# Question 1b172

Oct 5, 2015

You need $\textcolor{b l u e}{{\text{5.86 mol of O}}_{2}}$.

#### Explanation:

${\text{4Fe" + "3O"_2 → "2Fe"_2"O}}_{3}$

This tells you that ${\text{2 mol of Fe"""_2"O}}_{3}$ require ${\text{3 mol of O}}_{2}$.

This is called the molar ratio of ${\text{Fe"_2"O}}_{3}$ to ${\text{O}}_{2}$.

You want to convert the given moles of ${\text{Fe"_2"O}}_{3}$ to moles of ${\text{O}}_{2}$.

We can use the molar ratio to create a conversion factor.

It will be either $\left({\text{2 mol Fe"""_2"O"_3)/("3 mol O}}_{2}\right)$ or $\left({\text{3 mol O"""_2)/("2 mol Fe"""_2"O}}_{3}\right)$.

We choose the one that will give us the correct units in the answer.

It will be the second one. Then

3.91 color(red)(cancel(color(black)("mol Fe"_2"O"_3))) × ("3 mol O"""_2)/(2 color(red)(cancel(color(black)("mol Fe"_2"O"_3)))) = "5.86 mol O"""_2#

Notice that the units cancelled to give the desired units of $\text{mol O"""_2}$.

If we had chosen the other conversion factor, we would not have gotten the correct units.