Find solubility in terms of $\mathrm{mol} \mathrm{L}^{-1}$ if solubility product of silver bromide is $6.4…

Find solubility in terms of $\mathrm{mol} \mathrm{L}^{-1}$ if solubility product of silver bromide is $6.4 \times 10^{-13}$.
  1. $4.0 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1}$
  2. $8.0 \times 10^{-7} \mathrm{~mol} \mathrm{~L}^{-1}$
  3. $7.5 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1}$
  4. $6.4 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}$

Solution

$\begin{array}{ll} & \mathrm{AgBr}_{(\mathrm{s})} \rightleftharpoons \mathrm{Ag}_{(\mathrm{aq})}^{+}+\mathrm{Br}_{(\mathrm{sq})}^{-} \\ \therefore \quad & x=1, y=1 \\ & \mathrm{~K}_{\mathrm{sp}}=x^x y^y \mathrm{~S}^{x+y}=(1)^1(1)^1 \mathrm{~S}^{1+1}=\mathrm{S}^2 \\ \therefore \quad & \mathrm{S}=\sqrt{\mathrm{K}_{\mathrm{sp}}}=\sqrt{6.4 \times 10^{-13}}=\sqrt{64 \times 10^{-14}} \\ & =8 \times 10^{-7} \mathrm{~mol} \mathrm{~L}^{-1}\end{array}$

Asked in: MHT CET 2023 (10 May Shift 2)

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