What you'll learn

• What chemists mean by amount of substance and the mole.
• How the Avogadro constant links moles to numbers of particles.
• How to convert between mass, molar mass and amount in mol.
• How to use concentration in mol dm⁻³ with solution volumes.

Why chemists use the mole

Atoms, ions and molecules are far too small to count one by one in the lab. Instead, chemists count them in very large “packets” called moles.

This is a bit like counting eggs in dozens: you rarely want one egg number at a time, so you use a convenient counting unit. A mole is the chemist’s counting unit — just much, much bigger.

The word particle here means the entity you have chosen to count: atoms, molecules, ions, electrons, or formula units.

A formula unit is the simplest whole-number ratio represented by an ionic formula. For example, one formula unit of NaCl represents one Na⁺ ion and one Cl⁻ ion.

The mole and the Avogadro constant

In calculations, you may see:

$$N_A\approx 6.022\times 10^{23}{mol}^{-1}$$

That means 1 mol contains about 602 200 000 000 000 000 000 000 particles.

What can one mole apply to?

A mole can be used for different types of chemical particles:

• 1 mol of helium atoms contains $N_A$ helium atoms.
• 1 mol of water molecules contains $N_A$ H₂O molecules.
• 1 mol of chloride ions contains $N_A$ Cl⁻ ions.
• 1 mol of electrons contains $N_A$ electrons.
• 1 mol of MgCl₂ formula units contains $N_A$ MgCl₂ formula units.

Using the Avogadro constant

The relationship between number of particles, $N$, and amount in mol, $n$, is:

$$\begin{array}{rl}N& =n{N}_A\\ n& =\frac{N}{N_A}\end{array}$$

Here, $N$ is the number of particles and has no unit, although you should name the particle in your answer.

Moles in chemical equations

A balanced chemical equation shows the reacting ratio in particles, but because moles are proportional to particles, it also shows the reacting ratio in moles.

For example:

2H₂ + O₂ → 2H₂O

This means:

• 2 mol of H₂ reacts with 1 mol of O₂.
• 2 mol of H₂O is formed.
• The mole ratio H₂ : O₂ : H₂O is 2 : 1 : 2.

From mass to moles

In the lab, you usually measure mass, not individual particles. To convert mass into moles, you use molar mass.

For example, CO₂ has:

$$M=12.0+(2\times 16.0)=44.0{g\; mol}^{-1}$$

So 1 mol of CO₂ has a mass of 44.0 g.

The key equations are:

$$\begin{array}{rl}n& =\frac{m}{M}\\ m& =nM\end{array}$$

where $m$ is mass in g, $M$ is molar mass in g mol⁻¹, and $n$ is amount in mol.

Concentration in solution

A solution is formed when a solute dissolves in a solvent. For example, in sodium chloride solution, sodium chloride is the solute and water is the solvent.

The key equation is:

$$c=\frac{n}{V}$$

which can be rearranged to:

$$n=cV$$

where:

• $c$ is concentration in mol dm⁻³
• $n$ is amount in mol
• $V$ is volume in dm³

The volume must be in dm³ when using mol dm⁻³.

$$V({dm}^3)=\frac{V({cm}^3)}{1000}$$

The diagram below shows the three main mole calculation routes: particles, mass and solution concentration.

Standard form and significant figures

The Avogadro constant is very large, so particle numbers are usually written in standard form, such as $3.01\times 10^{23}$.

For measured quantities, your final answer should usually be given to an appropriate number of significant figures. A calculated result cannot be more precise than the least precise measurement used to calculate it.