Which of the following equations represents the relation between solubility and solubility product for salt…

Which of the following equations represents the relation between solubility and solubility product for salt $\mathrm{BA}_3$ ?
  1. $\mathrm{S}=\left(\frac{\mathrm{K}_{\mathrm{sp}}}{27}\right)^{1 / 4}$
  2. $\mathrm{S}=\left(27 \times \mathrm{K}_{\mathrm{sp}}\right)^{1 / 4}$
  3. $\mathrm{S}=\left(\frac{\mathrm{K}_{\mathrm{sp}}}{4}\right)^{1 / 4}$
  4. $\quad \mathrm{S}=\left(4 \times \mathrm{K}_{\mathrm{sp}}\right)^{1 / 4}$

Solution

$\mathrm{BA}_3$ ionises in the following manner: $\mathrm{BA}_3 \longrightarrow \mathrm{~B}^{3+}+3 \mathrm{~A}^{-}$
The relationship between solubility and solubility product is as follows: $\begin{array}{ll} \therefore & \mathrm{K}_{\mathrm{sp}}=(\mathrm{S}) \times(3 \mathrm{~S})^3=27 \mathrm{~S}^4 \\ \therefore & \mathrm{~S}=\sqrt[4]{\frac{\mathrm{K}_{\mathrm{sp}}}{27}}=\left(\frac{\mathrm{K}_{\mathrm{sp}}}{27}\right)^{1 / 4} \end{array}$

Asked in: MHT CET 2024 (03 May Shift 1)

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