Question

What will be the molar solubility $S$ of a solid salt with general formula $M_x^{p+}{X}_y^{q-}$ ?

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

Answer 1

Answer: (C)

A solid salt of the general formula, $M_x^{p+}{X}_y^{q-}$ with molar solubility $S$ in equilibrium with its saturated solution may be represented by the equation,
$M_x{X}_y(s)⟶x{M}^{p+}(aq)+y{X}^{q-}(aq)$
$($, where $x\times p^{+}=y\times q^{-})$
and its solubility product constant is given by
$K_{sp}={\left[M^{p+}\right]}^x{\left[X^{q-}\right]}^y=(xS{)}^x(yS{)}^y$
$K_{sp}=x^x\cdot y^y\cdot S^{(x+y)}$
$S^{(x+y)}=\frac{K_{sp}}{x^x\cdot y^y}$
or $S={\left(K_{sp}/x^x\cdot y^y\right)}^{1/x+y}$