Chemical and Ionic Equilibrium 2 Question 36
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36. The $K_{\text {sp }}$ of $\mathrm{Ag}{2} \mathrm{CrO}{4}$ is $1.1 \times 10^{-12}$ at $298 \mathrm{~K}$. The solubility (in $\mathrm{mol} / \mathrm{L}$ ) of $\mathrm{Ag}{2} \mathrm{CrO}{4}$ in a $0.1 \mathrm{M} \mathrm{AgNO}_{3}$ solution is
======= ####36. The $K_{\text {sp }}$ of $\mathrm{Ag}{2} \mathrm{CrO}{4}$ is $1.1 \times 10^{-12}$ at $298 \mathrm{~K}$. The solubility (in $\mathrm{mol} / \mathrm{L}$ ) of $\mathrm{Ag}{2} \mathrm{CrO}{4}$ in a $0.1 \mathrm{M} \mathrm{AgNO}_{3}$ solution is
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed (a) $1.1 \times 10^{-11}$
(b) $1.1 \times 10^{-10}$
(c) $1.1 \times 10^{-12}$
(d) $1.1 \times 10^{-9}$
(2013 Adv.)
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Solution:
- PLAN In presence of common ion (in this case $\mathrm{Ag}^{+}$ion) solubility of sparingly soluble salt is decreased.
Let solubility of $\mathrm{Ag}{2} \mathrm{CrO}{4}$ in presence of $0.1 \mathrm{M}$
$$ \begin{aligned} & \mathrm{AgNO}{3}=x \ & \mathrm{Ag}{2} \mathrm{CrO}{4} \rightleftharpoons 2 \mathrm{Ag}^{+}+\underset{x}{\mathrm{CrO}{4}^{2-}} \ & \mathrm{AgNO}{3} \rightleftharpoons \underset{0.1}{\mathrm{Ag}^{+}}+\underset{0.1}{\mathrm{NO}{3}^{-}} \end{aligned} $$
Total $\left[\mathrm{Ag}^{+}\right]=(2 x+0.1) \mathrm{M} \approx 0.1 \mathrm{M}$
$$ \text { as } x«<0.1 \mathrm{M} $$
$\left[\mathrm{CrO}_{4}^{2-}\right]=x \mathrm{M}$
Thus, $\quad\left[\mathrm{Ag}^{+}\right]^{2}\left[\mathrm{CrO}{4}^{2-}\right]=K{\text {sp }}$
$$ (0.1)^{2}(x)=1.1 \times 10^{-12} $$
$$ \because \quad x=1.1 \times 10^{-10} \mathrm{M} $$
