Certainly! Let’s calculate the number of iron (Fe) atoms in a 100.0 g sample of iron(III) oxide ([tex]\( Fe_2O_3 \)[/tex]) in a step-by-step manner.
1. Determine the molar mass of iron(III) oxide ([tex]\( Fe_2O_3 \)[/tex]):
- The molar mass ([tex]\(M\)[/tex]) of iron(III) oxide ([tex]\( Fe_2O_3 \)[/tex]) is given as 159.687 g/mol.
2. Calculate the number of moles of [tex]\( Fe_2O_3 \)[/tex] in the sample:
- Mass of the sample ([tex]\(m\)[/tex]) provided is 100.0 g.
- Use the formula to find the number of moles ([tex]\(n\)[/tex]):
[tex]\[
n = \frac{m}{M}
\][/tex]
[tex]\[
n = \frac{100.0 \text{ g}}{159.687 \text{ g/mol}} \approx 0.6262 \text{ mol} \quad \text{(to four significant digits)}
\][/tex]
3. Determine the number of molecules of [tex]\( Fe_2O_3 \)[/tex] in the sample:
- Avogadro's number ([tex]\(N_A\)[/tex]) is [tex]\(6.022 \times 10^{23}\)[/tex] molecules/mol.
- Using Avogadro's number, calculate the number of molecules:
[tex]\[
\text{Number of molecules} = n \times N_A
\][/tex]
[tex]\[
\text{Number of molecules} = 0.6262 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 3.7702 \times 10^{23} \text{ molecules}
\][/tex]
4. Determine the number of iron atoms in the sample:
- Each molecule of [tex]\( Fe_2O_3 \)[/tex] contains 2 atoms of iron (Fe).
- Therefore, the number of iron atoms:
[tex]\[
\text{Number of iron (Fe) atoms} = \text{Number of molecules} \times 2
\][/tex]
[tex]\[
\text{Number of iron (Fe) atoms} = 3.7702 \times 10^{23} \text{ molecules} \times 2 = 7.5404 \times 10^{23} \text{ atoms}
\][/tex]
5. Round the answer to 4 significant digits:
- The rounded result is:
[tex]\[
7.540 \times 10^{23}
\][/tex]
So, the number of iron ([tex]\(Fe\)[/tex]) atoms in a 100.0 g sample of iron(III) oxide ([tex]\( Fe_2O_3 \)[/tex]) is [tex]\(7.540 \times 10^{23}\)[/tex] atoms.
