Question

Which of the following molecules has the largest mass?

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

Answer 1

The answer is `"A) 1.5 moles O"_2`

Explanation:

For starters, you know that diatomic oxygen, `"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 `"32.0 g"`, it follows that you will get `1/2` moles of oxygen molecules in `"16.0 g"` of `"O"_2`.

Therefore, you can say that

`"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 * 10^(24)` atoms of oxygen will be equivalent to `1/2 * 1.24 * 10^(24)` molecules of oxygen.

Therefore, you have

`1.24 * 10^(24)color(white)(.)"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 * 10^(23)` molecules of that substance.

This means that the samples you have at point `"C"` and `"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))))`

`= 6.20/6.022 color(white)(.)"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))))`

`= 6.06/6.022 color(white)(.)"moles O"_2`

You can now say that the four samples contain

• `"A: " "1.5 moles O"_2`
• `"B: " "0.5 moles O"_2`
• `"C: " 6.20/6.022color(white)(.)"moles O"_2`
• `"D: " 6.06/6.022 color(white)(.)"moles O"_2`

Therefore, sample `"A"` will have the larger mass because it contains the biggest number of oxygen molecules.