Mole - the measure of a substance

In 1971, mole was accepted as an SI unit for ’measure of a substance‘.

Avogadro’s Law

The road to this adoption goes back to Amedeo Avogadro who hypothesised in 1811 that equal volumes of gases at standard pressure and temperature would have same number of particles.

Volume $\propto$ number of particles

V $\propto$ n

$V_1/n_1=V_2/n_2$

This is Avogadro’s Law for ideal gases. In case the gas is compressed at high pressures, this law will not apply as it is based on the fact that at standard pressure the molecules will be so far apart that their molecular measures will be irrelevant.

Hence there was no need to understand the actual atomic masses or sizes to make volume estimates for gases in ideal conditions. The understanding about electrons, etc came later in 1900s from JJ Thompson’s discovery.

Avogadro’s law however does not apply to liquids and solids because the closeness of particles meant that the atomic sizes became more relevant.

When it comes to liquids and solids, the density of the element comes into play as

$Volume\propto Mass/Density$

Avogadro’s Constant

Based on the Avogadro’s Law, Johann Josef Loschmidt in 1865 estimated the number of particles in a given volume of gas.

The precise value of number of particles in a given volume was determined by Jean Baptiste Perrin in 1909 during his Brownian Motion experiments. Jean attributed this constant number as ‘Avogadro’s Constant’. Jean was awarded a Nobel Prize in Physics for his contributions.

So now we know,

$N_A=6.02214076\times 10^{23}$

Unlike the law, being a constant, $N_A$ applies across all states of matters like solid, liquid, and gases.

Mole

Finally we comes to the concept of ‘mole’.

So mole is a made up concept by us humans, same as kilogram and every other measure. We say 1 mole is same as the number of atoms in 12g of $C^{12}$, which is equal to the Avogadro’s Constant of $6.02214076\times 10^{23}$.

So 1 mole of any entity (say it be atoms, molecules, ions, or even grains of rice) would be equal to $6.02214076\times 10^{23}$.

However we use this unit specifically for atomic or molecular measures as 1 mole of rice if calculated would be $1.5\times 10^{19}kg$ which is absurd. Hence we stick to kilograms for rice.

If we calculate molecule gram equivalent for some known molecules, we will get,

• 1 mole H₂O (liquid): 18 g → ~18 mL (since density ~1 g/mL)
• 1 mole olive oil: ~282 g (as ‘triolein molecule’) → ~300 mL depending on density
• 1 mole C (graphite): 12 g → ~5 mL (density ~2.2 g/cm³)
• 1 mole Fe (solid): 56 g → ~7 mL (density ~7.9 g/cm³)