Question

$P t(s)\left|II_2( g )(1 bar )\right| II^{+}(a q)(1 M)|| M^{3+}(a q), M^{+}(a q) \mid P t(s)$ The $E _{\text {cell }}$ for the given cell is $01115 V$ at $298 K$ when $\frac{\left[M^{+}(a q)\right]}{\left[M^{3+}(a q)\right]}=10^{\circ}$ The value of $a$ is _____ Given : $E ^\theta M ^{3+} M ^{+}=02 V$ $\frac{2303 R T}{F}=0059 V$

Answer 1

Correct Answer: 3

The correct answer is 3.
Overall reaction :-
$H_{2(g)}+M_{\text{(aq)}}^{3+}>M_{\text{(aq)}}^{+}+2H_{\text{(aq)}}^{+}$
$E_{\text{Cell}}=E_{\text{Cathode}}^o-E_{\text{anode}}^{\circ }-\frac{0.059}{2}\log \frac{\left[M^{+}\right]\times 1^2}{\left[M^{+3}\right]1}$
$0.1115=0.2-\frac{0.059}{2}\log \frac{\left[M^{+}\right]}{\left[M^{+3}\right]}$
$3=\log \frac{\left[M^{+}\right]}{\left[M^{+3}\right]}$
$\therefore a=3$