Which from the following equations represents the relation between solubility ( $\mathrm{mol}…

Which from the following equations represents the relation between solubility ( $\mathrm{mol} \mathrm{L}^{-1}$ ) and solubility product for a salt $\mathrm{B}_3 \mathrm{~A}_2$ ?
  1. $\mathrm{S}=\left(\frac{\mathrm{K}_{\mathrm{sp}}}{108}\right)^{\frac{1}{5}}$
  2. $\quad \mathrm{S}=\left(108 \times \mathrm{K}_{\mathrm{sp}}\right)^{1 / 5}$
  3. $\mathrm{S}=\left(\frac{\mathrm{K}_{\mathrm{sp}}}{27}\right)^{\frac{1}{5}}$
  4. $\mathrm{S}=\left(27 \times \mathrm{K}_{\mathrm{sp}}\right)^{1 / 5}$

Solution

$\begin{aligned} & \mathrm{B}_3 \mathrm{~A}_{2(\mathrm{s})}\rightleftharpoons 3 \mathrm{~B}^{2+}+2 \mathrm{~A}^{3-} \\ & \mathrm{K}_{\mathrm{sp}}=(3)^3(2)^2\left[\mathrm{~B}^{2+}\right]^3\left[\mathrm{A}^{3-}\right] \{\mathrm{A}^2] \\ & \mathrm{K}_{\mathrm{sp}}=27 \times 4 \times(\mathrm{S})^5\end{aligned}$ $\mathrm{S}=\left(\frac{\mathrm{K}_{\mathrm{sp}}}{108}\right)^{\frac{1}{5}}$

Asked in: MHT CET 2024 (10 May Shift 2)

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