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Deviation from Ideal Gas Law

The Ideal Gas Law (PV = nRT) provides a simplified model of gas behavior, assuming no intermolecular forces and negligible molecular volume. Real gases, however, deviate from ideal behavior, especially under high pressure and low temperature conditions.

Causes of Deviation​

  1. Intermolecular Forces:

    • Attractive forces between molecules reduce the pressure exerted by the gas on the container.
    • More significant for polar molecules or gases with hydrogen bonding.

  2. Finite Molecular Volume:

    • Gas molecules occupy space; at high pressures, the volume of molecules becomes significant compared to the total volume, causing deviation.

Van der Waals Equation​

To account for deviations, the Van der Waals equation modifies the Ideal Gas Law:

(P + a(n/V)²)(V − nb) = nRT

Where:

  • a = measure of intermolecular attraction
  • b = volume occupied by gas molecules
  • n = number of moles
  • V = volume
  • R = gas constant
  • T = temperature

Behavior at Different Conditions​

  • Low Pressure and High Temperature: Gases behave nearly ideally; deviations are minimal.
  • High Pressure: Molecular volume becomes important; gas is less compressible than predicted.
  • Low Temperature: Intermolecular attractions dominate; gas condenses more easily than ideal predictions.

Importance​

Understanding deviations from ideality is essential for:

  • Accurate calculations in chemical engineering and laboratory work
  • Predicting real gas behavior in reactions and industrial processes
  • Explaining condensation, liquefaction, and other phase transitions

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