# Entropy of Phase Changes

We would expect that a phase change would be accompanied by a change in entropy. For example, when a liquid boils, a compact condensed phase is converted into a widely dispersed vapour phase. Clearly, the molecular disorder in a gas will be greater than that in a liquid, so there must be an entropy increase upon vapourisation.

Likewise, when a liquid freezes the mobile molecules of the liquid phase are forced to assume fixed positions in the solid phase. This will  normally reduce the molecular disorder of the system, so there will usually be an entropy decrease that accompanies freezing.

We consider a system and its surroundings at the normal transition temperature, Ttrs, for a given phase change. (This is the temperature at which the two phases involved in the transition are in equilibrium at 1atm pressure. e.g. 273 K (0ºC) for ice and liquid water in equilibrium)

At the transition temperature, any transfer of heat between the system and its surroundings is reversible, because the two phases in the system are in equilibrium.

At constant pressure, q  =  ΔHtrs , which is defined as the enthalpy change accompanying the transition. The molar entropy change of the transition is thus given by:

If the phase transition is exothermic  (ΔHtrs < 0 , e.g. freezing or condensing) then the entropy change is negative, reflecting the greater ordering in the phase that is formed during the transition. (e.g. a solid is formed from a liquid during the freezing phase transition, a negative entropy change confirms that the solid is more ordered than the liquid.)
If the phase transition is endothermic (ΔHtrs > 0 , e.g. melting or vapourisation) then the entropy change is positive, reflecting the higher degree of disorder in the phase that is formed during the transition.

An interesting experimental observation has been formulated as Trouton’s Rule. This rule states that a wide range of liquids give approximately the same standard entropy of vapourisation, about + 85 J K-1 mol-1.

The reason behind this is associated with the large increase in translational freedom in the gas phase compared to the liquid phase. Small variations in the degree of order in the liquid phases of different elements or compounds are insignificant compared to the large increase in disorder generated upon vapourisation. Thus most liquids show roughly the same increase in entropy on going from a liquid to a gas, and hence have similar entropies of vapourisation.

Exceptions to the rule occur when there is an anomalously high degree of structural organisation in the liquid phase (e.g. in water, where the extensive hydrogen bonding between molecules provides the unusually high degree of structure), or when the entropy of the gas phase is somehow anomalous. Commonly, the entropy of the gas phase is rather low if the molecules are light (e.g. in methane). The reason behind this is somewhat complicated, but lies with the fact that rotational energy levels of light molecules are widely spaced, making it hard to excite them and reducing the contribution to the entropy that comes from the distribution of molecules among these energy levels.

The use of this rule is purely in estimating the value of ΔSvap for a liquid where it is unknown. If there is no obvious reason why the liquid phase should be unusually ordered or the entropy of the gas phase should be anomalous, then ΔSvap  =  + 85 J K-1 mol-1 is often a good approximation.

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