The vapor pressure of dichloromethane at 260 K is 71 torr. What is the vapor pressure at 310 K, given that ΔHvap = 31.4 kJ/mol?

• A. 350 torr
• B. 450 torr
• C. 250 torr
• D. 150 torr

Answer: (A)

Verified step by step guidance

1. Identify the given values: initial temperature (T1) = 260 K, initial vapor pressure (P1) = 71 torr, final temperature (T2) = 310 K, and enthalpy of vaporization (ΔHvap) = 31.4 kJ/mol.
2. Convert the enthalpy of vaporization from kJ/mol to J/mol by multiplying by 1000, since the Clausius-Clapeyron equation requires energy in joules.
3. Use the Clausius-Clapeyron equation to relate the vapor pressures and temperatures: \( \ln \left( \frac{P2}{P1} \right) = \frac{\Delta H_{vap}}{R} \left( \frac{1}{T1} - \frac{1}{T2} \right) \), where R is the ideal gas constant (8.314 J/mol·K).
4. Rearrange the equation to solve for the final vapor pressure (P2): \( P2 = P1 \times \exp \left( \frac{\Delta H_{vap}}{R} \left( \frac{1}{T1} - \frac{1}{T2} \right) \right) \).
5. Substitute the known values into the equation and calculate the expression to find the vapor pressure at 310 K.