Question

How many mols of aluminum atoms are in `1.42 xx 10^24` atoms?

Am I doing this right?

1.42x1024 x 26.98 = 3.83x1025

Answer 1

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"`.

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