Question #928c8

1 Answer
Feb 20, 2017

Answer:

Compound #AX_2# will have the smallest #K_sp# value.

Explanation:

The relation between solubility and #K_(sp)# is not a fixed one, but depends on the particular solid. Here's why

If the solid is of form #AX#, it will dissolve, producing one cation #A^+# and one anion #X^-#.

#AX(s) rightleftharpoons A^+ + X^-#

and the #K_(sp)# expression is #K_(sp)=[A^+][X^-]#

If you let #x# be the solubility, you can show that the ion concentrations will both be equal to #x#, and the #K_(sp)# expression is given by #x^2#.

On the other hand, both #A_2X# and #AX_2# dissolve to form three ions, and the #K_(sp)# expression is either

#K_(sp)=[A^+]^2[X^-]# or #K_(sp)=[A^+][X^-]^2#

In either case, using the same assignment of #x# equal to the solubility, you get to the same expression, the #K_(sp)# expression is equal to #4x^3#.

Since all three solubilities are on the order of #10^(-4)#, the #K_(sp)# of AX will be on the order of #10^(-8)#, while the other two will be on the order of #10^(-12)#.

To break the tie, you look at the size of the numbers. #AX_2# at #1.20xx10^(-4)# is smaller than #1.53xx10^(-4)#, and so, will generate the smaller #K_(sp)# value.