Question

One method for preparing pure iron from \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is by reaction with carbon monoxide. \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g)\) (a) Balance the equation. (b) How many grams of \(\mathrm{CO}\) are needed to react with \(3.02 \mathrm{~g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) ? (c) How many grams of \(\mathrm{CO}\) are needed to react with \(1.68 \mathrm{~mol}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3} ?\)

Short answer

Balanced equation is \( \mathrm{Fe}_{2} \mathrm{O}_{3} + 3\mathrm{CO} \rightarrow 2\mathrm{Fe} + 3\mathrm{CO}_{2} \); 1.587 g of CO for 3.02 g of \( \mathrm{Fe}_{2} \mathrm{O}_{3} \); 141.13 g of CO for 1.68 mol of \( \mathrm{Fe}_{2} \mathrm{O}_{3} \).

Step-by-step solution

Balance the Chemical Equation

We start by balancing the given chemical equation: \( \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \rightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g) \). First, balance the iron atoms. There are 2 iron atoms on the left side, so we need 2 iron atoms on the right: \( \mathrm{Fe}_{2} \mathrm{O}_{3} + \mathrm{CO} \rightarrow 2\mathrm{Fe} + \mathrm{CO}_{2} \). Next, balance the oxygen atoms. There are 3 oxygen atoms in \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) and 2 carbon monoxide yield 3 oxygen in \( \mathrm{CO}_{2} \), so the balanced equation is: \[ \mathrm{Fe}_{2} \mathrm{O}_{3}(s) + 3\mathrm{CO}(g) \rightarrow 2\mathrm{Fe}(s) + 3\mathrm{CO}_{2}(g) \].

Calculate Moles of Fe2O3 from Grams

Convert the given grams of \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) to moles. First, find the molar mass of \( \mathrm{Fe}_{2} \mathrm{O}_{3} \): \( 2 \times 55.85 + 3 \times 16.00 = 159.7 \, \mathrm{g/mol} \). For \( 3.02 \, \mathrm{g} \): \[ \text{Moles of } \mathrm{Fe}_{2} \mathrm{O}_{3} = \frac{3.02}{159.7} \approx 0.0189 \, \text{mol} \].

Calculate Moles and Grams of CO for 3.02g of Fe2O3

According to the balanced equation, \( 1 \) mole of \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) reacts with \( 3 \) moles of \( \mathrm{CO} \). Therefore, \( 0.0189 \, \text{mol of } \mathrm{Fe}_{2} \mathrm{O}_{3} \) will need: \[ 0.0189 \, \text{mol} \times 3 = 0.0567 \, \text{mol of } \mathrm{CO} \]. Convert moles of \( \mathrm{CO} \) to grams using molar mass of \( \mathrm{CO} \) (\( 28.01 \, \mathrm{g/mol} \)): \[ 0.0567 \, \text{mol} \times 28.01 \, \mathrm{g/mol} \approx 1.587 \, \mathrm{g} \].

Calculate Grams of CO for 1.68 mol of Fe2O3

For \( 1.68 \, \text{mol of } \mathrm{Fe}_{2} \mathrm{O}_{3} \), use the balanced equation to determine the moles of \( \mathrm{CO} \). As before, \( 1 \) mole of \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) requires \( 3 \) moles of \( \mathrm{CO} \), therefore: \[ 1.68 \, \text{mol of } \mathrm{Fe}_{2} \mathrm{O}_{3} \times 3 = 5.04 \, \mathrm{mol of } \mathrm{CO} \]. Convert this to grams of \( \mathrm{CO} \): \[ 5.04 \, \mathrm{mol} \times 28.01 \, \mathrm{g/mol} = 141.13 \, \mathrm{g} \].

Key concepts

Balancing Chemical Equations

Balancing chemical equations is a foundational skill in chemistry that ensures the law of conservation of mass is upheld. This law states that matter cannot be created or destroyed in a chemical reaction. Consequently, the number of atoms for each element must be the same on both the reactant and product sides of an equation.
To balance a chemical equation, start by comparing the number of atoms of each element on both sides. For example, in the equation \( \mathrm{Fe}_{2} \mathrm{O}_{3} + \mathrm{CO} \rightarrow \mathrm{Fe} + \mathrm{CO}_{2} \), first balance the iron atoms by making sure there are two iron atoms in the products, just as there are in the reactants. This is done by placing a coefficient '2' in front of \( \mathrm{Fe} \).
Next, balance the oxygen atoms. The original equation has three oxygen atoms in \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) and requires three \( \mathrm{CO} \) molecules to convert those to three \( \mathrm{CO}_{2} \) molecules on the product side. The balanced equation becomes: \[\mathrm{Fe}_{2} \mathrm{O}_{3}(s) + 3\mathrm{CO}(g) \rightarrow 2\mathrm{Fe}(s) + 3\mathrm{CO}_{2}(g)\]
Balancing equations often involves trial and error, as you adjust coefficients to achieve balance without altering the chemical formulas of the substances involved.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To calculate it, simply sum the atomic masses of all atoms in a chemical formula using the periodic table. Knowing the molar mass helps in translating between the mass of substances and the amount of substance in moles, a crucial step in stoichiometry.
Let's consider the compound \( \mathrm{Fe}_{2} \mathrm{O}_{3} \). The molar mass is calculated by adding the atomic masses of its constituent elements. Iron (Fe) has an atomic mass of approximately 55.85 g/mol, and oxygen (O) is about 16 g/mol. The calculation for \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) is:

• 2 atoms of Fe: \( 2 \times 55.85 = 111.7 \)
• 3 atoms of O: \( 3 \times 16 = 48 \)

Adding these gives a molar mass of 159.7 g/mol for \( \mathrm{Fe}_{2} \mathrm{O}_{3} \). Calculating the molar mass accurately is essential for determining the correct proportions of reactants and products in a chemical reaction.

Mole-to-Gram Conversion

Converting between moles and grams is a common requirement in stoichiometry because chemical reactions are often understood in terms of moles. To convert, you use the formula:\[\text{Mass} = \text{Number of moles} \times \text{Molar mass (g/mol)}\]
For instance, to find out how many grams of carbon monoxide (CO) are needed to react with 0.0189 moles of \( \mathrm{Fe}_{2} \mathrm{O}_{3} \), you first need to know how many moles of CO are required and then use the molar mass of CO. The balanced chemical equation shows that one mole of \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) requires three moles of CO. Therefore, 0.0189 moles of \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) needs:

• 0.0189 moles \( \times 3 = 0.0567 \) moles of CO

Using the molar mass of CO, which is 28.01 g/mol, the conversion to grams is:\[0.0567 \, \text{moles} \times 28.01 \, \text{g/mol} = 1.587 \, \text{grams}\]
This conversion is crucial for practical applications, such as determining the exact amount of reactants to use in a reaction.

Chemical Reaction

A chemical reaction involves the transformation of one or more substances into new substances, changing their chemical compositions. This process is represented by a chemical equation that shows reactants changing into products. The essence of a chemical reaction is the breaking of bonds in the reactants and the formation of new bonds in the products, leading to a different configuration of atoms and molecules.
In the case of reducing iron (III) oxide (\( \mathrm{Fe}_{2} \mathrm{O}_{3} \)) with carbon monoxide (CO) to produce iron (Fe) and carbon dioxide (CO₂), a redox reaction occurs. The iron in \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) is reduced as it loses oxygen, while CO is oxidized as it gains oxygen to become CO₂. This type of reaction is crucial in metallurgy for extracting metals from their ores.
Understanding the details of how atoms rearrange during a chemical reaction helps chemists manipulate conditions to optimize the formation of desired products. Emphasizing the changes at the molecular level provides insight into the principles driving these reactions, making stoichiometry an invaluable tool in both educational and industrial chemistry.