Problem 95 - General Chemistry

Question

When a mixture of aluminum powder and iron(III) oxide is ignited, it produces molten iron and aluminum oxide. In an experiment, \(5.40 \mathrm{~g}\) of aluminum was mixed with \(18.50 \mathrm{~g}\) of iron(III) oxide. At the end of the reaction, the mixture contained \(11.17 \mathrm{~g}\) of iron, \(10.20 \mathrm{~g}\) of aluminum oxide, and an undetermined amount of unreacted iron(III) oxide. No aluminum was left. What is the mass of the iron(III) oxide?

Step-by-Step Solution

Answer

The mass of unreacted iron(III) oxide is 2.53 g.

Step 1: Understand the Chemical Reaction

The chemical reaction between aluminum (Al) and iron(III) oxide (Fe₂O₃) is known as the thermite reaction. The balanced chemical equation is \[\text{2Al} + \text{Fe}_2\text{O}_3 \rightarrow \text{2Fe} + \text{Al}_2\text{O}_3\]. This means that 2 moles of aluminum react with 1 mole of iron(III) oxide to produce 2 moles of iron and 1 mole of aluminum oxide.

Step 2: Calculate the Moles of Aluminum Used

Given that the molar mass of aluminum is approximately 26.98 g/mol, determine the moles of aluminum that reacted. \[ \text{Moles of Al} = \frac{5.40 \text{ g}}{26.98 \text{ g/mol}} \approx 0.200 \text{ mol} \]

Step 3: Determine Moles of Iron(III) Oxide Needed

From the balanced equation, we see that 2 moles of Al react with 1 mole of Fe₂O₃. Therefore, \(0.200\) moles of Al will react with \(0.100\) moles of Fe₂O₃ (since \(\frac{0.200}{2} = 0.100\)).

Step 4: Calculate Grams of Iron(III) Oxide Consumed

The molar mass of Fe₂O₃ is approximately 159.7 g/mol. Thus, the mass of Fe₂O₃ that reacted is given by: \[ \text{Mass of Fe}_2\text{O}_3 = 0.100 \text{ mol} \times 159.7 \text{ g/mol} = 15.97 \text{ g} \]

Step 5: Determine Original and Unreacted Mass of Iron(III) Oxide

Initially, there were 18.50 g of Fe₂O₃. \[ \text{Unreacted Fe}_2\text{O}_3 = 18.50 \text{ g} - 15.97 \text{ g} = 2.53 \text{ g} \] Thus, the mass of unreacted iron(III) oxide is 2.53 g.

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that deals with the calculation of reactants and products in a chemical reaction. It relies heavily on the law of conservation of mass, which implies that matter is neither created nor destroyed in a chemical reaction. Consequently, stoichiometry allows chemists to predict the quantities of substances required or produced in a given reaction.

• In our exercise, stoichiometry helps us understand the relationship between aluminum and iron(III) oxide in the thermite reaction. Here, we use the balanced chemical equation to determine how much of each reactant is needed to fully react without any leftover.
• We see that 2 moles of aluminum react with 1 mole of iron(III) oxide. This molar ratio is crucial for calculating the amounts of reactants and products involved in the reaction efficiently.
• The stoichiometric coefficients in front of the chemical formulas (like 2 for aluminum in our equation) indicate the proportions in which the reactants combine and products form.

By understanding and applying stoichiometry, we can solve problems like determining how much reactant is left unreacted or how much product is formed.

Molar Mass Calculation

Molar mass is a key concept to convert between mass and moles, which is essential for stoichiometric calculations. It is the mass of one mole of a substance and is expressed in g/mol.

• The molar mass enables us to translate grams into moles, allowing us to use the stoichiometric coefficients from a balanced chemical equation effectively.
• For example, the molar mass of aluminum (Al) is 26.98 g/mol, and the molar mass of iron(III) oxide (Fe₂O₃) is 159.7 g/mol.
• In our solution, we calculated the moles of aluminum using its molar mass: \[ \text{Moles of Al} = \frac{5.40 \text{ g}}{26.98 \text{ g/mol}} \approx 0.20 \text{ mol} \]
• Similarly, we calculated the mass of iron(III) oxide that reacted by finding its moles, using the stoichiometric relationship from the reaction equation, and multiplying by its molar mass.

Understanding molar mass ensures accurate conversions and is a building block for many chemical calculations.

Chemical Equation Balancing

Balancing chemical equations is a skill that allows us to ensure the conservation of atoms in a chemical reaction, which is a reflection of the law of conservation of mass. An equation is balanced when the number of each type of atom on the reactant side equals the number on the product side.

• For our thermite reaction, it starts as: \[ 2\text{Al} + \text{Fe}_2\text{O}_3 \rightarrow 2\text{Fe} + \text{Al}_2\text{O}_3 \]
• This equation is already balanced because there are equal numbers of aluminum atoms (2 on each side), iron atoms (2 on each side), and oxygen atoms (3 on each side).
• Balanced equations like this help in forming stoichiometric relationships, enabling us to precisely calculate the amounts of reactants needed and products formed.
• If a chemical equation is not balanced, any stoichiometric calculations based on it will be inaccurate because they won't respect the conservation of mass.

Being proficient in balancing chemical equations is essential for any stoichiometric computation and insightful experimentation.