Question

The molar solubility of a sparingly soluble salt $M_x{X}_y$ in its saturated solution at a given temperature is $S$. The correct relation between $S$ and $K_{sp}$ of it is ($K_{sp}$ = solubility product).

• A. $S={\left(\frac{K_{sp}}{x^x.y^y}\right)}^{\frac{1}{x+y}}$
• B. $S=\frac{K_{sp}}{x^x.y^y}$
• C. $S={\left(\frac{K_{sp}}{x^x.y^y}\right)}^{x+y}$
• D. $S=\frac{x^x.y^y}{K_{sp}}$

Answer 1

The correct option is A $S={\left(\frac{K_{sp}}{x^x.y^y}\right)}^{\frac{1}{x+y}}$

$M_x{X}_y$ solubility is $S$.

$M_x{Y}_y\leftrightharpoons x{M}^{y+}+y{Y}^{x-}$

Thus, concentration of $M=xS$

Concentration of $X=yS$

$K_{sp}=\left[M{]}^x\right[X{]}^y$

$K_{sp}=\left[xS{]}^x\right[yS{]}^y$

$K_{sp}=x^x{y}^y{S}^{x+y}$

$S={\left(\frac{K_{sp}}{x^x.y^y}\right)}^{\frac{1}{x+y}}$