Revisiting the Clausius/Clapeyron Equation and the Cause of Linearity

In general, for an organic compound a plot of the log vapor pressure versus inverse temperature is linear over a wide temperature range. This however can lead to a point of confusion in an undergraduate thermodynamics course. This linear behavior is typically explained using the Clausius/Clapeyron equation. That is, starting with the Clapeyron equation one first assumes (1) that change in compressibility upon vaporization is approximately 1, or equivalently that the vapor phase may be treated as an ideal gas where the molar volume of the vapor is much greater than that of the liquid, which may be assumed negligible. And second (2), that the enthalpy of vaporization is constant. While the resulting linear behavior is captured, the underlying assumptions are not applicable over the wide range of temperature of interest. Here we discuss the shortcomings of the conventional explanation of the Clausius/Clapeyron equation. We further demonstrate that a simple solution is to instead assume that the enthalpy of vaporization relative to the change in compressibility upon vaporization is constant. We provide a series of examples and MATLAB code that can be used in an undergraduate thermodynamics course.