Chapter 21, Problem 64PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# The overall reaction involved in the industrial synthesis of nitric acid is NH 3 ( g ) + 2  O 2 ( g ) → HNO 3 (aq) + H 2 O( l ) Calculate ΔrG° for this reaction and its equilibrium constant at 25°C.

Interpretation Introduction

Interpretation:

The free energy change for the given reaction has to be calculated.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔG. The expression for the free energy change is:

ΔrG°=nΔfG°(products)nΔfG°(reactants)

ΔG is also related to the equilibrium constant K by the equation,

ΔrG=RTlnKp

The rearranged expression is,

Kp=eΔrGRT

Explanation

The Î”rGÂ° and the equilibrium constant for the reaction of ammonia and oxygen is calculated below.

Given:

Refer to Appendix L for the values of standard free energies.

The standard free energy of HNO3(aq) is âˆ’111.25Â J/Kâ‹…mol.

The standard free energy of H2O(l) is âˆ’237.15Â J/Kâ‹…mol.

The standard free energy of NH3(g) is âˆ’16.37Â J/Kâ‹…mol.

The standard free energy of O2(g) is 0Â J/Kâ‹…mol.

The balanced chemical equation is:

Â NH3(g)+2O2(g)â†’HNO3(aq)+H2O(l)

The Î”rGÂ° can be calculated by the following expression,

Î”rGÂ°=âˆ‘nÎ”fGÂ°(products)âˆ’âˆ‘nÎ”fGÂ°(reactants)=[[(1Â molÂ HNO3(aq)/mol-rxn)Î”fGÂ°[HNO3(aq)]+(1Â molÂ H2O(l)/mol-rxn)Î”fGÂ°[H2O(l)]]âˆ’[(1Â molÂ NH3(g)/mol-rxn)Î”fGÂ°[NH3

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