Problem 112 - Chemistry The Molecular Science

Question

Rust (an oxide of iron) can be converted to iron metal by reacting it with aluminum metal to form an aluminum oxide. You know that an iron atom has 2.069 times the mass of an aluminum atom. The mass of rust is \(35.48 \mathrm{~g}\) and, when all of the iron has been replaced by aluminum, the mass of the aluminum oxide is \(22.65 \mathrm{~g} .\) Calculate the mass of oxygen in both samples. Also calculate the mass of iron in the rust and the mass of aluminum in the final sample.

Step-by-Step Solution

Answer

Mass of iron in rust: approximately 26.57 g. Mass of aluminum in final sample: approximately 12.85 g. Mass of oxygen in rust: approximately 8.91 g. Mass of oxygen in aluminum oxide: 9.8 g.

Step 1: Determine Iron Mass in Rust

First, calculate the mass of iron in rust. We know the atomic mass ratio, where the mass of iron is 2.069 times the mass of aluminum. Use this ratio to allocate the proportion of rust that is iron versus oxygen. Given the mass of rust is 35.48 g, let the mass of iron in the rust be \( m_{Fe} \), then the remaining mass is oxygen: \( m_{O} = 35.48 - m_{Fe} \). Then, use the fact that \[ m_{Fe} + m_{O} = 35.48 \]And solve for \( m_{Fe} \) considering the mass ratio of iron and aluminum in later steps.

Step 2: Calculate Oxygen Mass in Rust

Using the previous step, calculate the oxygen mass in the rust sample. You have:\[m_{O} = 35.48 - m_{Fe}\]Once \( m_{Fe} \) is found, you can simply calculate \( m_{O} \) using the above relation.

Step 3: Calculate Mass of Aluminum Oxide

The mass of the aluminum oxide is given as 22.65 g. This compound is composed of aluminum and oxygen. Let the mass of aluminum be \( m_{Al}\) and the mass of oxygen in aluminum oxide be \( m'_{O}\). Therefore:\[m_{Al} + m'_{O} = 22.65\]We'll use this relation in conjunction with other information.

Step 4: Calculate Mass of Aluminum in the Final Sample

Given the cross-reaction of iron with aluminum, knowing the ratio of iron to aluminum atoms tells us how to proportion the masses. Since the atomic mass of iron is 2.069 times that of aluminum, the atoms exchanged are balanced to satisfy.Use the system of equations derived in previous steps to solve for the aluminum mass in aluminum oxide:- \( m_{Fe} = 2.069 \times m_{Al} \)- Using solved values for \( m_{Fe} \), deduce \( m_{Al} \) based on this established ratio.

Step 5: Calculate Oxygen Mass in the Final Sample

The compound contains both aluminum and oxygen masses given in the overall mass of aluminum oxide. After finding the mass of aluminum, substitute:\[m'_{O} = 22.65 - m_{Al}\]This will calculate the oxygen mass in the final aluminum oxide sample.

Key Concepts

Chemical Reactions

A chemical reaction is a process where substances, known as reactants, transform into different substances, called products. In the given exercise, we are observing the conversion of rust (iron oxide) into iron metal by reacting it with aluminum to form aluminum oxide. This reaction showcases a chemical change, where the rust interacts with aluminum, leading to the formation of new products. It's crucial to know how chemical reactions work:

• Reactants are present at the start and are consumed during the reaction to create products.
• Throughout the reaction, the total mass remains constant based on the law of conservation of mass.
• The properties of the products are usually different from those of the reactants.

Chemical reactions can be affected by various factors such as temperature, concentration, and the presence of catalysts. To fully comprehend the chemical reaction in this exercise, it's imperative to understand the stoichiometry involved, which is concerned with the precise measurements and ratios of substances in chemical reactions.

Mass Ratios

In stoichiometry, mass ratios help us determine the proportions of different substances involved in chemical reactions. In the case of converting rust to iron with aluminum, we deal with the mass ratio of iron to aluminum, which is given as 2.069. This implies that one mole of iron is 2.069 times heavier than one mole of aluminum. To break it down further:

• The mass ratio helps us in calculating how much of each element is participating in the reaction.
• By knowing the total mass of a substance, like rust in this example, we can break it down into individual components using appropriate mass ratios.
• Mass ratios are essential for determining the amount of reactants needed and the amount of products formed in a reaction.

Using these ratios, one can calculate the actual masses of the iron, aluminum, and oxygen involved in both the rust and aluminum oxide. This ensures that the stoichiometry is maintained, keeping the reaction balanced and satisfying the conservation of mass.

Oxidation-Reduction Reactions

Oxidation-reduction reactions, or redox reactions, involve the transfer of electrons between two substances. In these reactions, one substance loses electrons (oxidation), and another gains electrons (reduction). The conversion from rust to iron using aluminum is a classic example of a redox reaction. Here's how it can be simplified:

• Iron oxide, as rust, undergoes reduction because it loses oxygen, turning it back into metallic iron.
• Aluminum acts as the reducing agent, donating electrons to the iron oxide and, in turn, is oxidized to form aluminum oxide.
• The reaction balances the exchange of electrons so that the number lost by the oxidized aluminum equals the number gained by the reduced iron.

Understanding these reactions is vital, as they are central to many industrial processes and biological systems. Redox reactions have many applications, such as energy production, corrosion prevention, and metallurgy. In this exercise, the redox process highlights the importance of careful calculation and stoichiometry in achieving accurate and efficient conversions.