Calculate solubility $\left(\mathrm{moldm}^{-3}\right)$ of a sparingly soluble electrolyte AB at 298 K if…

Calculate solubility $\left(\mathrm{moldm}^{-3}\right)$ of a sparingly soluble electrolyte AB at 298 K if its solubility product is $1.6 \times 10^{-5}$ ?
  1. $1.6 \times 10^{-3}$
  2. $2.5 \times 10^{-3}$
  3. $4.0 \times 10^{-3}$
  4. $8.0 \times 10^{-3}$

Solution

$\begin{aligned} & \text { For } \mathrm{AB}, \\ & \mathrm{AB}_{(\mathrm{s})} \rightleftharpoons \mathrm{A}_{(\mathrm{aq})}^{+}+\mathrm{B}_{(\mathrm{aq})}^{-} \\ & \text {Here }^{-} x=1, \mathrm{y}=1 \\ \therefore \quad & \mathrm{~K}_{\mathrm{sp}}=x^x \mathrm{y}^{\mathrm{y}} \mathrm{S}^{x+\mathrm{y}}=(1)^1(1)^1 \mathrm{~S}^{1+1}=\mathrm{S}^2\end{aligned}$ $\begin{aligned} \therefore \quad \mathrm{S} & =\sqrt{\mathrm{K}_{\mathrm{sp}}} \\ & =\sqrt{1.6 \times 10^{-5}}=\sqrt{16 \times 10^{-6}} \\ & =4.0 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3}\end{aligned}$

Asked in: MHT CET 2024 (10 May Shift 1)

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