Determine the formation constant, Kf, of AC5 and the Ksp of AB

Question

a)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 and [C]=0.0150 M. Determine the formation constant, Kf, of AC5.

b) The solubility of AB(s) in a 1.000 M solution of C(aq) is found to be 0.122 M

What is the K sp of AB?

Answer 1

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

Kf = [AC₅]/[A][C]⁵

It seems as though something has been omitted from the question, as we do not know the equilibrium [AC₅], so we have 2 unknowns. Did they not give you this value? If they did, just plug it in along with the other concentrations and solve for Kf.

For Ksp, we have the following reaction:

AB(s) + 5C(aq) <===> AC₅(aq) + B(aq)

0.122...1.000................0............0.........Initial

-0.122...1-5*0.122.......+0.122...+0.122.....Change (the change is equal to the solubility)

Then we have K = [AC₅][B] / [C]⁵

K = (0.122)(0.122) / [1 - (5x0.122)]⁵ = 0.01488 / 0.00902 = 1.6497

Since K = Ksp x Kf, you would then divide this value of K by the Kf found in part 1 to obtain the Ksp.

To clarify this relationship, see below:

Kf: A + 5C < == > AC5

Ksp: AB <==> A + B

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K: AB + 5C <==> AC5 + B