   Chapter 17, Problem 105CP

Chapter
Section
Textbook Problem

# Using data from Appendix 4, calculate ∆H°, ∆G°, and K (at 298 K) for the production of ozone from oxygen: 3 O 2 ( g ) ⇌ 2 O 3 ( g ) At 30 km above the surface of the earth, the temperature is about 230. K and the partial pressure of oxygen is about 1.0 × 10−3 atm. Estimate the partial pressure of ozone in equilibrium with oxygen at 30 km above the earth's surface. Is it reasonable to assume that the equilibrium between oxygen and ozone is maintained under these conditions? Explain.

Interpretation Introduction

Interpretation: The value of ΔHο , ΔGο and K for the production of ozone from oxygen is to be calculated. The partial pressure of ozone is estimated to be in equilibrium with oxygen at 30 km above the Earth’s surface. Whether it is reasonable to assume that the equilibrium between the oxygen and ozone is maintained under these conditions is to be stated with explanation.

Concept introduction: Thermodynamics is associated with heat, temperature and its relation with energy and work. It helps us to predict whether a process will take place or not. But, it gives no information about the time required for the process. The terms associated with thermodynamics are system, surrounding, entropy, spontaneity and many more.

To determine: The value of ΔHο , ΔGο and K for the production of ozone from oxygen and whether it is reasonable to assume that the equilibrium between the oxygen and ozone is maintained under these conditions with explanation.

Explanation

Explanation

The given reaction is,

3O2(g)2O3(g)

The standard enthalpy change ( ΔHο ) is calculated by the formula,

ΔHο=(Number of moles of products×ΔHfοProducts Number of moles of reactants×ΔHfοReactants)

The number of moles of products is 2 .

The number of moles of reactants is 3 .

ΔHfο Products =Standard enthalpy of formation of O3(g) = 143 kJ/mol .

ΔHfο Reactants =Standard enthalpy of formation of O2(g) = 0 kJ/mol .

Substitute the number of moles of reactants and products and their standard enthalpy of formation in the above equation.

ΔHο=(2×143 kJ/mol 3×0)=286 kJ/mol_

The standard energy change ( ΔGο ) is calculated by the formula,

ΔGο=(Number of moles of products×ΔGfο Products Number of moles of reactants×ΔGfο Reactants)

The number of moles of products is 2 .

The number of moles of reactants is 3 .

ΔGfο  Products =Standard enthalpy of formation of O3(g) = 163 kJ/mol .

ΔGfο  Reactants =Standard enthalpy of formation of O2(g) = 0 kJ/mol .

Substitute the number of moles of reactants and products and their standard enthalpy of formation in the above equation.

ΔGο=(2×163 kJ/mol 3×0)=326 kJ/mol

The relationship between ΔG , ΔGο  and Q is expressed by the equation,

ΔG=ΔGο +RTlnQ

Where,

• ΔG is the Gibbs free energy change

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