2 years ago
which has the greatest mass? a.) 3.88 x 10^22 moecules of O2, b.)1.00 g of O2, C.)0.0312 mol of O2, D.) All of these have the same mass

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- chestercat

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- Cuanchi

you have to convert all to the same units to be able compare. You can not compare meters with yards, kilometers or miles. You can not compare which is more expensive if the prices are in dollars, and euros

- Ciarán95

Welcome to OpenStudy @Chelsayanna !! :D
As @Cuanchi said, if we want to compare the magnitude of three different values to see which is greatest, we need to be in a position to make them directly comparable to one another. That means that all three values must be written in the same units. So, we have:
1.) 3.88 x 10^22 molecules of O2
2.) 1.00g of O2
3.) 0.0312 moles of O2
We're asked to identify which has the greatest MASS. Generally, we would express mass in grams (g), so that's what we're going to convert Sample 1.) and Sample 3.) to so that their magnitude is directly comparable with that of Sample 2.). On an aside, if we had a number of samples and were looking to find out which had the greatest number of molecules, for example, it would probably be best to convert their quantities into moles. We don't have to worry about that here though.
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I'm going to start be looking at Sample 3.) first:
0.0312 mol of O2
To convert moles to grams, we need to multiply our answer by the molecular weight of the species in question (O2). From the periodic table, we know that the atomic weight of oxygen (O) is given as 15.9994 g/mol (grams per mole). So, O2 (containing 2 oxygen atoms) will have a molecular weight of 31.9998 g/mol.
\[Number of Grams (g) = (Number of Moles(mol)) \times (Molecular Weight(g/mol))\]
\[= (0.0312 mol)\times(31.9998 g/mol)\]
\[= 0.99836256 g\]
We'll keep as many decimal places as possible at the moment until we can compare our samples to see which is the largest.
_____________________________________________________________________________________
Now, looking at Sample 1.):
3.88 x 10^22 molecules of O2
So, here we need to convert individual molecules to mass in grams. But, how do we do that?
Well, there's actually no direct way of doing it. But, what we can do is convert our 'number of molecules' into moles and then use this to convert to grams like what we did previously with Sample 3.).
A key definition in stoichiometry is that:
"1 mole of any substance (a sample of atoms, ions, molecules) will contain Avagadro's Number (approximately 6.022 x 10^23) individual units of that substance".
\[6.022 \times 10^{23} molecules = 1 mole\]
\[1 molecule = \frac{ 1 }{ 6.022 \times 10^{23} }moles\]
\[3.88 \times 10^{22} molecules = (\frac{ 1 }{ 6.022 \times 10^{23} })(3.88 \times 10^{22}) moles\]
\[= 0.06443042179 moles\]
So, now we know the number of moles of O2 in Sample 3.). Therefore, to convert to grams, we simply multiply by the molecular mass of O2, again 31.9998 g/mol.
This gives us:
\[2.06176011 g\]
_____________________________________________________________________________________
Now, the magnitude of our 3 samples are directly comparable:
1.) 0.99836256 g of O2
2.) 1.00g of O2
3.) 2.06176011 of O2
and we can see clearly now that Sample 3.) contains the greatest mass. Hope that helped you out! :)

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