Question

Write relation between solubility and solubility product of a2b type salt

Answer 1

Given

A salt of type $A_2B$

To Find

The relation between solubility product $K_{sp}$ and solubility S.

Concept

Solubility product is the equilibrium constant of a sparingly soluble salt. Let us understand by a simple salt AB.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: AB \rightleftharpoons A^+ + B^- \\ = > t = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 0 \: \: \: \: \: \: \: \: \: 0 \\ = > t = t _{eq} \: \: - S \: \: \: \: \: \: \: S \: \: \: \: \: \: \: \: \: S \\ \\ k _{sp} = \frac{[A^+]\: [B^-]}{[AB]} \\\\ Since\:[AB] = Constant\:,\\\\We\:take\:[AB] = 1. \\\\Hence, k _{sp} = [A^+] \:[B^-] \\ \\=> K_{sp} = S^2$

Solution

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: A _ 2 B \rightleftharpoons 2A^+ + B^- \\ = > t = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 0 \: \: \: \: \: \: \: \: \: 0 \\ = > t = t _{eq} \: \: - S \: \: \: \: \: \: \: 2S \: \: \: \: \: \: \: \: \: S \\ \\ \\=> k _{sp} = [A^+]^2 \: [B^-] \\\\=> K_{sp} = [2S]^2 [S] \\\\ => K_{sp} = 4s^3$

$\boxed{ \boxed{\orange{Hence,\:the\:relation\:between\:K_{sp}\:and\:S\:for\:the\:salt\:A_2B\:is\: K_{sp} = 4s^3 }}}$