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

1 Answer
Dec 10, 2015

Answer:

#"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")#