AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Ideal gas equation: pV = nRT for n moles and pV = NkT for N molecules.
Full specification wording
Ideal gases (A-level only): Ideal gas equation: pV = nRT for n moles and pV = NkT for N molecules.
The ideal gas equation relates pressure p, volume V, amount of gas in moles n or number of molecules N, and absolute temperature T. The two forms are pV = nRT and pV = NkT, where R is the molar…
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 3 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The ideal gas equation relates pressure p, volume V, amount of gas in moles n or number of molecules N, and absolute temperature T. The two forms are pV = nRT and pV = NkT, where R is the molar gas constant (8.31 J mol⁻¹ K⁻¹) and k is the Boltzmann constant (1.38 × 10⁻²³ J K⁻¹). The equation combines the gas laws: Boyle's law (p ∝ 1/V at constant T), Charles's law (V ∝ T at constant p), and Avogadro's law (V ∝ n at constant p and T). To use it, convert temperature to kelvin and ensure consistent SI units: p in Pa, V in m³, n in mol, N as a number. For example, a gas at 100 kPa in a 0.020 m³ container at 300 K has n = pV/(RT) = (100000 × 0.020)/(8.31 × 300) ≈ 0.80 mol. The equation is assessed through calculations and explanations of gas behaviour.
What earns the marks
- The ideal gas equation can be written as pV = nRT, where n is the number of moles and R is the molar gas constant.
- The alternative form is pV = NkT, where N is the number of molecules and k is the Boltzmann constant.
- The constants are related by R = N_A k, where N_A is the Avogadro constant.
- In calculations, pressure must be in pascals, volume in cubic metres, and temperature in kelvin.
- The equation assumes an ideal gas: negligible intermolecular forces and negligible molecular volume.
Common mistakes and how to put them right
Using temperature in degrees Celsius instead of kelvin.
Put it right: Convert to kelvin by adding 273.15.
Mixing units, such as using volume in cm³ or pressure in kPa without converting to m³ and Pa.
Put it right: Convert all quantities to SI base units before substitution.
Confusing n (number of moles) with N (number of molecules).
Put it right: Use n with R and N with k; remember N = n N_A.
Exam tips
- Write down the equation, rearrange algebraically before substituting numbers, and include units in your final answer.
- Check that the temperature is in kelvin and that the gas constant used matches the form of the equation (R for moles, k for molecules).
- For questions involving changes in state, use the combined gas law p₁V₁/T₁ = p₂V₂/T₂ when n is constant.
Try the lesson
The start of the Ideal gases (A-level only): Ideal gas equation: pV = nRT for n moles and pV = NkT for N molecules. lesson, made from checked teaching notes for this specification point.
Have a go first
Which equation relates the pressure p, volume V and thermodynamic temperature T of n moles of an ideal gas?
Listen
The ideal gas equation relates pressure p, volume V, amount of gas in moles n or number of molecules N, and absolute temperature T. The two forms are pV = nRT and pV = NkT, where R is the molar gas constant (8.31 J mol⁻¹ K⁻¹) and k is the Boltzmann constant (1.38 × 10⁻²³ J K⁻¹). The equation combines the gas laws: Boyle's law (p ∝ 1/V at constant T), Charles's law (V ∝ T at constant p), and Avogadro's law (V ∝ n at constant p and T). To use it, convert temperature to kelvin and ensure consistent SI units: p in Pa, V in m³, n in mol, N as a number. For example, a gas at 100 kPa in a 0.020 m³ container at 300 K has n = pV/(RT) = (100000 × 0.020)/(8.31 × 300) ≈ 0.80 mol. The equation is assessed through calculations and explanations of gas behaviour. A strong answer earns marks for these points. The ideal gas equation can be written as pV = nRT, where n is the number of moles and R is the molar gas constant. The alternative form is pV = NkT, where N is the number of molecules and k is the Boltzmann constant. The constants are related by R = N_A k, where N_A is the Avogadro constant. In calculations, pressure must be in pascals, volume in cubic metres, and temperature in kelvin. A common slip: Using temperature in degrees Celsius instead of kelvin. Instead, convert to kelvin by adding 273.15. Exam tip: Write down the equation, rearrange algebraically before substituting numbers, and include units in your final answer.
Key words
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Ideal gas equation
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Molar gas constant
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Boltzmann constant
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Avogadro constant
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See every definition
- Ideal gas equation
- Written as pV = nRT for n moles and pV = NkT for N molecules, relating pressure, volume, amount of gas and absolute temperature.
- Molar gas constant
- The constant R in pV = nRT, equal to 8.31 J mol⁻¹ K⁻¹.
- Boltzmann constant
- The constant k in pV = NkT, equal to 1.38 × 10⁻²³ J K⁻¹.
- Avogadro constant
- The constant N_A, which relates the molar gas constant and the Boltzmann constant by R = N_A k.
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