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Problem 26a
(a) Does the entropy of the surroundings increase for spontaneous processes?
Problem 26b
(b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of ΔSsurr?
Problem 26c
(c) During a certain reversible process, the surroundings undergo an entropy change, ΔSsurr = -78 J/K. What is the entropy change of the system for this process?
Problem 28
(a) What sign for Δ𝑆 do you expect when the pressure on 0.600 mol of an ideal gas at 350 K is increased isothermally from an initial pressure of 0.750 atm?
(b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process.
(c) Which of the following statements about this process are true? (i) The entropy change you calculated will be the same for at any other constant temperature. (ii) The value of Δ𝑆 you calculated is valid only if the compression is done irreversibly. (iii) If the number of moles of gas being compressed were decreased by a factor of three, the entropy change would increase by a factor of three.
Problem 29b
For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (b) Explain why no work is done by the system during this process.
Problem 30a
(a) What is the difference between a state and a microstate of a system?
Problem 30b
(b) As a system goes from state A to state B, its entropy decreases. What can you say about the number of microstates corresponding to each state?
Problem 30c
(c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of ΔSsurr?
Problem 31b
Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (b) decrease in volume
- (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)