Question

A saturated, aqueous solution of a salt having the formula, AX₃, is prepared. The equilibrium that is established is: AX₃(s) <------> A³⁺(aq)+3X^-(aq). At equilibrium, the concentration of X^- is found to be 2.74x10^-7 M.

What is the solubility product constant, K_sp, for AX₃?

What is the solubility of this compound in a solution that is 1.529x10^-2 M NaX (assume that NaX is a completely soluble compound).

Answer 1

Reaction: ICE

AX3 (s) --- >     A³⁺ (aq) +      3X^-(aq)

I                                         0                   0

C          -y (solubility)      +y                   +3y

E                                         y                     3y

Ksp = [A³⁺][X-]³

= y x (3y)³

= 9 y⁴

We know at equilibrium concentration of x = 2.74 E-7 M

At equilibrium 3y = 2.74 E-7

y = 2.74 E-7 / 3

= 9.11 E-8

y = 9.11E-8

Lets plug this value this value ksp expression

Ksp = 9 x ( 3 * 9.11E-8 )⁴

Ksp = 6.28 E-28

[NaX]= [X-]= 1.529x10^-2 M

We use concentration X- and use same method to get Ksp

3y = 1.529x10^-2 M

y = 0.0051

Lets plug this value in Ksp

Ksp = 9 y⁴

= 9 x (0.0051)⁴

= 6.072 E-9

Ksp = 6.072 E-9