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The mole and pV = nRT Cambridge International AS & A Level Physics revision

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In plain words

Atoms are far too small to count one at a time, so scientists count them in giant batches, the way eggs come in dozens. One batch is a mole: about 6 × 10²³ particles. Count a gas in moles and one tidy equation links its pressure, its volume and its temperature.

4 things to know

  1. Amount of substance is an SI base quantity, and its unit is the mole (mol). One mole contains 6.02 × 10²³ particles: this number is the Avogadro constant, N_A.
  2. Number of particles N = nN_A, where n is the number of moles. Mass = n × molar mass.
  3. The equation of state for an ideal gas: pV = nRT, where R = 8.31 J mol⁻¹ K⁻¹ is the molar gas constant and T is in kelvin.
  4. The Boltzmann constant k = R ÷ N_A = 1.38 × 10⁻²³ J/K. Since nR = Nk, pV = nRT is the same equation as pV = NkT.

Worked example

Find the volume of 1.0 mol of an ideal gas at a pressure of 1.01 × 10⁵ Pa and a temperature of 273 K.

  1. V = nRT ÷ p.
  2. = 1.0 × 8.31 × 273 ÷ 1.01 × 10⁵.
  3. = 0.022 m³, which is about 22 litres.

Tips and tricks

  • T must be in kelvin and V in m³. 1 litre is 10⁻³ m³, and 1 cm³ is 10⁻⁶ m³.
  • Molar masses are usually given in grams per mole. Change them to kilograms before finding the mass of a molecule in kg.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

The mole and pV = nRT: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. How many particles are there in one mole?
    • 6.02 × 10⁻²³
    • 1.38 × 10²³
    • 6.02 × 10²³ (the answer)
    • 8.31 × 10²³

    This is the Avogadro constant.

  2. In pV = nRT, what is n?
    • the number of moles (the answer)
    • the number of molecules
    • the number density
    • the Avogadro constant

    For the number of molecules, use pV = NkT.

  3. How is the Boltzmann constant k related to R?
    • k = R ÷ N_A (the answer)
    • k = RN_A
    • k = N_A ÷ R
    • k = R

    k is the gas constant for one molecule, R for one mole.

  4. A container holds 1.0 mol of gas. Another 1.0 mol is added at the same temperature and volume. What happens to the pressure?
    • It doubles. (the answer)
    • It halves.
    • It stays the same.
    • It becomes four times bigger.

    Pressure is proportional to n.

  5. Oxygen gas has a molar mass of 32 g/mol. What is the mass of 0.50 mol?
    • 8 g
    • 16 g (the answer)
    • 32 g
    • 64 g

    0.50 × 32.

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