Question

Aluminum metal and iron(III) oxide react to give aluminum oxide and iron metal. What is the maximum mass of iron that can be obtained from a reaction mixture containing \(2.5 \mathrm{g}\) of aluminum and \(9.5 \mathrm{g}\) of iron(III) oxide. What mass of the excess reactant remains?

Short answer

The maximum mass of iron that can be obtained is 10.39 g. The mass of the excess reactant, iron(III) oxide, that remains is 2.08 g.

Step-by-step solution

Write the balanced chemical equation

Aluminum (Al) reacts with Iron (III) oxide (Fe2O3) to give Aluminum oxide (Al2O3) and Iron (Fe). The balanced chemical equation is: \[2Al + Fe2O3 → Al2O3 + 2Fe\] This equation tells that 2 moles of Al react with 1 mole of Fe2O3 to produce 1 mole of Al2O3 and 2 moles of Fe.

Convert mass to moles

Molar mass of Al = 26.98 g/mol. Molar mass of Fe2O3 = 159.7 g/mol. So, Moles of Al = \(\frac{2.5}{26.98} = 0.093\, moles\), Moles of Fe2O3 = \(\frac{9.5}{159.7} = 0.0595\, moles\)

Identify the limiting reactant

The reaction requires 2 moles of Al to react with 1 mole of Fe2O3. Based on calculation, there are enough moles of Al for 0.0465 moles of Fe2O3 and enough moles of Fe2O3 for 0.0595 moles of Al. So, Al is the limiting reactant.

Determine the amount of iron formed

From the balanced equation, we know that 2 moles of Al form 2 moles of Fe. So, the amount of Fe formed = \(0.093 * 2 = 0.186\, moles\). The molar mass of Fe is 55.85 g/mol, so the mass of Fe formed = \(0.186 * 55.85 = 10.39\, g\)

Determine the excess reactant remaining

All the aluminum was used up. For Fe2O3, Initially, we had 0.0595 moles of Fe2O3. The reaction used = \(0.093/2 = 0.0465\, moles\). Remaining Fe2O3 = \(0.0595 - 0.0465 = 0.013\, moles\). Therefore, the mass of Fe2O3 remaining = \(0.013 * 159.7 = 2.08\, g\)

Key concepts

Limiting Reactant

Understanding the concept of the limiting reactant is crucial when we're dealing with chemical reactions. Imagine you're trying to make sandwiches—bread slices are like one reactant and cheese slices are like another. If you have 4 slices of bread and only 2 slices of cheese, you can only make 2 sandwiches. The cheese limits the process, and that's what a limiting reactant does in a chemical reaction.

A limiting reactant is the reactant that will be completely used up first, limiting the amount of product that can be formed. To identify it, we first need a balanced chemical equation. Then, by comparing the mole ratio of the reactants used, we can determine which reactant will run out first. Any remaining reactants are known as excess reactants. They're like those extra bread slices waiting in the pantry while the cheese has run out.

In our exercise, after converting the mass of Aluminum (Al) and Iron(III) oxide (Fe₂O₃) to moles, we discovered that Al would run out first during the reaction. This makes Al the limiting reactant, and thus it dictates the maximum amount of Iron (Fe) that can be produced.

Mole-to-Mass Conversion

Transitioning between moles and mass is a common task in chemistry, much like converting miles to kilometers. This process is known as mole-to-mass conversion and hinges on knowing the substance's molar mass—the weight of one mole of the substance. To determine the molar mass, we sum the atomic masses of all atoms in the molecule according to its chemical formula.

For the exercise, using the molar masses of Aluminum (26.98 g/mol) and Iron(III) oxide (159.7 g/mol), we convert the given masses into moles. This conversion enables us to use the balanced equation effectively, since it is expressed in moles. From this, we calculate that 2.5 grams of Al yields 0.093 moles, while 9.5 grams of Fe₂O₃ corresponds to 0.0595 moles. These mole quantities play a pivotal role in finding the limiting reactant and the eventual yield of Iron.

Balanced Chemical Equations

A balanced chemical equation is the Rosetta Stone of chemistry—it tells us the exact proportion of reactants that combine and the amount of products formed. Think of it as a recipe: for our sandwich, it would be '2 slices of bread + 1 slice of cheese → 1 sandwich'. Without balance, the equation would be incorrect, and the product could not be formed as expected.

In balancing equations, we ensure that the number of atoms for each element is equal on both the reactant and product sides. This respect for the Law of Conservation of Mass is fundamental; mass can neither be created nor destroyed in a chemical reaction. In the exercise, the balanced equation was \(2Al + Fe₂O₃ \rightarrow Al₂O₃ + 2Fe\). From this equation, we see that two moles of Aluminum react with one mole of Iron(III) oxide to form one mole of Aluminum oxide and two moles of Iron, guiding us through the stoichiometric process from reactants to products.