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

Oct 25, 2016

${\text{1.8 g CO}}_{2}$

#### Explanation:

Your strategy here will be to

• use the chemical formula of carbon dioxide to find the number of molecules of ${\text{CO}}_{2}$ 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, $1 \times \text{C}$
• two atoms of oxygen, $2 \times \text{O}$

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"))))

$= 2.4 \cdot {10}^{22} {\text{molecules CO}}_{2}$

Now, one mole of any molecular substance contains exactly $6.022 \cdot {10}^{22}$ 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))))

$= {\text{0.03985 moles CO}}_{2}$

Finally, carbon dioxide has a molar mass of ${\text{44.01 g mol}}^{- 1}$, 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))))

$= \textcolor{g r e e n}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1.8 g}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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.