Consider the following liquid-vapour equilibrium. Liquid Vapour W… - Vidyadip

MCQ

Consider the following liquid-vapour equilibrium.

Liquid $\rightleftharpoons $ Vapour

Which of the following relations is correct ?

A
$\frac{{d\,\ln \,P}}{{d{T^2}}}\, = \,\frac{{ - \Delta {H_v}}}{{{T^2}}}$
✓
$\frac{{d\,\ln \,P}}{{d{T}}}\, = \,\frac{{ \Delta {H_v}}}{{{RT^2}}}$
C
$\frac{{d\,\ln \,G}}{{d{T^2}}}\, = \,\frac{{ \Delta {H_v}}}{{{RT^2}}}$
D
$\frac{{d\,\ln \,P}}{{d{T}}}\, = \,\frac{{ - \Delta {H_v}}}{{{RT}}}$

✓

Answer

Correct option: B.

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

b
According to Clausius Claperon equation

$P=A e^{\frac{-\Delta M}{I R T}}$

$\ln P=\ln A+\ln e \frac{-\Delta M}{\operatorname{Irr}} \Rightarrow \ln p=\ln A-\frac{\Delta H}{R T} \ln e$

or $\ln p=\ln A-\frac{\Delta H}{R T}$

$\frac{d}{d T}(\ln P)=0+\frac{-\Delta H}{R} \frac{d}{d T}\left(T^{-1}\right)$

$\frac{d}{d T} \ln P=\frac{\Delta H v}{R T^{2}}$

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