Question

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

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

Answer 1

Answer: (A)

$\Delta G=\Delta H-n F T\left(\frac{d E}{d T}\right)_{p}$
and $\Delta G=\Delta T-T \Delta S$
$\therefore \frac{\Delta S}{n F}=\left(\frac{d E}{d T}\right)_{p}$
or $\frac{96.5}{2 \times 96500}=\left(\frac{d F}{d T}\right)_{p}$
$\therefore \left(\frac{d E_{\text {cell }}}{d T}\right)_{p}=\frac{1 \times 10^{-3}}{2}$
$=5 \times 10^{-4} VK ^{-1}$