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?

Verified step by step guidance

1. Identify the Clausius-Clapeyron equation: \( \ln \left( \frac{P_1}{P_2} \right) = \frac{\Delta H_{\text{vap}}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \), 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.
2. Convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature. Thus, \( T_1 = -25 + 273.15 \) K and \( T_2 = -6.4 + 273.15 \) K.
3. Recognize that at the boiling point, the vapor pressure \( P_2 \) is equal to 1 atm (or 760 torr). Therefore, \( P_1 = 344 \) torr and \( P_2 = 760 \) torr.
4. Substitute the known values into the Clausius-Clapeyron equation: \( \ln \left( \frac{344}{760} \right) = \frac{\Delta H_{\text{vap}}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \).
5. Solve for \( \Delta H_{\text{vap}} \) by rearranging the equation: \( \Delta H_{\text{vap}} = R \cdot \ln \left( \frac{344}{760} \right) \cdot \left( \frac{1}{T_2} - \frac{1}{T_1} \right)^{-1} \).

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It reflects the tendency of particles to escape from the liquid phase into the gas phase. Higher vapor pressure indicates a greater number of molecules escaping into the vapor phase, which is crucial for understanding the boiling point and the enthalpy of vaporization.

Boiling Point

The boiling point of a substance is the temperature at which its vapor pressure equals the external pressure surrounding the liquid. At this point, the liquid transitions to a gas. For methylamine, the boiling point of -6.4 °C indicates the temperature at which it can vaporize under standard atmospheric pressure, providing insight into its physical properties and behavior.

Enthalpy of Vaporization (ΔHvap)

The enthalpy of vaporization (ΔHvap) is the amount of energy required to convert a unit mass of a liquid into vapor at constant temperature and pressure. It is a critical thermodynamic property that can be calculated using the Clausius-Clapeyron equation, which relates vapor pressure and temperature, allowing for the determination of ΔHvap from known vapor pressures at different temperatures.