Question

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

Answer 1

`3.01 * 10^(26)"molecules CO"_2`

Explanation:

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

`color(blue)(ul(color(black)("1 mole CO"_2 = 6.022 * 10^(23)color(white)(.)"molecules CO"_2))) ->` Avogadro's constant

So, a mole is essentially a group of things. In this case, a mole of carbon dioxide will contain `6.022 * 10^(23)` molecules of carbon dioxide. In other words, in order to have `1` mole of carbon dioxide, you need to have `6.022 * 10^(23)` molecules of carbon dioxide.

You know that `5.00 * 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))))`

`= color(darkgreen)(ul(color(black)(3.01 * 10^(26)color(white)(.)"molecules CO"_2)))`

The answer is rounded to three sig figs.