Question

At what $\frac{\left[B{r}^{+}\right]}{\sqrt{\left[C{O}_3^{2-}\right]}}$ does the following cell have its reaction at equilibrium?
$Ag\left(s\right)|A{g}_{2}C{O}_3\left(s\right)|N{a}_{2}C{O}_3\left(aq\right)||KBr\left(aq\right)|AgBr\left(s\right)|Ag\left(s\right)$
$K_{sp}=8\times {10}^{-12}$ for $A{g}_{2}C{O}_2$ and $K_{sp}=4\times {10}^{-13}$ for AgBr.

• A. $\sqrt{1}\times {10}^{-7}$
• B. $\sqrt{2}\times {10}^{-7}$
• C. $\sqrt{3}\times {10}^{-7}$
• D. $\sqrt{4}\times {10}^{-7}$

Answer 1

Answer: (B)

$\sqrt{2}\times {10}^{-7}$

Anode: $Ag\left(s\right)\to A{g}^{+}\left(aq\right)+1e^{-}$
Cathode: $A{g}^{+}\left(aq\right)+1e^{-}\to Ag$
--------------------------------------------------------------
net: $A{g}_{AgBr}\stackrel{1e^{-}}{\leftarrow }A{g}_{A{g}_{2}C{O}_3}^{+}$
$0=0+\frac{0.059}{1}log\frac{\left(\frac{K_{sp}AgBr}{\left[B{r}^{-}\right]}\right)}{\sqrt{\frac{K_{sp}A{g}_{2}C{O}_3}{\left[C{O}_3^{-2}\right]}}}\Rightarrow \frac{K_{sp}AgBr}{\left[B{r}^{-}\right]}=\sqrt{\frac{K_{sp}A{g}_{2}C{O}_3}{\left[C{O}_3^{2-}\right]}}$
$=\frac{4\times {10}^{-13}}{\sqrt{8\times {10}^{-12}}}=\frac{\left[B{r}^{-}\right]}{\sqrt{\left[C{O}_3^{2-}\right]}}\Rightarrow \frac{\left[B{r}^{-}\right]}{\sqrt{\left[C{O}_3^{2-}\right]}}=\sqrt{2}\times {10}^{-7}$