# How many molecules of carbon dioxide exit your lungs when you exhale 5.00 xx 10^2 mol of carbon dioxide, "CO"_2 ?

Mar 4, 2017

$3.01 \cdot {10}^{26} {\text{molecules CO}}_{2}$

#### Explanation:

Your tool of choice here is Avogadro's constant, which essentially acts as the definition of a mole

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{\text{1 mole CO"_2 = 6.022 * 10^(23)color(white)(.)"molecules CO}}_{2}}}} \to$ Avogadro's constant

So, a mole is essentially a group of things. In this case, a mole of carbon dioxide will contain $6.022 \cdot {10}^{23}$ molecules of carbon dioxide. In other words, in order to have $1$ mole of carbon dioxide, you need to have $6.022 \cdot {10}^{23}$ molecules of carbon dioxide.

You know that $5.00 \cdot {10}^{2}$ molecules of carbon dioxide are exhaled from the lungs when we breathe out. You can use Avogadro's constant as a conversion factor to help you figure out how many molecules are present

5.00 * 10^2 color(red)(cancel(color(black)("moles CO"_2))) * (6.022 * 10^(23)color(white)(.)"molecules CO"_2)/(1color(red)(cancel(color(black)("mole CO"_2))))

$= \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{3.01 \cdot {10}^{26} \textcolor{w h i t e}{.} {\text{molecules CO}}_{2}}}}$

The answer is rounded to three sig figs.