   # Consider the reaction Fe 2 O 3 ( s ) + 3 H 2 ( g ) → 2 Fe ( s ) + 3 H 2 O ( g ) Assuming ∆H° and ∆ S ° do not depend on temperature, calculate the temperature where K = 1.00 for this reaction. ### 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 16, Problem 93AE
Textbook Problem
885 views

## Consider the reaction Fe 2 O 3 ( s ) + 3 H 2 ( g ) → 2 Fe ( s ) + 3 H 2 O ( g ) Assuming ∆H° and ∆S° do not depend on temperature, calculate the temperature where K = 1.00 for this reaction.

Interpretation Introduction

Interpretation: The reaction between Fe2O3(s) and H2(g) is given. The temperature at which the value of K is 1.00 is to be calculated.

ΔG°=RTln(K)

And,

ΔG°=ΔH°TΔS°

Hence,

ΔH°TΔS°=RTln(K)

### Explanation of Solution

The stated reaction is,

Fe2O3(s)+3H2(g)2Fe(s)+3H2O

Refer Appendix 4 .

The value of ΔH°(kJ) for the given reactant and product is,

 Molecules ΔH°(kJ) Fe2O3(s) −826 Fe(s) 0 H2(g) 0 H2O(g) −242

The formula of ΔH° is,

ΔH°=npΔH°(product)nfΔH°(reactant)

Where,

• ΔH° is the standard enthalpy of reaction.
• np is the number of moles of each product.
• nr is the number of moles each reactant.
• ΔH°(product) is the standard enthalpy of product at a pressure of 1atm .
• ΔH°(reactant) is the standard enthalpy of reactant at a pressure of 1atm .

Substitute all values from the table in the above equation.

ΔH°=npΔH°(product)nfΔH°(reactant)=[2(0)+3(242){(826)+3(0)}]kJ=100kJ_

Refer to Appendix 4 .

The value of ΔS°(J/K) for the given reactant and product is,

 Molecules ΔS°(J/K) Fe2O3(s) 90 Fe(s) 131 H2(g) 27 H2O(g) 189

The formula of ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

Where,

• ΔS° is the standard enthalpy of reaction.
• np is the number of moles of each product

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