Question

Calculate the vapour pressure of water at ${27}^{\circ }C$, when the aqueous tension at ${77}^{\circ }C$ is $314.1torr$. (Given: Heat of vapourisation of water is nearly $40kJ/mol$) [$e^{-2.3}=0.1$]

• A. $31.4torr$
• B. $62.8torr$
• C. $94.2torr$
• D. $15.7torr$

Answer 1

The correct option is A $31.4torr$

Given,
$\text{Temperature,}{T}_1={77}^{\circ }C=350K$
$\text{Temperature,}{T}_2={27}^{\circ }C=300K$
Aqueous tension is the vapour pressure of water, thus
$\text{Vapour pressure at}350K,P_1=314.1torr$
$\text{Molar heat of vaporisation of water,}\Delta H=40kJ/mol$

Effect of temperature on the vapour​ pressure of a liquid is given by​ Clausius – Clapeyron equation,
$ln\left(\frac{P_2}{P_1}\right)=\frac{\Delta H}{R}(\frac{1}{T_1}-\frac{1}{T_2})$
Substituting the given values, we get,
$ln\left(\frac{P_2}{314.1}\right)=\left(\frac{40000}{8.314}\right)(\frac{1}{350}-\frac{1}{300})$

$ln\left(\frac{P_2}{314.1}\right)=\left(4811.2\right)\times \left(\frac{-1}{2100}\right)ln\left(\frac{P_2}{314.1}\right)=-2.29\frac{P_2}{314.1}=0.1P_2=31.4torr$
$\text{Vapour pressure of water at}{57}^{\circ }C,P_2=31.4torr$