18.33 The enthalpy change when liquid methanol, CH3 OH, vaporizes at 25^∘ C is 38.0 kJ / mol. W

step 1 So during the condensation of one molar vapor of methanol to a liquid, the system is always at e

18.33 The enthalpy change when liquid methanol, CH3 OH,...

18.33 The enthalpy change when liquid methanol, $\mathrm{CH}_{3} \mathrm{OH}$, vaporizes at $25^{\circ} \mathrm{C}$ is $38.0 \mathrm{~kJ} / \mathrm{mol}$. What is the entropy change when 1.00 mol of vapor in equilibrium with liquid condenses to liquid at $25^{\circ} \mathrm{C}$ ? The entropy of this vapor at $25^{\circ} \mathrm{C}$ is $255 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K})$. What is the entropy of the liquid at this temperature?

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Key Concepts

Enthalpy Change

Enthalpy change represents the heat absorbed or released during a process at constant pressure. In phase transitions such as vaporization or condensation, the enthalpy change (often called latent heat) quantifies the energy required to overcome intermolecular forces when a substance changes its phase without a temperature change.

Entropy Change

Entropy is a measure of the disorder or randomness in a system. The entropy change during a phase transition reflects how the order of the system changes; for instance, vaporization increases molecular disorder, while condensation decreases it. The relation ?S = ?H/T for reversible processes allows one to link the heat absorbed or released to the change in entropy.

Phase Transition Equilibrium

During a phase transition occurring at equilibrium, such as between vapor and liquid at a boiling or condensation point, the system undergoes a reversible change. This equilibrium state ensures that the thermodynamic properties, like temperature, enthalpy, and entropy, can be interrelated through equilibrium relations, enabling calculations of unknown quantities when others are known.

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