Question

When a mixture of aluminium powder and iron (III) oxide is ignited, it produces molten iron and aluminium oxide. In an experiment, \(5.4 \mathrm{~g}\) of aluminium was mixed with \(18.5 \mathrm{~g}\) of iron (III) oxide. At the end of the reaction, the mixture contained \(11.2 \mathrm{~g}\) of iron, \(10.2 \mathrm{~g}\) of aluminium oxide, and an undetermined amount of unreacted iron (III) oxide. No aluminium was left. What is the mass of the iron (III) oxide left? (a) \(2.5 \mathrm{~g}\) (b) \(7.3 \mathrm{~g}\) (c) \(8.3 \mathrm{~g}\) (d) \(2.9 \mathrm{~g}\)

Short answer

The mass of the iron (III) oxide left is 7.3 g.

Step-by-step solution

Write down the masses of the substances

We are given the following masses: Aluminium (Al) = 5.4 g, Iron (III) oxide (Fe2O3) = 18.5 g, Iron (Fe) produced = 11.2 g, and Aluminium oxide (Al2O3) produced = 10.2 g.

Calculate the mass of iron (III) oxide that reacted

Since no aluminium is left, it all reacted to form aluminium oxide. We use the law of conservation of mass which states that the total mass of reactants is equal to the total mass of products. The mass of Fe2O3 that reacted can be determined by subtracting the mass of Al2O3 and Fe produced from the total initial mass of reactants: Mass of Fe2O3 reacted = (Mass of Al + Mass of Fe2O3) - (Mass of Fe + Mass of Al2O3).

Subtract the mass of reacted Fe2O3 from the initial mass

Calculate the mass of the unreacted Fe2O3: Mass of unreacted Fe2O3 = Initial mass of Fe2O3 - Mass of Fe2O3 that reacted.

Calculate the mass of unreacted Fe2O3

Plug in the values into the equation from Step 3 to find the mass of the unreacted Fe2O3.

Key concepts

Law of Conservation of Mass

Understanding the Law of Conservation of Mass is crucial when solving stoichiometry problems. This principle, formulated by Antoine Lavoisier in the 18th century, states that the mass in an isolated system must remain constant over time. In simpler terms, matter cannot be created or destroyed in an ordinary chemical reaction. This means that when a chemical reaction occurs, the total mass of the reactants must equal the total mass of the products.

Applying this law to our exercise, we initially have a mixture of aluminium and iron (III) oxide which, after the reaction, gets transformed into iron and aluminium oxide. Since no mass is lost or gained in the process, we can confidently set up an equation equating the mass of the reactants to the mass of the products. It's important to note that gases and energy, such as heat or light, can also be products or reactants in a chemical reaction, but since the problem doesn't indicate their involvement, we focus only on the solid substances here.

Chemical Reaction

A chemical reaction involves the conversion of one or more substances, the reactants, into new substances, the products. Reactions can vary greatly, producing different kinds of products, such as gases, precipitates, or new compounds like in our example of aluminium reacting with iron (III) oxide.

To represent a chemical reaction, we write a balanced chemical equation that shows both the reactants and products, along with their stoichiometric coefficients, which indicate the relative numbers of molecules involved. The balanced equation provides a ratio that is used to calculate the theoretical yield—the amount of product that could be formed from given amounts of reactants under perfect conditions. In our exercise, the chemical equation would illustrate the reaction between aluminium and iron (III) oxide to form iron and aluminium oxide.

Theoretical Yield Calculation

The theoretical yield calculation is an essential aspect of stoichiometry. It estimates the maximum amount of product expected from a given amount of reactants, assuming complete conversion based on the stoichiometric ratios from the balanced chemical equation. To perform this calculation, one usually identifies the limiting reactant, the reactant that will be completely consumed first, dictating the maximum amount of product that can form.

However, in real-life scenarios like in our exercise, the reaction may not go to completion, or there may be side reactions leading to different products. To calculate the actual yield, you measure the mass of products obtained from the reaction. A comparison between the actual yield and the theoretical yield gives the efficiency of the reaction. In the problem provided, we focus on the mass of unreacted iron (III) oxide to deduce the extent of the reaction's progression.