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Difficulty: MediumDeviations of Real Gases from Ideal Gas Behavior

At extremely high pressures, the compressibility factor (Z=PVnRTZ = \frac{PV}{nRT}) of a real gas is observed to be greater than 1.01.0. Which assumption of the kinetic molecular theory breaks down to cause this positive deviation?

  1. The volume occupied by individual gas molecules is negligible compared to the total volume of the container.Answer
  2. B
    There are no attractive or repulsive intermolecular forces acting between the gas molecules.
  3. C
    Collisions between gas molecules and the container walls are perfectly elastic.
  4. D
    The average kinetic energy of gas molecules is directly proportional to the absolute temperature.

Answer

The assumption that the volume of individual gas molecules is negligible breaks down at extremely high pressures, causing the compressibility factor to exceed 1.0.
At extremely high pressures, gas particles are forced close together so that the actual volume occupied by the gas molecules becomes significant relative to the container volume. This breaks the ideal gas postulate of zero molecular volume, making the actual molar volume larger than ideal and resulting in Z>1.0Z > 1.0.

Step-by-Step Solution

1
Analyze the compressibility factor equation Z=PVnRTZ = \frac{PV}{nRT}.
For an ideal gas, Z=1.0Z = 1.0. When Z>1.0Z > 1.0, the real volume occupied by the gas is larger than predicted by the ideal gas law (Vreal>VidealV_{\text{real}} > V_{\text{ideal}}).
Understanding ZZ allows identification of whether volume exclusion or attractive forces dominate.
2
Identify the cause of positive deviation (Z>1.0Z > 1.0) at very high pressure.
At very high pressures, molecules are compressed into a small container volume. The finite volume of the gas molecules themselves (bb in van der Waals equation) can no longer be ignored.
The Kinetic Molecular Theory postulate stating gas particles have negligible volume breaks down under high pressure.

Key Concept

Compressibility Factor and Molecular Volume Exclusion in Real Gases
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Topics

Deviations of Real Gases from Ideal Gas Behavior

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