Real Gasses

The ideal gas law (PV = nRT) is a strong approximation for most gas behavior, but it rests on assumptions that no real gas perfectly satisfies. This article covers how real gases differ from ideal gases at the particle level, the conditions under which that difference becomes significant, and the van der Waals equation, which corrects the ideal gas law for real-gas behavior.

Key Takeaways

• Ideal gas particles are assumed to have no volume, no intermolecular interactions, and perfectly elastic collisions; real gas particles have nonnegligible volume, measurable intermolecular attractions, and lose energy in collisions.

• Real gases behave most like ideal gases at high temperature and low pressure, and deviate most at high pressure (low volume) or low temperature.

• At high pressure, particle volume becomes significant relative to total gas volume, making actual volume less than the ideal gas law predicts.

• At low temperature, slower-moving particles give intermolecular attractive forces more effect, pulling particles together in a way the ideal gas law doesn't account for.

• The van der Waals equation, (P + an²/V²)(V − nb) = nRT, corrects the ideal gas law: the a term corrects for intermolecular attraction (larger for bigger/more polarizable/polar molecules), and the b term corrects for molecular volume (larger for bigger molecules).

Ideal Gases vs. Real Gases

The ideal gas law assumes gas particles have no volume and no interactions with each other, and that their collisions are perfectly elastic — no kinetic energy is lost. Real gases don't meet these assumptions:

• Real gas particles occupy nonnegligible volume. They aren't points in space.

• Real gas particles interact with each other in measurable ways — intermolecular attractions exist between them.

• Energy is lost in real-gas collisions, unlike the perfectly elastic collisions assumed for an ideal gas.

When Do Real Gases Deviate from Ideal Behavior?

In general, the ideal gas law is a good approximation of real gas behavior, but every real gas deviates from ideal behavior to some extent:

• Real gases behave most like ideal gases at high temperature and low pressure.

• Real gases deviate most from ideal behavior at high pressure (low volume) or at low temperature.

Why Pressure Causes Deviation

As the pressure on a gas increases, its particles are pushed closer together. At high pressure, the particles are squeezed into a much smaller space, and the volume the particles themselves occupy becomes significant compared to the total volume of the gas — it can no longer be treated as negligible. This means the actual volume available to the gas is less than what the ideal gas law predicts.

Why Temperature Causes Deviation

At lower temperatures, gas particles have less kinetic energy and move more slowly than they do at higher temperatures. This slower movement gives intermolecular attractive forces more time to act: particles spend more time in close proximity to each other, allowing attractions to pull them together. This deviation, driven by intermolecular attraction, isn't accounted for in the ideal gas law.

The Van der Waals Equation

Several gas equations attempt to correct for the ways real gases deviate from ideal behavior. The van der Waals equation is the most commonly used:

(P + an²/V²)(V − nb) = nRT

Compared to the ideal gas law, a term is added to pressure and a term is subtracted from volume. The constants a and b are physical constants determined experimentally for each gas:

• The a term corrects for intermolecular attractive forces. It's smaller for gases that are small and less polarizable (like helium), larger for gases that are larger and more polarizable (like Xe or N₂), and largest for polar molecules (like HCl and ammonia).

• The b term corrects for the volume of the molecules themselves. Larger molecules have larger values of b.

Worked example — carbon dioxide has van der Waals constants a = 3.59 L²·atm/mol² and b = 0.0427 L/mol. What pressure does the van der Waals equation predict for 1.00 mol of CO₂ in a 1.00 L container at 300 K, and how does it compare to the ideal gas law's prediction?

Solving the van der Waals equation for pressure:

• P = nRT/(V − nb) − an²/V²

• nRT = (1.00 mol)(0.0821 L·atm/(mol·K))(300 K) = 24.63 L·atm

• V − nb = 1.00 L − (1.00 mol)(0.0427 L/mol) = 0.9573 L

• nRT/(V − nb) = 24.63 / 0.9573 ≈ 25.73 atm

• an²/V² = (3.59 L²·atm/mol²)(1.00 mol)² / (1.00 L)² = 3.59 atm

• P = 25.73 atm − 3.59 atm ≈ 22.1 atm

The ideal gas law, by contrast, predicts P = nRT/V = 24.63/1.00 ≈ 24.6 atm. The van der Waals pressure is lower — at this high particle density, intermolecular attraction pulls the gas's real pressure below the ideal gas law's prediction.

Common MCAT Mistakes

• Assuming all gases deviate from ideal behavior the same amount. Deviation depends on the gas's own a and b values — polar, large, or highly polarizable molecules (like NH₃ or Xe) deviate more than small, nonpolar ones (like He).

• Forgetting which direction pressure correction goes. The van der Waals equation adds an²/V² to the measured pressure (because attraction lowers the pressure a gas actually exerts) — don't subtract it when solving for the corrected pressure.

• Assuming high pressure and low temperature affect ideality through the same mechanism. High pressure causes deviation mainly through nonnegligible particle volume; low temperature causes deviation mainly through increased effect of intermolecular attraction. They're related but distinct causes.

• Treating "ideal gas" as a real substance. No real gas is perfectly ideal — it's a limiting model that real gases approach under specific conditions (high T, low P), not a gas that exists in nature.

MCAT-Style Concept Check

Question: Under which of the following conditions would a real gas be expected to behave most like an ideal gas?

• A) High pressure, low temperature

• B) Low pressure, high temperature

• C) High pressure, high temperature

• D) Low pressure, low temperature

Answer: B

Explanation: Real gases approximate ideal behavior best at low pressure (particles are far apart, so their own volume is negligible relative to the container) and high temperature (particles move fast enough that intermolecular attractions have little time to act). High pressure and/or low temperature push a gas further from ideal behavior.

FAQ

Why do real gases deviate from the ideal gas law?

Real gas particles have nonnegligible volume and experience intermolecular attractions, and their collisions aren't perfectly elastic — none of which the ideal gas law assumes. These effects become significant at high pressure (particle volume matters more) and low temperature (attractions have more time to act).

What do the a and b constants represent in the van der Waals equation?

The a constant corrects for intermolecular attractive forces — larger for bigger, more polarizable, or polar molecules. The b constant corrects for the physical volume the gas molecules themselves occupy — larger for bigger molecules.

Under what conditions does a real gas behave most ideally?

A real gas behaves most like an ideal gas at high temperature and low pressure, since these conditions keep particles far apart (making their own volume negligible) and moving quickly (minimizing the time intermolecular attractions have to act).

Is the van der Waals pressure always lower than the ideal gas law's prediction?

Not always — it depends on which effect dominates. When intermolecular attraction dominates (as in the CO₂ example), the van der Waals pressure comes out lower than the ideal gas law predicts. At very high pressures, where the volume correction (b) dominates, the van der Waals pressure can instead exceed the ideal gas law's prediction.