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

Md Ariful Islam

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Md Ariful Islam

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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 .

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