Question

Using activities, find the concentration of Ba⁺² in a 0.100M (CH₃)₄N⁺ IO₃^- solution saturated with Ba(IO₃)₂. Assume Ba(IO₃)₂ makes a negligible contribution to the ionic strength and the K_sp value is 1.5 X 10^-9

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Answer 1

Ksp = [Ba2+] [ IO- 3]^2 = (s) (0.100 + 2s)^2 since the 0.100 is the contribution of [IO- 3] as a result of dissociation of (CH3)4NIO3 solution. Now assuming that the 2s is far lesser than 0.100 as 2s << 0.100 then we could let Ksp = (s)(0.100)^2

With the activity coefficients which are also denoted by the symbol gamma, Ksp = (s)(0.100)^2 times mean ionic activity coefficient.

Mean ionic activity coefficient = (0.38)(0.775)^2 = 0.228

So, Ksp / mean ionic activity coefficient = (s)(0.100)^2

Rearranging it gives s = Ksp / (0.01 x 0.228) = (1.5 E -9) / 0.00228 = 6.58 E -7 M

So, [Ba2+] = 6.58 E -7 mol/dm^3