The Clausius-Clapeyron equation is a relation named for Rudolf Clausius and Benoit Emile Clapeyron. The equation describes the phase transition between two phases of matter that have the same composition.

Thus, the Clausius-Clapeyron equation can be used to estimate vapor pressure as a function of temperature or to find the heat of the phase transition from the vapor pressures at two temperatures. When graphed, the relationship between temperature and pressure of a liquid is a curve rather than a straight line. In the case of water, for example, vapor pressure increases much faster than temperature. The Clausius-Clapeyron equation gives the slope of the tangents to the curve.

This example problem demonstrates using the Clausius-Clapeyron equation to predict the vapor pressure of a solution.

## Problem

The vapor pressure of 1-propanol is 10.0 torr at 14.7 °C. Calculate the vapor pressure at 52.8 °C.

Given:

Heat of vaporization of 1-propanol = 47.2 kJ/mol

## Solution

The Clausius-Clapeyron equation relates a solution's vapor pressures at different temperatures to the heat of vaporization. The Clausius-Clapeyron equation is expressed by

ln[P_{T1,vap}/P_{T2,vap}] = (ΔH_{vap}/R)[1/T_{2} - 1/T_{1}]

Where:

ΔH_{vap} is the enthalpy of vaporization of the solution

R is the ideal gas constant = 0.008314 kJ/K·mol

T_{1} and T_{2} are the absolute temperatures of the solution in Kelvin

P_{T1,vap} and P_{T2,vap} is the vapor pressure of the solution at temperature T_{1} and T_{2}

### Step 1: Convert °C to K

T_{K} = °C + 273.15

T_{1} = 14.7 °C + 273.15

T_{1} = 287.85 K

T_{2} = 52.8 °C + 273.15

T_{2} = 325.95 K

### Step 2: Find PT2,vap

ln[10 torr/P_{T2,vap}] = (47.2 kJ/mol/0.008314 kJ/K·mol)[1/325.95 K - 1/287.85 K]

ln[10 torr/P_{T2,vap}] = 5677(-4.06 x 10_{-4})

ln[10 torr/P_{T2,vap}] = -2.305

take the antilog of both sides 10 torr/P_{T2,vap} = 0.997

P_{T2,vap}/10 torr = 10.02

P_{T2,vap} = 100.2 torr

## Answer

The vapor pressure of 1-propanol at 52.8 °C is 100.2 torr.