The overall reaction and standard cell potential at 25^∘ C for the rechargeable nickel-cadmium a

step 1 We are given an overall cell reaction as well as the value of the cell potential, and we want to

The overall reaction and standard cell potential at 25^∘ C...

The overall reaction and standard cell potential at $25^{\circ} \mathrm{C}$ for the rechargeable nickel-cadmium alkaline battery is $\mathrm{Cd}(s)+\mathrm{NiO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$ $\mathrm{Ni}(\mathrm{OH})_{2}(s)+\mathrm{Cd}(\mathrm{OH})_{2}(s) \quad \mathscr{E}^{\circ}=1.10 \mathrm{~V}$ For every mole of Cd consumed in the cell, what is the maximum useful work that can be obtained at standard conditions?

The overall reaction and standard cell potential at $25^{\circ} \mathrm{C}$ for the rechargeable nickel-cadmium alkaline battery is
$\mathrm{Cd}(s)+\mathrm{NiO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$
$\mathrm{Ni}(\mathrm{OH})_{2}(s)+\mathrm{Cd}(\mathrm{OH})_{2}(s) \quad \mathscr{E}^{\circ}=1.10 \mathrm{~V}$
For every mole of Cd consumed in the cell, what is the maximum useful work that can be obtained at standard conditions?

Key Concepts

Faraday's Constant

Faraday's constant, often denoted as F, is approximately 96485 coulombs per mole of electrons. It is a fundamental constant in electrochemistry that relates the amount of electric charge carried per mole of electrons, providing a bridge between chemical and electrical quantities.

Reaction Stoichiometry

Reaction stoichiometry in electrochemistry is critical because it determines the number of electrons involved in the redox process. The number of electrons transferred (n) in the reaction is needed to calculate the Gibbs free energy change, which directly impacts the calculation of the maximum electrical work available from the reaction.

Standard Cell Potential

The standard cell potential is a measure of the voltage difference between the two electrodes of an electrochemical cell under standard conditions. It represents the driving force behind the electron flow during the electrochemical reaction and is a key indicator of the cell's ability to perform electrical work.

Gibbs Free Energy and Maximum Work

The maximum useful work obtainable from an electrochemical reaction is given by the negative change in Gibbs free energy, represented by the equation ?G° = -nFE°. This relationship connects the cell’s potential to the thermodynamic feasibility of the reaction, indicating how much electrical work can be performed when electrons are transferred during the reaction.

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