Multiple Choice
Determine the vapor pressure (in mm Hg) of a substance at 29°C, whose normal boiling point is 76°C and has a ΔHvap of 38.7 kJ/mol.
13. Liquids, Solids & Intermolecular Forces
Clausius-Clapeyron Equation
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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
Verified step by step guidance1
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.
Convert the enthalpy of vaporization from kJ/mol to J/mol by multiplying by 1000, since the Clausius-Clapeyron equation requires energy in joules.
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).
Rearrange the equation to solve for the final vapor pressure (P2): \( P2 = P1 \times \exp \left( \frac{\Delta H_{vap}}{R} \left( \frac{1}{T1} - \frac{1}{T2} \right) \right) \).
Substitute the known values into the equation and calculate the expression to find the vapor pressure at 310 K.
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