Fundamental questions about entropy III. A kind of mobile order in liquids : preferential contacts between molecular groups

At 25°C, in liquid alcohols and in water an O‐H proton follows an oxygen atom of a neighbouring molecule in its peregrinations during a fraction (1‐γ) of the time (more than 95% for the lower alcohols). During this time the proton can be found only in a part Vo of the standardized domain A> of the molecule. Neither Vo not A> are fixed. The highly preferential contacts create in the liquid a kind of mobile order that does not exist in crystalline substances. As a consequence of the mobile order the standardized possibilities A> of one molecule A of the liquid are reduced by a factor A mobile order > = γ−γ (1‐γ)γ‐1 (Vo/ A> 1‐γ. This factor is smaller than one. In the case of water there are two such factors, one for the first and the other for the second proton. The mobile order provokes a change in the molar entropy ΔSA mobile order = R In that is therefore negative. A> is the volume of the solution divided by the number of A molecules. In the series of the normal alcohols, up to hexanol, the changes of γ can be neglected. Vo and the effects of H‐bonding on the vibrations can also be considered as constant. As a consequence in this series one expects an increase of the negative value of the entropy of mobile order according to d(−ΔSA mobile order) = R d ln VA. This is confirmed by the differences between the standard entropies of the alcohols and of their homomorphous hydrocarbons. In the vapour phase where H‐bonding is negligible, the differences are positive and practically constant: 13.8 ± 0.7 JK−1 mole−1. For the liquids the differences are negative and increase with the molecular weight.