Practice Problems Thermodynamics

1. Why is the entropy change in a system not always a reliable predictor of whether the process producing the change is spontaneous?

2. How does the equilibrium constant K_eq resemble, and how does it differ from, K_c and K_p?

3. For each of the following reactions, indicate whether you would expect the entropy of the system to increase or decrease. If you cannot tell by inspecting the equation, explain why.

(a) CH₃OH(l) → CH₃OH(g)

(b) N₂O₄(g) → 2 NO₂(g)

(c) CO(g) + H₂O(g) → CO₂(g) + H₂(g)

(d) 2 KClO₃(s) → 2 KCl(s) + 3 O₂(g)

(e) CH₃COOH(l )→ CH₃COOH(s)

(f) N₂(g) + O₂(g) → 2 NO(g)

(g) N₂H₄(l) → N₂(g) + 2 H₂(g)

(h) 2 NH₃(g) + H₂SO₄(aq) → (NH₄)₂SO₄(aq)

4. Based on a consideration of entropy changes, why is it so difficult to eliminate environmental pollution such as the contamination of groundwater with water-soluble methyl tert-butyl ether?

5. Would you expect each of the following reactions to be spontaneous at low temperatures, high temperatures, all temperatures, or not at all? Explain.

(a) PCl₃(g) + Cl₂(g) → PCl₅(g) ΔH° = –87.9 kJ

(b) 2 NH₃(g) → N₂(g) + 3 H₂(g) ΔH° = +92.2 kJ

(c) 2 N₂O(g) → 2 N₂(g) + O₂(g) ΔH° = –164.1 kJ

(d) H₂O(g) + ½O₂(g) → H₂O₂(g)ΔH° = +105.5 kJ

(e) CH₄(g) + O₂(g) → CO₂(g) + 2 H₂O(g)ΔH° = –802.3 kJ

(f) 2 CO(g) + O₂(g) → 2 CO₂(g)ΔH° = –566.0 kJ

6. Use the data from the Table of Thermodynamic Quantities to determine ΔG° values for the following reactions at 25 °C.

(a) C₂H₄(g) + H₂(g) → C₂H₆(g)

(b) SO₃(g) + CaO(s) → CaSO₄(s)

7. Use the data from the Table of Thermodynamic Quantities to determine ΔH° and ΔS°, at 298 K, for the following reaction. Then determine ΔG° in two ways, and compare the results.

CS₂(l) + 3 O₂(g) → CO₂(g) + 2 SO₂(g)

8. Use data from the Table of Thermodynamic Quantities to determine ΔH° and ΔS°, at 298 K, for the following reaction. Then determine ΔG° in two ways and compare the results.

C(graphite) + H₂O(g) → CO(g) + H₂(g)

9. Estimate the normal boiling of heptane, C₇H₁₆, given that at this temperature ΔH°_vapn = 31.69 kJ/mol.

10. The normal boiling point of Br₂(l) is 59.47 °C. Estimate ΔH°_vapn of bromine. Compare your result with a value based on data from the Table of Thermodynamic Quantities.

11. Write K_eq expressions for the following reactions. Which, if any, of these expressions correspond to equilibrium constants that we have previously denoted as K_c, K_p, K_a, and so on?

(a) 2 NO(g) + O₂(g) → ← 2 NO₂(g)

(b) MgSO₃(s) → ← MgO(s) + SO₂(g)

(c) HCN(aq) + H₂O(l) → ← H₃O⁺(aq) + CN^–(aq)

12. Use the data from the Table of Thermodynamic Quantities to determine K_p at 298 K for these reactions.

(a) 2 SO₂(g) + O₂(g) → ← 2 SO₃(g)

(b) CH₄(g) + 2 H₂O(g) → ← CO₂(g) + 4 H₂(g)

13. Use data from the Table of Thermodynamic Quantities to determine K_p at 298 K for these reactions.

(a) 2 N₂O(g) + O₂(g) → ← 4 NO(g)

(b) 2 NH₃(g) + 2 O₂(g) → ← N₂O(g) + 3 H₂O(g)

14. The thermodynamic data listed below are for 298 K. Use these data and data from the Table of Thermodynamic Quantities to determine K_eq at 45 °C for the reaction

CO₂(g) + SF₄(g) → ← CF₄(g) + SO₂(g)

 ΔH_f°, kJ/mol S°, J mol^–1 K^–1

SF₄(g) –763 299.6

CF₄(g) –925 261.6

15. The following reaction is carried out on an industrial scale for the production of thionyl chloride, a chemical used in the manufacture of pesticides.

SO₃(g) + SCl₂(l) → ← OSCl₂(l) + SO₂(g)

The thermodynamic data listed below are for 298 K. Use these data and data from the Table of Thermodynamic Quantities to determine the temperature at which K_eq = 1.0×10¹⁵ for the reaction.

 ΔH_f°, kJ/mol S°, J mol^–1 K^–1

SCl₂(l) –5.0 184

OSCl₂(l) –245.6 121

16. On several occasions, we have made the assumption that ΔH° and ΔS° undergo little change with temperature. Why can we not make the same assumption about ΔG°? If we assume that ΔH°₂₉₈ and ΔS°₂₉₈ do not change with temperature, is it possible for a reaction that is nonspontaneous under standard-state conditions to become spontaneous both at some higher temperature and some lower temperature? Explain.

17. Following are values of K_p at different temperatures for the reaction, 2 SO₂(g) + O₂(g) → ← 2 SO₃(g).

At 800 K, K_p = 9.1×10²; at 900 K, K_p = 4.2×10¹; at 1000 K, K_p = 3.2; at 1100 K, K_p = 0.39; and at 1170 K, K_p = 0.12. Construct a plot to determine ΔH° for this reaction.

18. Use thermodynamic data to determine K_eq for the following reaction

Mg(OH)₂(s) + 2 NH₄⁺(aq) → ← Mg²⁺(aq) + 2 NH₃(aq) + 2 H₂O(l)

Then obtain K_eq from other tabulated equilibrium constants and compare the results.

19. Use thermodynamic data to obtain a value of K_sp for Ag₂SO₄, and compare your result with the one found in the table of solubility product constants.

Answers