The ratios n = m/M and n = N/Na

Two ways of determining the amount of substance

The amount of substance n (in moles) is never measured directly: it is calculated from a quantity that can be measured or counted. There are two key relationships, depending on which quantity is used as the starting point: mass, or the number of particles.

Starting from a mass: n = m/M

If we know the mass m (in g) of a sample and the molar mass M (in g/mol) of the substance, the amount of substance is calculated as:

n = m / M

Example: what amount of substance is represented by 36.0 g of water, given that M(H₂O) = 18.0 g/mol?

n = 36,0 / 18,0 = 2,0 mol

Starting from a number of particles: n = N/Na

If we know (or are seeking) the number N of particles (atoms, molecules, ions), the relationship with Avogadro’s number Na is n = N / Na, or equivalently N = n × Na.

Example: how many molecules are there in these 2.0 mol of water?

N = n x Na = 2,0 x 6,02 x 10^23 = 1,204 x 10^24 molécules

Choosing the right formula

The best approach is to identify what the question gives you: a mass in grams -> use n = m/M; a number of particles -> use n = N/Na. Both relationships share the same quantity, n, which allows you to convert from one to the other.

Common mistake

The most common mistake is to reverse the formula, for example calculating M = m/n instead of n = m/M, or forgetting to convert a mass given in milligrams or kilograms to grams before dividing by M (which is always in g/mol).