   # Iron ore is converted to iron metal in a reaction with carbon. 2 Fe 2 O 3 (s) + 3 C(s) → 4 Fe(s) + 3 CO 2 (g) If 6.2 mol of Fe 2 O 3 (s) is used, what amount of C(s) is needed, and what amounts of Fe and CO 2 are produced? ### 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 4, Problem 8PS
Textbook Problem
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## Iron ore is converted to iron metal in a reaction with carbon.2 Fe2O3(s) + 3 C(s) → 4 Fe(s) + 3 CO2(g)If 6.2 mol of Fe2O3(s) is used, what amount of C(s) is needed, and what amounts of Fe and CO2 are produced?

Interpretation Introduction

Interpretation:

It should be determined that the amount of carbon required to complete the given reaction and the amount of products formed in the reaction. An amounts table for the given reaction also has to be set up.

Concept introduction:

• The number of moles of any substance can be determined  using the equation,

Numberofmole=GivenmassofthesubstanceMolarmass

• The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mol (g/mol).
• For chemical reaction balanced chemical reaction equation written in accordance with the Law of conservation of mass.
• Law of conservation of mass states that for a reaction total mass of the reactant and product must be equal.
• Amounts table is a table that shows the amounts of substances (reactants and products) in moles involved in the chemical reaction.

### Explanation of Solution

Balanced chemical equation for the given reaction is,

2Fe2O3(s)+3C(s)4Fe(s)+3CO2(g)

From the balanced equation it is clear that Fe2O3andC are reacting in the ratio of 2:3

So,

The amount of C require to complete the reaction can be calculated from the amount of Fe2O3

Therefore,

The amount of C required    =     6.2molFe2O3×3molC2molFe2O3=9.3molC

Similar to the above calculation it is possible to determine the amount of products produced in the reaction easily.

Here the stoichiometric ratio between the products (FeandCO2 ) and reactant Fe2O3 is 4:3:2

Therefore,

The amount of Fe produced =   6.2molFe2O3×4molFe2molFe2O3=12.4molFe

The amount of CO2 produced =   6.2molFe2O3×3molCO22molFe2O3=9

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