Open Question
Methylamine has a vapor pressure of 344 torr at -25 °C and a boiling point of -6.4 °C. What is the ΔHvap for methylamine?
13. Liquids, Solids & Intermolecular Forces
Clausius-Clapeyron Equation
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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.
A
96 mm Hg
B
48 mm Hg
C
21 mm Hg
D
13 mm Hg
Verified step by step guidance1
Identify the known values: the normal boiling point (T1) is 76°C, the vapor pressure at this temperature (P1) is 760 mm Hg (since it's the boiling point), the temperature of interest (T2) is 29°C, and the enthalpy of vaporization (ΔHvap) is 38.7 kJ/mol.
Convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature. T1 = 76 + 273.15 K and T2 = 29 + 273.15 K.
Use the Clausius-Clapeyron equation to relate the vapor pressures and temperatures: \( \ln \left( \frac{P2}{P1} \right) = -\frac{\Delta H_{vap}}{R} \left( \frac{1}{T2} - \frac{1}{T1} \right) \), where R is the ideal gas constant (8.314 J/mol·K).
Rearrange the equation to solve for P2, the vapor pressure at 29°C: \( P2 = P1 \times \exp \left( -\frac{\Delta H_{vap}}{R} \left( \frac{1}{T2} - \frac{1}{T1} \right) \right) \).
Substitute the known values into the equation and calculate P2. Remember to convert ΔHvap from kJ/mol to J/mol by multiplying by 1000.
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