A fuel cell designed to react grain alcohol with oxygen has the following net reaction: C 2 H 5 OH ( l ) + 3 O 2 ( g ) → 2 CO 2 ( g ) + 3 H 2 O ( l ) The maximum work that 1 mole of alcohol can do is 1.32 × 10 3 kJ. What is the theoretical maximum voltage this cell can achieve at 25°C?

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Interpretation Introduction Interpretation: The reaction taking place in grain alcohol and Oxygen in a fuel cell is given. The theoretical maximum voltage that given cell can achieve at 25 ° C for the given amount of maximum work is to be calculated. Concept introduction: Gibbs free energy is basically the maximum amount of non-expansion work done. Therefore, it is represented as, W max = Δ G ° The maximum amount of work that is done by an electrochemical cell is given as, W max = n F E ° cell The relationship between Gibbs free energy change and equilibrium constant is given by the formula, Δ G ° = − n F E ° cell To determine: The value of theoretical maximum voltage that given cell can achieve at 25 ° C . Explanation Given, The reaction between grain alcohol and oxygen is, C 2 H 5 OH ( l ) + 3 O 2 ( g ) → 2 CO 2 ( g ) + 3 H 2 O ( l ) The maximum amount of work done is 1.32 × 10 3 kJ . Conversion of kJ to J is done as, 1 kJ = 1000 J Conversion of 1.32 × 10 3 kJ to J is, 1.32 × 10 3 kJ = 1.32 × 10 3 × 1000 J = 132 × 10 4 J The number of moles of alcohol is 1 The reaction taking place at the cathode is, 3 O 2 + 12 H + + 12 e − → 6 H 2 O The reaction taking place at the anode is, C 2 H 5 OH + 3 H 2 O → 12 H + + 12 e − + 2 CO 2 The reaction involves the transfer of 12 moles of electrons. The relationship between Gibbs free energy change and cell potential is given by the formula, Δ G ° = − n F E ° cell Where, Δ G ° 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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Chemistry: An Atoms First Approach

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Steven S. Zumdahl + 1 other

Publisher: Cengage Learning

ISBN: 9781305079243

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Interpretation Introduction

Interpretation:

The reaction taking place in grain alcohol and Oxygen in a fuel cell is given. The theoretical maximum voltage that given cell can achieve at 25 °C for the given amount of maximum work 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

To determine: The value of theoretical maximum voltage that given cell can achieve at 25 °C .

Explanation of Solution

Given,

The reaction between grain alcohol and oxygen is,

C2H5OH(l)+3O2(g)→2CO2(g)+3H2O(l)

The maximum amount of work done is 1.32×103 kJ .

Conversion of kJ to J is done as,

1 kJ=1000 J

Conversion of 1.32×103 kJ to J is,

1.32×103 kJ=1.32×103×1000 J=132×104 J

The number of moles of alcohol is 1

The reaction taking place at the cathode is,

3O2+12H++12e−→6H2O

The reaction taking place at the anode is,

C2H5OH+3H2O→12H++12e−+2CO2

The reaction involves the transfer of 12 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

A fuel cell designed to react grain alcohol with oxygen has the following net reaction: C 2 H 5 OH ( l ) + 3 O 2 ( g ) → 2 CO 2 ( g ) + 3 H 2 O ( l ) The maximum work that 1 mole of alcohol can do is 1.32 × 10 3 kJ. What is the theoretical maximum voltage this cell can achieve at 25°C?

Chemistry: An Atoms First Approach

Solutions

Chemistry: An Atoms First Approach

A fuel cell designed to react grain alcohol with oxygen has the following net reaction:

C 2 H 5 OH ( l ) + 3 O 2 ( g ) → 2 CO 2 ( g ) + 3 H 2 O ( l )

The maximum work that 1 mole of alcohol can do is 1.32 × 10³ kJ. What is the theoretical maximum voltage this cell can achieve at 25°C?

Explanation of Solution

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A fuel cell designed to react grain alcohol with oxygen has the following net reaction: C 2 H 5 OH ( l ) + 3 O 2 ( g ) → 2 CO 2 ( g ) + 3 H 2 O ( l ) The maximum work that 1 mole of alcohol can do is 1.32 × 10 3 kJ. What is the theoretical maximum voltage this cell can achieve at 25°C?

Chemistry: An Atoms First Approach

Solutions

Chemistry: An Atoms First Approach