Problem 48 - Chemistry Matter and Change

Question

When aluminum is mixed with iron (III) oxide, iron metal and aluminum oxide are produced, along with a large quantity of heat. What mole ratio would you use to determine moles of Fe if moles of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is known? \begin{equation} \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})+ heat\end{equation}

Step-by-Step Solution

Answer

The mole ratio to determine moles of Fe from Fe2O3 is 1:2.

Step 1: Write the Balanced Chemical Equation

Let's start by ensuring we have the balanced chemical equation for the reaction. From the given information, we have \( \text{Fe}_2 \text{O}_3(s) + 2 \text{Al}(s) \rightarrow 2 \text{Fe}(s) + \text{Al}_2 \text{O}_3(s) + \text{heat} \). This equation is already balanced.

Step 2: Identify the Substances Involved

In the reaction, \( \text{Fe}_2 \text{O}_3 \) is the reactant and \( \text{Fe} \) is one of the products. We are interested in the mole ratio between these two substances.

Step 3: Determine the Mole Ratio from Balanced Equation

From the balanced equation, \( 1 \) mole of \( \text{Fe}_2 \text{O}_3 \) reacts to produce \( 2 \) moles of \( \text{Fe} \). Therefore, the mole ratio between \( \text{Fe}_2 \text{O}_3 \) and \( \text{Fe} \) is \( 1:2 \).

Key Concepts

Balanced Chemical Equation

To understand stoichiometry and its applications, it's crucial to start with the concept of a balanced chemical equation. A balanced equation means that the number of atoms of each element is the same on both sides of the equation. This balance reflects the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction.
For the given exercise, we have the equation: \[ \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s}) + 2 \mathrm{Al}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\mathrm{s}) + \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s}) + \text{heat} \]This equation is balanced because:

• There are 2 iron (Fe) atoms on each side.
• 2 aluminum (Al) atoms are used to form one molecule of aluminum oxide (Al₂O₃).
• 3 oxygen (O) atoms are present in both the reactant and product sides.

Understanding this balance is vital for solving problems related to stoichiometry, as it allows us to accurately calculate mole ratios and predict the outcome of reactions.

Mole Ratio

Mole ratio is a fundamental concept in stoichiometry used to relate the amounts of reactants and products in a chemical reaction. From a balanced equation, we derive these ratios to convert between moles of different substances.
The given balanced equation allows us to find the mole ratio between iron (III) oxide, \( \mathrm{Fe}_2 \mathrm{O}_3 \), and iron, \( \mathrm{Fe} \). According to the equation:

• 1 mole of \( \mathrm{Fe}_2 \mathrm{O}_3 \) reacts with 2 moles of aluminum to produce 2 moles of iron.

The mole ratio of \( \mathrm{Fe}_2 \mathrm{O}_3 \) to \( \mathrm{Fe} \) is therefore \( 1:2 \).
This ratio is crucial when predicting how much product you'll get from a given amount of reactant, or vice-versa, when balancing future reactions and ensuring that all materials are fully used without excess waste.

Chemical Reactions

Chemical reactions, like the one presented in the exercise, involve the transformation of reactants into products. The key aspects to consider include reactants, products, and the type of reaction. In this case, we deal with a reaction between aluminum and iron (III) oxide.
Important characteristics to note about this reaction:

• It's an exothermic reaction, indicated by the release of heat.
• Aluminum and iron (III) oxide, both solids, react to form iron and aluminum oxide, also solid substances.

The reaction not only follows the conservation of mass principle but also illustrates a displacement type of chemical reaction, commonly seen in metallurgical processes like the thermite reaction, where aluminum acts as a reducing agent to extract metal.

Redox Reaction

Redox reactions are a type of chemical reaction involving the transfer of electrons, resulting in changes in oxidation states of the substances involved. In the context of the exercise, when aluminum reacts with iron (III) oxide, it is a redox reaction.
Here's how the redox process works here:

• Oxidation: Aluminum loses electrons and gets oxidized to form aluminum oxide \( \mathrm{Al}_2 \mathrm{O}_3 \).
• Reduction: Iron (III) oxide gains electrons as it is reduced to iron \( \mathrm{Fe} \).

The oxidation and reduction processes happen simultaneously, characterized by:

• Oxidizing agent: The \( \mathrm{Fe}_2 \mathrm{O}_3 \) (iron is reduced from a +3 to 0 oxidation state).
• Reducing agent: The \( \mathrm{Al} \) (aluminum is oxidized from 0 to a +3 oxidation state).

Understanding redox reactions is crucial in various fields, especially in industrial applications where metal extraction and energy production via controlled reactions is critical.