How many mols of aluminum atoms are in 1.42 xx 10^241.42×1024 atoms?

Am I doing this right?

1.42x1024 x 26.98 = 3.83x1025

1 Answer
Aug 31, 2016

What you did was multiply the molar mass of aluminum atom by the number of atoms, which physically doesn't make sense; it gives you:

"g"/"mol" xx "atoms" = ("g"cdot"atoms")/"mol"gmol×atoms=gatomsmol.

The atoms "unit" has to cancel so that you get into the units of "mol"mols. So, you have to use a relationship between "mol"mols and "atoms"atoms and achieve:

cancel("atoms") xx "mol"/cancel("atoms")

How I would do it is to recall that "1 mol" of anything is 6.022xx10^23 of that thing. It could be spoons, watches, atoms, pencils, whatever. It could also be "Al" atoms, "C" atoms, "H" atoms, etc.

So if you have 1.42xx10^24 "atoms" of aluminum, practically speaking, you should have between 2 and 3 "mols" of aluminum atoms because (1.42xx10^24)/(6.022xx10^23) ~~ 2.

That's just an estimate, but it gives you an idea of what we expect to get.

1.42xx10^24 cancel"atoms" xx "1 mol"/(6.022xx10^23 cancel"atoms") = 14.2/6.022 = bb("2.36 mols") of aluminum atoms.

A "mol" is just like a dozen. A dozen eggs means 12 eggs, and 1 dozen eggs is larger in absolute quantity than 1 egg.

Similarly, "1 mol" of eggs is larger in absolute quantity than "1" egg. So, if you have a large number of atoms that you are converting to "mol"s, you should expect the number of "mol"s to be smaller, not larger, than your number of atoms.