19.1 Explain what is meant by a spontaneous process. Give two examples each
of spontaneous and nonspontaneous processes.
19.2 Which of the following processes are spontaneous and which are nonspontaneous?
(a) dissolving table salt (NaCl) in hot soup; (b) climbing Mt. Everett; (c) spread-
ing fragrance in room by removing the cap from a perfume bottle; (d) separating
235UF6 from 238UF6 by gaseous effusion (see Section 5.8).
19.5 Define entropy. What the units of entropy?
19.6 How does the entropy of a system change for each of the following processes?
(a) A solid melts.
(b) A liquid freezes.
(c) A liquid boils.
(d) A vapor is converted to a solid.
(e) A vapor condenses to a liquid.
(f) A solid sublimes.
19.10 Using the data in Appendix 3, calcultae the standard entropy change for the following
reactions at 25ºC:
(a) S(s) + O2(g) Æ SO2(g)
(b) MgCO3(s) Æ MgO(s) + CO2(g)
(c) H2(g) + CuO(s) Æ Cu(s) + H2O(g)
(d) 2Al(s) + 3ZnO(s) Æ Al2O3(s) + 3Zn(s)
(e) CH4(g) + 2O3(g) Æ CO2(g) + 2H2O(l)
19.12 Discuss qualitatively the sign of the entropy change expected for each of the
following processes.
(a) PC13(l) + Cl2(g) Æ PCl5(s)
(b) 2HgO(s) Æ 2Hg(l) + O2(g)
(c) H2(g) Æ 2H(g)
(d) U(s) = 3F2(g) Æ UF6(s)
19.13 Predict whether the entropy change is positivbe or negative for each of the
following reactions:
(a) Zn(s) + 2HCl(aq) Æ ZnCl2(aq) + H2(g)
(b) O(g) + O(g) Æ O2(g)
(c) NH4NO3(s) Æ N2O(g) + 2H2O(g)
(d) Ba2+(aq) + SO42-(aq) Æ BaSO4(s)
(e) 2H2O2(l) Æ 2H2O(l) + O2(g)
19.14 The reaction NH3(g) + HCl(g) Æ NH4CL(s) proceeds spontaneously at
25ºC even though there is a decrease in disorder in the system (gases re
converted to a solid). Explain.
19.15 Define free energy. What are its units?
19.19 Calculate DGº for the combustion of ethane:
2C2H6(g) + 7O2(g)
4CO2(g) + 6H2O(l)See tables for thermodynamic data.
19.20 From the following DH and DS values, predit whether each of the reactions
would be spontaneous at 25ºC. If not, at what temperature might the
reaction become spontaneous? Reaction A:DH = 10.5 kJ, DS = 30 J/K;
Reaction B:DH = 1.8 kJ, DS = -113 J/K; Reaction C: DH = -26 kJ,
DS = 84 J/K; Reaction D: DH = -11.7 kJ, DS = -105 J/K.
19.21 The molar heat of vaporization of ethanol is 39.3 kJ/mol and the boiling point
of ethanol is 78.3ºC. Calculate DS for the vaporization of 0.50 mol ethanol.
19.23 A certain reaction is known to have a DGº value of -122 kJ. Will the reaction
necessarily occur if the reagents are mixed together?
19.25 Explain clearly the difference between DG and DGº.
19.26 For the reaction
H2(g) + I2(g)
2HI(g)DGº = 2.60 kJ. Calculate Kp for the reaction at 25ºC.
19.28 Consider the following reaction at 25ºC:
Fe(OH)2(s) Fe2+(aq) + 2OH-(aq)
Calculate DGº for the reaction. Ksp for Fe(OH)2 is 1.6 x 10-14.
19.30 Calculate Kp for the following reaction at 25ºC:
N2(g) + O2(g) 2NO(g)
From your result, what can you conclude about the stability of a mixture
of O2 and N2 gases in the atmosphere?
19.33 (a) Calculate DGº and Kp for the following equilibrium reaction at 25ºC.
The DGºf values are, for Cl2(g), 0; for PCl3(g), -286 kJ/mol; and for PCl5(g),
-325 kJ/mol.
PCl5(g) PCl3(g) + Cl2(g)
(b) Calculate DG for the reaction if the partial pressures of the initial mixture
are PPCl5 = 0.0029 atm, PPCl3 = 0.27 atm, and PCL2 = 0.40 atm.
19.43 Predict the signs of DH, DS, and DG of the system for the following processes
at 1 atm: (a) ammonia melts at -60ºC, (b) ammonia melts at -77.7ºC, (c)
ammonia melts at -100ºC. (The normal melting point of ammonia is -77.7ºC.)
19.46 Ammonium nitrate dissolves spontaneously and endothermically in water.
What can you deduce about the sign of DS for the solution process?
19.48 Consider the following facts: Water freezes spontaneously at -5ºC and 1 atm,
and ice has a more ordered structure than liquid water. Explain how a
spontaneous process can lead to a decrease in entropy.
19.51 (a) Trouton's rule states that the ratio of the molar heat of vaporization of a
liquid (DHvap) to its boiling point in kelvins is approximately 90 J/K o mol.
Show that this is the case with the following data:
tbp(ºC) DHcap(kJ/mol)
Benzene 80.1 31.0
Hexane 68.7 30.8
Mercury 357 59.0
Toluene 110.6 35.2
and explain why this rule holds true. (b) Use the values in Table 11.6 to calculate
the same ratio for ethanol and water. Explain why Trouton's rule does not apply
to these two substances as well as it does to other liquids.
19.52 Referring to the above problem, explain why the ratio is considerably smaller
than 90 J/K o mol for the HF liquid.
19.58 Water gas is a fuel made by reacting steam with red-hot coke (coke is the product
of coal distillation):
H2O(g) + C(s) Æ CO(g) + H2(g)
From the data in Appendix 3, estimate the temperature at which the reaction
becomes favorable.
19.64 The internal engine of a car of mass 1200 kg is designed to run on octane
(C8H18), whose enthalpy of combustion is 5510 kJ/mol. Calculate the
maximum height (in meters) to which the car can be driven on 1.0 gallon of the
fuel. Assume that the engine cylinder temperature is 2200ºC and the exit
temperature is 760ºC and neglect all forms of friction. The mass of 1 gallon
of fuel is 3.1 kg. [Hint: See the Chemistry in Action essay on p. 745. The
work done in moving the car over a vertical distance is mgh, where m is the
mass of the car in kg, g the acceleration due to gravity (9.81 m/s2), and h
the height in meters.]