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The reaction of iron(III) oxide with aluminum to give molten iron is known as the thermite reaction (page \(172)\). $$\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\ell)+\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})$$ What amount of \(\mathrm{Al}\), in moles, is needed for complete reaction with 3.0 mol of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) ? What mass of \(\mathrm{Fe},\) in grams, can be produced?

Short Answer

Expert verified
6.0 moles of Al are needed and 335.10 grams of Fe can be produced.

Step by step solution

01

Understanding the Problem

We need to calculate the amount of aluminum, in moles, required to completely react with 3.0 moles of iron(III) oxide according to the given chemical equation.
02

Analyze the Balanced Equation

The balanced chemical equation is: \[\mathrm{Fe}_{2}\mathrm{O}_{3}(\mathrm{s}) + 2 \mathrm{Al}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\ell) + \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})\]. It shows that 1 mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) reacts with 2 moles of \(\mathrm{Al}\).
03

Calculate Moles of Aluminum Needed

Since 3.0 moles of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) are reacting, and according to the stoichiometry of the reaction, we need \(2 \times 3.0 = 6.0\) moles of \(\mathrm{Al}\) for a complete reaction.
04

Calculate Moles of Iron Produced

The balanced equation also indicates that 1 mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) produces 2 moles of \(\mathrm{Fe}\), hence 3.0 moles of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) produce \(2 \times 3.0 = 6.0\) moles of \(\mathrm{Fe}\).
05

Determine Mass of Iron Produced

The molar mass of iron (Fe) is approximately 55.85 g/mol. Therefore, the mass of iron produced is \(6.0 \text{ moles} \times 55.85 \text{ g/mol} = 335.10\) grams.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermite Reaction
The thermite reaction is a very intense exothermic reaction that produces a large amount of heat. It occurs between a metal oxide and a more reactive metal. In this context, we are looking at a reaction between iron(III) oxide (Fe extsubscript{2}O extsubscript{3}) and aluminum (Al).
This reaction, famously used for welding and cutting metals, results in the formation of molten iron and aluminum oxide (Al extsubscript{2}O extsubscript{3}). Here is the balanced chemical equation:
- \[\text{Fe}_{2}\text{O}_{3}(\text{s}) + 2 \text{Al}(\text{s}) \rightarrow 2 \text{Fe}(\ell) + \text{Al}_{2}\text{O}_{3}(\text{s})\]
- It clearly outlines that for every mole of Fe extsubscript{2}O extsubscript{3}, two moles of aluminum are required. The thermite reaction is instrumental in situations where high heat is needed immediately without external input, such as in welding railway tracks.
Chemical Equations
Chemical equations serve as a universal language for chemists by depicting chemical reactions using symbols and formulae. The equation for the thermite reaction is a classic example. A balanced chemical equation has equal numbers of each type of atom on both sides of the equation. This satisfies the law of conservation of mass, where matter cannot be created or destroyed in a chemical reaction.
In our case:
- Iron(III) oxide and aluminum are reactants, while molten iron and aluminum oxide are the products.
- The equation \[\text{Fe}_{2}\text{O}_{3}(\text{s}) + 2 \text{Al}(\text{s}) \rightarrow 2 \text{Fe}(\ell) + \text{Al}_{2}\text{O}_{3}(\text{s})\] tells us that all the aluminum atoms combine with oxygen atoms from iron oxide, forming aluminium oxide and iron metal in the process.
Learning to read and write balanced chemical equations is essential for solving stoichiometry problems.
Mole Calculations
In chemistry, the mole is a basic counting unit used to calculate the amount of substances involved in reactions. When dealing with the thermite reaction, mole calculations enable us to predict exactly how much of each reactant is needed to form a certain amount of product.
If you have 3.0 moles of \(\text{Fe}_{2}\text{O}_{3}\) and, according to the balanced equation, 1 mole of \(\text{Fe}_{2}\text{O}_{3}\) needs 2 moles of aluminum, you can calculate that:
- You need \(3.0 \text{ moles of } \text{Fe}_{2}\text{O}_{3} \times 2 = 6.0 \text{ moles of } \text{Al}\) .Moreover, knowing that each mole of \(\text{Fe}_{2}\text{O}_{3}\) produces 2 moles of iron, 3.0 moles of \(\text{Fe}_{2}\text{O}_{3}\) yield 6.0 moles of iron.
Mass-to-Mole Conversions
Mass-to-mole conversions involve converting a given mass of a substance to moles using its molar mass. This is a crucial step in stoichiometry that allows chemists to work with measurable quantities.
For instance, suppose you calculated that the reaction produces 6.0 moles of iron. To find the mass, you use the molar mass of iron, which is approximately 55.85 g/mol.
Here’s how it's done:
  • Multiply the number of moles by the molar mass: \(6.0 \text{ moles} \times 55.85 \text{ g/mol} = 335.10 \text{ grams}\)
This tells you that 6.0 moles of iron weighs 335.10 grams. Mastering mass-to-mole conversions is essential for analyzing the quantitative aspects of chemical reactions.

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Most popular questions from this chapter

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