   # Consider the reaction Fe 2 O 3 ( s ) + 3 H 2 ( g ) → 2 Fe ( s ) + 3 H 2 O ( g ) a. Use Δ G f ∘ values in Appendix 4 to calculate ∆G ° for this reaction. b. Is this reaction spontaneous under standard conditions at 298 K? c. The value of ∆H ° for this reaction is 100. kJ. At what temperatures is this reaction spontaneous at standard conditions? Assume that ∆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 16, Problem 61E
Textbook Problem
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## Consider the reaction Fe 2 O 3 ( s ) + 3 H 2 ( g ) → 2 Fe ( s ) + 3 H 2 O ( g ) a. Use Δ G f ∘ values in Appendix 4 to calculate ∆G° for this reaction.b. Is this reaction spontaneous under standard conditions at 298 K?c. The value of ∆H° for this reaction is 100. kJ. At what temperatures is this reaction spontaneous at standard conditions? Assume that ∆H° and ∆S° do not depend on temperature.

(a)

Interpretation Introduction

Interpretation: The value of ΔGο for the given reaction is to be calculated. The spontaneity under standard conditions is to be predicted and the temperature for the same condition is to be stated. The independency of ΔHο and ΔSο on the temperature is to be assumed.

Concept introduction: The term ΔGο is a thermodynamic function. The superscript on this function represents its standard form. The term Δ represents the change. This function is known as the standard Gibb’s free energy change. It correlates the enthalpy and entropy of the system in a mathematical formula.

To determine: The value of ΔGο for the given reaction by the use of ΔGfο values given in appendix 4 .

### Explanation of Solution

Given

The reaction is given as,

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

The values of ΔGfο given is appendix 4 are as follows,

SubstanceΔGfο(kJ/mol)Fe(s)0H2O(g)229Fe2O3(s)740H2(g)0

The value of standard Gibb’s free energy ΔGο of the given reaction is calculated by the formula,

ΔGο=npΔGfο(products)nrΔGfο(reactants)

Where,

• ΔGfο(reactants) are the standard free energy of formation for the reactants.
• ΔGfο(products) are the standard free energy of formation for the products.
• np is the number of products molecule.
• nr is the number of reactants molecule.
• is the symbol of summation

(b)

Interpretation Introduction

Interpretation: The value of ΔGο for the given reaction is to be calculated. The spontaneity under standard conditions is to be predicted and the temperature for the same condition is to be stated. The independency of ΔHο and ΔSο on the temperature is to be assumed.

Concept introduction: The term ΔGο is a thermodynamic function. The superscript on this function represents its standard form. The term Δ represents the change. This function is known as the standard Gibb’s free energy change. It correlates the enthalpy and entropy of the system in a mathematical formula.

To determine: Whether the reaction is spontaneous under standard conditions at 298K .

(c)

Interpretation Introduction

Interpretation: The value of ΔGο for the given reaction is to be calculated. The spontaneity under standard conditions is to be predicted and the temperature for the same condition is to be stated. The independency of ΔHο and ΔSο on the temperature is to be assumed.

Concept introduction: The term ΔGο is a thermodynamic function. The superscript on this function represents its standard form. The term Δ represents the change. This function is known as the standard Gibb’s free energy change. It correlates the enthalpy and entropy of the system in a mathematical formula.

To determine: The temperature at which the given reaction is spontaneous at standard conditions.

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