Question

The cell potential $\left(E_{cell}\right)$ of a reaction is related as $\Delta G=nF{E}_{cell}$, where $\Delta G$ represents maximum useful electrical work.
n = no. of moles of electrons exchanged during the reaction.
For reversible cell reaction $d\left(\Delta G\right)=\left(\Delta V\right)dp-\left(\Delta S\right)dT$
At const. P, $d\left(\Delta G\right)=-\left(\Delta S\right)dT$
At const. P, $\Delta G=\Delta H-T\Delta S$. (1)
$\therefore \Delta G=\Delta H+T{\left(\frac{d\left(\Delta G\right)}{\Delta T}\right)}_P$. (2)
${\left(\frac{d{E}_{cell}}{dT}\right)}_p$ is known as temperature coefficient of the emf of the cell.

The temperature coefficient of the emf the cell, ${\left(\frac{dE}{dT}\right)}_p$ is given by

• A. $\frac{nF}{\Delta S}$
• B. $\frac{\Delta S}{nF}$
• C. $\frac{\Delta S}{nFT}$
• D. $-nFE$

Answer 1

The correct option is B $\frac{\Delta S}{nF}$

From equations (1) and (2)
$-\Delta S=\frac{d\left(\Delta G\right)}{dT}=\frac{d(-nFE)}{dT}$
$\Delta S=nF=\frac{dE}{dT}or\frac{dE}{dT}=\frac{\Delta S}{nF}$