Chapter 3: Problem 142
One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron, is $$ \mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO} \longrightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_{2} $$ Suppose that \(1.64 \times 10^{3} \mathrm{~kg}\) of Fe is obtained from a \(2.62 \times 10^{3}-\mathrm{kg}\) sample of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). Assuming that the reaction goes to completion, what is the percent purity of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the original sample?
Short Answer
Step by step solution
Calculate Molar Masses
Use Stoichiometry of the Reaction
Calculate Moles of Fe
Calculate Moles of Fe2O3 Needed
Calculate Mass of Pure Fe2O3
Calculate Percent Purity
Conclusion
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Stoichiometry
- For instance, in a balanced chemical equation \( ext{Fe}_2 ext{O}_3 + 3 ext{CO} \rightarrow 2 ext{Fe} + 3 ext{CO}_2\), it tells us that 1 mole of \( ext{Fe}_2 ext{O}_3\) will produce 2 moles of \( ext{Fe}\), and consume 3 moles of carbon monoxide (CO) producing 3 moles of carbon dioxide (CO\(_2\)).
- The mole ratio is crucial for converting between moles of different substances in a reaction.
Molar Mass
- For example, the molar mass of \(\text{Fe}_2 \text{O}_3\) is calculated by taking the sum of the masses of 2 iron (Fe) atoms and 3 oxygen (O) atoms. Iron has an atomic mass of approximately 55.85 g/mol and oxygen has an atomic mass of 16.00 g/mol. Thus, the molar mass of \(\text{Fe}_2 \text{O}_3\) is \(2 \times 55.85 + 3 \times 16.00 = 159.7 \text{ g/mol}\).
- Similarly, the molar mass of iron (Fe) alone is 55.85 g/mol.
Chemical Reactions
- For the reaction \(\text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2\), the iron oxide (Fe\(_2\)O\(_3\)) reacts with carbon monoxide (CO) to produce iron (Fe) and carbon dioxide (CO\(_2\)).
- This specific reaction takes place in a blast furnace and is essential in the manufacture of iron from iron ore.
Iron Production
- In a blast furnace, the \(\text{Fe}_2\text{O}_3\) is reduced by carbon monoxide derived from the coke. The reaction, \(\text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2\), describes this iron extraction process.
- Here, the iron is produced as a molten material that can be tapped from the bottom of the furnace.
- The operation of the blast furnace requires precise control of the chemical reactions and is highly dependent on the purity of the input materials to optimize yield and efficiency.