Question

How do I calculate the number of molecules in a 300g sample of Fe2O3?

Answer 1

To calculate the number of molecules in a 300 g sample of iron(III) oxide (Fe₂O₃), you can follow these steps:

1. **Calculate the molar mass of Fe₂O₃**:
- The atomic mass of iron (Fe) is approximately 55.85 g/mol.
- The atomic mass of oxygen (O) is approximately 16.00 g/mol.
- The molar mass of Fe₂O₃ can be calculated as follows:
\[
\text{Molar mass of Fe₂O₃} = (2 \times 55.85) + (3 \times 16.00)
\]
\[
= 111.70 + 48.00 = 159.70 \text{ g/mol}
\]

2. **Calculate the number of moles in the 300 g sample**:
\[
\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{300 \text{ g}}{159.70 \text{ g/mol}} \approx 1.876 \text{ mol}
\]

3. **Use Avogadro's number to find the number of molecules**:
Avogadro's number is \(6.022 \times 10^{23}\) molecules/mol. Therefore, the number of molecules can be calculated as follows:
\[
\text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number}
\]
\[
= 1.876 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.13 \times 10^{24} \text{ molecules}
\]

In summary, a 300 g sample of Fe₂O₃ contains approximately \(1.13 \times 10^{24}\) molecules.