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?

1 Answer
Nov 22, 2016

Answer:

#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?