Question

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

Answer 1

`"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 * 10^(23)` molecules of that substance - this is known as Avogadro's number.

Notice that you're dealing with more than `6.022 * 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 `"44.01 g/mol"`, which means that every mole of `"CO"_2` will have a mass of `"44.01 g"`.

In your case, `2.491 * 10^2` moles of `"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 `"CO"_2`, the answer will be

`m_(CO_2) = color(green)("110 g")`