What mass of #CO_2# contains #4.8 xx 10^22# oxygen atoms?

1 Answer
Oct 25, 2016

Answer:

#"1.8 g CO"_2#

Explanation:

Your strategy here will be to

  • use the chemical formula of carbon dioxide to find the number of molecules of #"CO"_2# that would contain that many atoms of oxygen
  • use Avogadro's constant to convert the number of molecules to moles of carbon dioxide
  • use the molar mass of carbon dioxide to convert the moles to grams

So, you know that one molecule of carbon dioxide contains

  • one atom of carbon, #1 xx "C"#
  • two atoms of oxygen, #2 xx "O"#

This means that the given number of atoms of oxygen would correspond to

#4.8 * 10^(22) color(red)(cancel(color(black)("atoms O"))) * "1 molecule CO"_2/(2color(red)(cancel(color(black)("atoms O"))))#

# = 2.4 * 10^(22)"molecules CO"_2#

Now, one mole of any molecular substance contains exactly #6.022 * 10^(22)# molecules of that substance -- this is known as Avogadro's constant.

In your case, the sample of carbon dioxide molecules contains

#2.4 * 10^(22) color(red)(cancel(color(black)("molecules CO"_2))) * "1 mole CO"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules CO"_2))))#

#= "0.03985 moles CO"_2#

Finally, carbon dioxide has a molar mass of #"44.01 g mol"^(-1)#, which means that your sample will have a mass of

#0.03985 color(red)(cancel(color(black)("moles CO"_2))) * "44.01 g"/(1color(red)(cancel(color(black)("mole CO"_2))))#

# = color(green)(bar(ul(|color(white)(a/a)color(black)("1.8 g")color(white)(a/a)|)))#

The answer is rounded to two sig figs, the number of sig figs you have for the number of atoms of oxygen present in the sample.