Problem 87 - Chemistry: An Atoms-Focused Approach

Question

Iron is oxidized in a number of chemical weathering processes. How many moles of \(\mathrm{O}_{2}\) are consumed when one mole of magnetite (Fe \(_{3} \mathrm{O}_{4}\) ) is converted into hematite \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right) ?\)

Step-by-Step Solution

Answer

Answer: Half a mole of oxygen gas (0.5 moles) is consumed when one mole of magnetite is converted into hematite.

Step 1: Write the balanced chemical equation

We are given that magnetite (Fe3O4) is converted into hematite (Fe2O3) and we need to determine the amount of oxygen gas (O2) consumed in this process. The balanced chemical equation for this process would be: Fe3O4 + \(\frac{1}{2}\) O2 \(\rightarrow\) 2 Fe2O3 This equation states that one mole of magnetite (Fe3O4) reacts with half a mole of oxygen gas (O2) to produce two moles of hematite (Fe2O3).

Step 2: Calculate moles of O2 consumed

Now, we can use stoichiometry to determine the number of moles of oxygen gas (O2) consumed when one mole of magnetite (Fe3O4) is converted into hematite (Fe2O3). According to the balanced chemical equation: 1 mole of Fe3O4 \(\times\) \(\frac{1/2\,\text{mole O}_2}{1\,\text{mole Fe}_3\text{O}_4}\) After performing the calculation, we can see that it comes out to: \(1\,\text{mole Fe}_3\text{O}_4 \times \frac{1}{2} = \frac{1}{2}\,\text{mole O}_2\) So, when one mole of magnetite (Fe3O4) is converted into hematite (Fe2O3), half a mole of oxygen gas (O2) is consumed.

Key Concepts

Stoichiometry

Stoichiometry is an essential part of chemistry that involves the calculation of reactants and products in chemical reactions. To solve problems like the one given in the exercise, we use stoichiometry to determine how much of a reactant is needed or how much product can be formed. It relies on the concept of the mole, which is a unit to measure amount of substance, similar to dozen or gross but for atoms and molecules.

In the context of our exercise, stoichiometry helps us evaluate how many moles of oxygen gas \( \text{O}_2 \) are consumed when a certain reaction takes place. By using the proportions given in the balanced chemical equation, we know that one mole of magnetite \( \text{Fe}_3\text{O}_4 \) reacts with half a mole of \( \text{O}_2 \).

When you have a balanced chemical equation, like the one in our exercise, you can identify the mole ratio between the different substances involved. In this example:

• 1 mole of \( \text{Fe}_3\text{O}_4 \) is required
• 0.5 moles of \( \text{O}_2 \)
• Produces 2 moles of \( \text{Fe}_2\text{O}_3 \)

By knowing these ratios, stoichiometry allows us to predict quantities of chemicals reacting and forming.

Oxidation

Oxidation refers to the chemical process where a substance loses electrons, often to oxygen. It's a crucial concept in understanding various chemical reactions, especially those involving metals. In nature, oxidation can lead to the weathering and rusting of metals, impacting everything from geology to construction.

The exercise mentions the oxidation of magnetite to hematite. Here, the oxidation process involves the change in the oxidation states of iron. Magnetite \( \text{Fe}_3\text{O}_4 \) experiences oxidation as it reacts with oxygen, forming hematite\( \text{Fe}_2\text{O}_3 \).

In our example, oxidation occurs as part of a broader chemical reaction involving oxygen gas:

• Magnetite starts with different iron oxidation states
• Oxygen plays the role of the electron acceptor
• Hematite, with iron fully oxidized, is the result

This transformation signifies the oxygen has been used to "pull away" electrons from the iron in magnetite, fully oxidizing it to form hematite. This oxidation is crucial in understanding how elemental cycles and transformations occur in nature.

Balanced Chemical Equations

Balanced chemical equations are essential for accurately representing chemical reactions. They indicate the proportions of reactants and products involved and ensure that matter is conserved—an expression of the law of conservation of mass. Every reaction must be balanced to correctly reflect that no atoms are lost or gained, just rearranged.

In our problem, the balanced equation is crucial for finding out how much oxygen gas is consumed in the conversion of magnetite to hematite.The balanced equation given in the solution is:\[\text{Fe}_3\text{O}_4 + \frac{1}{2}\,\text{O}_2 \rightarrow 2\,\text{Fe}_2\text{O}_3\]

This equation is balanced because the number of iron and oxygen atoms is the same on both sides. Balancing equations involves:

• Counting the atoms of each element on both sides of the equation
• Using coefficients to adjust the number of molecules, ensuring each side is equal
• Ensuring total mass remains the same throughout the reaction

Without a balanced equation, it would be tough to determine the exact amounts of reactants and products, and stoichiometry would be ineffective. Always remember: balancing a chemical equation is a primary step in solving any stoichiometry problem.