UPSC Combined Geo-Scientist, Mains · 2019 · Mains Paper II

Q1(g). Single-ion activity coefficients

Question

Calculate the activity coefficients of Zn²⁺ and Cl⁻ in 1.0 mM ZnCl₂ at 25° C, given Debye–Huckel A=0.51 M^-1/2.

γ_(Zn²⁺)≈0.773 and γ_(Cl⁻)≈0.938 in the limiting-law model.

Complete dissociation gives concentrations 0.0010 M zinc and 0.0020 M chloride. Ionic strength is I=1/2[0.0010(2)²+0.0020(1)²]=0.0030 M.
The limiting law is log₁₀ γᵢ=-Azᵢ²√I. Thus log γ_(Zn²⁺)=-0.51(4)√(0.003)=-0.11174, giving 0.773.
For chloride, log γ=-0.51√(0.003)=-0.027934, giving 0.938. These are model-based single-ion coefficients; experimentally accessible mean ionic coefficients do not require an arbitrary single-ion convention.

The full model answer

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CoversSingle-ion activity coefficientsElectrolyte solutions