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The rusting of iron is represented by the equation below. If you have a [tex]1.67 \, \text{mol}[/tex] sample of iron, how many moles of Iron (III) oxide will be produced after the iron has rusted completely?

[tex]4 \, \text{Fe} + 3 \, \text{O}_2 \rightarrow 2 \, \text{Fe}_2\text{O}_3[/tex]

A. 0.557 mol
B. 0.835 mol
C. 1.11 mol
D. 1.67 mol
E. 2.51 mol



Answer :

GinnyAnswer
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].

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