# How many grams are there in 1.5 * 10^26 molecules of CO_2?

Dec 10, 2015

$\text{110 g}$

#### Explanation:

Your strategy here will be to

• use Avogadro's number to calculate how many moles of carbon dioxide would contain that many molecules

• use carbon dioxide's molar mass to determine how many grams would contain that many moles

As you know, one mole of any substance contains exactly $6.022 \cdot {10}^{23}$ molecules of that substance - this is known as Avogadro's number.

Notice that you're dealing with more than $6.022 \cdot {10}^{23}$ molecules of carbon dioxide, which means that you'll also be dealing with more than one mole of the compound.

More specifically, you'll have

1.5 * 10^(26) color(red)(cancel(color(black)("molecules"))) * "1 mole CO"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules")))) = 2.491 * 10^2"moles CO"_2

Now, a substance's molar mass tells what the mass of one mole of that substance is. In carbon dioxide's case, its molar mass is equal to $\text{44.01 g/mol}$, which means that every mole of ${\text{CO}}_{2}$ will have a mass of $\text{44.01 g}$.

In your case, $2.491 \cdot {10}^{2}$ moles of ${\text{CO}}_{2}$ would have a mass of

2.491 * 10^2 color(red)(cancel(color(black)("moles CO"_2))) * "44.01 g"/(1 color(red)(cancel(color(black)("mole CO"_2)))) = "109.63 g"

Rounded to two sig figs, the number of sig figs you have for the number of molecules of ${\text{CO}}_{2}$, the answer will be

${m}_{C {O}_{2}} = \textcolor{g r e e n}{\text{110 g}}$