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Show that the freezing-point depression of a real solution in which the solvent of molar mass M has activity aA obeys dInaA/d (T) = - M/Kf and use the Gibbs-Duhem equation to show that dInaB/d (T) = - 1/bBKf where aB is the solute activity and bB is its molality. Use the Debye-HUckel limiting law to show that the osmotic coefficient (I/J, Problem 5.21) is given by I/J= 1- 1/3 A'I with A' = 2.303A and I = blbo.

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