   Chapter 19, Problem 112SCQ

Chapter
Section
Textbook Problem

The free energy change for a reaction, ΔrG°, is the maximum energy that can be extracted from the process as work, whereas ΔrH° is the total chemical potential energy change. The efficiency of a fuel cell is the ratio of these two quantities. Efficiency =  Δ r G ° Δ r H ° × 100 % Consider the hydrogen-oxygen fuel cell, where the net reaction is H 2 ( g )  +  1 2  O 2 ( g ) →  H 2 O ( l ) (a) Calculate the efficiency of the fuel cell under standard conditions. (b) Calculate the efficiency of the fuel cell if the product is water vapor instead of liquid water. (c) Does the efficiency depend on the state of the reaction product? Why or why not?

(a)

Interpretation Introduction

Interpretation:

The efficiency of fuel cell under standard conditions has to be determined.

Concept introduction:

The free energy change for a reaction  ΔrGo is a thermodynamic potential that can be used to calculate maximum reversible work. The system is held at constant temperature and pressure and is closed.

The heat evolved or absorbed when a reaction takes place at a constant pressure under the standard condition is called standard enthalpy change, ΔrHo of the reaction.

The efficiency of a fuel cell is given as,

Efficiency=ΔrGΔrH×100%

Explanation

The efficiency of the fuel cell under standard conditions is calculated below.

Given:

The hydrogen-oxygen fuel cell reaction is written as,

H2(g)+12O2(g)H2O(l)

Refer to the appendix L for the values of ΔrGo and ΔrHo.

The ΔrHo for liquid water is 285.83kJmol1.

The ΔrGo for liquid water is 237.15kJmol1

(b)

Interpretation Introduction

Interpretation:

The efficiency of a fuel cell if the product is water vapour instead of liquid water has to be determined.

Concept introduction:

The free energy change for a reaction  ΔrGo is a thermodynamic potential that can be used to calculate maximum reversible work. The system is held at constant temperature and pressure and is closed.

The heat evolved or absorbed when a reaction takes place at a constant pressure under the standard condition is called standard enthalpy change, ΔrHo of the reaction.

The efficiency of a fuel cell is given as,

Efficiency=ΔrGΔrH×100%

(c)

Interpretation Introduction

Interpretation:

The efficiency whether depends upon the reaction product or not has to be stated.

Concept introduction:

The free energy change for a reaction  ΔrGo is a thermodynamic potential that can be used to calculate maximum reversible work. The system is held at constant temperature and pressure and is closed.

The heat evolved or absorbed when a reaction takes place at a constant pressure under the standard condition is called standard enthalpy change, ΔrHo of the reaction.

The efficiency of a fuel cell is given as,

Efficiency=ΔrGΔrH×100%

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