Problem 162 - Chemistry Matter and Change

Question

Iron Three naturally occurring iron compounds are pyrite (FeS \(_{2} )\) , hematite \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right),\) and siderite \(\left(\mathrm{FeCO}_{3}\right)\) Which contains the greatest percentage of iron?

Step-by-Step Solution

Answer

Hematite contains the greatest percentage of iron at 70%.

Step 1: Calculate Molar Mass of Pyrite

Pyrite is composed of one iron (Fe) atom and two sulfur (S) atoms. Iron has an atomic mass of approximately 56 g/mol and sulfur has an atomic mass of approximately 32 g/mol. Therefore, the molar mass of pyrite, FeS\[_{2}\], is calculated as: \[\text{{Molar mass of FeS}}_{2} = 56 + 2 \times 32 = 56 + 64 = 120\ ext{{g/mol}}\]

Step 2: Calculate Iron Percentage in Pyrite

To find the percentage of iron in pyrite, divide the atomic mass of Fe by the molar mass of pyrite and multiply by 100:\[\text{{Percentage of Fe}} = \left( \frac{56}{120} \right) \times 100 \approx 46.67\%\]

Step 3: Calculate Molar Mass of Hematite

Hematite is composed of two iron (Fe) atoms and three oxygen (O) atoms. Oxygen has an atomic mass of approximately 16 g/mol. Therefore, the molar mass of hematite, Fe\_{2}\ O\_{3}\, is calculated as:\[\text{{Molar mass of Fe}}_{2}\text{{O}}_{3} = 2 \times 56 + 3 \times 16 = 112 + 48 = 160 \text{{ g/mol}}\]

Step 4: Calculate Iron Percentage in Hematite

To find the percentage of iron in hematite, divide the total mass of iron by the molar mass of hematite and multiply by 100:\[\text{{Percentage of Fe}} = \left( \frac{112}{160} \right) \times 100 = 70\%\]

Step 5: Calculate Molar Mass of Siderite

Siderite is composed of one iron (Fe) atom, one carbon (C) atom, and three oxygen (O) atoms. Carbon has an atomic mass of approximately 12 g/mol. Therefore, the molar mass of siderite, FeCO\_{3}\, is calculated as:\[\text{{Molar mass of FeCO}}_{3} = 56 + 12 + 3 \times 16 = 56 + 12 + 48 = 116 \text{{ g/mol}}\]

Step 6: Calculate Iron Percentage in Siderite

To find the percentage of iron in siderite, divide the atomic mass of Fe by the molar mass of siderite and multiply by 100:\[\text{{Percentage of Fe}} = \left( \frac{56}{116} \right) \times 100 \approx 48.28\%\]

Step 7: Compare Percentages

Now, compare the iron percentages calculated for each compound: - Pyrite: 46.67% - Hematite: 70% - Siderite: 48.28% Hematite has the highest percentage of iron among the three compounds.

Key Concepts

Molar Mass Calculation

When carrying out a chemical composition analysis, a fundamental procedure is calculating the molar mass of a compound. The molar mass is the total mass of all atoms present in one mole of a compound, expressed in grams per mole (g/mol). To determine this, you sum the atomic masses of each element in the compound, multiplied by the number of atoms of that element.

For example, in the compound pyrite (FeS\(_{2}\)), you have:

• 1 atom of Iron (Fe) with an atomic mass of 56 g/mol.
• 2 atoms of Sulfur (S) with an atomic mass of 32 g/mol each.

The molar mass is calculated as:\[ ext{Molar mass of FeS}_{2} = 56 + 2 \times 32 = 120 \ ext{g/mol}\]This process is repeated similarly for hematite (Fe\(_{2}\)O\(_{3}\)) and siderite (FeCO\(_{3}\)), taking into account the atomic masses of iron, oxygen, and carbon involved.

Iron Compounds

Iron compounds are widespread and important in various fields such as geology, chemistry, and industry. The three common naturally occurring iron compounds are pyrite, hematite, and siderite, each with unique compositions and properties.

• **Pyrite (FeS\(_{2}\))**, also known as "fool's gold," consists of iron and sulfur and is often found in sedimentary rock formations.
• **Hematite (Fe\(_{2}\)O\(_{3}\))**, is a primary ore of iron, found in iron-rich rocks and is a crucial component in steel manufacturing.
• **Siderite (FeCO\(_{3}\))**, is composed of iron, carbon, and oxygen, and occurs in sedimentary deposits.

Each of these compounds exhibits different physical and chemical properties that make them valuable for various applications, particularly in materials science and metallurgical processes.

Percentage Composition

To understand how much of a particular element is present in a compound, calculating its percentage composition is necessary. This calculation tells us the proportion of each element in a compound by mass.

For instance, let's look again at pyrite (FeS\(_{2}\)) to determine its percentage composition in terms of iron. First, calculate the total molar mass:\[ ext{Molar mass of FeS}_{2} = 120 \ ext{g/mol}\]Then, calculate the contribution of iron:\[ ext{Percentage of Fe} = \left( \frac{56}{120} \right) \times 100 \approx 46.67\%\]This process can be applied to other iron compounds, like hematite and siderite, to determine the most iron-rich compound. Thus, by comparing the percentage compositions of these compounds, you can identify that hematite contains the greatest percentage of iron at 70%.