To determine the number of grams of iron(III) chloride ([tex]\(\text{FeCl}_3\)[/tex]) produced from 56.7 grams of iron (Fe) with sufficient chlorine (Cl[tex]\(_2\)[/tex]), follow these steps:
1. Identify the Molar Masses:
- Molar mass of iron ([tex]\(\text{Fe}\)[/tex]): 55.845 g/mol.
- Molar mass of iron(III) chloride ([tex]\(\text{FeCl}_3\)[/tex]): 162.204 g/mol.
2. Calculate the Number of Moles of Iron:
[tex]\[
\text{Moles of Fe} = \frac{\text{Mass of Fe}}{\text{Molar Mass of Fe}} = \frac{56.7 \, \text{g}}{55.845 \, \text{g/mol}} \approx 1.0153 \, \text{moles}
\][/tex]
3. Determine the Mole Ratio:
From the balanced chemical equation:
[tex]\[
2 \, \text{Fe} + 3 \, \text{Cl}_2 \rightarrow 2 \, \text{FeCl}_3
\][/tex]
The mole ratio of [tex]\(\text{Fe}\)[/tex] to [tex]\(\text{FeCl}_3\)[/tex] is 1:1. Therefore, the moles of [tex]\(\text{FeCl}_3\)[/tex] produced will be the same as the moles of [tex]\(\text{Fe}\)[/tex] used:
[tex]\[
\text{Moles of FeCl}_3 = 1.0153 \, \text{moles}
\][/tex]
4. Calculate the Mass of [tex]\(\text{FeCl}_3\)[/tex]:
[tex]\[
\text{Mass of FeCl}_3 = \text{Moles of FeCl}_3 \times \text{Molar Mass of FeCl}_3 = 1.0153 \, \text{moles} \times 162.204 \, \text{g/mol} \approx 164.687 \, \text{grams}
\][/tex]
5. Adjust for Significant Figures:
The given mass of iron (56.7 g) has three significant figures. Therefore, the final mass of [tex]\(\text{FeCl}_3\)[/tex] should also be reported with three significant figures:
[tex]\[
\text{Mass of FeCl}_3 = 164.687 \, \text{grams}
\][/tex]
To conclude, the mass of [tex]\(\text{FeCl}_3\)[/tex] produced from 56.7 grams of iron is approximately [tex]\(164.687\)[/tex] grams.
