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Difficulty: MediumDeviations of Real Gases from Ideal Gas Behavior

In the van der Waals equation of state for real gases, (P+an2V2)(V−nb)=nRT\left(P + \frac{a n^2}{V^2}\right)(V - n b) = n R T, which physical property of real gas molecules is corrected by the parameter aa?

  1. Intermolecular attractive forces between the gas moleculesAnswer
  2. B
    The finite volume occupied by the gas molecules themselves
  3. C
    The kinetic energy lost during inelastic molecular collisions
  4. D
    The increase in molecular speed under elevated pressure

Answer

The parameter aa in the van der Waals equation accounts for the intermolecular attractive forces between gas molecules.
In ideal gas theory, intermolecular forces are assumed to be non-existent. However, real gas molecules exert weak attractive forces on one another. These cohesive forces pull inward on molecules approaching the container wall, reducing the measured pressure. The term an2V2\frac{a n^2}{V^2} is added to the measured pressure to account for these intermolecular attractive forces, where aa is a characteristic constant for the specific gas.

Step-by-Step Solution

1
Analyze the kinetic theory assumption vs. real gas behavior
Ideal gases assume zero intermolecular forces, but real gas molecules attract each other.
Intermolecular attraction reduces the force of impact of molecules against the container walls, resulting in a lower real pressure than ideal pressure.
2
Identify the role of term an2V2\frac{a n^2}{V^2} in the van der Waals equation
The pressure correction term Pideal=Preal+an2V2P_{\text{ideal}} = P_{\text{real}} + \frac{a n^2}{V^2} adds a pressure factor proportional to intermolecular attraction (aa).
The constant aa specifically measures the strength of attraction between molecules of a given real gas.

Key Concept

Van der Waals Equation and Corrections for Real Gases
Estimated Time:1m 0s
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Topics

Deviations of Real Gases from Ideal Gas Behavior

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