The mole and the Avogadro constant

This page covers a single Form 4 content standard: the mole and the Avogadro constant. The mole is the chemist’s counting unit, and it is the idea that connects the invisible world of atoms to quantities you can actually weigh and measure. Once you are comfortable converting between moles and number of particles, the rest of the mole concept, mass, gas volume, formulae and equations, is just adding one more step to the same skill, so it is worth building this foundation carefully as you work through SPM Chemistry.

What a mole is

Atoms, molecules and ions are far too small and far too numerous to count one by one, so chemists group them into a standard-sized package called the mole. The mole is the SI unit for the amount of substance, in the same way that a dozen is a unit for counting eggs, except that a mole is a very large number chosen to suit the size of atoms. Whenever you have “one mole” of something, you have a fixed, known number of its particles.

The Avogadro constant

The number of particles in one mole is called the Avogadro constant (symbol NA). Its value is The Avogadro constant is 6.02 x 10²³ mol⁻¹. In other words, one mole of any substance contains 6.02 x 10²³ mol⁻¹ particles, the same count whether the particles are atoms of iron, molecules of water, or sodium ions. The unit of the Avogadro constant is mol⁻¹ (“per mole”), because it tells you how many particles there are per mole.

The word particle is deliberately general. One mole of a substance could mean:

• atoms, one mole of helium contains 6.02 x 10²³ mol⁻¹ helium atoms;
• molecules, one mole of water contains 6.02 x 10²³ mol⁻¹ water molecules;
• ions, one mole of sodium chloride contains 6.02 x 10²³ mol⁻¹ sodium ions and 6.02 x 10²³ mol⁻¹ chloride ions;
• electrons, one mole of electrons is 6.02 x 10²³ mol⁻¹ electrons.

Because “one mole” can refer to different particles, you must always say which particle you mean. This is one of the most heavily marked points in the whole chapter.

The key relationship

To convert between an amount in moles and an actual count of particles, use:

Number of particles = number of moles (n) × Avogadro constant (NA)

and, rearranged,

Number of moles (n) = number of particles ÷ Avogadro constant (NA)

Everything on this standard comes back to these two forms of the same equation.

Worked example

Question. Calculate the number of molecules in 2.5 mol of carbon dioxide, CO₂. Then state the number of oxygen atoms present. [NA = 6.02 x 10²³ mol⁻¹ mol⁻¹]

Step 1, Identify the particle and the amount. The particle is the CO₂ molecule, and the amount is 2.5 mol.

Step 2, Apply number of particles = n × NA. Number of CO₂ molecules = 2.5 × 6.02 x 10²³ mol⁻¹ = 1.505 × 10²⁴ molecules.

Step 3, Scale up to atoms if asked. Each CO₂ molecule contains 2 oxygen atoms, so the number of oxygen atoms = 2 × 1.505 × 10²⁴ = 3.01 × 10²⁴ oxygen atoms.

Answer. 2.5 mol of CO₂ contains 1.505 × 10²⁴ molecules and 3.01 × 10²⁴ oxygen atoms.

Practice question

Question. A sample contains 3.01 × 10²³ atoms of sodium. How many moles of sodium atoms is this? [NA = 6.02 x 10²³ mol⁻¹ mol⁻¹]

Answer. n = number of particles ÷ NA = (3.01 × 10²³) ÷ (6.02 x 10²³ mol⁻¹) = 0.5 mol of sodium atoms. (The sample is exactly half of the Avogadro constant, so it is half a mole.)

Exam tip

Two habits protect the marks here. First, write down which equation you are using and substitute clearly, examiners award method marks even if the final arithmetic slips. Second, read the particle in the question exactly: if it asks for atoms but gives you molecules, you must multiply by the number of atoms per molecule (as with the two oxygen atoms in CO₂). A frequent trap is a diatomic gas such as O₂ or Cl₂, one mole of O₂ molecules contains two moles of oxygen atoms. Keeping “molecules” and “atoms” separate in your working is what turns a half-right answer into a full-mark one.

Why the mole matters

The whole point of the mole is that it links the countable (a number of particles) with the weighable (a mass you can put on a balance) and, for gases, with a measurable volume. On its own, this standard only takes you between moles and particle counts, but it is the hinge for everything that follows: in the next standard you will attach a mass to a mole through molar mass, and after that a gas volume through molar volume. Because the same relationship, multiply by NA one way, divide by NA the other, reappears in every one of those calculations, practising it until it is automatic pays back across the whole chapter and into stoichiometry in later chapters.

A sense of scale

It helps to appreciate just how large the Avogadro constant is. If you could count particles at one per second without stopping, counting a single mole would take far longer than the age of the universe. That is exactly why chemists never count particles directly and instead work in moles: the mole packages an unimaginably large number into a quantity small enough to weigh out in the laboratory. This is also why one mole of a light substance and one mole of a heavy substance contain the same number of particles but have very different masses, a point that leads naturally into the idea of molar mass in the next standard.

Where this fits

This is content standard 3.2 of the The Mole Concept, Chemical Formula and Equation chapter, sitting between relative mass and molar mass. Consolidate the definition and the NA conversions with the revision notes, and test yourself with the practice questions. In our online 1-to-1 SPM Chemistry lessons, taught in English, from RM50/hr, our teachers make sure you never lose marks by confusing atoms with molecules and can move confidently in both directions between moles and particle counts.

Quick recap

• The mole is the SI unit for amount of substance; a fixed, known number of particles.
• The Avogadro constant is The Avogadro constant is 6.02 x 10²³ mol⁻¹: the number of particles in one mole.
• Number of particles = n × NA; number of moles = number of particles ÷ NA.
• Always state the particle (atom, molecule, ion or electron); watch diatomic gases.