   # Calculate Δ r G ° for the decomposition of sulfur trioxide to sulfur dioxide and oxygen. 2 SO 3 (g) ⇄ 2 SO 2 (g) + O 2 (g) (a) Is the reaction product-favored at equilibrium at 25 °C? (b) If the reaction is not product-favored at 25 °C, is there a temperature at which it will become so? Estimate this temperature. (c) Estimate the equilibrium constant for the reaction at 1500 °C. ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 18, Problem 55GQ
Textbook Problem
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## Calculate ΔrG° for the decomposition of sulfur trioxide to sulfur dioxide and oxygen.2 SO3(g) ⇄ 2 SO2(g) + O2(g) (a) Is the reaction product-favored at equilibrium at 25 °C? (b) If the reaction is not product-favored at 25 °C, is there a temperature at which it will become so? Estimate this temperature. (c) Estimate the equilibrium constant for the reaction at 1500 °C.

(a)

Interpretation Introduction

Interpretation:

It should be identified that whether the given reaction is product favoured at equilibrium of temperature 25oC.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrGo. It can be calculated in a similar manner as entropy and enthalpy. The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)

It is related to entropy and entropy by the following expression,

ΔGo= ΔHo- TΔSo

Here, ΔrHo is the change in enthalpy and ΔrSo is the change in entropy.

ΔrGo is related to the equilibrium constant Kp by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

### Explanation of Solution

The value of ΔrGo for the decompositon of sulfur trioxide is calculated below.

Given:

The Appendix L referred for the values of standard free energy values.

The given reaction is,

2SO3(g)2SO2(g)+O2(g)

The ΔrGo for SO2(g) is 300.13 kJ/mol.

The ΔrGo for O2(g) is 0 kJ/mol.

The ΔrGo for SO3(g) is 371.04 kJ/mol.

ΔrG°fG°(products)fG°(reactants)=[[(2 mol SO2(g)/mol-rxn)ΔfG°[SO2(

(b)

Interpretation Introduction

Interpretation:

The temperature at which given reaction is product favoured should be identified.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrGo. It can be calculated in a similar manner as entropy and enthalpy. The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)

It is related to entropy and entropy by the following expression,

ΔGo= ΔHo- TΔSo

Here, ΔrHo is the change in enthalpy and ΔrSo is the change in entropy.

ΔrGo is related to the equilibrium constant Kp by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

(c)

Interpretation Introduction

Interpretation:

The equilibrium constant for the given reaction should be calculated at 1500oC.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrGo. It can be calculated in a similar manner as entropy and enthalpy. The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)

It is related to entropy and entropy by the following expression,

ΔGo= ΔHo- TΔSo

Here, ΔrHo is the change in enthalpy and ΔrSo is the change in entropy.

ΔrGo is related to the equilibrium constant Kp by the equation,

ΔrGo= -RTlnKp

The rearranged expression is,

Kp= eΔrGoRT

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