In simple terms
A friendly intro before the formal notes — no formulas yet.
The Rules of Gas Behaviour
Gases are mostly empty space with particles in constant, random motion. The ideal gas law is a simple but powerful equation that describes how a gas's pressure, volume, and temperature are all interconnected.
Imagine a large, empty hall with a few hyperactive dancers. The dancers are the gas particles. They move in straight lines until they bounce off a wall (creating pressure) or each other. The speed of their dancing is their temperature. The ideal gas law is like the rulebook that connects the size of the hall, the number of dancers, the force of their wall collisions, and the tempo of the music.
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Ideal gas: particles far apart, random motion, elastic collisions.
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Boyle’s law: p ∝ 1/V at constant T (n fixed).
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Charles’s law: V ∝ T at constant p; Gay-Lussac: p ∝ T at constant V.
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Ideal gas equation: pV = nRT (R = 8.31 J mol⁻¹ K⁻¹).
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Key formulas
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Full topic notes
Formal explanation with the rigour you need for the exam.
The Kinetic-Molecular Theory and Ideal Gases
The kinetic-molecular theory provides a model to explain the properties of gases. An 'ideal gas' is a hypothetical gas that perfectly follows all the assumptions of this theory. While no gas is truly ideal, this model is extremely useful for predicting gas behaviour under many conditions.
Gas particles are in continuous, random, straight-line motion.
The volume of the gas particles is negligible compared to the volume of the container.
There are no attractive or repulsive forces between gas particles.
Collisions between particles and with the container walls are perfectly elastic (no kinetic energy is lost).
The average kinetic energy of the gas particles is directly proportional to the absolute temperature (in Kelvin).
The Ideal Gas Equation
The relationships between pressure (p), volume (V), number of moles (n), and temperature (T) for an ideal gas are combined into a single, powerful equation. This is known as the ideal gas equation. It builds upon the work of scientists like Boyle, Charles, and Gay-Lussac.
pV = nRT
In this equation, 'R' is a constant of proportionality called the molar gas constant. Its value is 8.31 J mol⁻¹ K⁻¹. It is crucial to use the correct SI units for all variables to ensure your calculation is valid. Pressure must be in Pascals (Pa), volume in cubic metres (m³), and temperature in Kelvin (K).
Memorise the key unit conversions: 1 kPa = 1000 Pa, 1 m³ = 1000 dm³, and 1 dm³ = 1000 cm³. The most common mistake is forgetting to convert volume from cm³ or dm³ into m³, or pressure from kPa into Pa. Always convert temperature to Kelvin by adding 273 to the Celsius value.
Real Gases vs. Ideal Gases
The ideal gas model is a simplification. Real gases, like oxygen or carbon dioxide, have particles that do occupy a small but finite volume, and they do experience weak intermolecular forces (van der Waals forces). These factors cause real gases to deviate from ideal behaviour, particularly under specific conditions.
Deviation is greatest at high pressure: The volume of particles is no longer negligible as they are forced closer together. The measured volume is larger than an ideal gas would predict.
Deviation is greatest at low temperature: Particles have low kinetic energy, so intermolecular forces become significant. Particles are pulled together, reducing the frequency and force of collisions with the container walls. This results in a lower pressure than an ideal gas would exert.
Worked examples
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Calculate the volume occupied by 0.500 mol of nitrogen gas at a pressure of 150 kPa and a temperature of 25 °C. (R = 8.31 J mol⁻¹ K⁻¹)
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Step 1: List the variables and convert units. p = 150 kPa = 150 × 10³ Pa = 150,000 Pa V = ? n = 0.500 mol T = 25 °C = 25 + 273 = 298 K R = 8.31 J mol⁻¹ K⁻¹
A cylinder contains 250 cm³ of a gas at 1.00 × 10⁵ Pa and 300 K. The gas is compressed to a volume of 100 cm³ and heated to 350 K. What is the new pressure inside the cylinder?
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Step 1: Since the amount of gas (n) is constant, we can use the combined gas law, which is a rearrangement of the ideal gas equation: p₁V₁/T₁ = p₂V₂/T₂.
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What are the two main assumptions made for an ideal gas?
- The gas particles themselves have negligible volume (they are point masses). 2. There are no intermolecular forces of attraction or repulsion between the particles.
Key takeaways
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Gas particles are in continuous, random, straight-line motion.
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The volume of the gas particles is negligible compared to the volume of the container.
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There are no attractive or repulsive forces between gas particles.
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Collisions between particles and with the container walls are perfectly elastic (no kinetic energy is lost).
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The average kinetic energy of the gas particles is directly proportional to the absolute temperature (in Kelvin).
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