The Clausius-Clapeyron equation relates the vapor pressure of a liquid at two different temperatures to its enthalpy of vaporization. It can be written as:
ln(P2/P1) = (-ΔHvap/R) x (1/T2 - 1/T1)
where P1 and T1 are the known vapor pressure and temperature of the liquid at one temperature, P2 is the vapor pressure of the liquid at the other unknown temperature T2, ΔHvap is the enthalpy of vaporization for the liquid, and R is the gas constant.
To use this equation to calculate the vapor pressure of methanol at a specific temperature, we need to know the vapor pressure of methanol and its enthalpy of vaporization at another temperature. For example, suppose we know that the vapor pressure of methanol at 25°C (298.15 K) is 13.02 kPa and its enthalpy of vaporization is 35.2 kJ/mol. We can use this information to calculate the vapor pressure of methanol at a higher temperature, such as 77.2°C (350.35 K).
Using the equation and the known values, we get:
ln(P2/13.02 kPa) = (-35.2 kJ/mol / (8.314 J/(mol.K))) x (1/350.35 K - 1/298.15 K)
Solving for P2:
P2 = 74.55 kPa
Therefore, the vapor pressure for methanol at 77.2°C is approximately 74.55 kPa.