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  4. textPt( s ) H 2( g )(1 bar )| H +( aq )(1 M )|| M 3+( aq ), M +( aq )| textPt( s ) The E text cell for the given cell is 0.1115 V at 298 K when ([ M +( aq )]/[ M 3+( aq )])=10 a The value of a is Given: E M 3+ / M +θ=0.2 V (2.303 RT / F )=0.059 V

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Q. $\text{Pt}( s ) H _2( g )(1 bar )\left| H ^{+}( aq )(1 M )\right|\left| M ^{3+}( aq ), M ^{+}( aq )\right| \text{Pt}( s )$
The $E _{\text {cell }}$ for the given cell is $0.1115 V$ at $298 K$ when $\frac{\left[ M ^{+}( aq )\right]}{\left[ M ^{3+}( aq )\right]}=10^{ a }$
The value of $a$ is ____
Given : $E _{ M ^{3+} / M ^{+}}^\theta=0.2\, V$
$\frac{2.303 RT }{ F }=0.059\, V$

JEE MainJEE Main 2023Electrochemistry

Solution:

Overall reaction :-
$ H _{2( g )}+ M _{\text {(aq) }}^{3+} > M _{\text {(aq) }}^{+}+2 H _{\text {(aq) }}^{+}$
$ E _{\text {Cell }}= E _{\text {Cathode }}^{ o }- E _{\text {anode }}^{\circ}-\frac{0.059}{2} \log \frac{\left[ M ^{+}\right] \times 1^2}{\left[ M ^{+3}\right] 1} $
$ 0.1115=0.2-\frac{0.059}{2} \log \frac{\left[ M ^{+}\right]}{\left[ M ^{+3}\right]} $
$ 3=\log \frac{\left[ M ^{+}\right]}{\left[ M ^{+3}\right]}$
$\therefore a =3$