Chapter 15, Problem 15.157QP

(a) Use the van’t Hoff equation in Problem 15.146 to derive the following expression, which relates the equilibrium constants at two different temperatures:

$\ln \frac{k_1}{k_2}=\frac{\Delta H^{\circ }}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$

How does this equation support the prediction based on Le Châtelier’s principle about the shift in equilibrium with temperature? (b) The vapor pressures of water are 31.82 mmHg at 30°C and 92.51 mmHg at 50°C. Calculate the molar heat of vaporization of water.