A sparingly soluble salt having general formula A{_{x}}^{p+},B{_{y}}^{q-} and molar solubility S is in equilibrium with its saturated solution. Derive a relationship between the solubility and solubility product for such salt.

Answers (1)

In order to derive the relationship between the solubility and solubility product for such a salt we will take the following steps,

We will assume the solubility to be S.

Initially, we will assume that 1 mole of AxBy was present. Out of it, S moles were dissolved in order to give xS and yS moles of Ap+ and Bq- respectively. We can understand it better through the following equation: -

A^{p+}\times B^{q-} y \leftrightharpoons xA^{+p} + yB^{-q}

At t=0, 1 0 0

At Equilibrium, 1-S,xS \; Ys

We know that, solubility product(K_{sp}) = [A^{+p}]\times [B^{-q}]^{y}

= (xS)\times (yS)^{y}

=x^{x}Y^{y}S^{x+y}

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