The solubility of AB(s) in a 1.000 M solution of C(aq) is found to be 0.114 M. What is the Ksp of AB?

Question

The generic metal A forms an insoluble salt AB(s) and a complex AC5(aq). The equilibrium concentrations in a solution of AC5 were found to be [A]=0.100 M, [C]=0.0210 M, and [AC5]=0.100 M.Determine the formation constant, Kf, of AC5.

That is Part A of the question and I got Kf = 244851927. For Part B, when I calculate Ksp I got 4.0 x 10-9 but it says it is incorrect.

Answer 1

For Kf, we can look at the formation of the complex as A + 5C <==> AC₅

Kf = [AC₅]/[A][C]⁵

Substituting the values given, I also find a Kf = 244,851,927.

Next, for Ksp, we have the following:

AB(s) + 5C(aq) <==> AC₅(aq) + B(aq)

0.114......1.000................0.............0...........Initial

-0.114....1 - (5x0.114)....+0.114...+0.114.....Change (change is the solubility)

0..............0.43................0.114......0.114......Equilibrium

Keq = [AC₅][B] / [C]⁵ = (0.114)(0.114) / (0.43)⁵

Keq = 0.884

K = Ksp x Kf

Ksp = K / Kf = 0.884 / 244,851,927

Ksp = 3.61x10^-9 (pretty close to what you got).

Not sure where you and I differ as you didn't post your procedure. But be sure to check the math for both your solution as well as for mine.