Question

A salt, `AB_3`, expresses an aqueous solubility of `0.0750*mol*L^-1` with respect to the given solubility? What is `K_"sp"` for this solute?

Answer 1

`K_(sp)=[A^(3+)][B^-]^3=27xx0.0750^4`

Explanation:

We examine the following equilibrium:

`AB_3(s) rightleftharpoons A^(3+)+3B^-`

Since the solid cannot express a concentration, we write the following expression to represent the `"solubility product:"`

`K_(sp)=[A^(3+)][B^-]^3`

As is usual in these problems, we raise each concentration to the power of the stoichiometric coefficient in the solubility expression, and thus we have the product `[A^(3+)]^1xx[B^-]^3`.

But we are given that `[AB_3(aq)]=0.0750*mol*L^-1,` and thus we are in a position to evaluate `K_"sp"` directly.

And thus `[A]=0.0750*mol*L^-1,` and `[B^-]=3xx0.0750*mol*L^-1`.

`K_(sp)=[0.0750][3xx0.0750]^3=27xx0.0750^4`

Are you happy with this?