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

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