   # Consider the cell described below: Al | Al 3+ ( 1.00 M ) | | Pb 2+ ( 1.00 M ) | Pb Calculate the cell potential after the reaction has operated long enough for the [Al 3+ ] to have changed by 0.60 mol/L. (Assume T = 25°C.) ### 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 74E
Textbook Problem
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## Consider the cell described below: Al | Al 3+ ( 1.00   M ) |   | Pb 2+ ( 1.00 M ) | Pb Calculate the cell potential after the reaction has operated long enough for the [Al3+] to have changed by 0.60 mol/L. (Assume T = 25°C.)

Interpretation Introduction

Interpretation:

The standard line notation for a cell is given. The cell potential after the reaction has operated long enough for the [Al3+] to have changed by 0.60mol/L is to be calculated.

Concept introduction:

The relationship between reduction potential and standard reduction potential value and activities of species present in an electrochemical cell at a given temperature is given by the Nernst equation.

The value of Ecell is calculated using Nernst formula,

E=E°(RTnF)ln(Q)

At room temperature the above equation is specifies as,

E=E°(0.0591n)log(Q)

To determine: The cell potential after the reaction has operated long enough for the [Al3+] to have changed by 0.60mol/L .

### Explanation of Solution

Given

The standard line notation is,

Al|Al3+(1.00M)||Pb2+(1.00M)|Pb

The reaction taking place on cathode,

Pb2++2ePbE°red=0.13V

The reaction taking place at anode,

AlAl3++3eE°ox=1.66V

Multiply reduction half-reaction with a coefficient of 3 and oxidation half-reaction with a coefficient of 2 and then add both the reduction half and oxidation half-reaction.

3Pb2++6e3Pb2Al2Al3++6e

The final equation is,

3Pb2++2Al3Pb+2Al3+

The overall cell potential is calculated as,

E°cell=E°ox+E°red=1

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