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

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

Sol: This is Clausius$-$Clapeyron equation.
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P=Ae-ΔHv/RT 

lnP = lnA - ΔHv/RT

d (lnP)/dT = 0 -ΔHv/RTdT 

d (lnP) /dT = [-ΔHv/R] (T-1)/dT

d (lnP) /dT = ΔHv/RT2

Ans : (B) 

This is "Clausius-Clapeyron Equation".

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