 0.\u201d The second column contains the following: \u201cSpontaneous,\u201d \u201cnonspontaneous ( spontaneous in opposite direction ),\u201d and, \u201creversible ( system is at equilibrium ).\u201d\">\n<thead>\n<tr>\n<th colspan=\"2\" data-align=\"center\">The Second Law of Thermodynamics<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>\u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &gt; 0<\/td>\n<td>spontaneous<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>\u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &lt; 0<\/td>\n<td>nonspontaneous (spontaneous in opposite direction)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>\u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> = 0<\/td>\n<td>at equilibrium<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-idp172517200\">For many realistic applications, the surroundings are vast in comparison to the system. In such cases, the heat gained or lost by the surroundings as a result of some process represents a very small, nearly infinitesimal, fraction of its total thermal energy. For example, combustion of a fuel in air involves transfer of heat from a system (the fuel and oxygen molecules undergoing reaction) to surroundings that are infinitely more massive (the earth\u2019s atmosphere). As a result, <em data-effect=\"italics\">q<\/em><sub>surr<\/sub> is a good approximation of <em data-effect=\"italics\">q<\/em><sub>rev<\/sub>, and the second law may be stated as the following:<\/p>\n<div id=\"fs-idp179481536\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1987\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-300x39.png\" alt=\"\" width=\"338\" height=\"44\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-300x39.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-768x100.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-65x8.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-225x29.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-350x45.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e.png 1025w\" sizes=\"auto, (max-width: 338px) 100vw, 338px\" \/><\/div>\n<p id=\"fs-idp5341920\">We may use this equation to predict the spontaneity of a process as illustrated in <a class=\"autogenerated-content\" href=\"#fs-idp33042160\">(Figure)<\/a>.<\/p>\n<div id=\"fs-idp33042160\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp271291696\"><strong>Will Ice Spontaneously Melt? <\/strong><\/p>\n<p>The entropy change for the process<\/p>\n<div id=\"fs-idp179791152\" style=\"padding-left: 40px\" data-type=\"equation\">H<sub>2<\/sub>O(<em>s<\/em>) \u27f6 H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\n<p id=\"fs-idp175389120\">is 22.1 J\/K and requires that the surroundings transfer 6.00 kJ of heat to the system. Is the process spontaneous at \u221210.00 \u00b0C? Is it spontaneous at +10.00 \u00b0C?<\/p>\n<p id=\"fs-idp54282352\"><strong>Solution:<\/strong><\/p>\n<p>We can assess the spontaneity of the process by calculating the entropy change of the universe. If \u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> is positive, then the process is spontaneous. At both temperatures, \u0394<em data-effect=\"italics\">S<\/em><sub>sys<\/sub> = 22.1 J\/K and <em data-effect=\"italics\">q<\/em><sub>surr<\/sub> = \u22126.00 kJ.<\/p>\n<p id=\"fs-idp9805936\">At \u221210.00 \u00b0C (263.15 K), the following is true:<\/p>\n<div id=\"fs-idp170559696\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1988\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3f-300x49.png\" alt=\"\" width=\"355\" height=\"58\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3f-300x49.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3f-1024x167.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3f-768x125.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3f-65x11.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3f-225x37.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3f-350x57.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3f.png 1163w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/div>\n<p id=\"fs-idp43894736\"><em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &lt; 0, so melting is nonspontaneous (<em data-effect=\"italics\">not<\/em> spontaneous) at \u221210.0 \u00b0C.<\/p>\n<p id=\"fs-idp156182416\">At 10.00 \u00b0C (283.15 K), the following is true:<\/p>\n<div id=\"fs-idm42720272\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1989\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3g-300x88.png\" alt=\"\" width=\"294\" height=\"86\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3g-300x88.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3g-768x226.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3g-65x19.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3g-225x66.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3g-350x103.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3g.png 945w\" sizes=\"auto, (max-width: 294px) 100vw, 294px\" \/><\/div>\n<p id=\"fs-idp34700864\"><em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &gt; 0, so melting <em data-effect=\"italics\">is<\/em> spontaneous at 10.00 \u00b0C.<\/p>\n<p id=\"fs-idp54808912\"><strong>Check Your Learning:<\/strong><\/p>\n<p>Using this information, determine if liquid water will spontaneously freeze at the same temperatures. What can you say about the values of <em data-effect=\"italics\">S<\/em><sub>univ<\/sub>?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp106254880\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp105321744\">Entropy is a state function, so \u0394<em data-effect=\"italics\">S<\/em><sub>freezing<\/sub> = \u2212\u0394<em data-effect=\"italics\">S<\/em><sub>melting<\/sub> = \u221222.1 J\/K and <em data-effect=\"italics\">q<\/em><sub>surr<\/sub> = +6.00 kJ. At \u221210.00 \u00b0C spontaneous, +0.7 J\/K; at +10.00 \u00b0C nonspontaneous, \u22120.9 J\/K.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idp45100816\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>The Third Law of Thermodynamics<\/strong><\/h3>\n<p id=\"fs-idm3499504\">The previous section described the various contributions of matter and energy dispersal that contribute to the entropy of a system. With these contributions in mind, consider the entropy of a pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K). This system may be described by a single microstate, as its purity, perfect crystallinity and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (<em data-effect=\"italics\">W<\/em> = 1). According to the Boltzmann equation, the entropy of this system is zero.<\/p>\n<div id=\"fs-idp179521936\" style=\"padding-left: 40px\" data-type=\"equation\"><em>S<\/em> = <em>k<\/em> ln <em>W<\/em>= <em>k<\/em> ln <span style=\"font-size: 1em\">(1) =0\u00a0<\/span><\/div>\n<p id=\"fs-idm15206896\">This limiting condition for a system\u2019s entropy represents the <strong>third law of thermodynamics<\/strong>: <em data-effect=\"italics\">the entropy of a pure, perfect crystalline substance at 0 K is zero.<\/em><\/p>\n<p id=\"fs-idp12220368\">Careful calorimetric measurements can be made to determine the temperature dependence of a substance\u2019s entropy and to derive absolute entropy values under specific conditions. <span data-type=\"term\"><strong>Standard entropies<\/strong> (<em data-effect=\"italics\">S<\/em>\u00b0)<\/span> are for one mole of substance under standard conditions (a pressure of 1 bar and a temperature of 298.15 K; see details regarding standard conditions in the thermochemistry chapter of this text). The <span data-type=\"term\"><strong>standard entropy change<\/strong> (\u0394<em data-effect=\"italics\">S<\/em>\u00b0)<\/span> for a reaction may be computed using standard entropies as shown below:<\/p>\n<div id=\"fs-idp35409536\" style=\"padding-left: 40px\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1990\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-300x31.png\" alt=\"\" width=\"348\" height=\"36\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-300x31.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-1024x105.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-768x79.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-65x7.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-225x23.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-350x36.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h.png 1190w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><\/div>\n<p id=\"fs-idm44012816\">where \u03bd represents stoichiometric coefficients in the balanced equation representing the process. For example, \u0394<em data-effect=\"italics\">S<\/em>\u00b0 for the following reaction at room temperature<\/p>\n<div id=\"fs-idm48571920\" style=\"padding-left: 40px\" data-type=\"equation\"><em>m<\/em>A + <em>n<\/em>B \u27f6 <em>x<\/em>C + <em>y<\/em>D,<\/div>\n<p id=\"fs-idp156085024\">is computed as:<\/p>\n<div id=\"fs-idp34261696\" style=\"padding-left: 40px\" data-type=\"equation\">\u0394<em data-effect=\"italics\">S<\/em>\u00b0 = [<em>xS<\/em>\u00b0(C) + <em>yS<\/em>\u00b0(D)] &#8211; [<em>mS<\/em>\u00b0(A) + <em>nS<\/em>\u00b0(B)]<\/div>\n<p id=\"fs-idp43524064\">A partial listing of standard entropies is provided in <a class=\"autogenerated-content\" href=\"#fs-idm78597984\">(Figure)<\/a>, and additional values are provided in Appendix G. The example exercises that follow demonstrate the use of <em data-effect=\"italics\">S<\/em>\u00b0 values in calculating standard entropy changes for physical and chemical processes.<\/p>\n<table id=\"fs-idm78597984\" style=\"height: 300px;width: 406px\" summary=\"The table has two columns and twenty rows. The first row is a header row and it labels the columns, \u201cSubstance,\u201d and \u201cS subscript 298 superscript degree symbol ( J mol superscript negative 1 K superscript negative 1 ).\u201d The second row spans both columns and contains the word, \u201cCarbon.\u201d Under the \u201cSubstance\u201d column for carbon are the following: C ( s, graphite ), C ( s, diamond ), C O ( g ), C O subscript 2 ( g ), C H subscript 4 ( g ), C subscript 2 H subscript 4 ( g ), C subscript 2 H subscript 6 ( g ), C H subscript 3 O H ( l ), and C subscript 2 H subscript 5 O H ( l ). Under the \u201cS subscript 298 superscript degree symbol ( J mol superscript negative 1 K superscript negative 1 )\u201d column for carbon are the following: 5.740, 2.38, 197.7, 213.8, 186.3, 219.5, 229.5, 126.8, and 160.7. The twelfth row spans both columns and contains the word, \u201cHydrogen.\u201d Under the \u201cSubstance\u201d column for hydrogen are the following: H subscript 2 ( g ), H ( g ), H subscript 2 O ( g ), H subscript 2 O ( l ), H C I ( g ), and H subscript 2 S ( g ). Under the \u201cS subscript 298 superscript degree symbol ( J mol superscript negative 1 K superscript negative 1 )\u201d column for hydrogen are the following: 130.57, 114.6, 188.71, 69.91, 186.8, and 205.7. The nineteenth row spans both columns and contains the word, \u201cOxygen.\u201d Under the \u201cSubstance\u201d column for oxygen is O subscript 2 ( g ). Under the \u201cS subscript 298 superscript degree symbol ( J mol superscript negative 1 K superscript negative 1 )\u201d column for oxygen is 205.03.\">\n<caption>Standard entropies for selected substances measured at 1 atm and 298.15 K. (Values are approximately equal to those measured at 1 bar, the currently accepted standard state pressure.)<\/caption>\n<tbody>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\"><strong data-effect=\"bold\">Substance<\/strong><\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"left\"><strong data-effect=\"bold\">S\u00b0(J mol<sup>\u22121<\/sup> K<sup>\u22121<\/sup>)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 391.042px\" colspan=\"2\"><strong>carbon<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C(<em data-effect=\"italics\">s<\/em>, graphite)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">5.740<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C(<em data-effect=\"italics\">s<\/em>, diamond)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">2.38<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">CO(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">197.7<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">CO<sub>2<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">213.8<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">CH<sub>4<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">186.3<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C<sub>2<\/sub>H<sub>4<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">219.5<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C<sub>2<\/sub>H<sub>6<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">229.5<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">CH<sub>3<\/sub>OH(<em data-effect=\"italics\">l<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">126.8<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">C<sub>2<\/sub>H<sub>5<\/sub>OH(<em data-effect=\"italics\">l<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">160.7<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 391.042px\" colspan=\"2\" data-align=\"left\"><strong>hydrogen<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H<sub>2<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">130.57<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">114.6<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H<sub>2<\/sub>O(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">188.71<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H<sub>2<\/sub>O(<em data-effect=\"italics\">l<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">69.91<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">HCI(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">186.8<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">H<sub>2<\/sub>S(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">205.7<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 391.042px\" colspan=\"2\" data-align=\"left\"><strong>oxygen<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 96.2604px\" data-align=\"left\">O<sub>2<\/sub>(<em data-effect=\"italics\">g<\/em>)<\/td>\n<td style=\"height: 15px;width: 281.823px\" data-align=\"center\">205.03<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-idp173892208\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp155406304\"><strong>Determination of \u0394<em data-effect=\"italics\">S<\/em>\u00b0 <\/strong><\/p>\n<p>Calculate the standard entropy change for the following process:<\/p>\n<div id=\"fs-idp582800\" style=\"padding-left: 40px\" data-type=\"equation\">H<sub>2<\/sub>O(<em>g<\/em>) \u27f6 H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp180269712\"><strong>Solution: <\/strong><\/p>\n<p>Calculate the entropy change using standard entropies as shown above:<\/p>\n<div id=\"fs-idm7244112\" style=\"padding-left: 40px\" data-type=\"equation\">\u0394S\u00b0 = (1 mol)(70.0 Jmol<sup>\u22121<\/sup>K<sup>\u22121<\/sup>) &#8211; (1 mol)(188.8 Jmol<sup>\u22121<\/sup>K<sup>\u22121<\/sup>) = \u2212118.8 J\/K<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm47317216\">The value for \u0394<em data-effect=\"italics\">S<\/em>\u00b0 is negative, as expected for this phase transition (condensation), which the previous section discussed.<\/p>\n<p id=\"fs-idp319200\"><strong>Check Your Learning:<\/strong><\/p>\n<p>Calculate the standard entropy change for the following process:<\/p>\n<div id=\"fs-idp43728512\" style=\"padding-left: 40px\" data-type=\"equation\">H<sub>2<\/sub>(<em>g<\/em>) + C<sub>2<\/sub>H<sub>4<\/sub>(<em>g<\/em>) \u27f6 C<sub>2<\/sub>H<sub>6<\/sub>(<em>g<\/em>)<\/div>\n<div data-type=\"equation\"><\/div>\n<div id=\"fs-idp34672944\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm48282704\">\u2212120.6 J\/K<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp34274768\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idp44594448\"><strong>Determination of \u0394<em data-effect=\"italics\">S<\/em>\u00b0 <\/strong><\/p>\n<p>Calculate the standard entropy change for the combustion of methanol, CH<sub>3<\/sub>OH:<\/p>\n<div id=\"fs-idp22586368\" style=\"padding-left: 40px\" data-type=\"equation\">2CH<sub>3<\/sub>OH(<em>l<\/em>) + 3O<sub>2<\/sub>(<em>g<\/em>) \u27f6 2CO<sub>2<\/sub>(<em>g<\/em>) + 4H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idp118976224\"><strong>Solution:<\/strong><\/p>\n<p>Calculate the entropy change using standard entropies as shown above:<\/p>\n<div id=\"fs-idp26460064\" style=\"padding-left: 40px\" data-type=\"equation\"><span style=\"font-size: 1em\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1990\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-300x31.png\" alt=\"\" width=\"367\" height=\"38\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-300x31.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-1024x105.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-768x79.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-65x7.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-225x23.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-350x36.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h.png 1190w\" sizes=\"auto, (max-width: 367px) 100vw, 367px\" \/><\/span><\/div>\n<div style=\"padding-left: 40px\" data-type=\"equation\"><span style=\"font-size: 1em\">[(2 mol)(<em>S\u00b0<\/em>(CO<sub>2<\/sub>(<em>g<\/em>)) + (4 mol)<em>S\u00b0<\/em>(H<sub>2<\/sub>O(<em>l<\/em>))] -[(2 mol)(<em>S\u00b0<\/em>(CH<sub>3<\/sub>OH(<em>l<\/em>)) + (3 mol)(<em>S\u00b0<\/em>(O<sub>2<\/sub>(<em>g<\/em>))] = [2(213.8 J\/K) + 4(70.0 J\/K)] &#8211; [2(126.8 J\/K) + 3(205.03 J\/K)] = -161.1 J\/K\u00a0<\/span><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm27377968\"><strong>Check Your Learning:<\/strong><\/p>\n<p>Calculate the standard entropy change for the following reaction:<\/p>\n<div id=\"fs-idp53679664\" style=\"padding-left: 40px\" data-type=\"equation\">Ca(OH)<sub>2<\/sub>(<em>s<\/em>) \u27f6CaO(<em>s<\/em>) + H<sub>2<\/sub>O(<em>l<\/em>)<\/div>\n<div data-type=\"equation\"><\/div>\n<div id=\"fs-idp174350576\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idp170733152\">24.7 J\/K<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idp139289936\" class=\"summary\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\n<p id=\"fs-idp116042384\">The second law of thermodynamics states that a spontaneous process increases the entropy of the universe, <em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &gt; 0. If \u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> &lt; 0, the process is nonspontaneous, and if \u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> = 0, the system is at equilibrium. The third law of thermodynamics establishes the zero for entropy as that of a perfect, pure crystalline solid at 0 K. With only one possible microstate, the entropy is zero. We may compute the standard entropy change for a process by using standard entropy values for the reactants and products involved in the process.<\/p>\n<\/div>\n<div id=\"fs-idp50875552\" class=\"key-equations\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Key Equations<\/strong><\/h3>\n<ul id=\"fs-idp170583392\" data-bullet-style=\"bullet\">\n<li><span style=\"font-size: 1em\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1990\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-300x31.png\" alt=\"\" width=\"367\" height=\"38\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-300x31.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-1024x105.png 1024w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-768x79.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-65x7.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-225x23.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h-350x36.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3h.png 1190w\" sizes=\"auto, (max-width: 367px) 100vw, 367px\" \/><\/span><\/li>\n<li>\u0394<em data-effect=\"italics\">S<\/em><sub>univ<\/sub> = \u0394<em data-effect=\"italics\">S<\/em><sub>sys<\/sub> + \u0394<em data-effect=\"italics\">S<\/em><sub>surr<\/sub><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1987\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-300x39.png\" alt=\"\" width=\"338\" height=\"44\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-300x39.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-768x100.png 768w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-65x8.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-225x29.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e-350x45.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/16.3e.png 1025w\" sizes=\"auto, (max-width: 338px) 100vw, 338px\" \/><\/li>\n<\/ul>\n<\/div>\n<div id=\"fs-idm53180608\" class=\"exercises\" data-depth=\"1\">\n<div id=\"fs-idp127896592\" data-type=\"exercise\">\n<div id=\"fs-idp209528688\" data-type=\"solution\">\n<p id=\"fs-idp209528944\">\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\" data-type=\"glossary\">\n<h3 data-type=\"glossary-title\"><strong>Glossary<\/strong><\/h3>\n<dl id=\"fs-idp194754048\">\n<dt>second law of thermodynamics<\/dt>\n<dd id=\"fs-idp194754688\">all spontaneous processes involve an increase in the entropy of the universe<\/dd>\n<\/dl>\n<dl id=\"fs-idp170415152\">\n<dt>standard entropy (<em data-effect=\"italics\">S<\/em>\u00b0)<\/dt>\n<dd id=\"fs-idp170416304\">entropy for one mole of a substance at 1 bar pressure; tabulated values are usually determined at 298.15 K<\/dd>\n<\/dl>\n<dl id=\"fs-idp85418944\">\n<dt>standard entropy change (\u0394<em data-effect=\"italics\">S<\/em>\u00b0)<\/dt>\n<dd id=\"fs-idp85420096\">change in entropy for a reaction calculated using the standard entropies<\/dd>\n<\/dl>\n<dl id=\"fs-idp90512720\">\n<dt>third law of thermodynamics<\/dt>\n<dd id=\"fs-idp90513360\">entropy of a perfect crystal at absolute zero (0 K) is zero<\/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-864","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":848,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/864","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":4,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/864\/revisions"}],"predecessor-version":[{"id":2182,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/864\/revisions\/2182"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/parts\/848"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/864\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/media?parent=864"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapter-type?post=864"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/contributor?post=864"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/license?post=864"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}