   # The major industrial use of hydrogen is in the production of ammonia by the Haber process: 3H 2 ( g ) + N 2 ( g ) → 2NH 3 ( g ) a. Using data from Appendix 4, calculate ∆ H °, ∆ S °, and ∆ G ° for the Haber process reaction. b. Is the reaction spontaneous at standard conditions? c. At what temperatures is the reaction spontaneous at standard conditions? Assume ∆ H ° and ∆ S ° do not depend on temperature. ### 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 19, Problem 12E
Textbook Problem
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## The major industrial use of hydrogen is in the production of ammonia by the Haber process: 3H 2 ( g ) + N 2 ( g ) → 2NH 3 ( g ) a. Using data from Appendix 4, calculate ∆H°, ∆S°, and ∆G° for the Haber process reaction.b. Is the reaction spontaneous at standard conditions?c. At what temperatures is the reaction spontaneous at standard conditions? Assume ∆H° and ∆S° do not depend on temperature.

(a)

Interpretation Introduction

Interpretation: Reaction of commercial production of ammonia is given. The value of ΔH° and ΔS° is to be calculated for the given reaction. If the reaction is spontaneous is to be identified. The temperature at which this reaction is spontaneous is to be calculated.

Concept introduction: The expression to calculate ΔH° is,

ΔH°=npΔH°(product)nfΔH°(reactant)

The expression to calculate ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

A reaction is said to be spontaneous if the value of ΔG° is negative.

### Explanation of Solution

Explanation

The stated reaction is,

3H2(g)+N2(g)2NH3(g)

Refer to Appendix 4

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

 Molecules ΔH°(kJ/mol) NH3(g) −46 N2(g) 0 H2(g) 0

The formula of ΔH° is,

ΔH°=npΔH°(product)nfΔH°(reactant)

Where,

• ΔH° 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 the values from the table in the above equation.

ΔH°=npΔH°(product)nfΔH°(reactant)=[2(46){3(0)+(0)}]kJ=92kJ_

The value of ΔS° for the given reaction is 199J/K_

(b)

Interpretation Introduction

Interpretation: Reaction of commercial production of ammonia is given. The value of ΔH° and ΔS° is to be calculated for the given reaction. If the reaction is spontaneous is to be identified. The temperature at which this reaction is spontaneous is to be calculated.

Concept introduction: The expression to calculate ΔH° is,

ΔH°=npΔH°(product)nfΔH°(reactant)

The expression to calculate ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

A reaction is said to be spontaneous if the value of ΔG° is negative.

(c)

Interpretation Introduction

Interpretation: Reaction of commercial production of ammonia is given. The value of ΔH° and ΔS° is to be calculated for the given reaction. If the reaction is spontaneous is to be identified. The temperature at which this reaction is spontaneous is to be calculated.

Concept introduction: The expression to calculate ΔH° is,

ΔH°=npΔH°(product)nfΔH°(reactant)

The expression to calculate ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

A reaction is said to be spontaneous if the value of ΔG° is negative.

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