Question 11.2.5: Use the two-point version of the Clausius–Clapeyron equation......
Use the two-point version of the Clausius–Clapeyron equation.
The vapor pressure of liquid aluminum is 400. mm Hg at 2590 K. Assuming that ΔH_{\text{vap}} for Al (296 kJ/mol) does not change significantly with temperature, calculate the vapor pressure of liquid Al at 2560 K.
You are asked to calculate the vapor pressure of a liquid at a given temperature.
You are given the vapor pressure of the liquid at a different temperature and the enthalpy of vaporization for the liquid.
Use the alternative form of the Clausius–Clapeyron equation (Equation 11.2) along with pressure, temperature, and ΔH_{\text{vap}} data to calculate the vapor pressure of aluminum at 2560 K.
P_{1} = 400. mm Hg T_{1} = 2590 K
P_{2} = ? T_{2} = 2560 K
ΔH_{\text{vap}} = 296 kJ/mol
\ln\frac{P_{2}}{400. \text{mm Hg}} =\frac{-\left(296\text{ kJ/mol}\right) }{8.3145 \times 10^{-3} \text{kJ/K} \cdot \text{mol}} \left(\frac{1}{2560\text{ K}}-\frac{1}{2590\text{ K}} \right)\ln (P_{2}) – \ln (400. mm Hg) = -0.1611
\ln (P_{2})= 5.830
P_{2} = e^{5.830} = 340. mm Hg
Is your answer reasonable? Notice that the vapor pressure has decreased because the temperature decreased (T_{2} < T_{1}).