   # The overall reaction and standard cell potential at 25°C for the rechargeable nickel-cadmium alkaline battery is For every mole of Cd consumed in the cell, what is the maximum useful work that can be obtained at standard conditions? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 17, Problem 126AE
Textbook Problem
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## The overall reaction and standard cell potential at 25°C for the rechargeable nickel-cadmium alkaline battery is For every mole of Cd consumed in the cell, what is the maximum useful work that can be obtained at standard conditions?

Interpretation Introduction

Interpretation:

The overall reaction and standard cell potential at 25°C for the rechargeable Nickel-Cadmium alkaline battery is given. The maximum useful work that can be obtained for every mole of Cadmium consumed at standard conditions is to be calculated.

Concept introduction:

Gibbs free energy is basically the maximum amount of non-expansion work done. Therefore, it is represented as,

Wmax=ΔG°

The maximum amount of work that is done by an electrochemical cell is given as,

Wmax=nFE°cell

The relationship between Gibbs free energy change and equilibrium constant is given by the formula,

ΔG°=nFE°cell

The work is done by the system over the surroundings; therefore the work is taken as a negative term.

To determine: The maximum useful work that can be obtained for every mole of Cadmium consumed at standard conditions.

### Explanation of Solution

Given,

The value of E°cell is 1.10V .

The reaction taking place at cathode is,

NiO2+2H2O+2eNi(OH)2+2OH

The reaction taking place at anode is,

Cd+2OHCd(OH)2+2e

The overall reaction is,

Cd(s)+NiO2(s)+2H2O(l)Ni(OH)2(s)+Cd(OH)2(s)

The reaction involves the transfer of 2 moles of electrons.

The relationship between Gibbs free energy change and cell potential is given by the formula,

ΔG°=nFE°cell

Where,

• ΔG° is the Gibbs free energy change at the standard conditions.
• n is the number of moles of electrons that are involved in the reaction

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