Q82 / 160 · JIPMER 2011 · Chemistry

The expression for the solubility product of $\mathrm{Ag}_2 \mathrm{CO}_3$ will be

  • A
    $K_{\mathrm{sp}}=s^2$
  • Correct answer
    B
    $K_{\mathrm{sp}}=4 s^3$
  • C
    $K_{\mathrm{sp}}=27 s^4$
  • D
    $K_{\mathrm{sp}}=s$

Solution

$\begin{aligned} & \mathrm{Ag}_2 \mathrm{CO}_3(s) \rightleftharpoons \underset{2 s}{2 \mathrm{Ag}^{+}}+\underset{s}{\mathrm{CO}_3^{2-}} \\ & K_{\mathrm{sp}}=\left[\mathrm{Ag}^{+}\right]^2\left[\mathrm{CO}_3^{2-}\right]=(2 s)^2 \cdot s \\ & \therefore \quad K_{\mathrm{sp}}=4 s^3 \\ & \end{aligned}$

Hence, the correct answer is option: 'B'.

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