Chloroform, \(\mathrm{CHCl}_{3}\), was once used as an anesthetic. In spy movies it is the liquid put in handkerchiefs to render victims unconscious. Its vapor pressure is \(197 \mathrm{~mm} \mathrm{Hg}\) at \(23^{\circ} \mathrm{C}\) and \(448 \mathrm{~mm} \mathrm{Hg}\) at \(45^{\circ} \mathrm{C}\). Estimate its (a) heat of vaporization. (b) normal boiling point.

To work with the temperatures in the Clausius-Clapeyron equation, we need to convert them to Kelvin. Add 273.15 to the Celsius temperatures: \(T_1 = 23^{\circ} \mathrm{C} + 273.15 = 296.15 \mathrm{K}\) \(T_2 = 45^{\circ} \mathrm{C} + 273.15 = 318.15 \mathrm{K}\)

Rearrange the Clausius-Clapeyron equation to solve for the heat of vaporization: \(L = -R(\frac{\ln(\frac{P_2}{P_1})}{\frac{1}{T_2} - \frac{1}{T_1}})\) Input the given values for vapor pressures, temperatures, and the gas constant \(R = 8.314 \mathrm{J/(mol \cdot K)}\): \(L = -8.314 \frac{\ln(\frac{448}{197})}{\frac{1}{318.15} - \frac{1}{296.15}}\) Calculate the heat of vaporization: \(L \approx 29570 \mathrm{J/mol}\) (a) The heat of vaporization of chloroform is approximately \(29.57 \mathrm{kJ/mol}\).

The normal boiling point is the temperature at which the vapor pressure of a liquid equals the atmospheric pressure. In this case, we will use 760 mm Hg as the atmospheric pressure. Rearrange the Clausius-Clapeyron equation to solve for the boiling point temperature: \(T_2 = \frac{1}{\frac{1}{T_1} -\frac{R}{L}\ln(\frac{P_2}{P_1})}\) Use the previously calculated heat of vaporization, \(L \approx 29570 \mathrm{J/mol}\), and plug in the values: \(T_2 = \frac{1}{\frac{1}{296.15} -\frac{8.314}{29570}\ln(\frac{760}{197})}\) Calculate the boiling point temperature in Kelvin: \(T_2 \approx 334.5 K\) Now convert the temperature to Celsius: \(T_2 = 334.5 - 273.15 = 61.35^{\circ} \mathrm{C}\) (b) The normal boiling point of chloroform is approximately \(61.35^{\circ} \mathrm{C}\).