The ideal gas equation Edexcel International A Level Physics revision
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In plain words
Squeeze a gas and its pressure rises. Heat it and it pushes harder, or swells. For a gas that isn't too cold or too squashed, a single equation ties its pressure, its volume, its temperature and the number of molecules together.
4 things to know
- For a fixed amount of an ideal gas, pV is proportional to T, with T in kelvin: pV ÷ T is constant.
- pV = NkT, where N is the number of molecules and k = 1.38 × 10⁻²³ J/K is the Boltzmann constant.
- At constant temperature, pV is constant: halve the volume and the pressure doubles. At constant volume, p is proportional to T. At constant pressure, V is proportional to T.
- Follow the pressure of a gas downwards as it cools and it would reach zero at absolute zero, 0 K, which is −273 °C. T in kelvin = θ in °C + 273.
Worked example
A gas at a pressure of 1.0 × 10⁵ Pa and a temperature of 300 K has a volume of 2.0 × 10⁻³ m³. Find the number of molecules in it.
- N = pV ÷ kT.
- = 1.0 × 10⁵ × 2.0 × 10⁻³ ÷ (1.38 × 10⁻²³ × 300).
- = 4.8 × 10²².
Tips and tricks
- Always change temperatures to kelvin before using a gas equation.
- For a fixed amount of gas before and after a change: p₁V₁ ÷ T₁ = p₂V₂ ÷ T₂.
It lands in your notebook with its questions as flashcards.
The ideal gas equation: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
In pV = NkT, what is N?
k is the constant for a single molecule.
The volume of a fixed amount of gas is halved at constant temperature. What happens to its pressure?
pV is constant.
What is 27 °C in kelvin?
Add 273.
A fixed amount of gas is heated at constant volume from 300 K to 600 K. What happens to its pressure?
At constant volume, p is proportional to T in kelvin.
What is k in pV = NkT?
1.38 × 10⁻²³ J/K.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 8 marks. Write your answers on paper, then check them.
The ideal gas equation
Edexcel International A Level Physics WPH · 8 marks · papermunch.org
Name ______________________________ Date ______________
A gas at 100 kPa has a volume of 6.0 litres. It is squeezed into 2.0 litres at the same temperature. Find the new pressure.[2]
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300 kPa.
A sealed container of gas at 27 °C and 1.0 × 10⁵ Pa is heated to 127 °C. Find the new pressure.[3]
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1.3 × 10⁵ Pa. 1.0 × 10⁵ × 400 ÷ 300. The temperatures must be in kelvin.
Describe how to investigate how the pressure of a gas depends on its volume at constant temperature.[3]
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Trap a fixed mass of air in a sealed syringe or tube joined to a pressure gauge. Change the volume in steps, slowly, so the temperature stays the same, and record the pressure and volume each time. A graph of p against 1 ÷ V should be a straight line through the origin.
Answers: The ideal gas equation
- 1. 300 kPa.
- 2. 1.3 × 10⁵ Pa. 1.0 × 10⁵ × 400 ÷ 300. The temperatures must be in kelvin.
- 3. Trap a fixed mass of air in a sealed syringe or tube joined to a pressure gauge. Change the volume in steps, slowly, so the temperature stays the same, and record the pressure and volume each time. A graph of p against 1 ÷ V should be a straight line through the origin.