Question

$AgBr\left(s\right)+2S_2{O}_3^{2-}(aq.)\rightleftharpoons Ag\left(S_2{O}_3{)}_2^{3-}\right(aq.)+B{r}^{-}(aq.)$
[Using: $K_{sp}\left(AgBr\right)=5\times {10}^{-13},K_f\left(Ag\right(S_2{O}_3{)}_2^{3-})=5\times {10}^{13}$]
What is the molar solubility of $AgBr$ in $0.1MN{a}_2{S}_2{O}_3$?

• A. $0.5M$
• B. $0.45M$
• C. $0.045M$
• D. None of these

Answer 1

Answer: (A)

$0.5M$

${AgBr}_{\left(s\right)}+{2S_2{O}_3^{2-}}_{\left(aq\right)}\leftrightharpoons {Ag(S_2{O}_3{)}_2^{3-}}_{\left(aq\right)}+{B{r}^{-}}_{\left(aq\right)}$

$a$ $a$

Now, $A{g}^{+}+2S_2{O}_3^{2-}\leftrightharpoons Ag(S_2{O}_3{)}_2^{3-}$

$K_f=\frac{\left[Ag\right(S_2{O}_3{)}_2^3]}{\left[A{g}^{+}\right][S_2{O}_3^{2-}{]}^2}$

and ${AgBr}_{\left(s\right)}\leftrightharpoons {A{g}^{+}}_{\left(aq\right)}+{B{r}^{-}}_{\left(aq\right)}$

$a$ $a$

$K_{sp}=\left[A{g}^{+}\right]\left[B{r}^{-}\right]$

$\therefore K_{sp}\times K_f=\frac{\left[Ag\right(S_2{O}_3{)}_2^3\left]\right[B{r}^{-}]}{[S_2{O}_3^{2-}{]}^2}$

Given that $\left[N{a}_2{S}_2{O}_3\right]=0.1$ $M$

$⟹\left[S_2{O}_3^{2-}\right]=0.1$ $M$

$\therefore 5\times {10}^{-13}\times 5\times {10}^{13}=\frac{a\times a}{(0.1{)}^2}$

$\therefore a^2=25\times {10}^{-2}$

$\therefore a=5\times {10}^{-1}$ $M=0.5$ $M$.

$\therefore a=5\times {10}^{-1}$ $M=0.5$ $M$

$\therefore$ Molar solubility of $AgBr=a=0.5$ $M$