To address the problem, we first need to understand how to express the molar mass of a compound as a conversion factor. A molar mass is the mass (in grams) of one mole of a substance. For iron (III) oxide [tex]\(\text{Fe}_2\text{O}_3\)[/tex], the molar mass is given as [tex]\(159.7 \, \text{g/mol}\)[/tex].
This means that:
- One mole of [tex]\(\text{Fe}_2\text{O}_3\)[/tex] weighs [tex]\(159.7 \, \text{g}\)[/tex].
To write this information as a conversion factor, we need to express the relationship in a way that shows the equivalence between grams and moles. The correct way to do this is to state:
- [tex]\(159.7 \, \text{g} \text{Fe}_2\text{O}_3\)[/tex] per [tex]\(1 \, \text{mol} \text{Fe}_2\text{O}_3\)[/tex].
This relationship can be written as a fraction:
[tex]\[
\frac{159.7 \, \text{g Fe}_2\text{O}_3}{1 \, \text{mol Fe}_2\text{O}_3}
\][/tex]
Now, let's examine the given options to identify the correct one:
1. [tex]\(\frac{159.7 \, \text{g Fe}_2\text{O}_3}{159.7 \, \text{mol Fe}_2\text{O}_3}\)[/tex] - This option is incorrect because it implies that 159.7 grams of [tex]\(\text{Fe}_2\text{O}_3\)[/tex] correspond to 159.7 moles, which is not correct. Instead, 159.7 grams correspond to only 1 mole.
2. [tex]\(\frac{1 \, \text{g Fe}_2\text{O}_3}{159.7 \, \text{mol Fe}_2\text{O}_3}\)[/tex] - This option is incorrect because it suggests that 1 gram of [tex]\(\text{Fe}_2\text{O}_3\)[/tex] corresponds to 159.7 moles, which is not correct. The relationship is 1 mole to 159.7 grams.
3. [tex]\(\frac{159.7 \, \text{g Fe}_2\text{O}_3}{1 \, \text{mol Fe}_2\text{O}_3}\)[/tex] - This is the correct conversion factor because it accurately reflects that one mole of [tex]\(\text{Fe}_2\text{O}_3\)[/tex] weighs 159.7 grams.
4. [tex]\(\frac{1 \, \text{g Fe}_2\text{O}_3}{1 \, \text{mol Fe}_2\text{O}_3}\)[/tex] - This option is incorrect because it implies that 1 gram corresponds to 1 mole, which is incorrect.
The correct way to write the molar mass of iron (III) oxide as a conversion factor is:
[tex]\[
\frac{159.7 \, \text{g Fe}_2\text{O}_3}{1 \, \text{mol Fe}_2\text{O}_3}
\][/tex]
Therefore, the correct choice is option 3.
