Question

The vapour pressure of a liquid at $500\text{K}$ is $150\text{torr}$. The vapour pressure in torr, at $1000\text{K}$ if the enthalpy of vapourisation of the substance is $4.157{\text{k J mol}}^{-1}$. (Given $e^{0.5}=1.65$) is

Answer 1

Effect of temperature on the vapour pressure of a liquid is given by Clausius – Clapeyron equation.

$\ln \left(\frac{P_2}{P_1}\right)=\frac{\Delta H}{R}(\frac{1}{T_1}-\frac{1}{T_2})$

where,

$\Delta H\text{is the enthalpy of vapourisation}=4.157\times {10}^{3}Jmo{l}^{-1}{P}_1\text{is the vapour pressure of the liquid at temperature}{T}_1=500K{P}_2\text{is the vapour pressure of the liquid at temperature}{T}_2=1000K$

Puting the values:

$\ln \left(\frac{P_2}{150}\right)=\frac{4.157\times {10}^3}{8.314{\text{J mol}}^{-1}{\text{K}}^{-1}}\times (\frac{1}{500}-\frac{1}{1000})$

$\ln \left(\frac{P_2}{150}\right)=\frac{1}{2}$

$\frac{P_2}{150}=e^{0.5}{P}_2=(1.65\times 150)\text{torr}{P}_2=247.5\text{torr}$