1. Tardigrade
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  3. Chemistry
  4. For the electrochemical cell, Mg(s)|Mg2+(aq, 1 M)||Cu2+ (aq, 1 M)|Cu(s) the standard emf of the cell is 2.70 V at 300 K. When the concentration of Mg2+ is changed to x M, the cell potential changes to 2.67 V at 300 K. The value of x is . (given, (F/R) = 11500 K V−1, where F is the Faraday constant and R is the gas constant, ln(10) = 2.30)

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

JEE AdvancedJEE Advanced 2018Electrochemistry

Solution:

Cell reaction,
$Mg ( s )+ Cu ^{2+}( aq ) \rightarrow Mg ^{2+}( aq )+ Cu ( s )$
$E _{\text {cell }}^{ o }=2.70; E _{\text {Cell }}=2.67;$
$Mg ^{2+}= x M ; Cu ^{2+}=1\, M$
$E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{R T}{n F} \ln x$
$2.67=2.70-\frac{ RT }{2 F } \ln x$
$-0.03=-\frac{ R \times 300}{2 F } \times \ln x$
$\ln x=\frac{0.03 \times 2}{300} \times \frac{F}{R}$
$\ln x=\frac{0.03 \times 2 \times 11500}{300 \times 1}$
$\ln x=2.30=\ln (10)$
$\therefore x=10$