Question #d7e9b

1 Answer
Aug 3, 2016

Answer:

The sample that contains #"20 g"# of neon.

Explanation:

Notice that the problem asks you which sample contains the same number of atoms as #"1 g"# of hydrogen gas, #"H"_2#, but that three of the sample actually contain molecules, not atoms.

Keep this in mind.

Also, it's worth noting that you're looking for how many moles of atoms are present in the samples. That is the case because a mole is simply a very large collection of atoms.

If you know how many moles of atoms you have, you automatically know how many atoms you have.

So, the problem provides you with a mass of hydrogen gas and the molar mass of the gas, which means that you can calculate how many moles of hydrogen gas are present in your sample

#1 color(red)(cancel(color(black)("g"))) * "1 mole H"_2/(2 color(red)(cancel(color(black)("g")))) = "0.5 moles H"_2#

Now, every mole of hydrogen gas contains #1# mole of hydrogen atoms, since

#0.5 color(red)(cancel(color(black)("moles H"_2))) * "2 moles atoms"/(1 color(red)(cancel(color(black)("mole H"_2)))) = "1 mole atoms"#

This means that you're looking for the sample that contains exactly #1# mole of atoms.

At this point, it should become clear that the answer is (c). You're dealing with #"20 g"# of neon, #"Ne"#, a gas that has a molar mass of #"20 g mol"^(-1)#.

This, of course, implies that the third sample contains

#20 color(red)(cancel(color(black)("g"))) * "1 mole Ne"/(20color(red)(cancel(color(black)("g")))) = "1 mole Ne"#

You can check the other samples if you want to make sure that the question does not have multiple answers. I'll show you how to do the first one.

For carbon dioxide, #"CO"_2#, you have

#22 color(red)(cancel(color(black)("g"))) * "1 mole CO"_2/(44color(red)(cancel(color(black)("g")))) = "0.5 moles CO"_2#

But every mole of carbon dioxide contains #3# moles of atoms, i.e. #1# of carbon atoms and #2# of oxygen atoms, and so

#0.5 color(red)(cancel(color(black)("moles CO"_2))) * "3 moles atoms"/(1color(red)(cancel(color(black)("mole CO"_2)))) = "1.5 moles atoms"#

You can use the same approach to see that sample (c) is indeed the only one that contains the same number of moles at the sample of hydrogen gas.

And remember, a mole is just a fixed number, #6.022 * 10^(23)# to be precise, of atoms / molecules / formula units, depending on the nature of the substance.