Sure, let's walk through the steps to find out how many moles of Iron (III) oxide ([tex]\( Fe_2O_3 \)[/tex]) will be produced from a 1.67 mol sample of iron ([tex]\( Fe \)[/tex]):
1. Write and interpret the balanced chemical equation:
[tex]\[
4 \text{Fe} + 3 \text{O}_2 \rightarrow 2 \text{Fe}_2\text{O}_3
\][/tex]
This balanced equation tells us that 4 moles of iron react with 3 moles of oxygen to produce 2 moles of Iron (III) oxide.
2. Determine the mole ratio between iron and Iron (III) oxide:
From the balanced chemical equation, we can see that:
[tex]\[
4 \text{mol Fe} \rightarrow 2 \text{mol Fe}_2\text{O}_3
\][/tex]
This simplifies to:
[tex]\[
2 \text{mol Fe} \rightarrow 1 \text{mol Fe}_2\text{O}_3
\][/tex]
3. Calculate the number of moles of Iron (III) oxide produced:
Given that we have 1.67 mol of iron, we need to determine how many moles of [tex]\( Fe_2O_3 \)[/tex] are produced:
[tex]\[
\text{Moles of } Fe_2O_3 = \left(\frac{1.67 \text{ mol Fe}}{2}\right)
\][/tex]
4. Simplify the calculation:
[tex]\[
\text{Moles of } Fe_2O_3 = 0.835 \text{ mol}
\][/tex]
Therefore, with 1.67 mol of iron, you will produce 0.835 mol of Iron (III) oxide.
Thus, the correct answer is [tex]\(0.835 \text{ mol}\)[/tex].
