Mole (mol)

Also called mol, Amount of substance

A mole is a counting unit. It denotes a fixed number of things, Avogadro's number of them, in the same way a dozen denotes twelve, so it measures neither a mass nor a volume.

A mole counts. It is the SI base unit for amount of substance, and the thing it measures is a population. One mole of anything is $N_0 = 6.02 \times 10^{23}$ of them, the value the AP Physics 2 table of information prints as Avogadro's number.

That makes converting between the two ways of counting a gas a plain multiplication:

N = n N_0

with $n$ the number of moles and $N$ the number of atoms. The two halves of the printed ideal gas law, $PV = nRT$ and $PV = Nk_BT$ , differ only in which count you use and which constant goes with it.

It is not a mass. One mole of helium fixes how many atoms there are and says nothing about kilograms until a molar mass is supplied. The AP Physics 2 tables print no molar masses at all, so a question that needs one states it in the stem.

It is not a volume either. The $22.4$ litres a chemistry course attaches to a mole is a result rather than a definition, and it holds at one particular temperature and pressure. Run it on the AP sheet's own numbers, one atmosphere as $1.0 \times 10^5$ Pa and $T = 273$ K:

V = \frac{nRT}{P} = \frac{(1)(8.31)(273)}{1.0 \times 10^5} = 0.0227\ \text{m}^3

which is $22.7$ L. Change either condition and the number moves, which is why no molar volume is printed anywhere on the sheet.

Mole is on one of the four AP unit-symbol tables, appearing as mol on the AP Physics 2 one.

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