A solid salt of the general formula, $A_x B_y$ with molar solubility ' $S$ ' in equilibrium with its

Question

A solid salt of the general formula, $A_x B_y$ with molar solubility ' $S$ ' in equilibrium with its saturated solution may be represented as:
$
A_x B_{y(s)} ightleftharpoons x A_{(a q)}^{y+}+y B_{(a q)}^{x-}
$
Its solubility product constant is given by :
$
K_{s p}=\left[A^{y+}ight]^x\left[\mathrm{~B}^{x-}ight]^y=(x S)^x(y S)^y=x^x \cdot y^y \cdot S^{(x+y)}
$\ What will be the solubility product of $A_2 X_3$ ?

Professor PC Thomas Classes · Answer

(a) : $A_2 X_3 \rightleftharpoons \underset{2 S}{2 A^{3+}}+\underset{3 S}{3 X^{2-}}$
$
K_{s p}=\left[A^{3+}\right]^2\left[X^{2-}\right]^3=(2 S)^2 \cdot(3 S)^3=108 S^5
$