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The mole and molar quantities is taught in the note for The Mole Concept. Read it below and look for the section on this topic.

The Mole Concept

12 min read

The mole and molar quantities

Atoms are far too small to count one by one, so chemists count them in large groups called moles. One mole of any substance contains 6.02 × 10²³ particles. This number is the Avogadro constant, written L. The molar mass M of a substance is the mass of one mole, in grams per mole. It is numerically equal to the relative atomic mass (Ar) or relative molecular mass (Mr).

The mole at the centreA diagram with the amount in moles in the centre. Mass in grams is moles times molar mass. Number of particles is moles times 6.02 times 10 to the 23. For a gas at room temperature, volume is moles times 24 litres.amount n (mol)mass m (g)particles Ngas volume V (dm³)n = m ÷ MN = n × 6.02×10²³V = n × 24 dm³
n = amount in moles, m = mass in grams, M = molar mass, N = number of particles, V = volume of a gas at room temperature and pressure (24 dm³ per mole; 22.4 dm³ at standard temperature and pressure).
  • amount of substance (mol)
  • molar mass (g/mol)
SubstanceFormulaMolar mass (g/mol)Working
WaterH₂O182(1) + 16
Carbon dioxideCO₂4412 + 2(16)
Sodium chlorideNaCl58.523 + 35.5
Calcium carbonateCaCO₃10040 + 12 + 3(16)
Sulphuric acidH₂SO₄982(1) + 32 + 4(16)
Worked exampleMoles and particles

How many moles are in 9 g of water, and how many molecules? (H = 1, O = 16)

  1. Molar mass of water: 18 g/mol.
  2. Number of molecules.

Answer: 0.5 mol, which is 3.01 × 10²³ molecules.

Avogadro's law

Avogadro's law
Equal volumes of all gases, at the same temperature and pressure, contain equal numbers of molecules.

So one mole of any gas takes up the same volume: 24 dm³ at room temperature and pressure (about 20 °C and 1 atmosphere). In a reaction between gases, the volumes combine in the same ratio as the moles in the equation. For example 2H₂ + O₂ → 2H₂O means 2 volumes of hydrogen react with 1 volume of oxygen.

Percentage composition

This tells how much of a compound is a given element, for example the nitrogen in a fertiliser.
Worked exampleNitrogen in a fertiliser

Find the percentage of nitrogen in ammonium nitrate, NH₄NO₃. (N = 14, H = 1, O = 16)

  1. Molar mass: 2(14) + 4(1) + 3(16) = 80 g/mol.
  2. Mass of nitrogen in one mole = 28 g.

Answer: Ammonium nitrate is 35% nitrogen.

Try itMoles, particles and gas volume

Choose a mass and a molar mass. See how many moles, molecules and cubic decimetres of gas it makes.

Check yourself How many moles are in 36 g of water? (H = 1, O = 16)
Check yourself What is the volume of 0.25 mol of any gas at room temperature and pressure?
Check yourself Which has the most molecules?

Key terms

Mole
The amount of substance that contains 6.02 × 10²³ particles.
Avogadro constant
6.02 × 10²³ per mole.
Molar mass
The mass of one mole of a substance, in g/mol.
Molar volume
The volume of one mole of gas: 24 dm³ at room temperature and pressure.

Summary

  • 1 mole contains 6.02 × 10²³ particles; molar mass is in g/mol.
  • n = m ÷ M; N = n × 6.02 × 10²³; V = n × 24 dm³ for gases at r.t.p.
  • Avogadro's law: equal volumes of gases contain equal numbers of molecules.
  • Percentage composition = mass of element ÷ molar mass × 100.
Avogadro's law