Question

Consider the following liquid-vapour equilibrium Liquid $\rightleftharpoons$ Vapour
Which of the following relations is correct ?

• A. $ \frac{d \, In \, P}{dT} = \frac{ - \Delta H_v}{RT}$
• B. $ \frac{d \, In \, P}{dT^2} = \frac{ - \Delta H_v}{T^2}$
• C. $ \frac{d \, In \, P}{dT} = \frac{ \Delta H_v}{RT^2}$
• D. $ \frac{d \, In \, G}{dT^2} = \frac{ \Delta H_v}{RT^2}$

Answer 1

Answer: (C)

Acc. To Clausius Claperon equation
$P = Ae^{\frac{-\Delta H}{RT}} $
$ l n P = l n A + ln e^{\frac{-\Delta H}{RT}} \Rightarrow lnp = lnA - \frac{\Delta H}{RT} lne$
or $ lnp = lnA - \frac{\Delta H}{RT} $
$ \frac{d}{dT} \left(ln P\right) = 0 + \frac{-\Delta H}{R} \frac{d}{dT} \left(T^{-1}\right) $
$\frac{d}{dT} lnP = \frac{\Delta H_{V}}{RT^{2}} $