Clausius-Clapeyron Equation

Vapor pressure increases exponentially with temperature rather than in a straight line. When vapor pressure is plotted directly against temperature, the curve rises sharply upward. However, when the natural logarithm of vapor pressure is plotted against reciprocal temperature, a linear relationship emerges, which is described by the Clausius-Clapeyron equation.

The slope of the line in a Clausius-Clapeyron plot equals the negative molar heat of vaporization divided by the gas constant. For example, if a plot of ethanol vapor pressure yields a slope of negative 4638 kelvins, you can calculate the molar heat of vaporization by multiplying the slope's absolute value by the gas constant, yielding 38,560 joules per mole.

If you know the molar heat of vaporization and vapor pressure at one temperature, use the two-point form of the Clausius-Clapeyron equation to calculate vapor pressure at another temperature. For water with enthalpy of vaporization of 40.7 kilojoules per mole and vapor pressure of 1 atm at 373 kelvins, the equation predicts 1.409 atm at 383 kelvins, demonstrating the non-linear increase in vapor pressure.

The constant A is the y-intercept of the Clausius-Clapeyron plot and is characteristic of each liquid. Its value depends on the chemical identity of the substance. While A remains constant for a given liquid across different temperatures, it varies between different liquids based on their molecular properties and intermolecular interactions.

The Clausius-Clapeyron equation uses absolute temperature in kelvins because the relationship between vapor pressure and temperature is fundamentally based on thermodynamic principles involving the gas constant R. Using kelvins ensures the mathematical relationships and proportionalities in the equation remain valid across all temperature ranges.

To use the two-point form, you need the molar heat of vaporization, vapor pressures at two different temperatures, those two temperatures in kelvins, and the gas constant. With these values, you can rearrange the equation to solve for an unknown vapor pressure at a new temperature or verify the relationship between vapor pressure and temperature for any liquid.

The Clausius-Clapeyron equation quantifies how vapor pressure—the pressure at which a liquid and its vapor are in equilibrium—changes with temperature. It predicts the rate at which vapor pressure increases per unit temperature increase, allowing chemists to understand and calculate the equilibrium conditions between liquid and vapor phases at different temperatures.