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.

substance formula α
sodium chloride NaCl 0.82
potassium sulfate K₂SO₄ 0.67
barium chloride BaCl₂ 0.77
cadmium sulfate CdSO₄ 0.35

substance	formula	α
sodium chloride	NaCl	0.82
potassium sulfate	K₂SO₄	0.67
barium chloride	BaCl₂	0.77
cadmium sulfate	CdSO₄	0.35

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)

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