Arrhenius strong electrolytes

In a paper on the dissociation of electrolytes in aqueous solution, Arrhenius presented data on a wide variety of solutes including materials we would class as non-electrolytes, strong electrolytes, and weak electrolytes. This exercise focuses on strong electrolyte salts. Arrhenius presented data on a quantity he called the activity coefficient (α) of several solutions, all containing 10. g solute in one liter of water.
substanceformulaα
sodium chlorideNaCl0.82
potassium sulfateK2SO40.67
barium chlorideBaCl20.77
cadmium sulfateCdSO40.35
Arrhenius's "activity coefficient" is the apparent ratio of dissociated solute molecules to total molecules of the solute (i.e., dissociated plus undissociated). It was determined from electrical conductance measurements. A modern physical chemist would understant that Arrhenius's "activity coefficient" α is a combination of a dissociation ratio and the activity coefficient γ introduced many years later by G. N. Lewis (the activity coefficient currently taught in physical chemistry courses).

Use the Debye-Hückel limiting law to estimate the mean ionic activity coefficient γ for each solution. How would γ vary with ionic charge and molar mass for 10.g/L solutions such as those Arrhenius used? Comment on the agreement between γ and α.

Reference

Svante Arrhenius, "On the Dissociation of Substances Dissolved in Water," Zeitschrift für physikalische Chemie 1, 631-48 (1887)
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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