Chemical and Ionic Equilibrium 2 Question 36

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36. The Ksp  of $\mathrm{Ag}{2} \mathrm{CrO}{4}is1.1 \times 10^{-12}at298 \mathrm{~K}.Thesolubility(in\mathrm{mol} / \mathrm{L})of\mathrm{Ag}{2} \mathrm{CrO}{4}ina0.1 \mathrm{M} \mathrm{AgNO}_{3}$ solution is

======= ####36. The Ksp  of $\mathrm{Ag}{2} \mathrm{CrO}{4}is1.1 \times 10^{-12}at298 \mathrm{~K}.Thesolubility(in\mathrm{mol} / \mathrm{L})of\mathrm{Ag}{2} \mathrm{CrO}{4}ina0.1 \mathrm{M} \mathrm{AgNO}_{3}$ solution is

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed (a) 1.1×1011

(b) 1.1×1010

(c) 1.1×1012

(d) 1.1×109

(2013 Adv.)

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Solution:

  1. PLAN In presence of common ion (in this case Ag+ion) solubility of sparingly soluble salt is decreased.

Let solubility of $\mathrm{Ag}{2} \mathrm{CrO}{4}inpresenceof0.1 \mathrm{M}$

$$ \begin{aligned} & \mathrm{AgNO}{3}=x \ & \mathrm{Ag}{2} \mathrm{CrO}{4} \rightleftharpoons 2 \mathrm{Ag}^{+}+\underset{x}{\mathrm{CrO}{4}^{2-}} \ & \mathrm{AgNO}{3} \rightleftharpoons \underset{0.1}{\mathrm{Ag}^{+}}+\underset{0.1}{\mathrm{NO}{3}^{-}} \end{aligned} $$

Total [Ag+]=(2x+0.1)M0.1M

 as x«<0.1M

[CrO42]=xM

Thus, $\quad\left[\mathrm{Ag}^{+}\right]^{2}\left[\mathrm{CrO}{4}^{2-}\right]=K{\text {sp }}$

(0.1)2(x)=1.1×1012

x=1.1×1010M