Question

What is the mass percent of iron in each of the following iron ores: \(\mathrm{Fe}_{2} \mathrm{O}_{3}, \mathrm{Fe}_{3} \mathrm{O}_{4}, \mathrm{FeS}_{2} ?\)

Short answer

Fe2O3: 69.94%Fe3O4: 72.35%FeS2: 46.54%

Step-by-step solution

- Determine the Molar Mass of Each Compound

Calculate the molar mass of Iron(III) oxide \(\text{Fe}_2\text{O}_3\). The molar mass of Fe is 55.85 g/mol and that of O is 16.00 g/mol:\(\text{Molar mass of Fe}_2\text{O}_3 = 2(55.85) + 3(16.00) = 159.70 \text{g/mol}\).

- Calculate the Mass Percent of Iron in \(\text{Fe}_2\text{O}_3\)

The mass percent of iron in \(\text{Fe}_2\text{O}_3\) is calculated as follows:\(\text{Mass percent of Fe} = \frac{2 \(55.85\)}{159.70} \times 100 = 69.94\%\).

- Determine the Molar Mass of \(\text{Fe}_3\text{O}_4\)

Calculate the molar mass of Iron(II,III) oxide \(\text{Fe}_3\text{O}_4\). The molar mass of Fe is 55.85 g/mol and that of O is 16.00 g/mol:\(\text{Molar mass of Fe}_3\text{O}_4 = 3(55.85) + 4(16.00) = 231.55 \text{g/mol}\).

- Calculate the Mass Percent of Iron in \(\text{Fe}_3\text{O}_4\)

The mass percent of iron in \(\text{Fe}_3\text{O}_4\) is calculated as follows:\(\text{Mass percent of Fe} = \frac{3 \(55.85\)}{231.55} \times 100 = 72.35\%\).

- Determine the Molar Mass of \(\text{FeS}_2\)

Calculate the molar mass of Iron disulfide \(\text{FeS}_2\). The molar mass of Fe is 55.85 g/mol and that of S is 32.07 g/mol:\(\text{Molar mass of FeS}_2 = 55.85 + 2(32.07) = 119.99 \text{g/mol}\).

- Calculate the Mass Percent of Iron in \(\text{FeS}_2\)

The mass percent of iron in \(\text{FeS}_2\) is calculated as follows:\(\text{Mass percent of Fe} = \frac{55.85}{119.99} \times 100 = 46.54\%\).

Key concepts

Molar Mass Calculation

Understanding how to calculate molar mass is crucial for determining the mass percent of elements in a compound. Molar mass is the sum of the masses of all the atoms in a molecule. It can be found by adding up the atomic masses of each element present in the molecule, multiplied by the number of times that element occurs. For example:

- Iron(III) oxide, \(\text{Fe}_2\text{O}_3\):
The molar mass of Fe is 55.85 g/mol and that of O is 16.00 g/mol. \[2(55.85) + 3(16.00) = 159.70 \text{g/mol}\]

- Iron(II,III) oxide, \(\text{Fe}_3\text{O}_4\):
The molar mass of Fe is 55.85 g/mol and that of O is 16.00 g/mol. \[3(55.85) + 4(16.00) = 231.55 \text{g/mol}\]

- Iron disulfide, \(\text{FeS}_2\):
The molar mass of Fe is 55.85 g/mol and that of S is 32.07 g/mol. \[55.85 + 2(32.07) = 119.99 \text{g/mol}\]
Once you know how to calculate molar mass, you can use it to determine the mass percent of each element. This makes it easier to understand the composition of different compounds.

Chemical Composition Analysis

Chemical composition analysis helps us understand the proportion of each element in a compound. To calculate the mass percent of an element within a compound, use the following formula:

\[\text{Mass percent of element} = \frac{\text{mass of element in the formula}}{\text{molar mass of the compound}} \times 100\]

Let's apply this to our previously calculated molar masses:

- For \(\text{Fe}_2\text{O}_3\), the mass percent of iron is:
\[\text{Mass percent of Fe} = \frac{2(55.85)}{159.70} \times 100 = 69.94\text{%}\]

- For \(\text{Fe}_3\text{O}_4\), the mass percent of iron is:
\[\text{Mass percent of Fe} = \frac{3(55.85)}{231.55} \times 100 = 72.35\text{%}\]

- For \(\text{FeS}_2\), the mass percent of iron is:
\[\text{Mass percent of Fe} = \frac{55.85}{119.99} \times 100 = 46.54\text{%}\]
This analysis helps in determining which compound has the highest amount of a particular element. So, it's incredibly useful in mining, chemistry, and various other fields.

Iron Compounds

Iron is found in different forms in nature, often combined with other elements. The most common iron ores are:

- Iron(III) oxide, \(\text{Fe}_2\text{O}_3\), also known as hematite
- Iron(II,III) oxide, \(\text{Fe}_3\text{O}_4\), known as magnetite
- Iron disulfide, \(\text{FeS}_2\), commonly called pyrite

Understanding their chemical composition helps us extract iron more effectively. For instance, hematite and magnetite are major sources of iron for the steel industry. Pyrite mainly provides sulfur but is less important as an iron source.

These iron compounds vary significantly in their iron content:

- Hematite (\text{Fe}_2\text{O}_3) has about 69.94% iron
- Magnetite (\text{Fe}_3\text{O}_4) has about 72.35% iron
- Pyrite (\text{FeS}_2) has about 46.54% iron

Knowing this information helps industries decide which ore to process for iron extraction. Iron is an essential element in modern infrastructure, so understanding its sources and composition is key.