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14.2.4Particle Model

Boyle’s Law

5 min read 6 parts Lesson 15 of 15 Unit quiz

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Section 1 of 6The Law

14.2.4 Boyle's Law

Boyle’s law gives a numerical form of the relationship between the pressure and volume of a gas.

Statement
  • For a fixed mass of gas at constant temperature, pressure multiplied by volume is a constant.
Equation
  • p₁V₁ = p₂V₂, where the subscripts show the initial and final conditions of the gas.
Unit freedom
  • Both volumes use the same unit and both pressures use the same unit, so conversion to SI units is optional.
Conditions
  • The law only applies when the mass and the temperature of the gas are constant.
Inverse relation
  • Pressure is inversely proportional to volume, so a graph of p against 1/V is a straight line through the origin.

Section 2 of 6Using the Equation

Follow the same short routine for every Boyle’s law question.

1
Write down the initial pressure and volume and the final value of whichever quantity is given.
2
Check that the temperature and mass of gas are stated to be constant.
3
Substitute the values into p₁V₁ = p₂V₂, keeping the units consistent on both sides.
4
Rearrange to find the unknown, for example p₂ = p₁V₁ ÷ V₂.
5
Check that the answer makes sense: a smaller volume should give a larger pressure.

Section 3 of 6Graphs

Graphs
p against V
  • The graph is a curve that falls steeply at small volumes and flattens at large volumes.
p against 1/V
  • Plotting pressure against the reciprocal of volume gives a straight line through the origin, showing inverse proportion.
pV against p
  • A graph of pV against p is a horizontal line, because the product stays constant.
Deviations
  • At very high pressure or low temperature a real gas departs from the law, but not within GCSE conditions.

Section 4 of 6Investigating the Law

Apparatus
  • A sealed tube of trapped air is connected to a pressure gauge and a foot pump or a hand-operated plunger.
Method
  • Change the pressure in steps, wait for the temperature to settle, and record the length of the air column each time.
Variables
  • The length of the column is proportional to the volume because the tube has a uniform cross-section.

Section 5 of 6Worked Example

Question

  • A syringe holds 600 cm³ of air at a pressure of 100 kPa.
  • The nozzle is sealed and the plunger is pushed in until the volume is 150 cm³, with no change in temperature.
  • Find the new pressure.

  1. p₁V₁ = p₂V₂, so p₂ = p₁V₁ / V₂.
  2. p₂ = (100 × 600) / 150.
  3. p₂ = 400 kPa.

Answer The pressure rises to 400 kPa, four times the original because the volume fell to one quarter.

Section 6 of 6Exam Checklist & Tips

14.2.4 – Key Points for the Exam

  • Boyle’s law At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume.
  • Inversely proportional A relationship in which the product of two quantities is constant.
  • Constant temperature A condition in which the average kinetic energy of the particles does not change.
  • Fixed mass A condition in which the gas amount does not change because the container is sealed.

Common Mistakes

  • Using the law when the temperature changes during the compression.
  • Mixing units, such as kPa for one pressure and Pa for the other.
  • Dividing instead of multiplyingpressure and volume have a constant product, not a constant ratio.
  • Forgetting that the gas must be sealed so that no particles escape.
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