The mole

Atoms, molecules and ions are far too small and numerous to count individually. Chemists therefore count them in large groups called moles. The mole, with symbol $$\mathrm{mol}$$, is the unit for amount of substance.

One mole contains $$6.02 \times 10^{23}$$ of the stated particles. This number is the rounded value of the Avogadro constant, which gives the number of particles in one mole.

A mole counts whatever entities have been named. For example, one mole of carbon atoms, one mole of carbon dioxide molecules and one mole of sodium ions each contain $$6.02 \times 10^{23}$$ of their respective particles. The particles are different, but their numbers are the same.

It is therefore important to state what is being counted: atoms, molecules, ions, electrons or formula units. One mole of carbon dioxide molecules is not the same as one mole of atoms, because each carbon dioxide molecule contains more than one atom.

Moles let chemists compare amounts by number of particles, rather than by mass. Equal numbers of different particles need not have equal masses.

Molar mass and mole calculations

The molar mass of a substance is the mass of one mole of that substance. It links an amount in moles to a mass that can be measured in grams.

A substance’s molar mass in grams per mole is numerically equal to its relative formula mass, $$M_r$$. For example, if $$M_r = 18$$, one mole has a mass of $$18\ \text{g}$$, so the molar mass is $$18\ \text{g/mol}$$. Relative formula mass has no unit; molar mass has a unit of mass per mole.

Finding the one-mole mass

Use the formula of the substance to find its relative formula mass: add the relative atomic masses of all the atoms shown in the formula. For water, $$\ce{H2O}$$, there are two hydrogen atoms and one oxygen atom. Using relative atomic masses of 1 for hydrogen and 16 for oxygen, $$M_r = (2 \times 1) + 16 = 18$$. Therefore, one mole of water has a mass of $$18\ \text{g}$$.

Converting between mass and moles

To find the amount in moles, divide the mass in grams by the molar mass in grams per mole:

For example, $$9\ \text{g}$$ of water is $$9 \div 18 = 0.5\ \text{mol}$$. This is half a mole because $$9\ \text{g}$$ is half the mass of one mole.

To find the mass in grams, multiply the amount in moles by the molar mass:

For example, $$2\ \text{mol}$$ of water has a mass of $$2 \times 18 = 36\ \text{g}$$. In either direction, use the molar mass calculated for the substance in the question.

Mole ratios in balanced equations

A balanced chemical equation shows the fixed ratio in which substances react and are formed. The numbers in front of the formulae, called coefficients, count particles, but they also represent amounts in moles. This is because one mole of any substance contains the same number of particles.

For example, the balanced equation for magnesium reacting with hydrochloric acid is:

A formula with no written coefficient has a coefficient of 1. The equation therefore gives the mole ratio of magnesium : hydrochloric acid : magnesium chloride : hydrogen as 1 : 2 : 1 : 1.

This means that 1 mole of magnesium reacts with 2 moles of hydrochloric acid to produce 1 mole of magnesium chloride and 1 mole of hydrogen. The same ratio applies to other amounts: 3 moles of magnesium require 6 moles of hydrochloric acid and, if the reaction goes to completion, produce 3 moles of hydrogen.

Using a mole ratio

When the amount of one substance is known, the coefficients show how to find the amount of another substance needed or produced. Select the two coefficients from the balanced equation and use their ratio to scale from the known amount to the unknown amount.

The ratio comes from the balanced equation, so the equation must be balanced before using it for an amount calculation.