Short on time? This page is the recap. For explanations, figures and worked examples, use the full study guide.
Recap
- PV = nRT rests on two KMT assumptions that real gases break: particles have no volume and particles do not attract each other.
- Attractions pull particles back as they approach the walls, so collisions are less frequent and less forceful. The measured pressure is lower than ideal.
- Particle volume reduces the free space the particles can move in. At very high pressure the measured volume (or pressure) is higher than ideal.
- Both effects are always present; the conditions decide which one dominates.
Key relationships
| Idea | What it tells you | When it matters most |
|---|---|---|
| P_ideal = nRT / V | the pressure an ideal gas would exert | compare with the measured pressure |
| PV/nRT = 1 | ideal behaviour | low pressure, high temperature |
| PV/nRT < 1 | attractions dominate | low T, moderate-to-high P, strong intermolecular forces |
| PV/nRT > 1 | particle volume dominates | extremely high P, large particles |
Assumptions and conditions
- Most ideal: high temperature and low pressure; small, nonpolar particles with few electrons (He is the classic example).
- Least ideal: close to condensation (low T, high P), and polar or hydrogen-bonded or large, highly polarisable molecules.
- A higher boiling point signals stronger intermolecular forces, and so a larger deviation from attractions at the same conditions.
Mistakes to avoid
- “Real pressure is always lower.” Only when attractions dominate.
- High pressure is not “more ideal”. Low pressure is.
- Low temperature is not “more ideal”. Slow particles feel attractions more.
- Collisions do not cause deviations. Ideal particles collide too.
- Name the force. Not “strong forces” but “hydrogen bonding between NH₃ molecules”.
- Intermolecular, not intramolecular. Bonds inside molecules are irrelevant here.
- PV/nRT = 1 at one pressure ≠ ideal. The effects may simply cancel.
Quick self-check
- A gas has PV/nRT = 0.90 at 50 atm. Which effect dominates? (Attractions)
- Which deviates more at 25 °C and 5 atm: N₂ or NH₃? Why? (NH₃: hydrogen bonding and dipole–dipole forces give stronger attractions)
- Why does PV/nRT exceed 1 for every gas at extremely high pressure? (The particles fill a large share of the volume, so the real volume is larger than ideal)
Next: practice questions.