{"id":7979,"date":"2021-06-08T21:58:26","date_gmt":"2021-06-08T21:58:26","guid":{"rendered":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/end-of-chapter-18-material\/"},"modified":"2021-10-27T16:30:51","modified_gmt":"2021-10-27T16:30:51","slug":"end-of-chapter-18-material","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/end-of-chapter-18-material\/","title":{"raw":"End-of-Chapter Material","rendered":"End-of-Chapter Material"},"content":{"raw":"
\r\n

Exercises<\/p>\r\n\r\n<\/header>\r\n

\r\n
    \r\n \t
  1. Classify each of the following as spontaneous or nonspontaneous processes:\r\n
      \r\n \t
    1. the browning of a cut apple slice on a snack tray over time<\/li>\r\n \t
    2. the rolling of a ball uphill<\/li>\r\n \t
    3. the formation of diamond from the graphite in your pencil<\/li>\r\n \t
    4. the melting of ice cubes in a glass of water you are holding<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    5. State the second law of thermodynamics.<\/li>\r\n \t
    6. What sign would you expect for \u0394S<\/em> for the following processes?\r\n
        \r\n \t
      1. water freezing in a lake during a cold Alberta winter<\/li>\r\n \t
      2. AB(s) + CD(s) \u2192 AC(g) + BD(g)<\/li>\r\n \t
      3. a balloon with a fixed amount of gas stretched to a larger volume<\/li>\r\n \t
      4. the sublimation of dry ice<\/li>\r\n \t
      5. 3E2<\/sub>F2<\/sub>(g) \u2192 E6<\/sub>F6<\/sub>(g)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
      6. Which of the following would you expect to have the higher standard molar entropy, S<\/em>\u00b0?\r\n
          \r\n \t
        1. Br2<\/sub>(\u2113<\/span>) or Br2<\/sub>(g)<\/li>\r\n \t
        2. NO2<\/sub>(g) or NO(g)<\/li>\r\n \t
        3. C2<\/sub>H6<\/sub>(g) or C5<\/sub>H12<\/sub>(g)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
        4. Calculate the \u0394S<\/em>\u00b0 of the following reactions using the values listed in the appendix.\r\n
            \r\n \t
          1. 4NH3<\/sub>(g) + 5O2<\/sub>(g) \u2192 6H2<\/sub>O(g)\u00a0 + 4NO(g)<\/li>\r\n \t
          2. 2HgO(s) \u2192 2Hg(\u2113<\/span>)\u00a0 + O2<\/sub>(g)<\/li>\r\n \t
          3. 3FeCl2<\/sub>(s) + KNO3<\/sub>(s) + 4HCl (aq) \u2192 3FeCl3<\/sub>(s) + KCl(s) + NO(g) + 2H2<\/sub>O(\u2113<\/span>)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
          4. Draw a diagram showing the approximate entropy change of water from \u2212100\u00b0C to 250\u00b0C.<\/li>\r\n \t
          5. A chemical reaction has \u0394H<\/em>\u00b0 = \u221243.5 kJ and \u0394S<\/em>\u00b0 = \u221265.8 J\/K. Calculate \u0394G<\/em>\u00b0 at 298 K. Is this a spontaneous process?<\/li>\r\n \t
          6. Using data from the appendix, determine \u0394G<\/em>\u00b0 for all reactions listed in question 5.<\/li>\r\n \t
          7. Find the standard Gibbs energy change for the reaction CaCO3<\/sub>(s)\u00a0\u2192 CaO(s)\u00a0+ CO2<\/sub>(g).\r\n

            The \u0394Gf<\/sub>\u00b0<\/em>\u00a0values for the three components of this reaction system are CaCO3<\/sub>(s): \u20131128\u00a0kJ\u00a0mol\u20131<\/sup>; CaO(s): \u2013603.5\u00a0kJ\/mol; CO2<\/sub>(g): \u2013137.2 kJ\/mol.[footnote]Question and solution from Chem1 Virtual Textbook, Stephen Lower\/CC-BY-SA-3.0[\/footnote]<\/p>\r\n<\/li>\r\n \t

          8. Using the appendix data, determine the approximate temperature at which the following processes are at equilibrium:\r\n
              \r\n \t
            1. CH2<\/sub>Cl2<\/sub>(\u2113<\/span>) \u2192 CH2<\/sub>Cl2<\/sub>(g)<\/li>\r\n \t
            2. CH3<\/sub>OH(\u2113<\/span>) \u2192 CH3<\/sub>OH(g)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
            3. Determine if the following reactions would be spontaneous at any temperature, nonspontaneous at any temperature, spontaneous at low temperature but not high temperature, or spontaneous at high temperature but not low temperature:\r\n
                \r\n \t
              1. \u0394H<\/em>\u00b0 = \u2212750 kJ and \u0394S<\/em>\u00b0 = 250 J\/K<\/li>\r\n \t
              2. \u0394H<\/em>\u00b0 = \u2212100 kJ and \u0394S<\/em>\u00b0 = \u2212300 J\/K<\/li>\r\n \t
              3. \u0394H<\/em>\u00b0 = 95 kJ and \u0394S<\/em>\u00b0 = \u221270 J\/K<\/li>\r\n \t
              4. \u0394H<\/em>\u00b0 = 400 kJ and \u0394S<\/em>\u00b0 = 500 J\/K<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
              5. The K<\/em>a<\/sub> for acetic acid, CH3<\/sub>COOH, is 1.75 \u00d7 10\u22125<\/sup> at 25\u00b0C.\r\n
                  \r\n \t
                1. Using the K<\/em>a<\/sub> value, determine the \u0394G<\/em>\u00b0 for the dissociation of acetic acid in aqueous solution.<\/li>\r\n \t
                2. What is the value of \u0394G <\/em>when [H+<\/sup>] is 7.5 \u00d7 10\u22122<\/sup> M, [CH3<\/sub>COO\u2212<\/sup>] is 2.5 \u00d7 10\u22122<\/sup> M, and [CH3<\/sub>COOH] is 0.10 M?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
                3. Calculate the equilibrium constant for the reaction H+<\/sup>(aq) + OH\u2212<\/sup>(aq) \u2192 H2<\/sub>O(\u2113<\/span>)\u00a0from the following data:\r\n\r\n\r\n\r\n\r\n\r\n
                  <\/td>\r\nH+<\/sup>(aq)<\/strong><\/td>\r\nOH\u2212<\/sup>(aq)<\/strong><\/td>\r\nH2<\/sub>(\u2113<\/span><\/em>)<\/strong><\/td>\r\n<\/tr>\r\n
                  \u0394H\u00b0f<\/sub><\/em>, kJ mol\u20131<\/sup><\/strong><\/td>\r\n0<\/td>\r\n\u2013230.0<\/td>\r\n\u2013285.8<\/td>\r\n<\/tr>\r\n
                  S<\/em><\/strong>\u00b0, J K\u20131<\/sup> mol\u20131<\/sup><\/strong><\/td>\r\n0*<\/td>\r\n\u201310.9<\/td>\r\n70.0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n*Note that the standard entropy of the hydrogen ion is zero by definition. This reflects the fact that it is impossible to carry out thermodynamic studies on a single-charged species. All ionic entropies are relative to that of H+<\/sup>(aq), which explains why some values (as for the aqueous hydroxide ion) are negative.[footnote]Question and solution from Chem1 Virtual Textbook, Stephen Lower\/CC-BY-SA-3.0[\/footnote]<\/li>\r\n \t
                4. Using data from the appendix, calculate the equilibrium constants at 298 K for all the reactions in question 5.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n
                  \r\n

                  Answers<\/p>\r\n\r\n<\/header>\r\n

                  \r\n
                    \r\n \t
                  1. \r\n
                      \r\n \t
                    1. spontaneous<\/li>\r\n \t
                    2. nonspontaneous<\/li>\r\n \t
                    3. nonspontaneous<\/li>\r\n \t
                    4. spontaneous<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n
                        \r\n \t
                      1. \r\n
                          \r\n \t
                        1. \u0394S<\/em> = \u2212<\/li>\r\n \t
                        2. \u0394S<\/em> = +<\/li>\r\n \t
                        3. \u0394S<\/em> = +<\/li>\r\n \t
                        4. \u0394S<\/em> = +<\/li>\r\n \t
                        5. \u0394S<\/em> = \u2212<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n
                            \r\n \t
                          1. \r\n
                              \r\n \t
                            1. [latex]\\phantom{start}[\/latex]\r\n[latex]\\begin{align*}\r\n\\Delta S^{\\circ}&=\\underset{\\text{products}}{\\sum n S^{\\circ}}-\\underset{\\text{reactants}}{\\sum m S^{\\circ}}\\\\\r\n&=(6\\ S^{\\circ}\\ \\ce{H2O(g)}+4\\ S^{\\circ}\\ \\ce{NO(g)})\\\\\r\n&\\phantom{=}-(4\\ S^{\\circ}\\ \\ce{NH3(g)}+5\\ S^{\\circ}\\ \\ce{O2(g)}) \\\\\r\n&=[(6\\times 188.8\\text{ J\/mol K})+(4\\times 210.8\\text{ J\/mol K})]\\\\ &\\phantom{=}-[(4\\times 192.8\\text{ J\/mol K})+(5\\times 205.2\\text{ J\/mol K})] \\\\\r\n&=178.8\\text{ J\/mol K}\r\n\\end{align*}[\/latex]<\/li>\r\n \t
                            2. [latex]\\phantom{start}[\/latex]\r\n[latex]\\begin{align*}\r\n\\Delta S^{\\circ}&=\\underset{\\text{products}}{\\sum n S^{\\circ}}-\\underset{\\text{reactants}}{\\sum m S^{\\circ}}\\\\\r\n&=(2 \\ S^{\\circ} \\ \\ce{Hg(\\ell)}+S^{\\circ} \\ \\ce{O2(g)})-(2 \\ S^{\\circ} \\ \\ce{HgO}) \\\\\r\n&=[(2\\times 75.9\\text{ J\/mol K})+(205.2\\text{ J\/mol K})] \\\\\r\n&\\phantom{=}-(2\\times 70.3\\text{ J\/mol K}) \\\\\r\n&=216.4\\text{ J\/mol K}\r\n\\end{align*}[\/latex]<\/li>\r\n \t
                            3. [latex]\\phantom{start}[\/latex]\r\n[latex]\\begin{align*}\r\n\\Delta S^{\\circ}&=\\underset{\\text{products}}{\\sum n S^{\\circ}}-\\underset{\\text{reactants}}{\\sum m S^{\\circ}}\\\\\r\n&=(3 \\ S^{\\circ} \\ \\ce{FeCl3(s)}+S^{\\circ} \\ \\ce{KCl(s)}+S^{\\circ} \\ \\ce{NO(g)}+2 \\ S^{\\circ} \\ \\ce{H2O(\\ell)})\\\\\r\n&\\phantom{=}-(3 \\ S^{\\circ} \\ \\ce{FeCl2(s)}+ \\ S^{\\circ} \\ \\ce{KNO3(s)}+4 \\ S^{\\circ} \\ \\ce{HCl(aq)}) \\\\\r\n&=[(3\\times 142.3\\text{ J\/mol K})+(82.6\\text{ J\/mol K})\\\\\r\n&\\phantom{=}+(210.8\\text{ J\/mol K})+(2\\times 70.0\\text{ J\/mol K})]\\\\\r\n&\\phantom{=}-[(3\\times 118.0\\text{ J\/mol K})+(133.1\\text{ J\/mol K})\\\\\r\n&\\phantom{=}+(4\\times 56.5\\text{ J\/mol K})] \\\\\r\n&=147.2\\text{ J\/mol K}\r\n\\end{align*}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n
                                \r\n \t
                              1. [latex]\\phantom{start}[\/latex]\r\n[latex]\\begin{align*}\r\n\\Delta G^{\\circ}&=\\Delta H^{\\circ}-T\\Delta S^{\\circ} \\\\\r\n&=-43.5\\text{ kJ}-[(298\\text{ K})(-65.8\\text{ J\/K})] \\\\\r\n&=-23.9\\text{ kJ}\r\n\\end{align*}[\/latex]\r\n\u0394G<\/em>\u00b0 is negative. Therefore, this is a spontaneous process.<\/li>\r\n<\/ol>\r\n
                                  \r\n \t
                                1. \u0394G<\/em>\u00b0 = (\u2013603.5 \u2013 137.2) \u2013 (\u20131128) kJ\/mol = +130.9 kJ\/mol, indicating that the process is not spontaneous under standard conditions (i.e., solid calcium carbonate will not form solid calcium oxide and CO2<\/sub> at 1 atm partial pressure at 25\u00b0C).<\/li>\r\n<\/ol>\r\n
                                    \r\n \t
                                  1. \r\n
                                      \r\n \t
                                    1. spontaneous at all temperatures<\/li>\r\n \t
                                    2. spontaneous at low temperatures, nonspontaneous at high temperatures<\/li>\r\n \t
                                    3. nonspontaneous at all temperatures<\/li>\r\n \t
                                    4. spontaneous at high temperatures, nonspontaneous at low temperatures<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n
                                        \r\n \t
                                      1. [latex]\\phantom{start}[\/latex]\r\n[latex]\\begin{align*}\r\n\\Delta H^{\\circ}&=\\underset{\\text{products}}{\\sum \\Delta H^{\\circ}{}_{\\text{f}}}-\\underset{\\text{reactants}}{\\sum\\Delta H^{\\circ}{}_{\\text{f}}} \\\\\r\n&=(-285.8)-(-230) \\\\\r\n&=-55.8\\text{ kJ\/mol} \\\\ \\\\\r\n\\Delta S^{\\circ}&=\\underset{\\text{products}}{\\sum\\Delta S^{\\circ}}-\\underset{\\text{reactants}}{\\sum\\Delta S^{\\circ}} \\\\\r\n&=(70.0)-(-10.9) \\\\\r\n&=+80.8\\text{ J\/mol K}\r\n\\end{align*}[\/latex]\r\nThe value of \u0394G<\/em>\u00b0 at 298 K is:\r\n[latex]\\begin{align*}\r\n\\Delta H^{\\circ}-T\\Delta S^{\\circ}&=(-55,800)-(298)(80.8)=-79,900\\text{ J\/mol} \\\\\r\nK&=\\text{exp}\\left(\\dfrac{-79,900}{8.314\\times 298}\\right)=e^{-32.2}=1.01\\times 10^{-14}\r\n\\end{align*}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>","rendered":"
                                        \n
                                        \n

                                        Exercises<\/p>\n<\/header>\n

                                        \n
                                          \n
                                        1. Classify each of the following as spontaneous or nonspontaneous processes:\n
                                            \n
                                          1. the browning of a cut apple slice on a snack tray over time<\/li>\n
                                          2. the rolling of a ball uphill<\/li>\n
                                          3. the formation of diamond from the graphite in your pencil<\/li>\n
                                          4. the melting of ice cubes in a glass of water you are holding<\/li>\n<\/ol>\n<\/li>\n
                                          5. State the second law of thermodynamics.<\/li>\n
                                          6. What sign would you expect for \u0394S<\/em> for the following processes?\n
                                              \n
                                            1. water freezing in a lake during a cold Alberta winter<\/li>\n
                                            2. AB(s) + CD(s) \u2192 AC(g) + BD(g)<\/li>\n
                                            3. a balloon with a fixed amount of gas stretched to a larger volume<\/li>\n
                                            4. the sublimation of dry ice<\/li>\n
                                            5. 3E2<\/sub>F2<\/sub>(g) \u2192 E6<\/sub>F6<\/sub>(g)<\/li>\n<\/ol>\n<\/li>\n
                                            6. Which of the following would you expect to have the higher standard molar entropy, S<\/em>\u00b0?\n
                                                \n
                                              1. Br2<\/sub>(\u2113<\/span>) or Br2<\/sub>(g)<\/li>\n
                                              2. NO2<\/sub>(g) or NO(g)<\/li>\n
                                              3. C2<\/sub>H6<\/sub>(g) or C5<\/sub>H12<\/sub>(g)<\/li>\n<\/ol>\n<\/li>\n
                                              4. Calculate the \u0394S<\/em>\u00b0 of the following reactions using the values listed in the appendix.\n
                                                  \n
                                                1. 4NH3<\/sub>(g) + 5O2<\/sub>(g) \u2192 6H2<\/sub>O(g)\u00a0 + 4NO(g)<\/li>\n
                                                2. 2HgO(s) \u2192 2Hg(\u2113<\/span>)\u00a0 + O2<\/sub>(g)<\/li>\n
                                                3. 3FeCl2<\/sub>(s) + KNO3<\/sub>(s) + 4HCl (aq) \u2192 3FeCl3<\/sub>(s) + KCl(s) + NO(g) + 2H2<\/sub>O(\u2113<\/span>)<\/li>\n<\/ol>\n<\/li>\n
                                                4. Draw a diagram showing the approximate entropy change of water from \u2212100\u00b0C to 250\u00b0C.<\/li>\n
                                                5. A chemical reaction has \u0394H<\/em>\u00b0 = \u221243.5 kJ and \u0394S<\/em>\u00b0 = \u221265.8 J\/K. Calculate \u0394G<\/em>\u00b0 at 298 K. Is this a spontaneous process?<\/li>\n
                                                6. Using data from the appendix, determine \u0394G<\/em>\u00b0 for all reactions listed in question 5.<\/li>\n
                                                7. Find the standard Gibbs energy change for the reaction CaCO3<\/sub>(s)\u00a0\u2192 CaO(s)\u00a0+ CO2<\/sub>(g).\n

                                                  The \u0394Gf<\/sub>\u00b0<\/em>\u00a0values for the three components of this reaction system are CaCO3<\/sub>(s): \u20131128\u00a0kJ\u00a0mol\u20131<\/sup>; CaO(s): \u2013603.5\u00a0kJ\/mol; CO2<\/sub>(g): \u2013137.2 kJ\/mol.[1]<\/sup><\/a><\/p>\n<\/li>\n

                                                8. Using the appendix data, determine the approximate temperature at which the following processes are at equilibrium:\n
                                                    \n
                                                  1. CH2<\/sub>Cl2<\/sub>(\u2113<\/span>) \u2192 CH2<\/sub>Cl2<\/sub>(g)<\/li>\n
                                                  2. CH3<\/sub>OH(\u2113<\/span>) \u2192 CH3<\/sub>OH(g)<\/li>\n<\/ol>\n<\/li>\n
                                                  3. Determine if the following reactions would be spontaneous at any temperature, nonspontaneous at any temperature, spontaneous at low temperature but not high temperature, or spontaneous at high temperature but not low temperature:\n
                                                      \n
                                                    1. \u0394H<\/em>\u00b0 = \u2212750 kJ and \u0394S<\/em>\u00b0 = 250 J\/K<\/li>\n
                                                    2. \u0394H<\/em>\u00b0 = \u2212100 kJ and \u0394S<\/em>\u00b0 = \u2212300 J\/K<\/li>\n
                                                    3. \u0394H<\/em>\u00b0 = 95 kJ and \u0394S<\/em>\u00b0 = \u221270 J\/K<\/li>\n
                                                    4. \u0394H<\/em>\u00b0 = 400 kJ and \u0394S<\/em>\u00b0 = 500 J\/K<\/li>\n<\/ol>\n<\/li>\n
                                                    5. The K<\/em>a<\/sub> for acetic acid, CH3<\/sub>COOH, is 1.75 \u00d7 10\u22125<\/sup> at 25\u00b0C.\n
                                                        \n
                                                      1. Using the K<\/em>a<\/sub> value, determine the \u0394G<\/em>\u00b0 for the dissociation of acetic acid in aqueous solution.<\/li>\n
                                                      2. What is the value of \u0394G <\/em>when [H+<\/sup>] is 7.5 \u00d7 10\u22122<\/sup> M, [CH3<\/sub>COO\u2212<\/sup>] is 2.5 \u00d7 10\u22122<\/sup> M, and [CH3<\/sub>COOH] is 0.10 M?<\/li>\n<\/ol>\n<\/li>\n
                                                      3. Calculate the equilibrium constant for the reaction H+<\/sup>(aq) + OH\u2212<\/sup>(aq) \u2192 H2<\/sub>O(\u2113<\/span>)\u00a0from the following data:
                                                        \n\n\n\n\n\n
                                                        <\/td>\nH+<\/sup>(aq)<\/strong><\/td>\nOH\u2212<\/sup>(aq)<\/strong><\/td>\nH2<\/sub>(\u2113<\/span><\/em>)<\/strong><\/td>\n<\/tr>\n
                                                        \u0394H\u00b0f<\/sub><\/em>, kJ mol\u20131<\/sup><\/strong><\/td>\n0<\/td>\n\u2013230.0<\/td>\n\u2013285.8<\/td>\n<\/tr>\n
                                                        S<\/em><\/strong>\u00b0, J K\u20131<\/sup> mol\u20131<\/sup><\/strong><\/td>\n0*<\/td>\n\u201310.9<\/td>\n70.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                                        *Note that the standard entropy of the hydrogen ion is zero by definition. This reflects the fact that it is impossible to carry out thermodynamic studies on a single-charged species. All ionic entropies are relative to that of H+<\/sup>(aq), which explains why some values (as for the aqueous hydroxide ion) are negative.[2]<\/sup><\/a><\/li>\n

                                                      4. Using data from the appendix, calculate the equilibrium constants at 298 K for all the reactions in question 5.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n
                                                        \n
                                                        \n

                                                        Answers<\/p>\n<\/header>\n

                                                        \n
                                                          \n
                                                        1. \n
                                                            \n
                                                          1. spontaneous<\/li>\n
                                                          2. nonspontaneous<\/li>\n
                                                          3. nonspontaneous<\/li>\n
                                                          4. spontaneous<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n
                                                              \n
                                                            1. \n
                                                                \n
                                                              1. \u0394S<\/em> = \u2212<\/li>\n
                                                              2. \u0394S<\/em> = +<\/li>\n
                                                              3. \u0394S<\/em> = +<\/li>\n
                                                              4. \u0394S<\/em> = +<\/li>\n
                                                              5. \u0394S<\/em> = \u2212<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n
                                                                  \n
                                                                1. \n
                                                                    \n
                                                                  1. \"\phantom{start}\"\n

                                                                      <\/span>   <\/span>\"\begin{align*}<\/p>\n<\/li>\n

                                                                  2. \"\phantom{start}\"\n

                                                                      <\/span>   <\/span>\"\begin{align*}<\/p>\n<\/li>\n

                                                                  3. \"\phantom{start}\"\n

                                                                      <\/span>   <\/span>\"\begin{align*}<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                                      \n
                                                                    1. \"\phantom{start}\"\n

                                                                        <\/span>   <\/span>\"\begin{align*}<\/p>\n

                                                                      \u0394G<\/em>\u00b0 is negative. Therefore, this is a spontaneous process.<\/li>\n<\/ol>\n

                                                                        \n
                                                                      1. \u0394G<\/em>\u00b0 = (\u2013603.5 \u2013 137.2) \u2013 (\u20131128) kJ\/mol = +130.9 kJ\/mol, indicating that the process is not spontaneous under standard conditions (i.e., solid calcium carbonate will not form solid calcium oxide and CO2<\/sub> at 1 atm partial pressure at 25\u00b0C).<\/li>\n<\/ol>\n
                                                                          \n
                                                                        1. \n
                                                                            \n
                                                                          1. spontaneous at all temperatures<\/li>\n
                                                                          2. spontaneous at low temperatures, nonspontaneous at high temperatures<\/li>\n
                                                                          3. nonspontaneous at all temperatures<\/li>\n
                                                                          4. spontaneous at high temperatures, nonspontaneous at low temperatures<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n
                                                                              \n
                                                                            1. \"\phantom{start}\"\n

                                                                                <\/span>   <\/span>\"\begin{align*}<\/p>\n

                                                                              The value of \u0394G<\/em>\u00b0 at 298 K is:<\/p>\n

                                                                                <\/span>   <\/span>\"\begin{align*}<\/p>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                                                              1. Question and solution from Chem1 Virtual Textbook, Stephen Lower\/CC-BY-SA-3.0 ↵<\/a><\/li>
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