   # Write a balanced equation that depicts the formation of 1 mol of Fe 2 O 3 (s) from its elements. What is the standard free energy of formation of 1.00 mol of Fe 2 O 3 (s)? What is the value of Δ G ° when 454 g (1 lb) of Fe 2 O 3 (s) is formed from the elements? ### 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 38GQ
Textbook Problem
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## Write a balanced equation that depicts the formation of 1 mol of Fe2O3(s) from its elements. What is the standard free energy of formation of 1.00 mol of Fe2O3(s)? What is the value of ΔG° when 454 g (1 lb) of Fe2O3(s) is formed from the elements?

Interpretation Introduction

Interpretation:

The balanced equation for formation of 1molFe2O3(s) should be written. The standard free energy change for the formation of 1molFe2O3(s) from its elements and the value of ΔGo for formation of 454 gFe2O3(s) should be calculated.

Concept introduction:

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

ΔrG°=nΔfG°(products)nΔfG°(reactants)

• Chemical equation is the representation of a chemical reaction, in which the reactants and products of the reactions are represented left and right side of an arrow respectively by using their respective chemical formulas.
• Reactant of a chemical reaction is the substrate compounds or the compounds which undergo a chemical reaction.
• Product of a chemical reaction is the produced compounds or the compounds formed after a chemical reaction.
• Balanced chemical equation of a reaction is written according to law of conservation of mass.

Moles: One mole is equivalent to the mass of the substance consists same number of units equal to the atoms present in 12g of 12C.

From given mass of substance moles could be calculated by using the following formula,

Molesofsubstance GivenmassofsubstanceMolecularmass

### Explanation of Solution

The given reaction is, Fe(s) + O2(g)Fe2O3(s)

The balanced chemical reaction obtained by multiplying 2 before Fe and 32 before O2

2Fe(s) + 32O2(g)Fe2O3(s)

The standard free energy change for the formation of Fe2O3(s) from its elements and the value of ΔrG when 454 g of Fe2O3(s) from its elements is calculated below.

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

The ΔfG° for Fe2O3(s) is 742.2 kJ/mol.

The ΔfG° for O2(g) is 0 kJ/mol.

The ΔfG° for Fe(s) is 0 kJ/mol.

ΔrG°=nΔfG°(products)nΔfG°(reactants)=[(1 mol Fe2O3(s)/mol-rxn)ΔfG°[Fe2O3(s)][(1.5 mol O2(g)/mol-rxn)ΔfG°[O2(g)]+(1 mol Fe(s)/mol-rxn)ΔfG°[Fe(s)]]]

Substituting the values,

ΔrG°=[(1 mol Fe2O3(s)/mol-rxn)(742

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