$Pt ( s ) H _2( g )(1 bar )\left| H ^{+}( aq )(1 M )\right|\left| M ^{3+}( aq ), M ^{+}( aq )\right| Pt ( s )$

$298\,K$ પર જ્યારે $\frac{\left[M^*(a q)\right]}{\left[M^{3 *}(a q)\right]}=10^a$ હોય ત્યારે આપેલ કોષ નો $E_{\text {cell }}$ એ $0.1115\,V$ છે. $a$ નું મૂલ્ય $............$ છે.આપેલ : $E _{ M }^\theta{ }^{3+} M ^{+}=0.2\,V$

$\frac{2.303\,R T}{F}=0.059\,V$

Question

$Pt ( s ) H _2( g )(1 bar )\left| H ^{+}( aq )(1 M )\right|\left| M ^{3+}( aq ), M ^{+}( aq )\right| Pt ( s )$

$298\,K$ પર જ્યારે $\frac{\left[M^*(a q)\right]}{\left[M^{3 *}(a q)\right]}=10^a$ હોય ત્યારે આપેલ કોષ નો $E_{\text {cell }}$ એ $0.1115\,V$ છે. $a$ નું મૂલ્ય $............$ છે.આપેલ : $E _{ M }^\theta{ }^{3+} M ^{+}=0.2\,V$

$\frac{2.303\,R T}{F}=0.059\,V$

A$2$
B$6$
C$8$
D$3$

JEE MAIN 2023, Diffcult

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Solution

d
Overall reaction :-

$H _{2( g )}+ M _{( aq )}^{3+} \longrightarrow M _{( aq )}^{+}+2 H _{( aq )}^{+}$

$E _{\text {Coll }}= E _{\text {Cathode }}^{\circ}- E _{\text {amode }}^{\circ}-\frac{0.059}{2} \log \frac{\left[ M ^{+}\right] \times 1^2}{\left[ M ^{+3}\right] 1}$

$0.1115=0.2-\frac{0.059}{2} \log \frac{\left[ M ^{+}\right]}{\left[ M ^{+3}\right]}$

$\quad 3=\log \frac{\left[ M ^{+}\right]}{\left[ M ^{+3}\right]}$

$\therefore a =3$

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