A non-ergodic thermodynamics based not on concentrations but on time fractions. Application to conductance problems of solutions of lithium salts in ethers

Hydrogen bonds or strong dipole-dipole interactions lead to the formation of transient chain-association in solution. The interaction has a given molar energy: Delta H-bond. In an open chain as for instance in alcohols O-H-O-H-O-H-O-H-O-H, only the completely inserted molecules are in possession of this energy during the whole time they are inserted. The head and the tail are transient forms during the life-time of which Delta H-bond is transferred from the medium to the molecule or vice-versa. In the ensemble at a given time they have no definite energy and their concentrations cannot be calculated by means of a Boltzmann equation. But in a time schedule they can be considered half of the time as possessing Delta H-bond and half of the time as free. The classical Guldberg and Waage equilibrium expression using concentrations has to be replaced by another one where time fractions gamma appear. In an alcohol the time fraction gamma during which the molecule escapes from H-bonding and becomes vaporizable is given by the equation (1-gamma)/gamma = K-A C-alcohol. The new equations derived from these principles allow to predict correctly the vapor pressures of the alcohols and the solubilities of foreign substances in these solvents and provide a completely new quantitative explanation for the hydrophobicity of alkanes. Non-ergodic association also occurs between ion pairs as LiCl in moderately polar solvents as tetrahydrofuran THF (epsilon(293) = 7.53) or tetrahydropyran THP (epsilon(293) = 5.71), which can form open dimers LiClLiCl or higher associates in these solvents. The formation of these dimers is accompanied by the appearance in the solution of triple anions and cations between which there exists via the neutral dimer a perpetual exchange of a LiCl molecule according to: LiClLi+ + Cl- <-> LiClLiCl <-> Li+ ClLiCl-. The triple ions formed in this way cannot be considered as separated thermodynamic entities and do not follow the Guldberg and Waage equilibrium expression. The LiCl group which they have in common is sometimes involved in a positive ion and sometimes in a negative one. Only in the neutral dimer it may be considered as in possession of the insertion bond. On the other hand LiCl may also be involved in a dissociation where the Li+ ion becomes specifically solvated by the ether, giving: LiCl <-> LiS4+ + Cl- However this specific solvation is incompatible with the formation of triple ions because it would prevent the oscillation of LiCl between the triple ions. As a consequence one has to distinguish in the time schedule of a given LiCl a fraction of the time xi degrees during which it dissociates in an anion and a solvated cation, and the fraction of the time (1-xi degrees) during which it is involved in a dimerization process and where triple ions can be formed. One has: (1-xi degrees)/xi degrees = K-ass(K-d-1/2)C-LiCl(3/2) where K-ass is the non-ergodic constant governing the association of the ion pairs and Kd the classical dissociation constant, C-LiCl being the concentration of the salt. The quantitative equations based on this theory allow to explain the peculiarities of the conductance of LiCl solutions and the paradoxical effects of the addition of LiCl on the conductivity of Polystyryl(-)Li(+) solutions and on the kinetics of the anionic polymerization.