The origin of gas pressure, and the ideal gas model
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explain the origin of pressure in a gas in terms of collisions between gas molecules and the wall of the container … understand that ideal gases have zero particle volume and no intermolecular forces of attraction.
Pressure as the result of countless tiny impacts
Gas particles move constantly and randomly, in straight lines, until they hit each other or the walls of their container. When a particle hits a wall it bounces back. The wall has to push the particle to turn it round, so the particle pushes on the wall with an equal force.
Each collision gives only a tiny force, but billions of particles hit every square centimetre of wall every second. Pressure is the total force of these collisions between gas molecules and the wall, per unit area of wall:
When you explain gas pressure in an exam, use this wording: gas molecules collide with the walls of the container, and the force of these collisions per unit area is the pressure.
Each particle-wall collision delivers a tiny, momentary force. Summed over the huge number of collisions happening every second across the whole wall, the result is a steady, measurable pressure.
- More particles in the same container: more collisions with the wall per second → higher pressure.
- The same particles in a smaller container: each particle reaches a wall more often, so there are more collisions per second → higher pressure.
- Higher temperature: particles move faster, so each collision pushes harder and collisions happen more often → higher pressure.
The ideal gas equation, later in this note, puts all three statements into one line.
The ideal gas model: two deliberate simplifications
Real gas particles take up some space, and they attract each other weakly. The ideal gas model ignores both. This makes the maths simple, and for most gases at everyday conditions the answers are very close to the real values. An ideal gas has:
- zero particle volume — each particle is treated as a point;
- no intermolecular forces of attraction between the particles.
These are the only two assumptions the syllabus asks for. The particles still have mass — without it they could not push on the wall when they hit it.
An ideal gas particle is a dimensionless point with no pull toward its neighbours; a real gas particle actually takes up space and is weakly attracted to nearby particles by van der Waals' forces — the two simplifications the ideal model makes.
When a real gas stops behaving like an ideal one
The two assumptions stop being true under two conditions:
- High pressure. The particles are pushed close together. Their own volume is now a noticeable part of the container's volume, and being close lets them attract each other.
- Low temperature. The particles move slowly, so the weak attractions between them have time to pull them together.
So a real gas behaves most like an ideal gas at high temperature and low pressure: the particles are fast and far apart, so their own volume and their attractions hardly matter.
The type of gas matters too. At the same temperature and pressure, a gas with stronger intermolecular forces deviates more, because "no forces between particles" is less true for it. Rank the gases using the forces from the "Intermolecular forces" section of the AS Chemical Bonding note: hydrogen bonding is stronger than permanent dipole–permanent dipole (pd–pd) forces, and both are stronger than the weak instantaneous dipole–induced dipole (id–id) forces of a small non-polar molecule.
A demonstration
Which gas behaves more like an ideal gas at room temperature and pressure: helium or hydrogen chloride?
Step 1 — conditions. Both gases are at the same temperature and pressure, so the conditions cannot decide.
Step 2 — compare the forces. Helium atoms are tiny and non-polar: only very weak id–id forces. is polar: pd–pd forces as well as id–id forces.
Step 3 — compare the particle sizes. A helium atom is also much smaller than an molecule, so its own volume matters less.
Step 4 — conclude. Helium has weaker forces and smaller particles, so helium is closer to ideal.
Identifying the two correct ideal-gas assumptions
Which assumptions are made about ideal gases?
- Ideal gases contain molecules with no mass.
- Ideal gases contain molecules with no volume.
- Ideal gases have no intermolecular forces.
Options
A 1, 2 and 3
B 1 and 2 only
C 1 and 3 only
D 2 and 3 only
Show full working
- 1
Statement 1 is false. The model assumes zero volume, not zero mass.
A particle with no mass could not push on the wall when it hits it, so there would be no pressure. This makes A, B and C wrong, since they all include 1.
- 2
Statement 2 is true: zero particle volume is the first assumption.
- 3
Statement 3 is true: no intermolecular forces is the second assumption.
D — 2 and 3 only
An ideal gas particle still has mass. Only its volume and the forces between particles are assumed to be zero.
Predicting which conditions make a real gas behave most ideally
Under which conditions will nitrogen behave most like an ideal gas?
| temperature | pressure | |
|---|---|---|
| A | low | high |
| B | high | low |
| C | low | low |
| D | high | high |
Show full working
- 1
Temperature: at high temperature the particles move fast, so the weak attractions between them have little effect. This rules out A and C.
Low temperature slows the particles down, so the attractions matter more and the gas is less ideal.
- 2
Pressure: at low pressure the particles are far apart, so their own volume is tiny compared with the container's. This rules out D.
High pressure squeezes the particles together, so their volume and their attractions both start to matter.
B — high temperature, low pressure
Comparing which gas deviates most, using intermolecular forces
Which gas will behave least like an ideal gas at and ?
Options
A ammonia
B fluorine
C krypton
D steam
Show full working
- 1
All four gases are at the same temperature and pressure, so the conditions cannot decide. The gas with the strongest intermolecular forces deviates most from ideal.
"No intermolecular forces" is least true for the gas with the strongest forces.
- 2
Krypton (single atoms) and fluorine (, non-polar) have only weak id–id forces, so B and C are out.
- 3
Ammonia and steam () both form hydrogen bonds. Water's are stronger: O is more electronegative than N, so the O–H bond is more polar. Each water molecule can also form two hydrogen bonds, on average twice as many as an ammonia molecule.
This is the reasoning from the "Intermolecular forces" section of the AS Chemical Bonding note, which also explains why water boils at 100 °C but ammonia at −33 °C.
- 4
Steam has the strongest intermolecular forces of the four, so it behaves least like an ideal gas.
D — steam
To compare how ideal gases are at the same conditions, rank their intermolecular forces: id–id only is weakest, hydrogen bonding is strongest, and water's hydrogen bonding is stronger than ammonia's.
Your turn
- 1
State the two assumptions of the ideal gas model.
Show solution
- 1
Ideal gas particles have zero volume.
Say "zero volume" or "negligible volume", not "zero size and mass": the particles still have mass.
- 2
There are no intermolecular forces of attraction between ideal gas particles.
Name the forces as intermolecular forces (between particles). "No bonds" is wrong: the atoms inside a molecule are still bonded.
AnswerZero particle volume; no intermolecular forces of attraction.
- 1
- 2
Explain, in terms of particle collisions, why increasing the temperature of a fixed mass of gas at constant volume increases its pressure.
Stuck? Show hint
Two separate effects of a higher temperature both push pressure up — find both.
Show solution
- 1
At a higher temperature, particles move faster on average, so each collision with the container wall delivers a greater force.
Faster particles hit the wall harder.
- 2
Faster-moving particles also collide with the walls more frequently in a given time.
They cross the container in less time, so they reach a wall more often.
- 3
Both a greater force per collision and more collisions per second increase the total force per unit area — the pressure.
Link back to the definition: pressure is the force of the collisions per unit area of wall.
AnswerParticles move faster (more force per collision) and collide more often — both increase pressure.
- 1
- 3
Ammonia, , is cooled from to at constant pressure. State and explain whether it becomes more or less like an ideal gas.
Stuck? Show hint
At low temperature, which ideal-gas assumption becomes less true?
Show solution
- 1
Ammonia molecules form hydrogen bonds with each other, so there are fairly strong intermolecular forces between them.
Start with what forces are present: the "no intermolecular forces" assumption is the one at risk.
- 2
At the molecules move more slowly, so the attractions between them have more effect.
Fast molecules collide briefly and separate before the attractions can act. Slow ones are pulled together.
- 3
So the assumption "no intermolecular forces" is less true, and ammonia becomes less like an ideal gas.
AnswerLess ideal: at lower temperature the slower molecules are affected more by the hydrogen bonding between them.
- 1
The rest of this note
Can you do all of these?
Explain gas pressure in terms of particle collisions with the container wall
State the ideal gas model's two assumptions, and identify when and why a real gas deviates from them
Use pV = nRT, converting kPa → Pa, cm³ or dm³ → m³ and °C → K as separate steps, including for gases mixed from two containers
Rearrange pV = nRT to find a relative molecular mass, a gas density or a molecular formula
Use p ∝ n at fixed V and T (e.g. a gas-phase decomposition), and the combined gas law p₁V₁/T₁ = p₂V₂/T₂ for a fixed amount of gas
Recognise Boyle's law's p–V graph shape
Describe the giant ionic, simple molecular, giant molecular (covalent) and giant metallic lattices, for every named example, including the 6 : 6 coordination in NaCl and the 4 : 2 bonding in SiO₂
Explain graphite's electrical conductivity and softness, and diamond's lack of conductivity, from their structures
Predict melting/boiling point, conductivity, solubility and malleability from a substance's structure and bonding, including the effect of ionic charge
Deduce a substance's structure and bonding from given data, giving the evidence for the structure and for the bonding separately