If the exact enthalpy change for the equilibrium phase transition of liquid water to steam ($\mathrm

Question

If the exact enthalpy change for the equilibrium phase transition of liquid water to steam ($\mathrm{H}_2\mathrm{O}_{(l)} ightleftharpoons \mathrm{H}_2\mathrm{O}_{(v)}$) is accurately measured as $+40 	ext{ kJ mol}^{-1}$ at $373 	ext{ K}$, what is the corresponding entropy change ($\Delta S$) for this specific process?

Professor PC Thomas Classes · Answer

(a) : During any reversible phase transition at its normal transition temperature (in this case, the normal boiling point), the two phases exist in dynamic equilibrium. Therefore, the Gibbs free energy change is strictly zero ($\Delta G = 0$). Applying the Gibbs equation: $\Delta G = \Delta H - T\Delta S \implies 0 = \Delta H - T\Delta S \implies \Delta S = \frac{\Delta H}{T}$. Substituting values: $\Delta S = \frac{40000 	ext{ J mol}^{-1}}{373 	ext{ K}} \approx 107.24 	ext{ J K}^{-1} 	ext{ mol}^{-1}$.