Multiple Choice
Benzene has a heat of vaporization of 30.72 kJ/mol and a normal boiling point of 80.1 °C. At what temperature does benzene boil when the external pressure is 577 mbar?
13. Liquids, Solids & Intermolecular Forces
Clausius-Clapeyron Equation
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The boiling point of liquid A is 75.5 °C at 1 atm (760.0 torr). Its vapor pressure at 15.5 °C is 205 torr. What is its ΔHvap in kJ/mol?
A
45.2 kJ/mol
B
31.5 kJ/mol
C
60.1 kJ/mol
D
52.8 kJ/mol
Verified step by step guidance1
Identify the Clausius-Clapeyron equation, which relates the vapor pressure and temperature to the enthalpy of vaporization: \( \ln \left( \frac{P_2}{P_1} \right) = -\frac{\Delta H_{\text{vap}}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \), where \( P_1 \) and \( P_2 \) are the vapor pressures at temperatures \( T_1 \) and \( T_2 \), respectively, and \( R \) is the ideal gas constant.
Convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature. Thus, \( T_1 = 75.5 + 273.15 \) K and \( T_2 = 15.5 + 273.15 \) K.
Substitute the known values into the Clausius-Clapeyron equation: \( P_1 = 760.0 \) torr, \( P_2 = 205 \) torr, \( T_1 \) and \( T_2 \) in Kelvin, and \( R = 8.314 \) J/mol·K.
Rearrange the equation to solve for \( \Delta H_{\text{vap}} \): \( \Delta H_{\text{vap}} = -R \cdot \frac{\ln \left( \frac{P_2}{P_1} \right)}{\left( \frac{1}{T_2} - \frac{1}{T_1} \right)} \).
Calculate \( \Delta H_{\text{vap}} \) using the rearranged equation and convert the result from J/mol to kJ/mol by dividing by 1000.
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