Question

Concentration of $A{g}^{+}$ ion in a saturated solution of $A{g}_{2}Cr{O}_4$ is $5.4\times {10}^{-6}$ g/litre when the salt is 50% dissociated. Then solubility product of $A{g}_{2}Cr{O}_4$ is

• A. $7.03\times {10}^{-17}$
• B. $6.25\times {10}^{-23}$
• C. $1.72\times {10}^{-23}$
• D. $2.15\times {10}^{-24}$

Answer 1

The correct option is A $7.03\times {10}^{-17}$

$A{g}_{2}Cr{O}_4\leftrightharpoons 2A{g}^{+}+Cr{O}_4^{2-}$

$c(1-s)$ $2cs$ $cs$

As, it is $50\%$ dissociated

$s=0.5$

and $2cs=5.4\times {10}^{-6}$ $g/L$

$c=5.4\times {10}^{-6}$ $g/L$

$K_{sp}=\left(2cs{)}^2\right(cs)$

$⟹K_{sp}=4c^3{s}^3$

$⟹K_{sp}=4(5.4\times {10}^{-6}{)}^3\times \frac{1}{8}$

$⟹K_{sp}=\frac{1}{2}\times (5.4{)}^3\times {10}^{-18}$

$⟹K_{sp}=7.8\times {10}^{-17}$