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19 Chemical Thermodynamics Solutions to Exercises 19.26 (a) Ga(I) Ga(s), is negative, less motional freedom (b) = Ga Ga Ga Ga = 4.81046 = 19.27 (a) For a spontaneous process, the entropy of the universe increases; for a reversible process, the entropy of the universe does not change. (b) In a reversible process, + = 0. If is positive, must be negative. (c) Since Suniv must be positive for a spontaneous process, must be greater than -42J/K. 19.28 (a) For a spontaneous process, Suniv > 0. For a reversible process, Suniv = 0. (b) is positive and greater than the magnitude of the decrease in (c) 19.29 Analyze. Consider for the isothermal expansion of 0.200 mol of an ideal gas at 27°C and an initial volume of 10.0 L. (a) Whenever an ideal gas expands isothermally, we expect an increase in entropy, or positive S, owing to the greater volume available for motion of the particles. (b) Plan. Use the relationship = nR Equation [19.3]. Solve. = 0.200 L/10.0 = 1.02 J/K. Check. We expect S to be positive when the motional freedom of a gas increases, and our calculation agrees with this prediction. (c) The temperature at which the expansion occurs is not needed to calculate the entropy change, as long as the process is isothermal. 19.30 (a) According to Boyle's law, pressure and volume are inversely proportional at constant amount and temperature. If the pressure of an ideal gas increases, volume decreases. We expect a decrease in entropy, or negative S, for the isothermal compression of an ideal gas, owing to the smaller volume available for motion of the particles. (b) According to Boyle's law, P₁ V₁ = at constant n and T. 0.750 atm V₁ = 1.20 atm V₂; V₂/V₁ = 0.750 atm/1.20 atm = 0.62500 = 0.625 = nR In (V₂/V₁) = 0.600 mol = -2.34 Check. An increase in pressure results in a decrease in volume at constant T, so we expect to be negative, and it is. (c) The temperature at which the compression (increase in pressure, decrease in volume) occurs is not needed to calculate the entropy change, as long as the process is isothermal. 582