Problem 7 - Chemistry The Molecular Nature of Matter

Question

How many moles of iron atoms are in one mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) ? How many iron atoms are in one mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) ?

Step-by-Step Solution

Answer

One mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) contains 2 moles of iron atoms. Thus, there are \(2 \times 6.022 \times 10^{23}\) iron atoms in one mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\).

Step 1: Understanding the Mole Concept

A mole is a unit of measurement used in chemistry to express amounts of a chemical substance. One mole of any substance contains Avogadro's number (\(6.022 \times 10^{23}\text{ entities/mole}\)) of molecules.

Step 2: Determining Moles of Iron in \(\mathrm{Fe}_{2}\mathrm{O}_{3}\)

The chemical formula \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) indicates that each molecule has 2 iron atoms. Thus, 1 mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) contains 2 moles of iron atoms.

Step 3: Calculating Number of Iron Atoms

Since 1 mole of a substance contains Avogadro's number of entities, 1 mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) contains 2 moles of iron atoms, which equals to \(2 \times 6.022 \times 10^{23}\) iron atoms.

Key Concepts

Understanding Avogadro's Number

Avogadro's number, named after the scientist Amedeo Avogadro, is a fundamental constant in chemistry. It represents the number of units, whether they are atoms, molecules, ions, or other particles, in one mole of a substance. The value is approximately \(6.022 \times 10^{23} \text{entities/mole}\), and it's this large number that enables chemists to count out atoms and molecules in a practical way, much like a dozen helps us count eggs.

For a student grappling with concepts like these, it's vital to appreciate that Avogadro's number gives us a bridge between the microscopic world of atoms and the macroscopic world we can measure. For instance, when the problem asks how many iron atoms are in one mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\), it is essentially asking us to envision a mole's worth of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) molecules, which is comparable to considering how two dozen donuts would give you 24 donuts in total. Thus, multiplying the moles of iron by Avogadro's number gives us the actual count of iron atoms.

Deciphering the Chemical Formula

The chemical formula \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) is like a recipe for making a compound; it tells us the ratio of elements present. In this case, the subscript '2' next to the iron (Fe) indicates there are two iron atoms for every one molecule of iron oxide (rust), and the '3' next to oxygen (O) tells us there are three oxygen atoms per molecule. What's crucial for students is to understand that these subscripts provide the stoichiometry, or the relative quantities of reactants and products in a chemical reaction.

Relating back to our exercise, knowing that each molecule of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) contains exactly two iron atoms allows you to determine that one mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) must inherently contain two moles of iron atoms. This insight offers the key to solving problems involving conversions between moles of compounds and moles of individual elements.

Mastering Stoichiometry

Stoichiometry is the aspect of chemistry that involves the calculation of relative quantities of reactants and products in chemical reactions. It is derived from two Greek words that mean 'element' and 'measure.' In practice, stoichiometry allows us to predict the amounts of substances consumed and produced in a given reaction.

For students, mastering stoichiometry entails understanding the mole concept and Avogadro's number, as this knowledge is fundamental to performing calculations correctly. In the exercise example, once we know there are two moles of iron atoms in a mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\), we apply stoichiometry to find that two moles of iron would contain \(2 \times 6.022 \times 10^{23}\) iron atoms. Without a clear understanding of stoichiometry, navigating the relationships between reactants and products would be a daunting task and solving chemistry problems accurately would be challenging.