Calculations with moles and particles

The number of moles in a sample links its mass to its relative particle mass:

moles = mass (g) ÷ relative formula mass M_r (or A_r for an element)

Rearranged, mass = moles × M_r. For example, 11 g of carbon dioxide (M_r 44) is 11 ÷ 44 = 0.25 mol. And 0.5 mol of sodium hydroxide (M_r 40) has a mass of 0.5 × 40 = 20 g. Always check that the mass is in grams before you start.

To count particles, use the Avogadro constant, 6.02 × 10²³ per mole: particles = moles × 6.02 × 10²³. Going the other way, moles = particles ÷ 6.02 × 10²³. So 0.25 mol contains 0.25 × 6.02 × 10²³ = 1.5 × 10²³ particles (2 significant figures), and 3.01 × 10²³ particles is 0.5 mol.

To find the number of particles in a given mass, work in two steps: change the mass into moles, then multiply by the Avogadro constant. To go from particles to mass, reverse the steps.