# Calculations around the molar mass of a chemical substance

## Definition

The molar mass (M) of a substance is the mass (m) expressed in grams of one mole of molecules.

For instance, the mass of $6.023\cdot 10^{23}$ molecules of water is $18\;g$, therefore
$ M_{H_2O}$ $=$ $18 \frac{g}{mol}$

## Relation between molar mass(M), mass(m) and number of moles(n)

The mass of a substance equals the number of moles multiplied by the mass of one mole( = molar mass)

For instance, the mass of 2 moles water is
$m$ $=$ $2\cdot M_{H_2O}$ $=$ $2\cdot 18.02$ $=$ $36.04 g$

For instance, 36.04 g water are
$n$ $=$ $\frac{36.04}{M_{H_2O}}$ $=$ $2 mol$

For instance, knowing that 36.04 g water are 2 mol , the molar mass of water is
$M_{H_2O}$ $=$ $\frac{36.04}{2}$ $=$ $18.02 \frac{g}{mol}$