15. Thermodynamics II Problems

Thermo II Problems

Michael Mombourquette

Thermodynamics and Equilibrium Problems

1. Which of the following processes would result in a decrease in the entropy of the system:

  1. boiling water to form steam;
  2. isothermal compression of a gas from 100 kPa to 300 kPa;
  3. mixing two gases in a container;
  4. freezing of water to form ice;
  5. cooling ice from 0℃ to −50℃.

2. Calculate the entropy change \Delta S of 50.0 g of water when it is heated from 25.0℃ to 35.0℃ at atmospheric pressure.

[6.90 J/K]

3. A piece of copper metal of mass 20.0 g at a temperature of 100.0℃ is dropped into 100.0 g of water at a temperature of 10.2℃ contained in a Dewar flask.  If the heat capacity of the Dewar flask is 10. J K−1, calculate the final temperature of the system, and the entropy changes of the copper, the water plus Dewar and of the universe.

[11.6℃, -2.08 J/K, +2.31 J/K, +0.23 J/K]

4. A sample of 2.0 dm3 of ethane gas, C2H6, at 100 kPa and 30.0℃ is compressed isothermally to a volume of .20 dm3, and then cooled to 0.0℃ at constant pressure.  Calculate the final pressure and entropy change of the qhole process, assuming that ethane is an ideal gas.

[901 kPa, -1.95 J/k]

5. For the decomposition of ammonium chloride, calculate Delta G and K at 25℃, and the equilibrium constant at 100.℃
NH4Cl(s) \rightleftarrows NH3(g) + HCl(g)

[+91.12 kJ/mol, 101×10-16, 1.7×10-16 ]

6. Calculate \Delta S^\circ and  \Delta G^\circ for the following reactions at 25℃.

  1. N2(g) + O2(g) → 2 NO(g)                             [+24.77 J/K.mol, +173.10 kJ/mol]
  2. 3O2(g) → 2O3(g)                                           [-137.55 J/K.mol, +326.4 kJ/mol]
  3. SO2(g) + 1/2 O2(g) → SO3(g)                       [-94.03 J/K.mol, -70.89 kJ/mol]
  4. N2(g) + 3H2(g) → 2NH3(g)                          [-198.76 J/K.mol, -32.90 kJ/mol]
  5. CH4(g) + 1/2 O2(g) → CH3OH(\ell)                [-162.0 J/K.mol, -155.55 kJ/mol]

7. From K_a of propanoic acid, Calculate \Delta G^\circ at 25℃ for the reaction
C2H5COOH(aq) \rightleftarrows H+(aq) + CH3COO–(aq)

[+27.7 kJ/mol]

8. From thermodynamic data tables, calculate \Delta G^\circ and K_b for ammonia at 25℃ for the reaction
NH3(aq) + H2O(\ell) \rightleftarrows NH4+(aq) + OH–(aq)

[+27.08 kJ/mol, 1.8×10-5 ]

9.  From thermodynamic data tables, calculate  \Delta G^\circ and   \Delta H^\circ at 25℃ for the reaction
H2O(\ell) \rightleftarrows H+(aq) + OH–(aq)
and hence, K_w for water at 25℃ and at 100℃ .

[+79.89 kJ/mol, +55.84 kJ/mol, 1.0×10-14, 9.2×10-13 ]

10. The Henry’s Law Constants (Found in Liquid and Solid Solution phase changes) are all large, and increase as the temperature increases. What does this imply for the signs of each of the Gibbs energy change of solution, the enthalpy change of solution and the entropy change of solution for these gases?

11. Calculate \Delta G^\circ and \Delta H^\circ for the dissolving of O2 gas in water at 25℃ from the Henry’s Law Constants and its temperature dependence.  Compare your answers with the data given in the thermodynamic data tables (appendix 5).

[+16.6 kJ/mol, -12.2 kJ/mol]

12. Calculate and compare the standard molar entropy changes for the following two processes at 25℃: (a) the condensation of water vapour to form liquid water, and (b) the dissolving of oxygen gas in liquid water.

[-118.91 J/K.mol, -94.2 J/K.mol]

13. From the Thermodynamic data, calculate the solubility product for barium sulfate at 25℃, and compare with the data in the Solubility data: 

    \[\mathrm{BaSO_4(s) \rightleftarrows \mathrm{Ba^{2+}(s)\;+\;SO_4^{2-}(aq)}}\]

[1.1×10-10]

14. From the Thermodynamic data, and your answer to the previous question, calculate the solubility product for barium sulfate at 80℃.

[5.7×10-10]

15. From the Thermodynamic data, calculate K for the water gas reaction at 25℃ and 1000. ℃.
C(s) + H2O(g) \rightleftarrows CO(g) + H2(g)
note that because the temperature range is so wide, the result of the calculation using the van’t Hoff equation will not be very accurate.

[9.8×10-17, 40.]

16. Calculate the vapour pressure of n-hexane at 25 ℃ from the Thermodynamic data.

[19.8 kPa]

17. Calculate the boiling point of n-hexane at a pressure of 100.0 kPa from the  Thermodynamic data. and compare with the data in The table of boiling points and Enthalpy of vaporization.

[341.6 K or 68.4℃]

18. At temperatures in the neighborhood of 25 ℃, the vapour presure of solid benzoic acid ahs been found to follow the relationship ln\frac{P}{P^\circ}=a-\frac{b}{T}, where a = 22.88 and b = 1.07\times10^4 K. Calculate \Delta H^\circ, \Delta G^\circ, and \Delta S^\circ for the sublimation of benzoic acid.

[89.0 kJ/mol, 32.2 kJ/mol, 190 J/mol.K]

19. It can be claimed tha tall oxides of nitrogen are thermodynamically unstable with respect ot decomposition into the elements. Explain why this is so by reference to the Thermodynamic data.

20. What is the relationship between the pKa of an acid and the standard Gibbs energy of ionization of the acid in aqueous solution?

21. Calculate \Delta G^\circ and \Delta H^\circ for the explosive decomposition of ammonium nitrate and lead azide.  Explain why these substances are explosives.  Can you come up with a general statement that might explain explosives?

[-273.27 kJ/mol. -118.08 kJ/mol]

 

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