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

Question

Consider the following liquid-vapour equilibrium.

Liquid $\rightleftharpoons$ Vapour

Which of the following relations is correct?

(a) ${d \ln P \over dT^2}={-\Delta H_v \over T^2}$

(b) ${d \ln P \over dT}={\Delta H_v \over RT^2}$

(c) ${d \ln G \over dT^2}={\Delta H_v \over RT^2}$

(d) ${d \ln P \over dT}={-\Delta H_v \over RT}$

Answer 1

Ans: (b) ${d\ln P \over dT}={ΔH_v \over RT^2}$

Sol: This is Clausius$-$Clapeyron equation.

Answer 2

P=Ae^-ΔH_v/RT 

lnP = lnA - ΔH_v/RT

d (lnP)/dT = 0 -ΔH_v/RTdT 

d (lnP) /dT = [-ΔH_v/R] (T^-1)/dT

d (lnP) /dT = ΔH_v/RT²

Ans : (B) 

This is "Clausius-Clapeyron Equation".