Question

If for the cell reaction, $Zn+{Cu}^{2+}\rightleftharpoons Cu+{Zn}^{2+}$, entropy change $\Delta S^o$ is $96.5$ $J{mol}^{-1}{K}^{-1}$, then temperature coefficient of the emf of a cell is :

• A. $5\times {10}^{-4}V{K}^{-1}$
• B. $1\times {10}^{-3}V{K}^{-1}$
• C. $2\times {10}^{-3}V{K}^{-1}$
• D. $9.65\times {10}^{-4}V{K}^{-1}$

Answer 1

Answer: (A)

$5\times {10}^{-4}V{K}^{-1}$

$\Delta G=\Delta H-nFT{\left(\frac{dE}{dT}\right)}_P$

and $\Delta G=\Delta H-T\Delta S$

$\therefore \frac{\Delta S}{nF}={\left(\frac{dE}{dT}\right)}_P$

or $\frac{96.5}{2\times 96500}={\left(\frac{dE}{dT}\right)}_P$

$\therefore {\left(\frac{d{E}_{cell}}{dT}\right)}_P=\frac{1\times {10}^{-3}}{2}=5\times {10}^{-4}V{K}^{-1}$