# 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

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:

$\text{g"/"mol" xx "atoms" = ("g"cdot"atoms")/"mol}$.

The atoms "unit" has to cancel so that you get into the units of $\text{mol}$s. So, you have to use a relationship between $\text{mol}$s and $\text{atoms}$ and achieve:

$\cancel{\text{atoms") xx "mol"/cancel("atoms}}$

How I would do it is to recall that $\text{1 mol}$ of anything is $6.022 \times {10}^{23}$ of that thing. It could be spoons, watches, atoms, pencils, whatever. It could also be $\text{Al}$ atoms, $\text{C}$ atoms, $\text{H}$ atoms, etc.

So if you have $1.42 \times {10}^{24}$ $\text{atoms}$ of aluminum, practically speaking, you should have between $2$ and $3$ $\text{mols}$ of aluminum atoms because $\frac{1.42 \times {10}^{24}}{6.022 \times {10}^{23}} \approx 2$.

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 $\text{mol}$ is just like a dozen. A dozen eggs means $12$ eggs, and $1$ dozen eggs is larger in absolute quantity than $1$ egg.

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