Hydrogen Bonding and Entropy

Abstract

A new general expression for the entropy S is given, based on the standard number 〈W〉 of “possibilities” of placing or moving for one molecule of a given kind. 〈W〉 is calculated in an independent way for all the different kinds of molecules present in the system. For a system containing N_A molecules A and N_B molecules of B, S = k ln 〈W_oneA〉^NA〈W_oneB〉^NB. This expression differs from that of Boltzmann but strictly agrees with that of Clausius, dS = dq_rev./T. For the calculation of the entropy of placing in a liquid mixture, one has to use the equation 〈W_placingA〉=x A^1/2ΦA^1/2 which combines the mole fraction x and the volume fraction Φ. The last term is related to the fact that in a liquid solution a given molecule has a larger volume at its disposal than its own one. During the fraction of time (l-γ_Ah) during which an hydroxyl proton is involved in H-bonding it renounces to the possibility of visiting its mobile domain, DomA, and remains confined in a small part V₀ at the border of it. This creates in the liquid a kind of mobile order and a decrease of the entropy that is related to the ratio V₀/〈DomA〉. The addition of an inert substance to the liquid increases 〈DomA〉, letting V₀ inaltered. This corresponds to a decrease of the entropy that constitutes the true origin of the hydrophobic effect. The quantitative treatment leads to an equation that, without the use of any adjustable constant, correctly predict the solubility of liquid alkanes in water.