Real gases Knowledge-Based Study

Study notes

1. Kinetic Molecular Theory and Real Gases

   The ideal gas equation, $PV = nRT$, is built on two core assumptions of the Kinetic Molecular Theory:

   • Gas particles occupy zero volume (they are treated as point masses).
   • There are no attractive or repulsive intermolecular forces between gas particles.

   In reality, actual gas molecules possess a finite, non-zero volume, and attractive forces exist between them. Gases that take these physical realities into account are called real gases.

   When Do Gases Deviate from Ideality?

   Real gases behave most like ideal gases under conditions of high temperature and low pressure:

   • High Temperature: High thermal kinetic energy minimizes the relative impact of intermolecular attractions, allowing particles to overcome attractive forces upon collision.
   • Low Pressure: Gas molecules are widely spaced, meaning the actual volume of the molecules is negligible compared to the total volume of the container.

   Conversely, significant deviations from ideal behavior occur under high pressure and low temperature:

   • At high pressure, molecules are forced close together, making molecular volume significant compared to container volume.
   • At low temperature, molecules move slowly, allowing intermolecular attractions to pull particles together and reduce collision force against container walls.

   Quantifying Non-Ideality: The Compressibility Factor (Z)

   The deviation of a real gas from ideal behavior is quantitatively evaluated using the compressibility factor (Z):

   $Z = \frac{PV}{nRT}$

   For an ideal gas, Z is exactly equal to 1 under all conditions. For real gases, Z varies with temperature and pressure:

   • $Z < 1$: Intermolecular attractive forces dominate. Attractions pull molecules inward, reducing the pressure exerted on the container walls below the ideal value.
   • $Z > 1$: Finite molecular volume dominates. The volume occupied by the particles themselves leaves less free space for movement, making the gas less compressible than an ideal gas.

   Accounting for Molecular Volume and Attractions

   Johannes van der Waals modified the ideal gas equation to correct for non-ideal behavior in real gases:

   $\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$

   This equation introduces two substance-specific constants:

   • Constant a (Pressure Correction): Accounts for intermolecular attractive forces. Stronger attractions lead to a larger a value.
   • Constant b (Volume Correction): Accounts for the finite volume excluded by one mole of gas particles. Larger molecules have greater b values.

   Molecules with weak intermolecular forces and small molecular sizes, such as helium and hydrogen, have very low a and b values and behave most closely to ideal gases.