Problem 17 - Chemistry and Chemical Reactivity

Question

In the thermite reaction, iron(III) oxide is reduced by aluminum to give molten iron. $$\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\ell)+\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})$$ If you begin with \(10.0 \mathrm{g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and \(20.0 \mathrm{g}\) of \(\mathrm{Al}\), (a) Which reactant is limiting? (b) What mass of Fe can be produced? (c) What mass of the excess reactant remains after the limiting reactant is consumed? (d) Set up an amounts table for this problem.

Step-by-Step Solution

Answer

(a) The limiting reactant is Fe2O3. (b) 6.99 g of Fe can be produced. (c) 16.62 g of Al remains. (d) An amounts table is set up accordingly.

Step 1: Determine Molar Masses

To solve this problem, we first need to calculate the molar masses of the compounds involved. - Molar mass of Fe2O3 = 2(55.85) + 3(16.00) = 159.7 g/mol - Molar mass of Al = 26.98 g/mol - Molar mass of Fe = 55.85 g/mol

Step 2: Convert Grams to Moles

Convert the masses of Fe2O3 and Al to moles using their molar masses.- Moles of Fe2O3 = \( \frac{10.0\ \text{g}}{159.7\ \text{g/mol}} = 0.0626\ \text{mol} \)- Moles of Al = \( \frac{20.0\ \text{g}}{26.98\ \text{g/mol}} = 0.741\ \text{mol} \)

Step 3: Identify Limiting Reactant

Using the stoichiometry of the balanced equation, identify the limiting reactant. From the equation, we know:- 1 mole of Fe2O3 reacts with 2 moles of Al.- Moles of Al required for 0.0626 moles of Fe2O3 = \( 0.0626\ \text{mol} \times 2 = 0.1252\ \text{mol} \)Since we have 0.741 moles of Al and need only 0.1252 moles, Fe2O3 is the limiting reactant.

Step 4: Calculate Mass of Iron Produced

Use the moles of the limiting reactant to calculate the mass of iron produced.- From the balanced equation, 1 mole of Fe2O3 produces 2 moles of Fe.- Moles of iron = \( 0.0626\ \text{mol Fe2O3} \times 2 = 0.1252\ \text{mol Fe} \)- Mass of iron = \( 0.1252\ \text{mol} \times 55.85\ \text{g/mol} = 6.99\ \text{g} \)

Step 5: Calculate Mass of Excess Reactant Remaining

To find the remaining mass of Al after the reaction:- Moles of Al reacted = 0.1252 moles- Moles of excess Al = 0.741 - 0.1252 = 0.6158 moles- Mass of remaining Al = \( 0.6158\ \text{mol} \times 26.98\ \text{g/mol} = 16.62\ \text{g} \)

Step 6: Set Up Amounts Table

Create an initial, change, and final amounts table for the reaction: | | Fe2O3 | Al | Fe | Al2O3 | |--------|-------|------|--------|-------| | Initial| 0.0626| 0.741| 0 | 0 | | Change | -0.0626| -0.1252| +0.1252| +0.0626| | Final | 0 | 0.6158| 0.1252| 0.0626|

Key Concepts

Thermite Reaction

The thermite reaction is a type of exothermic oxidation-reduction chemical reaction, highly favored for its high temperature output and the ability to produce molten metals. In this particular reaction, aluminum serves as the reducing agent, while iron(III) oxide acts as the oxidizing agent. When these two reactants come together, aluminum reduces iron(III) oxide to produce elemental iron and aluminum oxide. The reaction is represented by the balanced chemical equation:

• Fe₂O₃(s) + 2Al(s) → 2Fe(l) + Al₂O₃(s)

A key feature of this reaction is its ability to produce intense heat, often used for welding and creating metal alloys.
Despite its industrial utility, the thermite reaction is central in various chemistry problems, allowing students to explore concepts like limiting reactants, stoichiometry, and molar mass calculations.

Stoichiometry

Stoichiometry is a branch of chemistry focusing on the amount of substances involved in chemical reactions. It uses the balanced chemical equations to connect the quantities of reactants and products. In our thermite reaction example, stoichiometry helps determine how much of each reactant is needed and the expected amount of each product. It accomplishes this through the mole ratio, which is derived from the coefficients in the balanced equation:

• 1 mole of Fe₂O₃ requires 2 moles of Al to form 2 moles of Fe and 1 mole of Al₂O₃.

To solve problems related to the thermite reaction:

• First, convert all given reactant amounts to moles.
• Use the stoichiometric ratios to find the limiting reactant and calculate the resulting products.

Understanding stoichiometry thus allows for precise predictions about chemical reactions.

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry, crucial for converting grams of a substance to moles and vice versa. Each element's molar mass (derived from their atomic weights in atomic mass units) is found on the periodic table. For our thermite reaction:

• The molar mass of Fe₂O₃ is calculated as 2 times the molar mass of iron plus 3 times the molar mass of oxygen, which is 159.7 g/mol.
• The molar mass of aluminum is 26.98 g/mol.

These calculations are the cornerstone for translating the mass of each reactant into moles, a necessary step in stoichiometry to solve for reactants' and products' quantities. When tackling exercises, take care to perform accurate molar mass calculations, as errors can mislead your solution.

Excess Reactant

In chemical reactions, reactants are often not consumed completely, leading to excess reactants. Identifying the excess reactant is crucial, as it provides insights into the reaction's efficiency and economy. For the thermite reaction, the excess reactant is found using the limiting reactant concept:

• Calculate moles of each reactant.
• Use stoichiometry to find which reactant runs out first (the limiting reactant).
• Subtract the moles of the limiting reactant from the initial moles of other reactants to find the leftover or excess amount.

In our specific problem, aluminum acts as the excess reactant. After reacting with all available iron(III) oxide, not all aluminum is consumed, resulting in leftover aluminum. By calculating the precise amount of the remaining reactant, students better grasp the reaction's dynamics and efficiency.