Question

The overall reaction and standard cell potential at 25°Cfor the rechargeable nickel-cadmium alkaline battery is
$Cd\left(s\right)+Ni{O}_2\left(s\right)+2H_{2}O\left(l\right)\to Ni(OH{)}_2\left(s\right)+Cd(OH{)}_2\left(s\right) E^o=1.1 V$
For every mole of Cd consumed in the cell, what is themaximum useful work that can be obtained at standardconditions?

Short answer

The maximum work done for consuming each mole is Cd=-212.2 kJ.

Step-by-step solution

Relation of Gibbs free energy and potential

The relation can be written as:

$\Delta {G^o}_{cell}=-nF{E^o}_{cell}$

Maximum work gained and equal to free energy change

The standard cell potential at 25^oC can be:

$E^o=1.1 V$

The maximum work gained should be equal to free energy change at standard condition for every mole of consumption of Cd.

$$\begin{gathered} \Delta G^o=-nF{E}^o \\ n=2 \\ \Delta G^o=-(2 mole)(96485C/mole)(1.1 V) \\ \Delta G^o=-212.2 kJ \end{gathered}$$