Question

What is the concentration of $A{g}^{+}$ in a solution made by dissolving both $A{g}_{2}Cr{O}_4$ and $A{g}_2{C}_2{O}_4$ until saturation is reached with respect to both salts?
$\left[K_{sp}\right(A{g}_2{C}_2{O}_4)=2\times {10}^{-11},K_{sp}(A{g}_{2}Cr{O}_4)=2\times {10}^{-12}]$

• A. $2.80\times {10}^{-4}$
• B. $7.6\times {10}^{-5}$
• C. $6.63\times {10}^{-6}$
• D. $3.52\times {10}^{-4}$

Answer 1

Answer: (D)

$3.52\times {10}^{-4}$

$A{g}_2{C}_2{O}_4\to 2A{g}^{+}+C_2{O}_4^{-2}$

2x+2y x

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

2y+2x y

$K_{sp}ofA{g}_2{C}_2{O}_4=(2x+2y{)}^2\times x=2\times {10}^{11}$

$K_{sp}ofA{g}_{2}Cr{O}_4=(2x+2y{)}^2\times y=2\times {10}^{12}$

By solving this, we get $x=10y$

$y=1.6\times {10}^{-5}$ then, $x=10y=1.6\times {10}^{-4}$

Hence, $\left[A{g}^{+}\right]=2x+2y=3.52\times {10}^{-4}M$