Inthermodynamics,Trouton's rule states that the (molar)entropy of vaporization has almost the same value, about 85–88 J/(K·mol), for various kinds ofliquids at theirboiling points.^[1] The entropy ofvaporization is defined as the ratio between theenthalpy of vaporization and theboiling temperature. It is named afterFrederick Thomas Trouton.

It is expressed as a function of thegas constantR:

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

A similar way of stating this (Trouton's ratio) is that thelatent 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 usingBoltzmann's definition of entropy to the relative change in free volume (that is, space available for movement) between the liquid andvapour phases.^[2][3] It is valid for many liquids; for instance, theentropy of vaporization oftoluene is 87.30 J/(K·mol), that ofbenzene is 89.45 J/(K·mol), and that ofchloroform 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 ofwater,ethanol,formic acid andhydrogen fluoride are far from the predicted values. The entropy of vaporization ofXeF₆ at its boiling point has the extraordinarily high value of 136.9 J/(K·mol), or 16.5R.^[4] The characteristic of those liquids to which Trouton’s rule cannot be applied is their special interaction between molecules, such ashydrogen bonding. The entropy of vaporization of water and ethanol shows positive deviance from the rule; this is because the hydrogen bonding in the liquid phase lessens the entropy of the phase. In contrast, the entropy of vaporization of formic acid has negative deviance. This fact indicates the existence of an orderly structure in the gas phase; it is known that formic acid forms adimer structure even in the gas phase. Negative deviance can also occur as a result of a small gas-phase entropy owing to a low population of excited rotational states in the gas phase, particularly in small molecules such as methane – a smallmoment of inertiaI giving rise to a largerotational constantB, with correspondingly widely separated rotational energy levels and, according toMaxwell–Boltzmann distribution, a small population of excited rotational states, and hence a low rotational entropy. The validity of Trouton's rule can be increased by considering^{[citation needed]}

${\displaystyle \mathrm{\Delta }{\overline{S}}_{\text{vap}}\approx 4.5R+R\ln T.}$

Here, ifT = 400 K, the right-hand side of the equation equals10.5R, and we find the original formulation for Trouton's rule.

• Trouton, Frederick (1884)."On Molecular Latent Heat".Philosophical Magazine.18 (110):54–57.doi:10.1080/14786448408627563. - Publication of Trouton's rule
• Atkins, Peter (1978).Physical ChemistryOxford University PressISBN 0-7167-3539-3

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• Thermodynamic properties

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