Stoichiometric Conversions and Molar Ratios in Chemical Reactions

Q43. Given the following equation, which molar conversion factor would be used to find the number of moles of Fe needed to produce a known number of moles of Fe2O3?

4Fe(s) + 3O2(g) → 2Fe2O3(s)

Background

Topic: Stoichiometry and Molar Ratios

This question tests your understanding of how to use balanced chemical equations to set up conversion factors (mole ratios) for stoichiometric calculations. These ratios allow you to convert between moles of reactants and products.

Key Terms and Formulas

• Stoichiometry: The calculation of reactants and products in chemical reactions using balanced equations.

• Mole Ratio: A conversion factor derived from the coefficients of a balanced chemical equation, used to relate the amounts in moles of any two substances involved in the reaction.

For the reaction: 4Fe(s) + 3O2(g) → 2Fe2O3(s)

The possible mole ratios include:

• $\frac{4\ \text{mol Fe}}{2\ \text{mol Fe}_2\text{O}_3}$

• $\frac{4\ \text{mol Fe}}{3\ \text{mol O}_2}$

• $\frac{2\ \text{mol Fe}_2\text{O}_3}{4\ \text{mol Fe}}$

• $\frac{3\ \text{mol O}_2}{2\ \text{mol Fe}_2\text{O}_3}$

Step-by-Step Guidance

1. Start by identifying what you are given and what you are asked to find. In this case, you want to convert from moles of Fe2O3 (product) to moles of Fe (reactant).

2. Write the balanced chemical equation and note the coefficients for Fe and Fe2O3:

   $4\ \text{Fe} + 3\ \text{O}_2 \rightarrow 2\ \text{Fe}_2\text{O}_3$

3. Set up the mole ratio using the coefficients from the balanced equation. The ratio should relate moles of Fe to moles of Fe2O3:

   $\frac{4\ \text{mol Fe}}{2\ \text{mol Fe}_2\text{O}_3}$

4. Use this ratio as a conversion factor to multiply by the given number of moles of Fe2O3 to find the moles of Fe needed.

Try solving on your own before revealing the answer!

Final Answer: $\frac{4\ \text{mol Fe}}{2\ \text{mol Fe}_2\text{O}_3}$

This ratio comes directly from the coefficients in the balanced equation. It tells you that for every 2 moles of Fe2O3 produced, 4 moles of Fe are required.