Influence of H-bond chains in solvents on the solubility of inert substances. A new quantitative approach.

The classic thermodynamic treatments considering self-associated liquids A as multicomponent systems are unable to explain the solubilities of substances B in these liquids by effects directly related to the presence of H-bond chains. This is not the case when the hypothesis of successive equilibria between the i-mers is abandoned and replaced by a single equilibrium between bonded and free hydroxylic protons. In the new treatment presented here two combinatorial entropies are considered : that resulting from the exchange possibilities between bonded and non-bonded protons and that originating from the exchange between A and B molecules. For large values of φ_A, the volume fraction of the associated liquid, it is shown that the latter combinatorial entropy is practically equal to that calculated in absence of self-association. The fraction γ of the free hydroxylic protons depends on the molar enthalpy of the hydrogen bond ΔH_h and on the entropy of chain-reintegration ΔS_h. The latter depends on the formal concentration F_A of the associated substance and a quantitative treatment shows that dΔS_h/dlnF_A = R (gas constant). This conclusion is experimentally confirmed by the variation of the vapor pressure with F_A in the series of the primary alcohols. The introduction of an inert substance B causes F_A to decrease and enhances the lowering of the entropy of the bonded molecules with respect to the non-bonded molecules. This creates a hydrophobic effect that is at the origin of the lowering of the solubility φ_B of B in A. As a consequence, lnφ_B at the equilibrium is diminished by an amount equal to b_Aφ_A$\text{V}$_B/$\text{V}$_A, where $\text{V}$_B and $\text{V}$_A are the formal molar volumes of both substances. b_A is a so called “structuration factor” of the solvent A that nearly equals ?1 for strongly associated solvents with single H-bond chains, like alcohols, and ?2 for solvents with double chains like water. Taking for the combinatorial entropy between A and B an expression intermediate between the classic one in mole fractions and that of Flory-Huggins in volume fractions, one derives equations that predict the solubility of alkanes in water and in alcohols. Although these equations do not contain any adjustable parameter and that the experimental solubilities φ_B cover several orders or magnitude, the agreement between prediction and experiment is remarkable.