Real Gases and Deviations
Identify which ideal assumption fails under extreme conditions.
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Real-gas questions are explanation questions: name the condition (very high p or very low T), state which ideal assumption fails (no intermolecular forces or negligible particle volume), then link that failure to molecular behaviour.
Definitions (Must Know)
A. Ideal gas vs real gas
An ideal gas is a model that obeys pV = nRT exactly under all conditions.
A real gas is a real substance that only behaves approximately ideally, especially at low pressure and high temperature.
B. Ideal gas assumptions (what can fail)
The ideal gas model assumes:
- gas particles have negligible volume
- there are no intermolecular forces between particles
Key Ideas (What Earns Marks)
- Gases behave most ideally at low pressure and high temperature.
- Deviations become important at:
- very high pressure (molecular size and finite particle volume matter)
- very low temperature (intermolecular attractions matter)
- Intermolecular attractions can make the measured pressure lower than the ideal prediction.
- Finite particle volume can make the measured pressure higher than the ideal prediction.
- If you need the intermolecular-force language, revise Intermolecular Forces and Properties.
- Anchor every deviation explanation against the baseline assumptions in Ideal Gas Model and pV = nRT.
Pressure comes from gas particles colliding with the container walls. Anything that changes collisions (attractions, available volume) can change the pressure from the ideal prediction.
Detailed Explanations
A. How to explain a deviation (exam chain)
Write a complete chain:
- State the condition (high p / low T).
- State which ideal assumption fails (no IMFs / negligible volume).
- State the effect on collisions or free volume.
- State what happens to the measured pressure compared with the ideal prediction.
B. What low T does (attractions matter)
At very low temperature, particles have lower average kinetic energy, so intermolecular attractions are more significant relative to their motion.
When particles are being pulled back from the walls, their collisions with the walls are less frequent/less forceful, so the measured pressure is lower than the ideal prediction.
C. What high p does (particle volume matters)
At very high pressure, particles are close together. Their own volume is no longer negligible, so the “free volume” available for movement is smaller than the container volume V.
Less free volume means particles hit the walls more often, so the measured pressure is higher than the ideal prediction (compared with pV = nRT using the full V).
D. Which assumption fails, and what it does
- Very low T: the “no intermolecular forces” assumption fails. Attractions reduce momentum transfer at the walls, so pressure is lower than the ideal prediction.
- Very high p: the “negligible particle volume” assumption fails. Molecular size is significant, so free volume is smaller than V and pressure is higher than the ideal prediction.
See these effects on a graph of pV/nRT for three real gases, calculated from the van der Waals equation with their measured constants. Change the temperature and move along the pressure axis.
Graph of pV/nRT against pressure for three real gases at 320 K. At 10.0 MPa, pV/nRT is: helium 1.09, nitrogen 0.98, carbon dioxide 0.38. An ideal gas would give 1.
- Pressure
- — kPa
- Mass of gas
- — g
- Mr of the gas
- —
- nRT/V
- — kPa
- pV/nRT
- —
- p(N₂)
- — kPa
- p(He)
- — kPa
- Total pressure
- — kPa
- Mole fraction of N₂
- —
- pV/nRT for He
- 1.09
- pV/nRT for N₂
- 0.98
- pV/nRT for CO₂
- 0.38
Try this
0 of 5 doneHalve the volume of the gas at the same temperature and let the pressure settle. (not done yet)
The pressure doubles. In half the volume each particle hits the walls twice as often: p ∝ 1/V at constant n and T.
Double the absolute temperature at the same volume and let the pressure settle. (not done yet)
The pressure doubles. Faster particles hit the walls harder and more often: p ∝ T in kelvin, as pV = nRT says.
Mix helium with the nitrogen, then change the amount of helium. Compare the partial pressures with the total. (not done yet)
Each gas pushes on the walls as if it were alone, so p = p(N₂) + p(He), and p(N₂) = x(N₂) × p. The light, fast helium exerts the same pressure per mole as nitrogen.
Measure an unknown gas at two volumes or temperatures and work out its Mr from each reading. (not done yet)
Both readings give the same n = pV/RT, so the same Mr = mass ÷ n. Use p in Pa with V in m³ (or kPa with dm³) and T in kelvin.
Compare the real-gas curves at 330 K or below and at 800 K or above. (not done yet)
Real gases are most nearly ideal at high temperature and low pressure. Hot molecules move too fast for attractions to matter, and far-apart molecules take up a negligible share of the volume.
Your readings
| # | V / dm³ | p / kPa | 1/V / dm⁻³ | T / K | Remove |
|---|---|---|---|---|---|
| No readings yet. Set up a measurement, then record it. | |||||
Worked Examples
Modelled example 1
Conditions for ideal behaviour
Problem
State the conditions under which a real gas behaves most ideally, and explain why.
Study the worked solution
Lower the pressure
Method
Keep particles far apart.Reason
Particle volume and intermolecular attractions then become small relative to the container scale.
Working
Low pressure → large mean separation.
Raise the temperature
Method
Give particles high mean kinetic energy.Reason
Attractions are less significant relative to particle motion, so ideal assumptions are closer to true.
Working
Most ideal: low pressure and high temperature.
Common misconception 2
Lower-than-ideal pressure at low temperature
Learner claim
Identify the dominant non-ideal effect
View solution step by step
Strengthen the relative attraction effect
Method
Lower particle kinetic energy.Reason
Intermolecular attractions become more significant at low temperature.Working
Cooling → attractions matter more.Connect to wall collisions
Method
Reduce the frequency or force of wall collisions.Reason
Attractions pull particles toward one another, so measured pressure falls below the ideal prediction.Working
pᵣₑₐₗ < p_ideal.
Challenge 3
Higher-than-ideal pressure at high pressure
Deviation-direction transfer
Switch from attractions to excluded volume
Hints
Hint 1: crowding
Hint 2: collision consequence
View solution step by step
Account for particle volume
Method
Treat molecules as occupying a significant fraction of the container.Reason
The ideal model assumes negligible particle volume.Working
The free volume is smaller than V.Predict pressure direction
Method
Increase wall-collision frequency and measured pressure.Reason
Particles move within less available volume than the ideal equation assumes.Working
pᵣₑₐₗ > p_ideal.
Common Mistakes
- Saying gases deviate most at high temperature (raising temperature makes attractions less significant, so behaviour approaches ideality).
- Mentioning only one cause when the question asks about both very low temperature and very high pressure.
- Writing “real gases deviate because they are not ideal” without stating the failed assumption.
Exam Tips
- Always use the exact assumption language: “negligible volume” and “no intermolecular forces”.
- If the question asks “why is pressure lower than predicted?”, your default driver is intermolecular attractions.
- If the question asks “why is pressure higher than predicted at high pressure?”, your default driver is finite molecular volume.
- If the question just says “explain the deviation”, start by stating the condition (low T or high p) so the examiner knows which assumption you are targeting.
Mind Stretchers
Mind stretcher 1Extension
At the same temperature and pressure, which deviates more from ideal behaviour: He or NH₃? Explain.
Show Hint
Compare both the strength of intermolecular attractions and particle size; either can make an ideal assumption less valid.
Show Answer
Mark scheme:
- NH₃ has stronger intermolecular forces (including hydrogen bonding) and larger particles than He.
- So the “no intermolecular forces” and “negligible volume” assumptions fail more strongly for NH₃.
- Therefore NH₃ deviates more from ideal behaviour.
Mind stretcher 2: Explaining a reversal in deviationExtension
Question. For a fixed amount of gas at low temperature, the measured pressure is initially lower than the ideal-gas prediction. After the same sample is compressed much more strongly, its measured pressure becomes higher than the ideal prediction. Explain why the direction of deviation changes.
Show Hint
Treat the two observations separately: decide which failed ideal assumption explains each direction of pressure change.
Show Answer
At low temperature, intermolecular attractions are significant. They reduce the frequency or force of wall collisions, so the measured pressure is lower than the ideal prediction. After strong compression, particles are much closer and their finite molecular volume is no longer negligible. The free volume is then smaller than the container volume used in the ideal equation, increasing wall-collision frequency and producing a pressure above the ideal prediction. The dominant non-ideal effect has changed from attractions to finite particle volume.
Syllabus and review details
- GCE A-Level H2 Chemistry 9476-2027 · 9476-2027
9476 (2027), complete syllabus
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