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- (a) Using the heat of vaporization in Appendix B, calculate the entropy change for the vaporization of water at 25 °C and at 100 °C. (b) From your knowledge of microstates and the structure of liquid water, explain the difference in these two values.
Problem 32
Problem 34a
(a) In a chemical reaction, two gases combine to form a solid. What do you expect for the sign of ΔS?
Problem 34b
(b) How does the entropy of the system change in the processes described in Exercise 19.12?
- Does the entropy of the system increase, decrease, or stay the same when (a) a solid melts, (b) a gas liquefies, or (c) a solid sublimes?
Problem 35
- Does the entropy of the system increase, decrease, or stay the same when (a) the temperature of the system increases, (b) the volume of a gas increases, and (c) equal volumes of ethanol and water are mixed to form a solution?
Problem 36
- Indicate whether each statement is true or false. (a) The third law of thermodynamics says that the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal. (b) “Translational motion” of molecules refers to their change in spatial location as a function of time. (c) “Rotational” and “vibrational” motions contribute to the entropy in atomic gases like He and Xe. (d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.
Problem 37
Problem 38
Indicate whether each statement is true or false. (a) Unlike enthalpy, where we can only ever know changes in H, we can know absolute values of S. (b) If you heat a gas such as CO2, you will increase its degrees of translational, rotational and vibrational motions. (c) CO2(g) and Ar(g) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.
- For each of the following pairs, predict which substance has the higher entropy per mole at a given temperature: (a) Ar(l) or Ar(g) (b) He(g) at 3 atm pressure or He(g) at 1.5 atm pressure (c) 1 mol of Ne(g) in 15.0 L or 1 mol of Ne(g) in 1.50 L (d) CO2(g) or CO2(s)
Problem 39
Problem 41a
Predict the sign of the entropy change of the system for each of the following reactions: (a) N2(g) + 3 H2(g) → 2 NH3(g)
Problem 41b
Predict the sign of the entropy change of the system for each of the following reactions: (b) CaCO3(s) → CaO(s) + CO2(g)
Problem 41c
Predict the sign of the entropy change of the system for each of the following reactions: (c) 3 C2H2(g) → C6H6(g)
Problem 41d
Predict the sign of the entropy change of the system for each of the following reactions: (d) Al2O3(s) + 3 H2(g) → 2 Al(s) + 3 H2O(g)
Problem 42a
Predict the sign of ΔSsys for each of the following processes: (a) Molten gold solidifies.
Problem 42b
Predict the sign of ΔSsys for each of the following processes: (b) Gaseous Cl2 dissociates in the stratosphere to form gaseous Cl atoms.
Problem 42c
Predict the sign of ΔSsys for each of the following processes: (c) Gaseous CO reacts with gaseous H2 to form liquid methanol, CH3OH.
Problem 42d
Predict the sign of ΔSsys for each of the following processes: (d) Calcium phosphate precipitates upon mixing Ca(NO3)2(aq) and (NH4)3PO4(aq).
Problem 46
Cyclopropane and propylene are isomers that both have the formula C3H6. Based on the molecular structures shown, which of these isomers would you expect to have the higher standard molar entropy at 25 °C?
- Predict which member of each of the following pairs has the greater standard entropy at 25°C: (a) Sc(s) or Sc(g). Use Appendix C to find the standard entropy of each substance. (b) NH3(g) or NH3(aq). Use Appendix C to find the standard entropy of each substance. (c) O2(g) or O3(g). Use Appendix C to find the standard entropy of each substance. (d) C(graphite) or C(diamond). Use Appendix C to find the standard entropy of each substance.
Problem 47
- Predict which member of each of the following pairs has the greater standard entropy at 25°C: (a) C6H6(l) or C6H6(g). Use Appendix C to find the standard entropy of each substance. (b) CO(g) or CO2(g). Use Appendix C to find the standard entropy of each substance. (c) 1 mol N2O4(g) or 2 mol NO2(g). Use Appendix C to find the standard entropy of each substance. (d) HCl(g) or HCl(aq). Use Appendix C to find the standard entropy of each substance.
Problem 48
- Ammonium nitrate dissolves spontaneously and endothermally in water at room temperature. What can you deduce about the sign of ΔS for this dissolution process?
Problem 49
Problem 51
Using S° values from Appendix C, calculate ΔS° values for the following reactions. In each case, account for the sign of ΔS°.
(a) C2H4(g) + H2(g) → C2H6(g)
(b) N2O4(g) → 2 NO2(g)
(c) Be(OH)2(s) → BeO(s) + H2O(g)
(d) 2 CH3OH(g) + 3 O2(g) ⟶ 2 CO2(g) + 4 H2O(g)
Problem 53a
(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system?
Problem 53b
(b) For a certain process that occurs at constant T and P, the value of ΔG is positive. Is the process spontaneous?
- (a) Is the standard free-energy change, ΔG°, always larger than ΔG? (b) For any process that occurs at constant temperature and pressure, what is the significance of ΔG = 0? (c) For a certain process, ΔG is large and negative. Does this mean that the process necessarily has a low activation barrier?
Problem 54
Problem 55b
For a certain chemical reaction, ΔH° = -35.4 kJ and ΔS° = -85.5 J/K. (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system?
Problem 55c,d
For a certain chemical reaction, ΔH° = -35.4 kJ and ΔS° = -85.5 J/K. (c) Calculate ΔG° for the reaction at 298 K. (d) Is the reaction spontaneous at 298 K under standard conditions?
- A certain reaction has ΔH° = +23.7 kJ and ΔS° = +52.4 J>K. (c) Calculate ΔG° for the reaction at 298 K. (d) Is the reaction spontaneous at 298 K under standard conditions?
Problem 56
Problem 58
Use data in Appendix C to calculate ΔH°, ΔS°, and ΔG° at 25 °C for each of the following reactions.
a. 4 Cr(s) + 3 O2(g) → 2 Cr2O3(s)
b. BaCO3(s) → BaO(s) + CO2(g)
c. 2 P(s) + 10 HF(g) → 2 PF5(g) + 5 H2(g)
d. K(s) + O2(g) → KO2(s)
Problem 59
Using data from Appendix C, calculate ΔG° for the following reactions. Indicate whether each reaction is spontaneous at 298 K under standard conditions.
(a) 2 SO2(g) + O2(g) → 2 SO3(g)
(b) NO2(g) + N2O(g) → 3 NO(g)
(c) 6 Cl2(g) + 2 Fe2O3(s) → 4 FeCl3(s) + 3 O2(g)
(d) SO2(g) + 2 H2(g) → S(s) + 2 H2O(g)
Problem 60
Using data from Appendix C, calculate the change in Gibbs free energy for each of the following reactions. In each case, indicate whether the reaction is spontaneous at 298 K under standard conditions.
(a) 2 Ag(s) + Cl2(g) → 2 AgCl(s)
(b) P4O10(s) + 16 H2(g) → 4 PH3(g) + 10 H2O(g)
(c) CH4(g) + 4 F2(g) → CF4(g) + 4 HF(g)
(d) 2 H2O2(l) → 2 H2O(l) + O2(g)