Question

For the electrochemical cell,
$Mg\left(s\right)\left|M{g}^{2+}\left(aq,1M\right)\right|\left|C{u}^{2+}\left(aq,1M\right)\right|Cu\left(s\right)$
the standard emf of the cell is $2.70V$ at $300K$. When the concentration of $M{g}^{2+}$ is changed to $xM$, the cell potential changes to $2.67V$ at $300K$. The value of $x$ is ____.
(given, $\frac{F}{R}=11500K{V}^{-1}$, where $F$ is the Faraday constant and $R$ is the gas constant, $ln(10)=2.30$)

Answer 1

Answer: 10

Cell reaction,
$Mg(s)+C{u}^{2+}(aq)\to M{g}^{2+}(aq)+Cu(s)$
$E_{\text{cell }}^o=2.70;E_{\text{Cell }}=2.67;$
$M{g}^{2+}=xM;C{u}^{2+}=1M$
$E_{\text{cell }}=E_{\text{cell }}^{\circ }-\frac{RT}{nF}\ln x$
$2.67=2.70-\frac{RT}{2F}\ln x$
$-0.03=-\frac{R\times 300}{2F}\times \ln x$
$\ln x=\frac{0.03\times 2}{300}\times \frac{F}{R}$
$\ln x=\frac{0.03\times 2\times 11500}{300\times 1}$
$\ln x=2.30=\ln (10)$
$\therefore x=10$