Question

Given the values of AH and AS, which of the following changes will be spontaneous at constant T and P? (Select all that apply.)

a) AH=+25 kJ, AS = +6.0 J/K, T=300. K
b) AH=-10. KJ, AS = +4.0 J/K, T=281 K
c) AH=-10. KJ, AS=-40. J/K, T=100. K
d) AH = +24 kJ, AS = +100. J/K, T=300. K
e) None of the above.

Answer 1

Options (b), (c), and (d) represent changes that will be spontaneous at constant temperature and pressure because they result in a negative Gibbs free energy change. Option (a) is not spontaneous because the Gibbs free energy change is positive. Therefore, the correct options are (b), (c), and (d).

Step-by-step explanation:

To determine whether the changes given in the options provided will be spontaneous at constant temperature (T) and pressure (P), we must look at the sign of the Gibbs free energy change (ΔG). The standard free energy change is calculated using the formula ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, ΔS is the change in entropy, and T is the temperature in Kelvin. For a process to be spontaneous, ΔG should be negative.

• For option (a), ΔG = 25 kJ - (300 K)(0.006 kJ/K) = 25 kJ - 1.8 kJ = 23.2 kJ, which is positive, so it is not spontaneous.
• For option (b), ΔG = -10 kJ - (281 K)(0.004 kJ/K) = -10 kJ - 1.124 kJ = -11.124 kJ, which is negative, so it is spontaneous.
• For option (c), ΔG = -10 kJ - (100 K)(-0.04 kJ/K) = -10 kJ + 4 kJ = -6 kJ, which is negative, so it is spontaneous.
• For option (d), ΔG = 24 kJ - (300 K)(0.1 kJ/K) = 24 kJ - 30 kJ = -6 kJ, which is negative, so it is spontaneous.
• Option (e) is incorrect because options (b), (c), and (d) are spontaneous changes.