F or the electrochemical cell, Mg ( s ) Mg 2+ ( aq , 1 M ) \ Cu 2+ ( aq , 1 M ) Cu ( s ) 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 )

Chemistry · Electrochemistry

JEE Advanced 2018 — Paper 1 — Question 22

F or the electrochemical cell,

$\operatorname{Mg}(\mathrm{s})\left|\mathrm{Mg}^{2+}(\mathrm{aq}, 1 \mathrm{M}) \| \mathrm{Cu}^{2+}(\mathrm{aq}, 1 \mathrm{M})\right| \mathrm{Cu}(\mathrm{s})$

the standard emf of the cell is 2.70 V at 300 K . When the concentration of $\mathrm{Mg}^{2+}$ is changed to ${x} \mathrm{M}$ ,

the cell potential changes to 2.67 V at 300 K . The value of ${x}$ is $\_\_\_\_$ .

(given, $\frac{\mathrm{F}}{\mathrm{R}}=11500 \mathrm{~K} \mathrm{~V}^{-1}$ , where $F$ is the Faraday constant and $R$ is the gas constant, $\ln (10)=2.30$ )

Answer: 10

Numerical answer — enter this value.

Step-by-step solution

Case I: $\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{0}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{1}{1}$

$=2.7-0=2.7 \mathrm{~V}$

Case II: $\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{0}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\mathrm{x}}{1}$

$2.67=2.7-\frac{\mathrm{R} \times 300}{2 \mathrm{~F}} \ell \mathrm{nx}$

$-0.03=-\frac{\mathrm{R} \times 300}{2 \mathrm{~F}} \operatorname{lnx}$

$\ell \mathrm{nx}=\frac{0.03 \times 2 \times \mathrm{F}}{300 \times \mathrm{R}}=2.3$

$\mathrm{x}=10$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2018
Paper: Paper 1
Subject: Chemistry
Chapter: Electrochemistry
Topic: Nernst Equation and Electrochemical Series