What is the solubility of $\mathrm{AgCl}_{(\mathrm{s})}$ if its solubility product is $1.6 \times 10^{-10}$ ?

What is the solubility of $\mathrm{AgCl}_{(\mathrm{s})}$ if its solubility product is $1.6 \times 10^{-10}$ ?
  1. $1.26 \times 10^{-5} \mathrm{M}$
  2. $1.00 \times 10^{-9} \mathrm{M}$
  3. $2.6 \times 10^{-5} \mathrm{M}$
  4. $1.56 \times 10^{-9} \mathrm{M}$

Solution

$\begin{aligned} & \mathrm{AgCl}_{(\mathrm{s})} \rightleftharpoons \mathrm{Ag}_{\text {(aq) }}^{+}+\mathrm{Cl}_{\text {(aq) }}^{-} \\ & x=1, \mathrm{y}=1 \\ & \mathrm{~K}_{\text {sp }}=x^x \mathrm{y}^{\mathrm{y}} \mathrm{S}^{x+\mathrm{y}}=(1)^1(1)^1 \mathrm{~S}^{1+1}=\mathrm{S}^2 \\ & \mathrm{~S}=\sqrt{\mathrm{K}_{\mathrm{sp}}}=\sqrt{1.6 \times 10^{-10}} \\ & \quad=1.26 \times 10^{-5} \mathrm{M}\end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 2)

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