Trouton's rule

In thermodynamics, Trouton's rule states that the (molar) entropy of vaporization is almost the same value, about 85–88 J/(K·mol), for various kinds of liquids at their boiling points.^[1] The entropy of vaporization is defined as the ratio between the enthalpy of vaporization and the boiling temperature. It is named after Frederick Thomas Trouton.

It is expressed as a function of the gas constant R:

${\displaystyle \Delta {\bar {S}}_{\text{vap}}\approx 10.5R.}$

A similar way of stating this (Trouton's ratio) is that the latent heat is connected to boiling point roughly as

${\displaystyle {\frac {L_{\text{vap}}}{T_{\text{boiling}}}}\approx 85{-}88\ {\frac {\text{J}}{{\text{K}}\cdot {\text{mol}}}}.}$

Trouton’s rule can be explained by using Boltzmann's definition of entropy to the relative change in free volume (that is, space available for movement) between the liquid and vapour phases.^[2][3] It is valid for many liquids; for instance, the entropy of vaporization of toluene is 87.30 J/(K·mol), that of benzene is 89.45 J/(K·mol), and that of chloroform is 87.92 J/(K·mol). Because of its convenience, the rule is used to estimate the enthalpy of vaporization of liquids whose boiling points are known.

The rule, however, has some exceptions. For example, the entropies of vaporization of