A LevelPhysicsAQARevision NotesFurther Mechanics & Thermal PhysicsIdeal GasesIdeal Gas Equation

Ideal Gas Equation (AQA A Level Physics): Revision Note

Exam code: 7408

Written by: Katie M

Reviewed by: Tim

Updated on 30 September 2026

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Understand this topic with deeper explanations and understanding checks.

Ideal gas equation

An ideal gas is a specific type of gas which:
- has molecules with negligible volume
- collisions which are elastic
- cannot be liquefied
- has no interactions between the molecules (except during collisions)
- obeys the (ideal) gas laws (Boyle's law, Charles’s law and pressure law)
All of these can occur at any temperature or pressure

The equation of state for an ideal gas (or the ideal gas equation) can be expressed as:

$p V = n R T$

Where:
- $p$ = pressure (Pa)
- $V$ = volume (m³)
- $n$ = number of moles (mol)
- $R$ = molar gas constant (= 8.31 J K^-1 mol^-1)
- $T$ = temperature (K)

The ideal gas equation can also be written in the form:

$p V = N k T$

Where:
- $p$ = pressure (Pa)
- $V$ = volume (m³)
- $N$ = number of molecules
- $k$ = Boltzmann constant (= 1.38 × 10^-23 J K^-1)
- $T$ = temperature (K)

An ideal gas is therefore defined as:
A gas which obeys the equation of state $p V = n R T$ at all pressures, volumes and temperatures

Worked Example

A storage cylinder of an ideal gas has a volume of 8.3 × 10³ cm³. The gas is at a temperature of 15 °C and a pressure of 4.5 × 10⁷ Pa. Calculate the amount of gas in the cylinder, in moles.

[2]

Answer:

Step 1: Write down the ideal gas equation

Since the number of moles ( $n$ ) is required, use the equation:

$p V = n R T$

Step 2: Rearrange for the number of moles n

$n = \frac{p V}{R T}$

Step 3: Substitute in values

$V = 8.3 \times 10^{3} {cm}^{3} = 8.3 \times 10^{3} \times 10^{- 6} = 8.3 \times 10^{- 3} m^{3}$ [1 mark]

$T = 15 ° C + 273.15 = 288.15 K$

$n = \frac{(4.5 \times 10^{7}) \times (8.3 \times 10^{- 3})}{8.31 \times 288.15}$

$n = 155.98 mol = 160 mol (2 s . f .)$ [1 mark]

Examiner Tips and Tricks

Don’t worry about remembering the values of $R$ and $k$ , they will both be given in the equation sheet in your exam.

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