Which of the following molecules has the largest mass?

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Can someone explain to me how to do question 62? Thanks!

1 Answer
Mar 17, 2017

Answer:

The answer is #"A) 1.5 moles O"_2#

Explanation:

For starters, you know that diatomic oxygen, #"O"_2#, has a molar mass equal to

#M_ ("M O"_2) = "32.0 g mol"^(-1)#

Now, each molecule of oxygen contains #2# atoms of oxygen, so right from the start, you can say that #1# mole of oxygen atoms will have a molar mass that is equal to half of the molar mass of diatomic oxygen

#M_ ("M O") = "16.0 g mol"^(-1)#

So, if #1# mole of oxygen molecules has a mass of #"32.0 g"#, it follows that you will get #1/2# moles of oxygen molecules in #"16.0 g"# of #"O"_2#.

Therefore, you can say that

#"16 g O"_2 = 1/2color(white)(.)"moles O"_2#

You can use the fact that each oxygen molecule contains #2# atoms of oxygen to say that #1.24 * 10^(24)# atoms of oxygen will be equivalent to #1/2 * 1.24 * 10^(24)# molecules of oxygen.

Therefore, you have

#1.24 * 10^(24)color(white)(.)"atoms O" = 6.20 * 10^(23)color(white)(.)"molecules O"_2#

Finally, you know that #1# mole of a molecular substance must contain #6.022 * 10^(23)# molecules of that substance.

This means that the samples you have at point #"C"# and #"D"# will be equivalent to a little less than #1# mole of oxygen molecules

#6.20 * 10^(23)color(red)(cancel(color(black)("molecules O"_2))) * "1 mole O"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules O"_2))))#

# = 6.20/6.022 color(white)(.)"moles O"_2#

and

#6.06 * 10^(23)color(red)(cancel(color(black)("molecules O"_2))) * "1 mole O"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules O"_2))))#

# = 6.06/6.022 color(white)(.)"moles O"_2#

You can now say that the four samples contain

  • #"A: " "1.5 moles O"_2#
  • #"B: " "0.5 moles O"_2#
  • #"C: " 6.20/6.022color(white)(.)"moles O"_2#
  • #"D: " 6.06/6.022 color(white)(.)"moles O"_2#

Therefore, sample #"A"# will have the larger mass because it contains the biggest number of oxygen molecules.