   # Explain the following relationships: Δ G and w , cell potential and w, cell potential and Δ G, cell potential and Q. Using these relationships, explain how you could make a cell in which both electrodes are the same metal and both solutions contain the same compound, but at different concentrations. Why does such a cell run spontaneously? ### 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 8ALQ
Textbook Problem
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## Explain the following relationships: ΔG and w, cell potential and w, cell potential and ΔG, cell potential and Q. Using these relationships, explain how you could make a cell in which both electrodes are the same metal and both solutions contain the same compound, but at different concentrations. Why does such a cell run spontaneously?

Interpretation Introduction

Interpretation:

A cell with the electrodes of the same metal and solution of the same compound but with a different solution concentration is given. The relationships between cell potential, Gibbs free energy change and wmax and their use for the construction of above cell is to be stated.

Concept introduction:

Concentration difference leads to the spontaneous reaction in a concentration cell because a higher difference in concentration leads to positive cell potential and therefore, the change in Gibbs free energy comes out to be negative which means a spontaneous reaction. The Gibbs free energy change is the maximum work done therefore concentration difference will lead to the maximum work that can be obtained.

To determine: The type of cell formed by the electrodes of the same metal and solutions of the same compound, but at different concentration; the relationships among w , ΔG , E , Q and the reason of spontaneous reaction taking place in the cell formed.

### Explanation of Solution

The various relationships can be represented as follows,

wmax = ΔG

Where, the change in free energies defines the maximum work done.

wmax = -qEmax

ΔG = -nFEcell

Ecell = E°cell - 2.303 (RTnF) log(Q)

The cell which consists of the same type of electrodes and the same type of solutions just varying in concentration is called concentration cell.

When the concentration difference is higher and the value of cell potential comes out to be positive, then ΔG will be negative and thus, the reaction will occur in the cell.

The various relationships are represented as follows,

wmax = ΔG

Where, the change in free energies defines the maximum work done.

wmax = -qEmax

ΔG = -nFEcell

Ecell = E°cell - 2

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