4.1 Gaseous State of Matter
🎯 Learning outcomes
After completing this lesson, you should be able to:
- explain the origin of pressure in a gas in terms of collisions between gas molecules and the walls of the container
- understand that ideal gases have zero particle volume and no intermolecular forces of attraction
- state and use the ideal gas equation, pV = nRT, in calculations, including in the determination of Mr
1🧊The three states of matter
Solids, liquids and gases differ in how close their particles are, how they’re arranged, and how freely they can move.
🧊 Solids
- fixed shape and volume
- particles touching — cannot be compressed
- usually a regular arrangement
- particles can only vibrate in place
💧 Liquids
- takes the shape of its container
- particles close together — fixed volume, only slightly compressible
- mostly randomly arranged
- limited movement from place to place
☁️ Gases
- no fixed shape or volume
- particles far apart — can be compressed
- randomly arranged
- move freely in all directions
2💨The kinetic theory of gases
The kinetic theory of gases is the idea that gas molecules are in constant, rapid, random motion.
The kinetic theory makes several simplifying assumptions about gas particles:
- gas molecules move rapidly and randomly
- the distance between molecules is much greater than the diameter of the molecules themselves, so the volume of the molecules is negligible
- there are no intermolecular forces of attraction or repulsion between the molecules
- all collisions between particles are elastic — no kinetic energy is lost in a collision
- the temperature of the gas is related to the average kinetic energy of its molecules
A theoretical gas that fits this description exactly is called an ideal gas. Real gases don’t fit the description perfectly, although some come very close — these are called real gases.
Noble gases with small atoms, such as helium and neon, come closest to ideal gas behaviour. Their atoms have very few electrons, so any instantaneous dipole–induced dipole forces between them are extremely weak — meaning intermolecular attraction is almost negligible, just as the ideal gas model assumes.
3⚖️Limitations of the ideal gas model
Accurate measurements show that real gases don’t always behave exactly as the ideal gas model predicts. This is because real gases break the kinetic theory’s assumptions in two ways:
- there is not zero attraction between the molecules
- the volume of the molecules themselves cannot always be ignored
Deviation from ideal behaviour is most noticeable at very high pressures and very low temperatures — this exact phrase is worth memorising, as it comes up repeatedly in exam mark schemes.
Under these conditions:
- the molecules are forced close to each other
- the volume of the molecules is no longer negligible compared with the volume of the container
- instantaneous dipole–induced dipole forces, or permanent dipole–permanent dipole forces, of attraction act between the molecules
- these attractive forces pull molecules towards each other and away from the container walls
- as a result, the pressure is lower than expected for an ideal gas
- and the effective volume of the gas is smaller than expected for an ideal gas
4🔵Gas pressure and Boyle’s Law
The pressure of a gas is caused by collisions between the gas molecules and the walls of the container.
If the volume of a gas is decreased at constant temperature, the same number of molecules are squashed into a smaller space. They hit the walls of the container more often, so the pressure of the gas increases.
Plotting the volume of a gas against the inverse of its pressure (1/p) gives a straight line through the origin — showing that volume is inversely proportional to pressure at constant temperature.
5🧮The ideal gas equation
The ideal gas equation links pressure, volume, temperature and the number of moles of a gas:
| Symbol | Quantity | Unit |
|---|---|---|
| p | pressure | pascals, Pa |
| V | volume | cubic metres, m³ (1 m³ = 1000 dm³) |
| n | number of moles | mol (n = m / Mr) |
| R | gas constant | 8.31 J K⁻¹ mol⁻¹ |
| T | temperature | kelvin, K (K = °C + 273) |
101 325 Pa = 1.0 atmosphere. If you substitute pressure in kPa, the volume calculated will come out in dm³. If you substitute pressure in Pa, the volume calculated will come out in m³ — the two must always be paired consistently.
Always convert temperature to kelvin before substituting into pV = nRT — forgetting to add 273 to a Celsius temperature is one of the most common errors in gas calculations. Since n = m/Mr, the same equation can be rearranged to find the relative molecular mass of an unknown gas from experimental p, V, T and mass data.
📌 Exam tips & quick summary
✅ Do remember
- gas pressure comes from collisions between molecules and the container walls
- ideal gas = zero particle volume + no intermolecular forces (learn this phrase exactly)
- real gases deviate most at high pressure and low temperature
- pV = nRT; R = 8.31 J K⁻¹ mol⁻¹; always use kelvin for T
- kPa pairs with dm³; Pa pairs with m³ — keep units matched
🚫 Do not confuse
- “ideal gas” is a theoretical model — no real gas is perfectly ideal, though small noble gases like He and Ne come close
- solids and liquids resist compression (particles already close/touching); gases compress easily (particles far apart)
- don’t forget to convert °C to K, or mix up kPa/dm³ with Pa/m³, when using pV = nRT
🔁 Quick recap
- Solid → Liquid → Gas: particles get further apart and more free to move
- Kinetic theory: rapid random motion, negligible volume, no IMFs, elastic collisions, T ∝ average KE
- Pressure: caused by molecule–wall collisions; ↓V → ↑collision frequency → ↑p
- pV = nRT: n = m/Mr, R = 8.31 J K⁻¹ mol⁻¹, T in kelvin