Kinetic Theory of Gases and the Gas Laws
The kinetic theory of matter models gas particles as small, moving in constant random motion at different speeds, and undergoing frequent collisions with each other and the walls of their container; gas pressure is caused by the total force from these collisions acting over the area of the container walls. Absolute temperature is measured in kelvin (K), related to Celsius by kelvin = Celsius + 273, and absolute zero (0 K, -273 degrees C) is the temperature at which particles have the minimum possible internal energy. The gas laws linking pressure, volume and temperature for a fixed mass of gas, including Boyle's law (pressure x volume = constant, at constant temperature) and the pressure law (pressure / temperature = constant, at constant volume), extend well beyond the core GCSE course, which typically only covers a qualitative explanation of gas pressure.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Convert any temperature given in degrees Celsius into kelvin using kelvin = Celsius + 273, since the gas laws only work with absolute temperature.
- Identify which quantity is held constant in the question: if temperature is constant, use Boyle's law; if volume is constant, use the pressure law.
- For Boyle's law, use pressure 1 x volume 1 = pressure 2 x volume 2 (P1V1 = P2V2), substituting the known values and rearranging to find the unknown pressure or volume.
- For the pressure law, use pressure 1 / temperature 1 = pressure 2 / temperature 2 (P1/T1 = P2/T2), making sure both temperatures are in kelvin before substituting.
- Use the kinetic theory to explain gas pressure and its changes: increasing temperature increases the average speed of the particles, so they collide with the walls more frequently and with greater force, increasing the pressure (at constant volume) or pushing the walls outward to increase the volume (at constant pressure).
- To explain a change in pressure at constant temperature (Boyle's law), use the kinetic theory idea that reducing the volume means the particles have less distance to travel between collisions with the walls, so they hit the walls more often per second, increasing the pressure, even though their average speed has not changed.
Worked example
A fixed mass of gas has a volume of 0.40 m^3 at a pressure of 150 kPa. The gas is compressed at constant temperature until its pressure is 200 kPa. Calculate the new volume of the gas.
- Write down Boyle's law: pressure 1 x volume 1 = pressure 2 x volume 2.
- Substitute the known values: 150 x 0.40 = 200 x volume 2.
- Calculate the left-hand side: 150 x 0.40 = 60.
- Rearrange to find volume 2: volume 2 = 60 / 200.
- Calculate: 60 / 200 = 0.30.
- State the final answer with its unit: the new volume is 0.30 m^3.
Practice questions
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Q1Convert 27 degrees C to kelvin.Show answer
Answer: 300 K (27 + 273).
Q2State what is meant by absolute zero.Show answer
Answer: The lowest possible temperature (0 K, -273 degrees C), at which particles have the minimum possible internal energy.
Q3Explain, using kinetic theory, why increasing the temperature of a gas at constant volume increases its pressure.Show answer
Answer: The particles move faster on average, so they collide with the container walls more frequently and with greater force, increasing the pressure.
Q4A gas has a volume of 2.0 m^3 at a pressure of 100 kPa. Use Boyle's law to calculate its pressure when compressed to 0.50 m^3 at constant temperature.Show answer
Answer: 400 kPa (100 x 2.0 = 200; 200/0.50 = 400).
Q5State the equation for the pressure law.Show answer
Answer: Pressure 1 / temperature 1 = pressure 2 / temperature 2 (with temperature in kelvin).
Q6A gas at 300 K has a pressure of 100 kPa in a sealed, rigid container. Calculate its pressure at 450 K.Show answer
Answer: 150 kPa (100/300 x 450 = 150).
Q7Explain, using kinetic theory, why reducing the volume of a gas at constant temperature increases its pressure.Show answer
Answer: The particles have less distance to travel between collisions with the walls, so they collide with the walls more frequently, increasing the pressure, even though their average speed is unchanged.
Exam-style questions
Written in the style of a IGCSE Science exam paper, with a full mark scheme.
A sealed, rigid gas cylinder contains gas at a pressure of 90 kPa and a temperature of 27 degrees C. The cylinder is heated until the temperature reaches 127 degrees C. Calculate the new pressure of the gas.
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A student uses a sealed syringe containing a fixed mass of air, connected to a pressure sensor, to investigate how the pressure of a gas depends on its volume at constant temperature. (a) Describe how the student should carry out the investigation to obtain a set of pressure and volume readings, and how the results should be processed to test whether the gas obeys Boyle's law. (4 marks) (b) Using kinetic theory, explain why decreasing the volume of the gas increases its pressure. (2 marks)
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Free printable worksheet
Want more practice on paper? Download the kinetic theory of gases and the gas laws worksheet pack - 5 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 29 of IGCSE Science Workbook, the whole course as one free printable PDF.
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