Q. The standard emf for the cell reaction, ${2Cu}^{+}\ (aq)\ \rightarrow \ 2Cu\ (s)\ + \ {Cu}^{+}\ (aq)$ is +0.36 V at 298 K. The equilibrium constant of the reaction is
A) $5\ \times \ 10^{6}$
B) $1.4\ \times \ 10^{12}$
C) $7.4\ \times \ 10^{12}$
D) $1.2\ \times \ 10^{6}$
Explanation
(d)
E = $E^{{^\circ}}$ - $\frac{0.059}{n}$ log $\left\lbrack \frac{M}{M^{n +}} \right\rbrack$
= $E^{{^\circ}}$ - $\frac{0.059}{n}$ log $\left\lbrack \frac{products}{reactants} \right\rbrack$
E = 0 at equilibrium
0 = $E^{{^\circ}}$ - $\frac{0.059}{n}$ log $K_{eq}$
Or log $K_{eq}$ = $\frac{{nE}^{{^\circ}}}{0.059}$
Or log $K_{eq}$ = $\frac{1\ \times 0.36}{0.059}$ = 6.09
$K_{eq}$ = 1.2 × $10^{6}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.