QJEEAdv18Ch87af: JEE Advanced 2018 Chemistry - Class 12 JEEAdv18Ch87af Solution: For the electrochemical cell, the standard of the cell is at…

Equation of cell reaction according to the cell notation given, is

Given, E $_{cell}^o$ = 2.70 V, T = 300 K with [Mg²⁺(aq)] = 1 M and [Cu²⁺(aq)] = 1 M and n = 2

Further, E_cell = 2.67 V with [Cu²⁺(aq)] = 1 M and [Mg²⁺(aq)] = xM and ${F \over R}$ = 11500 KV ^{$-$ 1} where F = Faraday constant, R = gas constant

From the formula,

E_cell = E $_{cell}^o$ $-$ ${{RT} \over {nF}}\ln {{[M{g^{2 + }}(aq)]} \over {[C{u^{2 + }}(aq)]}}$

After putting the given values

$2.67 = 2.70 - {{RT} \over {2F}}\ln {x \over 1}$

or $2.67 = 2.70 - {{R \times 300} \over {2F}} \times \ln x$

$- 0.03 = {{ - R \times 300} \over {2F}} \times \ln x$

or $\ln x = {{0.03 \times 2} \over {300}} \times {F \over R}$

$= {{0.03 \times 2 \times 11500} \over {300}} = 2.30$

So, $\ln x = 2.30$

or x = 10 (as given $\ln (10) = 2.30$ )