Question

A liquid at $500K$ has a vapour pressure of $200torr$. Calculate the vapour pressure at $1000K$ if the enthalpy of vapourisation of the substance is nearly $8.314kJmo{l}^{-1}$

• A. $382.9torr$
• B. $220.1torr$
• C. $897.4torr$
• D. $543.6torr$

Answer 1

The correct option is D $543.6torr$

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,

$\Delta H\text{is the enthalpy of vapourisation}=8.314\times {10}^{3}Jmo{l}^{-1}{P}_1\text{is the vapour pressure of the liquid at temperature}{T}_1=500K{P}_2\text{is the vapour pressure of the liquid at temperature}{T}_2=1000K$

Puting the values:

$\ln \left(\frac{P_2}{200}\right)=\frac{8.314\times {10}^3}{8.314Jmo{l}^{-1}{K}^{-1}}\times (\frac{1}{500}-\frac{1}{1000})$

$\ln \left(\frac{P_2}{200}\right)=1$

$\frac{P_2}{200}=e^1{P}_2=(e\times 200)torr{P}_2\approx 543.6torr$