Chapter 11, Problem 11.57SP

Interpretation Introduction

Interpretation:

Use any two temperatures and their corresponding vapour pressures from the given table to calculate $△H_{vap}$ for mercury in kJ/mol and compare the result with the value read from the plot in Problem 11.55.

Concept Introduction:

Vapour pressure is the pressure that is exerted on the walls of a sealed container when a substance in it gets into a gaseous state. To find the vapour pressure at a given temperature, the Clausius-Clapeyron equation is used. We can use the Clausius-Clapeyron equation to construct the entire vaporization curve.

The Clausius-Clapeyron equation is as follows:

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

where

R = Real gas constant or 8.314 J/(k.mol)
T₁=The temperature at which the vapour pressure is known
T₂= The temperature at which the vapour pressure is to be found
P₁ =The vapour pressures at the temperature T1
P₂ =The vapour pressures at the temperature T2
△H_vap= The enthalpy of vaporization of the mercury.

Given:

R= 8.314 J/(K.mol), P₁=39.3 mm Hg, P₂=68.5 mm Hg, ln P₁=3.6712, ln P₂=4.2268, T₁=500 K, T₂=520 K