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If the molar solubility (in $\mathrm{mol} \mathrm{L}^{-1}$ ) of a sparingly soluble salt $A B_4$ is $S$ and the corresponding solubility product is $K_{\text {sp }}$, then $s$ in terms of $K_{\mathrm{sp}}$ is given by the relation
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Verified Answer
The correct answer is:
$S=\left(\frac{K_{\mathrm{sp}}}{256}\right)^{1 / 5}$
For the reaction,
$\begin{array}{ccc}A B_4(s) \stackrel{(a q)}{\rightleftharpoons} & A^{4+}(a q)+4 B^{-}(a q) \\ - & S & 4 S\end{array}$
Molar solubility (in $\mathrm{mol} / \mathrm{L}$ ) of a sparingly soluble salt $A B_4$ is ' $S$ ' and corresponding solubility product is $K_{\mathrm{sp}}$.
$S$ in term of $K_{\mathrm{sp}}$ is given by above relation is
$$
\begin{aligned}
& K_{\text {sp }}=\left[A^{4+}\right]\left[B^{-}\right]^4 \\
& K_{\text {sp }}=S \times(4 S)^4 \\
& K_{\text {sp }}=256 S^5
\end{aligned}
$$
Hence, the molar solubility, $S=\left(\frac{K_{\mathrm{sp}}}{256}\right)^{\frac{1}{5}}$
$\begin{array}{ccc}A B_4(s) \stackrel{(a q)}{\rightleftharpoons} & A^{4+}(a q)+4 B^{-}(a q) \\ - & S & 4 S\end{array}$
Molar solubility (in $\mathrm{mol} / \mathrm{L}$ ) of a sparingly soluble salt $A B_4$ is ' $S$ ' and corresponding solubility product is $K_{\mathrm{sp}}$.
$S$ in term of $K_{\mathrm{sp}}$ is given by above relation is
$$
\begin{aligned}
& K_{\text {sp }}=\left[A^{4+}\right]\left[B^{-}\right]^4 \\
& K_{\text {sp }}=S \times(4 S)^4 \\
& K_{\text {sp }}=256 S^5
\end{aligned}
$$
Hence, the molar solubility, $S=\left(\frac{K_{\mathrm{sp}}}{256}\right)^{\frac{1}{5}}$
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