Real Gasses
High-Yield Summary
- Ideal gas law assumes zero particle volume, no intermolecular interactions, and perfectly elastic collisions — real gases violate all three.
- Real gases behave most ideally at high temperature and low pressure; deviate most at high pressure (low volume) or low temperature.
- High pressure: particle volume becomes significant relative to container volume, so real available volume < ideal prediction.
- Low temperature: slower particles give intermolecular attractions more time to act, pulling particles together — a deviation the ideal gas law ignores.
- Van der Waals equation (P + an²/V²)(V − nb) = nRT corrects for both: a corrects for intermolecular attraction, b corrects for molecular volume.
Key Terms
- Van der Waals equation
- (P + an²/V²)(V − nb) = nRT — corrects the ideal gas law for real-gas intermolecular attraction and molecular volume.
- a constant
- Corrects for intermolecular attractive forces; larger for bigger/more polarizable/polar molecules.
- b constant
- Corrects for the volume occupied by gas molecules themselves; larger for bigger molecules.
Van der Waals Equation
(P + an²/V²)(V − nb) = nRT
- a = constant correcting for intermolecular attraction (added to P)
- b = constant correcting for molecular volume (subtracted from V)
- n = moles
- Worked example: CO₂ (a = 3.59 L²·atm/mol², b = 0.0427 L/mol), 1.00 mol, 1.00 L, 300 K → van der Waals P ≈ 22.1 atm vs. ideal gas law's 24.6 atm.
- At high particle density, intermolecular attraction pulls real pressure below the ideal prediction.
Ideal vs. Real Gas Assumptions
| Ideal gas assumption | Real gas reality |
|---|---|
| No particle volume | Particles occupy nonnegligible volume |
| No intermolecular interactions | Measurable intermolecular attractions exist |
| Perfectly elastic collisions | Energy is lost in real collisions |
Must-Know Points
- Memorize the deviation conditions: real gases deviate MOST at high pressure/low volume OR low temperature; they behave MOST ideally at low pressure and high temperature.
- The a term (attraction) is largest for large, polarizable, or polar molecules (e.g., HCl, ammonia); smallest for small, nonpolar molecules (e.g., helium).
- The b term (molecular volume) simply scales with molecular size — bigger molecules, bigger b.
Common MCAT Trap
- Don't assume real gas pressure is always LOWER than ideal — at very high pressure, the volume-correction (b) term can dominate and push real pressure ABOVE the ideal prediction; at moderate high pressure/density, attraction (a) dominates and pushes it below.
- Don't forget: the a term is ADDED to pressure and the b term is SUBTRACTED from volume in the van der Waals equation — easy to invert the signs from memory.
- Low temperature causes deviation via intermolecular attraction, NOT via molecular volume — keep the two causes (pressure→volume effect, temperature→attraction effect) straight.
Quick Recall
Under what two conditions do real gases deviate most from ideal behavior?
In the van der Waals equation, what does the constant 'a' correct for?
Why does low temperature cause a gas to deviate from ideal behavior?