Finding pKsp?

Question

Consider a salt of composition, A2B3. For this salt, pKsp = 86.909. What is the logarithm of the molar concentration of this salt?

Answer 1

A2B3 <===> 2A + 3B. Let [A2B3] in solution be x. Then [A] = 2x and [B] = 3x

Ksp = [A]^2[B]^3 = (2x)^2(3x)^3 = 36x^5

pKsp = -LogKsp

LogKsp = -86.909 = -87 + 0.091

Ksp = 1.23 x 10^-87

36x^5 = 1.23 x10^-87

x^5 = 3.4 x 10^-89 = 34 x 10^-90

x = 2.02 x 10^-18

Log x = 0.305 - 18 = -17.695, which is what was wanted