Jupiter2U School
Chapter 11

States of Matter & Gas Laws

High School
At a glance
Core ideaGas pressure is countless particles striking the container walls.
Key termIdeal gas law — PV = nRT.
You can…Solve for P, V, n or T with the combined gas laws.
Watch outTemperature must be in kelvin, never Celsius.
Theory

Kinetic theory and the gas laws

The kinetic-molecular theory models matter as particles in constant motion. In a solid particles vibrate in fixed positions (definite shape and volume); in a liquid they move past one another (fixed volume, no fixed shape); in a gas they move freely and far apart (neither fixed). Temperature is a measure of average kinetic energy.

For an ideal gas (point particles, no intermolecular forces, elastic collisions), pressure, volume, temperature and amount relate through the empirical gas laws, combined into the ideal gas equation:

PV = nRT   R = 8.314 J mol⁻¹ K⁻¹; T in kelvin
  • Boyle's law: at constant T, P ∝ 1/V.
  • Charles's law: at constant P, V ∝ T.
  • Gay-Lussac's law: at constant V, P ∝ T.
  • Avogadro's law: at constant T and P, V ∝ n.

Temperature must be in kelvin: T(K) = T(°C) + 273.15. Absolute zero (0 K) is where particle motion is minimal.

8.314
Gas constant R, J mol⁻¹ K⁻¹
273.15
Add to °C to get kelvin
0 K
Absolute zero (−273.15 °C)
22.4 L
Molar volume of a gas at STP
Explanation

Why gases push back

Gas pressure is nothing but the summed impacts of countless particles striking the container walls. Squeeze a gas into half the volume (Boyle) and each particle hits the walls twice as often — pressure doubles. Heat a gas (Charles) and its particles move faster, striking harder and more often; to keep pressure constant, the gas must expand. These are not arbitrary rules but direct, mechanical consequences of particles in motion.

Real gases deviate from ideality at high pressure (particles are squeezed close, so their own volume matters) and low temperature (they move slowly enough for intermolecular attractions to pull them together, eventually condensing). The ideal gas law is a superb approximation under everyday conditions and the correct starting point for reasoning.

Practical

Worked example — volume of a gas from PV = nRT

What volume does 0.50 mol of an ideal gas occupy at 25 °C and 1.0 × 10⁵ Pa? (R = 8.314 J mol⁻¹ K⁻¹.)

  1. Convert temperature to kelvin: T = 25 + 273 = 298 K.
  2. Rearrange the ideal gas law for volume: V = nRT / P.
  3. Substitute in SI units: V = (0.50 × 8.314 × 298) / (1.0 × 10⁵).
  4. Compute the numerator: 0.50 × 8.314 × 298 = 1238.8 J.
  5. Divide: V = 1238.8 ÷ 100000 = 0.0124 m³ = 12.4 L.
  6. Answer: about 12.4 litres — close to the familiar 24 L mol⁻¹ molar volume scaled by 0.50 mol at near-room conditions.
Q&A
A gas at 2.0 atm and 3.0 L is compressed to 1.0 L at constant temperature. Find the new pressure.

Boyle's law: P₁V₁ = P₂V₂. So P₂ = (2.0 × 3.0) ÷ 1.0 = 6.0 atm. Third the volume, triple the pressure.

Why must temperature be in kelvin for the gas laws?

The laws are proportionalities to absolute temperature. The Celsius scale has an arbitrary zero (the freezing point of water), so ratios like V ∝ T fail — a gas at 0 °C does not have zero volume. Kelvin starts at absolute zero, where extrapolated volume genuinely reaches zero, making the proportion valid.

Under what conditions do real gases deviate most from ideal behaviour?

At high pressure and low temperature. High pressure forces particles close, so their finite volume is no longer negligible; low temperature slows them so intermolecular attractions become significant. Both effects are ignored by the ideal model.

Explain, using kinetic theory, why a sealed can may burst when heated.

Heating raises the average kinetic energy of the gas particles inside. They strike the walls faster and more frequently, so (at fixed volume) pressure rises with temperature (Gay-Lussac). If the internal pressure exceeds the can's strength, it ruptures.

Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Kinetic theoryBoyle law P-VCharles law V-TIdeal gas PV=nRTAbsolutetemperatureMolar volumeGas Laws
Infographic

The key facts, visualised

PV = nRT
the ideal gas equation, R = 0.0821 L atm/mol K
Boyle
at fixed T, P and V are inversely related
Charles
at fixed P, V is proportional to absolute T
22.4 L
molar volume of an ideal gas at STP
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1Find the volume of 2.00 mol of gas at 273 K and 1.00 atm.

  1. Use PV = nRT, so V = nRT / P.
  2. V = (2.00 x 0.0821 x 273) / 1.00.
  3. Compute: 2.00 x 0.0821 x 273 = 44.8, divided by 1.00.

Example 2A gas at 2.0 atm and 3.0 L is compressed to 1.0 L at constant T. Find the new pressure.

  1. Boyle law: P1V1 = P2V2.
  2. Rearrange: P2 = P1V1 / V2 = (2.0 x 3.0) / 1.0.
  3. Compute: 6.0 / 1.0 = 6.0.
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1What happens to gas volume if you double the pressure at constant temperature?
The volume halves, because P and V are inversely related (Boyle law).
2Why must temperature be in kelvin for gas laws?
Because gas volume and pressure are proportional to absolute temperature, and kelvin starts at absolute zero.
3Convert 25 degrees C to kelvin.
298 K, because K = C + 273.
4What volume does 1 mol of ideal gas occupy at STP?
22.4 L, the standard molar volume.
5According to kinetic theory, what causes gas pressure?
Gas particles colliding with the container walls.
6In PV = nRT, what does n represent?
The number of moles of gas.