# Question 7883c

Oct 25, 2017

$2.62 \cdot {10}^{- 4}$ $\text{g}$

#### Explanation:

The first thing that you need to do here is to figure out how many moles of carbon dioxide are present in your sample.

As you know, $1$ mole of carbon dioxide contains $1$ mole of carbon and $2$ moles of oxygen.

This means that if you know the number of atoms of oxygen, you can calculate the number of moles of oxygen, which, in turn, will give you the number of moles of carbon dioxide.

Now, Avogadro's constant tells you that in order to have $1$ mole of atomic oxygen, you need to have $6.022 \cdot {10}^{23}$ atoms of oxygen.

This means that your sample contains

7.17 * 10^(18)color(red)(cancel(color(black)("atoms O"))) * "1 mole O"/(6.022 * 10^(23)color(red)(cancel(color(black)("atoms O")))) = 1.191 * 10^(-5)color(white)(.)"moles O"

You can thus say that your sample contains

1.191 * 10^(-5) color(red)(cancel(color(black)("moles O"))) * "1 mole CO"_2/(2color(red)(cancel(color(black)("moles O")))) = 5.955 * 10^(-6)color(white)(.)"moles CO"_2#

Finally, to find the mass of carbon dioxide that contains this many moles, you can use the molar mass of the compound.

$5.955 \cdot {10}^{- 6} \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles CO"_2))) * "44.01 g"/(1color(red)(cancel(color(black)("mole CO"_2)))) = color(darkgreen)(ul(color(black)(2.62 * 10^(-4)color(white)(.)"g}}}}$

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