Problem 4 - Chemistry and Chemical Reactivity

Question

The balanced equation for the reduction of iron ore to the metal using CO is $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g}) $$ (a) What is the maximum mass of iron, in grams, that can be obtained from \(454 \mathrm{g}(1.00 \mathrm{lb})\) of iron(III) oxide? (b) What mass of \(\mathrm{CO}\) is required to react with \(454 \mathrm{g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3} ?\)

Step-by-Step Solution

Answer

(a) 317.5 g of Fe; (b) 239.1 g of CO required.

Step 1: Determine the molar mass of Fe2O3

The molar mass of Fe is 55.85 g/mol and the molar mass of O is 16.00 g/mol. Therefore, the molar mass of Fe2O3 is calculated as:\[ 2(55.85) + 3(16.00) = 159.70 \text{ g/mol} \]

Step 2: Calculate moles of Fe2O3 in 454 g

To find the moles of Fe2O3, divide the given mass by its molar mass:\[ \text{Moles of Fe2O3} = \frac{454 \text{ g}}{159.70 \text{ g/mol}} \approx 2.844 \text{ mol} \]

Step 3: Use stoichiometry to find moles of Fe produced

From the balanced equation, 1 mole of Fe2O3 produces 2 moles of Fe. Therefore:\[ 2.844 \text{ mol Fe2O3} \times 2 \text{ mol Fe/mol Fe2O3} = 5.688 \text{ mol Fe} \]

Step 4: Convert moles of Fe to grams

Multiply the moles of Fe by its molar mass to find the mass of Fe:\[ 5.688 \text{ mol Fe} \times 55.85 \text{ g/mol} = 317.5 \text{ g Fe} \]

Step 5: Calculate moles of CO needed for reaction

According to the balanced equation, 1 mole of Fe2O3 reacts with 3 moles of CO. Hence, the moles of CO required are:\[ 2.844 \text{ mol Fe2O3} \times 3 \text{ mol CO/mol Fe2O3} = 8.532 \text{ mol CO} \]

Step 6: Find the mass of CO required

The molar mass of CO is 28.01 g/mol. Multiply the moles of CO by this to find the total mass:\[ 8.532 \text{ mol CO} \times 28.01 \text{ g/mol} = 239.1 \text{ g CO} \]

Key Concepts

Balanced chemical equations

In any chemical reaction, balanced chemical equations are fundamental for determining the relationship between reactants and products. They tell us the exact number of moles of each substance needed and produced in a reaction. This ensures that the law of conservation of mass is satisfied, which means the mass of reactants equals the mass of products.

Consider the chemical reaction given for the iron reduction process:\[\mathrm{Fe}_{2}\mathrm{O}_{3}(\mathrm{s}) + 3 \mathrm{CO}(\mathrm{g}) \rightarrow 2 \mathrm{Fe}(\mathrm{s}) + 3 \mathrm{CO}_{2}(\mathrm{g})\]This balanced equation provides a simple ratio between substances:

• One mole of \(\mathrm{Fe}_2\mathrm{O}_3\) reacts with three moles of \(\mathrm{CO}\).
• This produces two moles of \(\mathrm{Fe}\) and three moles of \(\mathrm{CO}_2\).

Such equations help in identifying how much of each reactant is needed to produce the desired amounts of products. In this case, they indicate exactly how much carbon monoxide is needed to fully react with the given iron(III) oxide.

Moles and molar mass

Moles and molar mass are essential concepts in stoichiometry. They help us translate between the macroscopic world of grams and the microscopic world of molecules and atoms.

The molar mass is the mass of one mole of a substance. It's a bridge between the atomic scale described by the molecular weight and the gram scale used in everyday chemistry. The molar mass (g/mol) is obtained from the periodic table for the elements that make up a compound. For example, the molar mass of \(\mathrm{Fe}_2\mathrm{O}_3\) is calculated as: \[2(55.85) + 3(16.00) = 159.70 \, \text{g/mol}\]Once the molar mass is known, it enables us to find the amount of substance in terms of moles. By dividing the mass of the compound by its molar mass, we find how many moles of the compound are present. This method assists in determining how many moles participate in or are produced by a chemical reaction, as seen in the iron reduction process.

Iron reduction process

The iron reduction process is an example of a redox (reduction-oxidation) reaction, specifically reducing iron from an ore using a carbon monoxide reducing agent.

In this process, iron(III) oxide (\(\mathrm{Fe}_2\mathrm{O}_3\)) is reduced to iron metal (\(\mathrm{Fe}\)) by carbon monoxide (\(\mathrm{CO}\)). As explained, the balanced chemical equation outlines that every mole of iron(III) oxide will produce two moles of iron when reacted with three moles of carbon monoxide.

• Step 1: The \(\mathrm{CO}\) acts as the reducing agent, donating electrons and reducing the iron ions in \(\mathrm{Fe}_2\mathrm{O}_3\) to elemental iron.
• Step 2: Carbon monoxide, in turn, is oxidized to carbon dioxide (emission).
• Step 3: This reaction is essential in the steel-making process, where such raw materials are key components.

Understanding this process provides insight into industrial chemistry practices involving the conversion of raw metal ores to usable metal forms, showcasing the crucial role of chemical reactions in industrial applications.