Mass, Moles and Particles

The mole is the bridge between a mass you can weigh and a number of particles you cannot count:

$$n = \frac{m}{M} \qquad N = n \times N_A$$

$9\ \mathrm{g}$ of water ($18\ \mathrm{g/mol}$) is 9 / 18 = $0.5\ \mathrm{mol}$, and 0.5 × $6.02 \times 10^{23}$ = $3.01 \times 10^{23}$ molecules.

9 g of water: half a mole

Particles back to mass: divide by N_A, then multiply by $M$.