A new basis for the analysis of ion activity coefficient data. I. The parabolic law^*

Chemistry Department, College of Science, the University of Texas, El Paso, Texas 79968.

Abstract

As is well known, over an extended concentration range a plot of the log of the mean molal activity coefficient vs. the square root of the modality of an electrolyte is not even approximately linear. In fact, γ_± itself (not log γ_±) is a parabolic function of [math] or [math] over the entire concentration range (0 to 3 molal) for all 1-1 strong electrolytes and for most others of different charge types. Thus, It will be shown that γ_± = αm + β[math] + δ. Evaluation of the constants α, β, and δ shown that δ = 1, β = — 2α[math], and α = (1 — γ₀)/m₀, where y₀ is the minimum activity coefficient observed at concentration m₀ for a particular 1-1 electrolyte. This leads to the general equation γ = 1 + (1 — γ₀) m/m₀ + 2 (γ₀ — 1) [math]/m₀, which can be put in the linear form (1 — γ)/[math] = 2 (1-γ₀)/ [math] — (1 — γ₀) [math]/[math]. Thus a plot of (1 — γ)/ [math] vs. [math] is a straight line of slope (γ₀ — 1)/m₀ and intercept 2 (1 — γ₀)/ [math]. From the slope (= α) and the Intercept (= β), one obtains m₀ = (β/2α)² and γ₀ = 1 — β2/4α. After passing through the minimum of the parabola, γ_± rises and again becomes unity (γ₁) at some higher molal concentration m₁, and It is shown that m₁ = 4m₀. The parameters γ₀, m₀, γ₁, and m₁ must have a profound significance in any detailed theory of electrolytic solutions, a significance we are currently investigating. The new equations are compared with detailed experimental data with excellent results.

Résumé

Dans un large domaine de concentrations, la relation entre log du coefficient d'activité moyen et racine carrée de la molalité d'un électrolyte n'est pas linéaire. En fait γ_± (et non log γ_±) est une fonction parabolique de [math] ou [math] dans tous le domaine (molalité 0 à 3) de concentrations pour tous les électrolytes forts 1-1 et la plupart des autres. On établit que γ_± = αm + β[math] + δ et l'évaluation d'α, β et δ en fonction de γ₀, coefficient minimal d'activité observé à la concentration m₀ pour un électrolyte 1-1 donné. On en tire une expression linéaire de γ en fonction de m, dont les pentes et ordonnée à l'origine fournissent γ_o et m_o ^; Lorsque γ_± remonte et atteint la valeur unité pour une concentration m₁ on montre que m₁ = 4m_o. L'accord est excellent entre les équations établies et l'expérience. La signification physique des diverses grandeurs calculées est en cours d'étude.