# Calculate the standard free-energy change at 25°C for the following reaction. 4 Al ( s ) + 3 O 2 ( g ) + 12 H + ( a q ) → 4 Al 3 + ( a q ) + 6 H 2 O ( l ) Use standard electrode potentials.

### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343

### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343

#### Solutions

Chapter
Section
Chapter 19, Problem 19.74QP
Textbook Problem
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## Calculate the standard free-energy change at 25°C for the following reaction. 4 Al ( s ) + 3 O 2 ( g ) + 12 H + ( a q ) → 4 Al 3 + ( a q ) + 6 H 2 O ( l ) Use standard electrode potentials.

Expert Solution
Interpretation Introduction

Interpretation:

The free energy change of given voltaic cell should be calculated by using standard reduction potentials.

Concept introduction:

Cell potential (EMF):

The maximum potential difference between two electrodes in the voltaic cell is known as cell potential.

If standard reduction potentials of electrodes are given the cell potential (EMF) is given by,

Ecell=Ecathode-Eanode

Where,

Ecathodeisthereductionhalfcell potentialEanodeistheoxidationhalfcell potential

Free energy change:

In thermodynamics the cell potential is known as  maximum work of the cell and it is equal to free energy change of the cell and it is given by,

ΔG=-nFEcell

Where,

### Explanation of Solution

Given:

4Al(s) + 3O2(g) + 12H+(aq)4Al3+(aq) + 6H2O(l)

The given voltaic cell is recorder as shown above.

To calculate the cell potential (EMF) of given cell

The standard reduction potentials of (SRQ) of half cell reactions are record from standard reduction potentials table and they are,

4Al(s) 4Al3+(aq) + 12e-SQR=-1.66 V3O2(g) + 12H+(aq) + 12e-6H2O(l)SQR=1.23V

The most positive SQR is considering as cathode potential.

The SQR of electrodes are plugged in the bellow equation to give cell potential of given voltaic cell.

Ecell=Ecathode-Eanode=1

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