Question

The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively:

• A. $X_{2}Y,2\times {10}^{-9}{M}^3$
• B. $X{Y}_2,1\times {10}^{-9}{M}^3$
• C. $X{Y}_2,4\times {10}^{-9}{M}^3$
• D. $XY,2\times {10}^{-6}{M}^3$

Answer 1

The correct option is C $X{Y}_2,4\times {10}^{-9}{M}^3$

$\text{(a)}{X}_2{Y}_{\left(s\right)}\rightleftharpoons 2X^{+}+Y^{2-}$
$K_{sp}=\left[X^{+}{]}^2\right[Y^{2-}]=4\times {10}^{-6}\times {10}^{-3}=4\times {10}^{-9}$

$\text{(b)}X{Y}_{2\left(s\right)}\rightleftharpoons X^{2+}+2Y^{-}$
$K_{sp}=\left[X^2\right]+[Y^{-}{]}^2={10}^{-3}\times 4\times {10}^{-6}=4\times {10}^{-9}$

$\text{(c)}X{Y}_{2\left(s\right)}\rightleftharpoons X^{2+}+2Y^{-}$
$K_{sp}=\left[X^2\right]+[Y^{-}{]}^2={10}^{-3}\times (2\times {10}^{-3}{)}^2=4\times {10}^{-9}$

$\text{(d)}X{Y}_{2\left(s\right)}\rightleftharpoons X^{+}+Y^{-}$
$K_{sp}=\left[X^{+}\right]+\left[Y^{-}\right]={10}^{-3}\times {10}^{-3}={10}^{-6}$