Question

What mass of `CO_2` contains `4.8 xx 10^22` oxygen atoms?

Answer 1

`"1.8 g CO"_2`

Explanation:

Your strategy here will be to

• use the chemical formula of carbon dioxide to find the number of molecules of `"CO"_2` that would contain that many atoms of oxygen
• use Avogadro's constant to convert the number of molecules to moles of carbon dioxide
• use the molar mass of carbon dioxide to convert the moles to grams

So, you know that one molecule of carbon dioxide contains

• one atom of carbon, `1 xx "C"`
• two atoms of oxygen, `2 xx "O"`

This means that the given number of atoms of oxygen would correspond to

`4.8 * 10^(22) color(red)(cancel(color(black)("atoms O"))) * "1 molecule CO"_2/(2color(red)(cancel(color(black)("atoms O"))))`

`= 2.4 * 10^(22)"molecules CO"_2`

Now, one mole of any molecular substance contains exactly `6.022 * 10^(22)` molecules of that substance -- this is known as Avogadro's constant.

In your case, the sample of carbon dioxide molecules contains

`2.4 * 10^(22) color(red)(cancel(color(black)("molecules CO"_2))) * "1 mole CO"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules CO"_2))))`

`= "0.03985 moles CO"_2`

Finally, carbon dioxide has a molar mass of `"44.01 g mol"^(-1)`, which means that your sample will have a mass of

`0.03985 color(red)(cancel(color(black)("moles CO"_2))) * "44.01 g"/(1color(red)(cancel(color(black)("mole CO"_2))))`

`= color(green)(bar(ul(|color(white)(a/a)color(black)("1.8 g")color(white)(a/a)|)))`

The answer is rounded to two sig figs, the number of sig figs you have for the number of atoms of oxygen present in the sample.