1. dln G/dT² = Δ H_v/RT² 2. dln P/dT = -Δ H_v/RT 3. dln P/dT² = -Δ H_v/T² 4. dln P/dT = Δ H_v/RT²

Topic: Gibbs energy change and equilibrium constant· Chemical Thermodynamics

Consider the following liquid - vapour equilibrium.Liquid ⇌ VapourWhich of the following relations is correct ?

1. $\frac{d\ln G}{dT^2} = \frac{\Delta H_v}{RT^2}$

2. $\frac{d\ln P}{dT} = \frac{-\Delta H_v}{RT}$

3. $\frac{d\ln P}{dT^2} = \frac{-\Delta H_v}{T^2}$

4. $\frac{d\ln P}{dT} = \frac{\Delta H_v}{RT^2}$

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Answer: 4. $\frac{d\ln P}{dT} = \frac{\Delta H_v}{RT^2}$

Key idea: this is the Clausius-Clapeyron equation for liquid-vapour equilibrium:

$$\frac{d\ln P}{dT}=\frac{\Delta H_v}{RT^2}$$

Vapour pressure rises with temperature, so the derivative must be positive. Options 2 and 3 have a negative sign, and option 1 uses $G$ instead of the vapour pressure P. So option 4.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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Consider the following liquid - vapour equilibrium.Liquid ⇌ VapourWhich of the following relations is correct ?

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