Entropy Free Energy and Equilibrium Part 2

59. Find the temperature at which the reaction N2O4(g)  2NO2(g) will be in equilibrium when both gases are present at partial pressures of 1.00 atm. NO2(g) N2O4(g) A) 300°C Ans: C  H°f (25°C) 33.85 kJ/mol 9.66 kJ/mol  G°f (25°C) 51.8 kJ/mol 98.29 kJ/mol B) 28°C C) 55°C D) 32°C E) 562°C 60. Predict the normal boiling point of triethylborane (C6H15B) using the following data: C6H15B(l) C6H15B(g) A) 92°C Ans: A  H°f (25°C) –194.6 kJ/mol –157.7 kJ/mol  G°f (25°C) 9.4 kJ/mol 16.1 kJ/mol B) –21°C C) 21°C D) 365°C E) 256°C 61. A sample of solid naphthalene is introduced into an evacuated flask. Use the data below to calculate the equilibrium vapor pressure of naphthalene (C10H8) in the flask at 35°C. C10H8(s) C10H8(g) A) B) C) Ans: 890. mmHg 0.21 mmHg 696 mmHg B  H°f (25°C) 78.5 kJ/mol 150.6 kJ/mol  G°f (25°C) 201.6 kJ/mol 224.1 kJ/mol D) E) 0.086 mmHg 833 mmHg 62. The standard free energy of formation of gaseous hydrogen iodide is 1.30 kJ/mol at 25°C. Find Kp for the reaction H2(g) + I2(s) 2HI(g) at this temperature. A) 7.0 B) 7100 C) 1.0 D) 2.4 E) 2.9 Ans: E 63. Find the temperature at which Kp = 4.00 for the reaction N2O4(g) 2NO2(g). [Given: at 25°C, for NO2(g), H°f = 33.85 kJ/mol, S° = 240.46 J/mol·K; for N2O4(g), H°f = 9.66 kJ/mol, S° = 304.3 J/mol·K; assume that H° and S° are independent of temperature.] A) 197 °C B) 56 °C C) 36 °C D) 79 °C E) 476°C Ans: D 64. Find the temperature at which Kp = 42.0 for the reaction H2(g) + I2(g) 2HI(g). [Given: at 25°C, for H2(g), H°f = 0, S° = 131.0 J/mol·K; for I2(g), H°f = 62.26 kJ/mol, S° = 260.6 J/mol·K; for HI(g), H°f = 25.9 kJ/mol, S° = 206.3 J/mol·K; assume that H° and S° are independent of temperature.] A) 1040 K B) 168 K C) 539 K D) 1400 K E) 34,200 K Ans: A 65. For the reaction HCONH2(g) NH3(g) + CO(g), Kc = 4.84 at 400 K. If reaction is 29 kJ/mol, find Kc at 500 K. A) 5.8 B) 0.17 C) 27 D) 0.88 E) 10.3 Ans: C H° for this 66. In the gas phase, formic acid forms a dimmer, 2HCOOH(g) (HCOOH)2(g). For this reaction, H° = –60.1 kJ/mol and G° = –13.9 kJ/mol at 25°C. Find the equilibrium constant (Kp) for this reaction at 75 °C. A) 8960 B) 273 C) 0.120 D) 8.33 E) 1.12 × 10–4 Ans: D 67. In the gas phase, methyl isocyanate (CH3NC) isomerizes to acetonitrile (CH3CN), H3C– N C (g) H3C–C N (g) with H° = –89.5 kJ/mol and G° = – 73.8 kJ/mol at 25°C. Find the equilibrium constant for this reaction at 100°C. D) 4.63 × 10–11 A) 1.68 × 10–10 E) 8.64 × 1012 B) 5.96 × 109 C) 2.16 × 1010 Ans: B 68. Using the thermodynamic data provided below, calculate the standard change in entropy when one mole of sodium nitrate is dissolved in water? S° (J/K·mol) NaNO3(s) 116.3 60.25 Na+(aq) 146.4 NO3–(aq) Will the solubility of sodium nitrate increase or decrease if the temperature of the system is increased? Ans: 90.4 J/K·mol; solubility increases with increasing temperature 69. Using the thermodynamic data provided below, calculate the standard change in entropy when one mole of sodium sulfate is dissolved in water? S° (J/K·mol) Na2SO4(s) 149.49 60.25 Na+(aq) 17.15 SO42–(aq) Will the solubility of sodium nitrate increase or decrease if the temperature of the system is increased? Ans: –11.84 J/K·mol; solubility decreases with increasing temperature 70. For the reaction CuS(s) + H2(g) H2S(g) + Cu(s), G°f (CuS) = –53.6 kJ/mol G°f (H2S) = –33.6 kJ/mol H°f (CuS) = –53.1 kJ/mol H°f (H2S) = – 20.6 kJ/mol Will this reaction proceed spontaneously at 298 K and 1 atm pressure? Ans: No 71. For the reaction CuS(s) + H2(g) H2S(g) + Cu(s), G°f (CuS) = –53.6 kJ/mol G°f (H2S) = –33.6 kJ/mol H°f (CuS) = –53.1 kJ/mol H°f (H2S) = – 20.6 kJ/mol Calculate the value of the equilibrium constant (Kp) for this reaction at 298 K. Ans: 3.11 × 10–4 72. For the reaction CuS(s) + H2(g) H2S(g) + Cu(s), G°f (CuS) = –53.6 kJ/mol G°f (H2S) = –33.6 kJ/mol H°f (CuS) = –53.1 kJ/mol H°f (H2S) = –20.6 kJ/mol Calculate G at 798 K and 1 atm pressure (assume S° and H° do not change with temperature). Ans: –1.02 kJ/mol 73. For the reaction CuS(s) + H2(g) H2S(g) + Cu(s), G°f (CuS) = –53.6 kJ/mol G°f (H2S) = –33.6 kJ/mol H°f (CuS) = –53.1 kJ/mol H°f (H2S) = –20.6 kJ/mol Calculate the value of the equilibrium constant (Kp) at 798 K and 1 atm pressure. Ans: 1.17 74. For the reaction SbCl5(g) SbCl3(g) + Cl2(g), G°f (SbCl5) = –334.34 kJ/mol G°f (SbCl3) = –301.25 kJ/mol H°f (SbCl5) = –394.34 kJ/mol H°f (SbCl3) = –313.80 kJ/mol Will this reaction proceed spontaneously at 298 K and 1 atm pressure? Ans: No 75. For the reaction SbCl5(g) SbCl3(g) + Cl2(g), G°f (SbCl5) = –334.34 kJ/mol G°f (SbCl3) = –301.25 kJ/mol H°f (SbCl5) = –394.34 kJ/mol H°f (SbCl3) = –313.80 kJ/mol Calculate the value of the equilibrium constant (Kp) for this reaction at 298 K. Ans: 1.58 × 10–6 76. For the reaction SbCl5(g) SbCl3(g) + Cl2(g), G°f (SbCl5) = –334.34 kJ/mol G°f (SbCl3) = –301.25 kJ/mol H°f (SbCl5) = –394.34 kJ/mol H°f (SbCl3) = –313.80 kJ/mol Calculate G at 800 K and 1 atm pressure (assume S° and H° do not change with temperature). Ans: –46.66 kJ/mol 77. For the reaction SbCl5(g) SbCl3(g) + Cl2(g), G°f (SbCl5) = –334.34 kJ/mol G°f (SbCl3) = –301.25 kJ/mol H°f (SbCl5) = –394.34 kJ/mol H°f (SbCl3) = –313.80 kJ/mol Calculate the value of the equilibrium constant (Kp) at 800 K and 1 atm pressure. Ans: 1.11 × 103 78. Assuming S° and H° do not vary with temperature, at what temperature will the reaction shown below become spontaneous? C(s) + H2O(g) H2(g) + CO(s) (S° = 133.6 J/K·mol; H° = 131.3 kJ/mol) Ans: 710°C 79. Rubidium has a heat of vaporization of 69.0 kJ/mol at its boiling point (686°C). Calculate S for this process, Rb(l) Rb(g), at 1 atm and 686°C. Ans: 71.9 J/K·mol 80. The free energy of formation of nitric oxide, NO, at 1000 K (roughly the temperature in an automobile engine during ignition) is about 78 kJ/mol. Calculate the equilibrium constant Kp for the reaction N2(g) + O2(g) 2NO(g) at this temperature. Ans: Kp = 7.1 × 10–9 81. Predict the signs (–, +, or 0) of Ans: +, + H and S, in that order, for the reaction: O2(g) 2O(g). 82. Under what conditions (always, never, high temperature only, low temperature only) is the reaction O2(g) 2O(g) expected to be spontaneous? Ans: high temperatures only 83. Predict the signs (–, +, or 0) of into a vacuum. Ans: 0, + H and S, in that order, for the expansion of an ideal gas 84. Under what conditions (always, never, high temperature only, low temperature only) is the expansion of an ideal gas into a vacuum expected to be spontaneous? Ans: always 85. Predict the signs (–, +, or 0) of H2O(s). Ans: –, – H and S, in that order, for the process: H2O(l) 86. Under what conditions (always, never, high temperature only, low temperature only) is the process: H2O(l) H2O(s) expected to be spontaneous? Ans: low temperature only 87. Predict the signs (–, +, or 0) of H and 6H2O(g) C6H12O6(g) + 6O2(g). Ans: +, – S, in that order, for the reaction: 6CO2(g) + 88. Under which of the following conditions (always, never, high temperature only, low temperature only) is the reaction: 6CO2(g) + 6H2O(g) C6H12O6(g) + 6O2(g) expected to be spontaneous? Ans: never 89. What is the free energy change for the reaction SiO2(s) + Pb(s) G°f (PbO2) = –217 kJ/mol G°f (SiO2) = –856 kJ/mol Ans: 639 kJ/mol PbO2(s) + Si(s)? 90. Is the reaction SiO2(s) + Pb(s) PbO2(s) + Si(s) spontaneous? G°f (PbO2) = –217 kJ/mol G°f (SiO2) = –856 kJ/mol Ans: No 91. For a certain reaction, G° = 87 kJ/mol, H° = 100 kJ/mol at STP. At what temperature, in K, is the reaction in equilibrium, assuming that S° and H° are temperatureindependent? Ans: 2,100 K 92. The heat of vaporization of water is 2.27 kJ/g. What is boiling point? Ans: 110. J/K·mol Svap per mole at the normal 93. Calculate the free energy of formation of NaBr(s) given the following information: NaBr(s) Na(s) + 1/2Br2(l), G° = 349 kJ/mol Ans: –349 kJ/mol 94. The following reaction is nonspontaneous at 25°C: Cu2O(s) 2Cu(s) + 1/2O2(g), G° = 141 kJ/mol If S° = 75.8 J/K·mol, what is the lowest temperature at which the reaction will be spontaneous? Ans: 2160 K 95. For the reaction 3H2(g) + N2(g) Ans: 29.4 kJ/mol 2NH3(g), Kc = 9.0 at 350°C. Calculate G° at 350°C. 96. For the reaction 3H2(g) + N2(g) 2NH3(g), Kc = 9.0 at 350°C. In what direction does this reaction proceed at 350°C under standard state conditions? Ans: right to left 97. For the reaction 3H2(g) + N2(g) 2NH3(g), Kc = 9.0 at 350°C. What is the value of G at this temperature when 1.0 mol NH3, 5.0 mol N2, and 5.0 mol H2 are mixed in a 2.5 L reactor? Ans: –35.2 kJ/mol 98. For the reaction 3H2(g) + N2(g) 2NH3(g), Kc = 9.0 at 350°C. In what direction does the reaction proceed when 1.0 mol NH3, 5.0 mol N2, and 5.0 mol H2 are mixed in a 2.5 L reactor? Ans: left to right 99. Consider the reaction CO(g) + 2H2(g) G°f (CO) = –137.3 kJ/mol G°f (CH3OH) = –166.3 kJ/mol H°f (CO) = –110.5 kJ/mol H°f (CH3OH) = –238.7 kJ/mol S°(CO) = 197.9 J/K·mol S°(CH3OH) = 126.8 J/K·mol Calculate G° at 25°C. Ans: –29.0 kJ/mol CH3OH(l) at 25°C. 100. Consider the reaction CO(g) + 2H2(g) CH3OH(l) at 25°C. G°f (CO) = –137.3 kJ/mol G°f (CH3OH) = –166.3 kJ/mol H°f (CO) = –110.5 kJ/mol H°f (CH3OH) = –238.7 kJ/mol S°(CO) = 197.9 J/K·mol S°(CH3OH) = 126.8 J/K·mol Calculate value of the equilibrium constant (Kp) for this reaction at 25°C. Ans: 1.21 × 10 5 101. Consider the reaction CO(g) + 2H2(g) G°f (CO) = –137.3 kJ/mol G°f (CH3OH) = –166.3 kJ/mol H°f (CO) = –110.5 kJ/mol H°f (CH3OH) = –238.7 kJ/mol S°(CO) = 197.9 J/K·mol S°(CH3OH) = 126.8 J/K·mol Calculate S°(H2(g)). Ans: 131 J/K·mol CH3OH(l) at 25°C. 102. For the reaction H2O2(g) H2O(g) + 1/2O2(g), H° = –106 kJ/mol and S° = 58 J/K·mol at 25°C. Calculate G° for this reaction at this temperature. Ans: –123 kJ/mol 103. For the reaction H2O2(g) H2O(g) + 1/2O2(g), H° = –106 kJ/mol and S° = 58 J/K·mol at 25°C. Is H2O2(g) stable with respect to dissociation into water vapor and oxygen gas at 25°C? Ans: No 104. Choose the substance with the higher entropy per mole at a given temperature: O2(g) at 5 atm or O2(g) at 0.5 atm. Ans: O2(g) at 0.5 atm 105. Choose the substance with the higher entropy per mole at a given temperature: Br2(l) or Br2(g). Ans: Br2(g) 106. Choose the substance with the higher entropy per mole at a given temperature: 1 mole of N2(g) in a 22.4 L container or 1 mole of N2(g) in a 2.24 L container. Ans: 1 mole of N2(g) in a 22.4 L container 107. Choose the substance with the higher entropy per mole at a given temperature: CO2(g) or CO2(aq). Ans: CO2(g) 108. Hvap for ethanol is 38.7 kJ/mol at its boiling point (78°C). What is of ethanol is boiled? Ans: –110 J/K·mol Ssurr when 1.00 mole 109. Using the thermodynamic data provided below, determine the temperature in °C at which the decomposition of solid calcium carbonate to form solid calcium oxide and oxygen becomes spontaneous. CO2(g) CaO(s) CaCO3(s) H°f (kJ/mol) –393.5 –635.6 –1206.9 S° (J/K·mol) 213.6 39.8 92.9 Ans: 834.6°C 110. Sulfur can be separated from lead in the mineral galena, PbS(s), by “roasting” the ore in the presence of oxygen as shown in the following reaction: 2PbS(s) + 3O2(g) 2PbO(s) + 2SO2(g) Determine G for the above reaction at 850°C. PbS(s) O2(g) PbO(s) SO2(g) H°f (kJ/mol) –94.3 0 –217.86 –296.4 S°(J/K·mol) 91.2 205.0 69.45 248.5 Ans: –660 kJ/mol 111. Given the following data, calculate the boiling point of HCOOH (formic acid). HCOOH(l) HCOOH(g) Ans: 115°C  H°f (kJ/mol) –410 –363 S° (J/K·mol) 130 251 112. Given the following data, estimate the boiling point of carbon disulfide, CS2, assuming that S° and H° are temperature-independent. CS2(g) CS2(l) H°f (kJ/mol) 115.3 87.3 S° (J/K·mol) 237.8 151.0 Ans: 49.4°C 113. Given the following data, estimate the boiling point of bromine, Br2, assuming that S° and H° are temperature-independent. Br2(g) Br2(l) H°f (kJ/mol) 30.91 0 S° (J/K·mol) 245.3 152.3 Ans: 59.2°C 114. At 700 K, the equilibrium constant for the reaction CO(g) + H2O(g) 5.10. What is G° for this reaction at this temperature? Ans: –9.48 kJ/mol CO2(g) + H2(g) is 115. Using the thermodynamic data provided below, calculate Ka for HCN(aq) at 25°. H+(aq) CN–(aq) HCN(aq) H°f (kJ/mol) 0 151.0 105.4 S° (J/K·mol) 0 117.99 128.9 Ans: 2.8 × 10–9 (compared to the experimental value of 4.9 × 10–10) 116. Using the thermodynamic data provided below, calculate Ka1 for H2CO3(aq) at 25°. H+(aq) H2CO3(aq) HCO3–(aq) CO32– (aq) H°f (kJ/mol) 0 –698.7 –691.11 –676.26 S° (J/K·mol) 0 191 95.0 –53.1 Ans: 5 × 10–7 (compared to the experimental value of 4.5 × 10–7) 117. Using the thermodynamic data provided below, calculate Ka2 for H2CO3(aq) at 25°. H+(aq) H2CO3(aq) HCO3–(aq) CO32– (aq) H°f (kJ/mol) 0 –698.7 –691.11 –676.26 S° (J/K·mol) 0 191 95.0 –53.1 Ans: 4.59 × 10–11 (which agrees well with the experimental value of 4.7 × 10–11) 118. Using the thermodynamic data provided below, calculate Ksp for ZnS(s) at 25°. Zn2+(aq) S2–(aq) ZnS(s) H°f (kJ/mol) –152.4 41.8 –203 S° (J/K·mol) –106.5 22 57.7 Ans: 2.4 × 10–24 (the experimental value is 2.0 × 10–22) 119. Using the thermodynamic data provided below, calculate Ksp for Mg(OH)2(s) at 25°. Mg2+(aq) OH–(aq) Mg(OH)2(s) H°f (kJ/mol) –461.96 –229.94 –924.66 S° (J/K·mol) –117.99 –10.5 63.1 Ans: 8.90 × 10–12 (agrees reasonably well with the experimental value of 1.2 × 10–11) 120. The standard entropy of any pure substance is 0 J/mol. Ans: False 121. The entropy of any pure substance at 0 K is 0 J/mol. Ans: False 122. The entropy of a perfectly ordered crystalline substance at 0 K is 0 J/mol. Ans: True 123. Melting an ionic solid always results in an increase in entropy. Ans: True 124. Dissolving an ionic solid in water always results in an increase in entropy. Ans: False 125. For a given substance the entropy always increases in the following order: S (gas) < S (liq) < S (solid). Ans: False 126. The entropy change S° for the reaction NH4Cl(s) Ans: False NH3(g) + HCl(g) will be negative. 127. The following reaction is spontaneous under standard state conditions at 25°C: AgCl(s) Ag+(aq) + Cl–(aq) (G° = 55 kJ/mol) Ans: False 128. For any pure substance, if Hf° = 0 and Gf° = 0, than S° = 0 Ans: False