# Which of the following molecules has the largest mass?

## Can someone explain to me how to do question 62? Thanks!

Mar 17, 2017

The answer is ${\text{A) 1.5 moles O}}_{2}$

#### Explanation:

For starters, you know that diatomic oxygen, ${\text{O}}_{2}$, has a molar mass equal to

M_ ("M O"_2) = "32.0 g mol"^(-1)

Now, each molecule of oxygen contains $2$ atoms of oxygen, so right from the start, you can say that $1$ mole of oxygen atoms will have a molar mass that is equal to half of the molar mass of diatomic oxygen

M_ ("M O") = "16.0 g mol"^(-1)

So, if $1$ mole of oxygen molecules has a mass of $\text{32.0 g}$, it follows that you will get $\frac{1}{2}$ moles of oxygen molecules in $\text{16.0 g}$ of ${\text{O}}_{2}$.

Therefore, you can say that

${\text{16 g O"_2 = 1/2color(white)(.)"moles O}}_{2}$

You can use the fact that each oxygen molecule contains $2$ atoms of oxygen to say that $1.24 \cdot {10}^{24}$ atoms of oxygen will be equivalent to $\frac{1}{2} \cdot 1.24 \cdot {10}^{24}$ molecules of oxygen.

Therefore, you have

$1.24 \cdot {10}^{24} \textcolor{w h i t e}{.} {\text{atoms O" = 6.20 * 10^(23)color(white)(.)"molecules O}}_{2}$

Finally, you know that $1$ mole of a molecular substance must contain $6.022 \cdot {10}^{23}$ molecules of that substance.

This means that the samples you have at point $\text{C}$ and $\text{D}$ will be equivalent to a little less than $1$ mole of oxygen molecules

6.20 * 10^(23)color(red)(cancel(color(black)("molecules O"_2))) * "1 mole O"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules O"_2))))

$= \frac{6.20}{6.022} \textcolor{w h i t e}{.} {\text{moles O}}_{2}$

and

6.06 * 10^(23)color(red)(cancel(color(black)("molecules O"_2))) * "1 mole O"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules O"_2))))

$= \frac{6.06}{6.022} \textcolor{w h i t e}{.} {\text{moles O}}_{2}$

You can now say that the four samples contain

• ${\text{A: " "1.5 moles O}}_{2}$
• ${\text{B: " "0.5 moles O}}_{2}$
• ${\text{C: " 6.20/6.022color(white)(.)"moles O}}_{2}$
• ${\text{D: " 6.06/6.022 color(white)(.)"moles O}}_{2}$

Therefore, sample $\text{A}$ will have the larger mass because it contains the biggest number of oxygen molecules.