1. Which of the Following Processes Are Spontaneous and Which Are Nonspontaneous: (A) Spreading

Chapter 19

1. Which of the following processes are spontaneous and which are nonspontaneous: (a) spreading of the fragrance of perfume through a room; (b) separation of N2 and O2 molecules in air from each other; (c) mending a broken clock; (d) the reaction of sodium metal with chlorine gas to form sodium chloride; (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid?

2. A nineteenth-century chemist, Marcellin Berthelot, suggested that all chemical processes that proceed spontaneously are exothermic. Is this correct? If you think not, offer some counterexamples.

3. The freezing of water to ice is an exothermic process. (a) In what temperature range is it a spontaneous process? (b) In what temperature range is it a nonspontaneous process? (c) Why isn’t this exothermic process always spontaneous?

4. When steam condenses to water at 90oC, the entropy of the system decreases. What must be true if the second law of thermodynamics is to be satisfied?

5. In a living cell, large molecules are assembled from smaller ones. Is this process consistent with the second law of thermodynamics?

6. How does the entropy of the system change when the following processes occur: (a) a solid is melted; (b) a liquid is vaporized; (c) a solid is dissolved in water; (d) a gas liquefied?

7. Why is the increase in entropy of the system greater for the vaporization of a substance than for its melting?

8. For each of the following pairs, choose the substance with the higher entropy (per model) at a given temperature: (a) O2(g) at 5 atm or O2 (g) at 0.5 atm; (b) Br2(g) or Br2 (l); (c) 1 mol of N2(g) in 22.4 L or 1 mol of N2(g) in 2.24 L; (d) CO2(g) or CO2(aq).

9. For each of the following pairs, indicate which substance you would expect to possess the larger standard entropy: (a) 1 mol of Cl2(g) at 273 K, 1 atm pressure, or 1 mol at 373 K, 1 atm pressure; (b) 1 mol of H2O(g) at 100oC, 1 atm pressure or 1 mol of H2O(l) at 100oC; (c) 1 mol of O2(g) at 300 K, 30.0 L volume, or 2 mol of O(g) at 300 K, 60.0 L volume; (d) 1 mol of KNO3 (s) at 40.00C or 1 mol KNO3(aq) at 40.00C. Explain the origin of the difference in entropy values in each case.

10. Using Appendix C, compare the standard entropies at 298 K for the substances in the following pairs: (a) CCL4(l) and CCL4(g); (b)C(diamond) and C(graphite); (c) 1 mol of N2O4(g) and 2 mol of NO2(g); (d) KClO3(s) and KClO3(aq). Explain in the origin of the difference in entropy values in each cas

11.Using Appendix C, compare the standard entropies at 298 K for the substances in the following pairs: (a) Si(g) and Si(s); (b) 1 mol of C6H12O6(s) and 6 mol C(graphite) plus 6 mol H2O(l); (c) 2 mol P2(g) and 1 mol of P4(g); (d) NaOH(s) and NaOH(aq).

12.Predict the sign of DS for the system in each of the following processes: (a) freezing of 1 mol of H2O(l); (b) evaporation of 1 mol of Br2(l); (c) precipitation of BaSO4 upon mixing Ba(NO3)2(aq) and H2SO4(aq); (d) oxidation of magnesium metal:

2Mg(s) + O2(g) 2MgO(s).

13. For each of the following processes, predict whether the entropy change in the system is positive or negative:

(a) 2C(s) + O2(g) 2CO(g)

(b) 2K(s) + Br2(l) 2KBr(s)

(d) O(g) + O2(g) O3(g)

14. Using tabulated So values from Appendix C, calculate So for each of the following reactions:

(a) 2HBr(g) + F2(g) 2HF(g) + Br2(g)

(b) NO(g) + O2(g) 2NO2(g)

(d) 4FeO(s) + O2(g) 2Fe2O3(s)

In each case, account for the sign of So.

15. (a) What is the significance of DG = 0 for any process in a system? (b) What is the meaning of the standard free-energy change in a process, DG0, as contrasted with simply the free-energy change, DG?

16. Using the data in Appendix C, calculate DH0, DS0, and DG0 at 250C for each of the following reactions. In each case show that DG0 = DH0 - TDS0.

(a) BaO (s) + CO2 (g) ® BaCO3 (s)

(b) 2 KClO3 (s) ® 2 KCl (s) + 3 O2 (g)

(d) NOCl (g) + Cl (g) ® NO (g) + Cl2 (g)

17. Using the data from Appendix C, calculate the change in Gibbs free energy for each of the following processes. In each case, indicate whether each reaction is spontaneous under standard conditions.

(a) 2 SO2 (g) + O2 (g) ® 2 SO3 (g)

(b) NO2 (g) + N2O (g) ® 3 NO (g)

(d) SO2 (g) + 2 H2 (g) ® S (s) + 2 H2O (g)

18. From the values given for DH0 and DS0, calculate DG0 for each of the following reactions at 298K. If the reaction is not spontaneous under standard conditions at 298K, at what temperature (if any) would the reaction become spontaneous?

(a) 2 PbS (s) + 3 O2 (g) ® 2 PbO (s) + 2 SO2 (g) DH0 = -844kJ; DS0 = -0.165 kJ/K

(b) 2 POCl3 (g) ® 2 PCl3 (g) + O2 (g) DH0 = 572 kJ; DS0 = 179 J/K

19. A certain reaction is spontaneous at 850C. The reaction is endothermic by 34 kJ. What is the minimum value of DS for the reaction?

20. Reactions in which a substance decomposes by losing CO2 are called decarboxylation reactions. The decarboxylation of acetic acid proceeds as follows:

CH3COOH (l) ® CH4 (g) + CO2 (g)

By using the data from Appendix C, calculate the minimum temperature at which this process will be spontaneous under standard conditions. (You may assume that DH and DS do not vary with temperature.)

21. (a) Using the data in Appendix C, predict how DG0 for the following process will change with increasing temperature:

SO3 (g) + H2 (g) ® SO2 (g) + H2O (g)

(b) Calculate DG0 at 600K, assuming that DH0 and DS0 do not change with variation in temperature.

22. Acetylene gas, C2H2, is used in welding. (a) How much heat is produced in burning a mole of C2H2 at standard conditions if both reactants and products are brought to 298K and H2O (l) is formed? (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

23. Indicate whether DG increases, decreases, or does not change when the partial pressure of H2 is increased in each of the following reactions:

(a) N2 (g) + 3 H2 (g) ® 2 NH3 (g)

(b) 2 HBr (g) ® H2 (g) + Br2 (g)

24. Consider the following reaction:

2 CO (g) + O2 (g) ® 2 CO2 (g)

(a) Using data from Appendix C, calculate DG0 for this reaction at 298K. (b) Calculate DG at 298K if the reaction mixture consists of 6.0 atm of CO, 300 atm of O2, and 0.10 atm of CO2.

25. Write the equilibrium expression and calculate the magnitude of the equilibrium constant for each of the following reactions at 298K, using data from Appendix C.

(a) NaHCO3 (s) « NaOH (s) + CO2 (g)

(b) 2 HBr (g) + Cl2 (g) « 2 HCl (g) + Br2 (g)

26. Consider the reaction: PbCO3 (s) ® PbO (s) + CO2 (g)

Using data from Appendix C, calculate the equilibrium pressure of CO2 in the system at (a) 250C and (b) 5000C.

27. (a) Given Kb for ammonia at 298K, calculate DG0 for the following reaction:

NH3 (aq) + H2O (l) ® NH4+ (aq) + OH- (aq)

(a) What is the value of DG at equilibrium? (c) What is the value of DG when

(b) [NH3] = 0.10 M, [NH4+] = 0.10 M, and [OH-] = 0.050 M?