Problem 88 - Chemistry The Molecular Science

Question

Three oxygen-containing compounds of iron are \(\mathrm{FeCO}_{3}\), \(\mathrm{Fe}_{2} \mathrm{O}_{3},\) and \(\mathrm{Fe}_{3} \mathrm{O}_{4} \cdot\) Calculate the percent iron by mass in each iron compound.

Step-by-Step Solution

Answer

Percent iron: FeCO3 ≈ 48.20%, Fe2O3 ≈ 69.94%, Fe3O4 ≈ 72.36%.

Step 1: Find Molar Mass of Compounds

First, calculate the molar mass of each compound using the atomic masses: Fe (55.85 g/mol), C (12.01 g/mol), O (16.00 g/mol). - For \( \mathrm{FeCO}_3 \): Molar mass = 55.85 (Fe) + 12.01 (C) + 3 \times 16.00 (O) = 115.86 \text{ g/mol}. - For \( \mathrm{Fe}_2 \mathrm{O}_3 \): Molar mass = 2 \times 55.85 (Fe) + 3 \times 16.00 (O) = 159.70 \text{ g/mol}. - For \( \mathrm{Fe}_3 \mathrm{O}_4 \): Molar mass = 3 \times 55.85 (Fe) + 4 \times 16.00 (O) = 231.55 \text{ g/mol}.

Step 2: Calculate Percent Iron in \( \mathrm{FeCO}_3 \)

To find the percent iron by mass in \( \mathrm{FeCO}_3 \), divide the mass of iron by the molar mass of the compound and multiply by 100. \[ \text{Percent Iron in } \mathrm{FeCO}_3 = \left( \frac{55.85}{115.86} \right) \times 100 \approx 48.20\% \]

Step 3: Calculate Percent Iron in \( \mathrm{Fe}_2 \mathrm{O}_3 \)

To find the percent iron by mass in \( \mathrm{Fe}_2 \mathrm{O}_3 \), calculate twice the mass of iron since there are two iron atoms, then divide by the molar mass of the compound and multiply by 100. \[ \text{Percent Iron in } \mathrm{Fe}_2 \mathrm{O}_3 = \left( \frac{2 \times 55.85}{159.70} \right) \times 100 \approx 69.94\% \]

Step 4: Calculate Percent Iron in \( \mathrm{Fe}_3 \mathrm{O}_4 \)

For \( \mathrm{Fe}_3 \mathrm{O}_4 \), calculate thrice the mass of iron, divide by the molar mass of the compound, and multiply by 100. \[ \text{Percent Iron in } \mathrm{Fe}_3 \mathrm{O}_4 = \left( \frac{3 \times 55.85}{231.55} \right) \times 100 \approx 72.36\% \]

Key Concepts

Molar Mass Calculation

Calculating the molar mass of compounds is essential to understand their composition. The molar mass tells us the mass of one mole of a compound in grams. To find it, we use the atomic masses of the elements involved. These atomic masses can be found on the periodic table and are expressed in grams per mole.

For example, in the compound \( \mathrm{FeCO}_3 \), we add together the atomic masses of iron (Fe), carbon (C), and oxygen (O). Iron has an atomic mass of 55.85 g/mol, carbon 12.01 g/mol, and oxygen 16.00 g/mol. In \( \mathrm{FeCO}_3 \), we have:

• 1 Iron atom: 55.85 g/mol
• 1 Carbon atom: 12.01 g/mol
• 3 Oxygen atoms: 3 × 16.00 g/mol

Adding these together gives us a molar mass of 115.86 g/mol for \( \mathrm{FeCO}_3 \). Similarly, we calculate the molar masses of other compounds such as \( \mathrm{Fe}_2 \mathrm{O}_3 \) and \( \mathrm{Fe}_3 \mathrm{O}_4 \). Understanding molar mass is crucial for further calculations like percent composition.

Iron Compounds

Iron compounds play a significant role in chemistry and various applications. Here, we look at three specific oxygen-containing compounds: \( \mathrm{FeCO}_3 \), \( \mathrm{Fe}_2 \mathrm{O}_3 \), and \( \mathrm{Fe}_3 \mathrm{O}_4 \).

• \( \mathrm{FeCO}_3 \) is known as iron(II) carbonate. It's a compound where iron is bonded with carbonate ions.
• \( \mathrm{Fe}_2 \mathrm{O}_3 \) is iron(III) oxide, commonly known as hematite. It's one of the main iron ores.
• \( \mathrm{Fe}_3 \mathrm{O}_4 \) is known as magnetite, which is a naturally occurring iron oxide with magnetic properties.

These compounds differ in their iron content, which is essential for determining their percent composition by mass. By calculating how much iron is present in each, we can understand their potential uses and recognize their importance in industrial processes.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's all about the numbers and how they relate to the chemical formulas of substances.

To understand how much of a substance we have, we often need to calculate the percent composition. This involves using stoichiometry to find how much of an element is present in a compound compared to the whole compound.

For instance, in \( \mathrm{Fe}_2 \mathrm{O}_3 \), we calculate the percent of iron by determining how much iron is present compared to the entire compound's molar mass. By using formulas like \( \text{Percent Iron} = \left( \frac{\text{mass of Fe}}{\text{molar mass of compound}} \right) \times 100 \), we get clear insights into the compound's composition. Such calculations are vital in real-world applications, where we need precise amounts of materials for manufacturing, mining, and more.