Under what conditions will a real gas behave like an ideal gas?
Reasons for Real Gases Showing Ideal Behavior at Extremely Low Pressure and High Temperature
For 1 mole of a real gas, the Van der Waals equation is given by:
(P +
aV2)(V − b) = RT
Under certain specific conditions, real gases deviate from this equation and exhibit ideal behavior. The underlying reasons are systematically explained below:
i. At Very Low Pressure
According to Boyle’s Law, at extremely low pressures, the volume of a gas becomes exceptionally large. Consequently, the distance between the gas molecules increases significantly, reducing the mutual intermolecular forces of attraction to a negligible state.
Due to the extremely small value of a and the vast magnitude of volume V, the value of the pressure correction term
P.
Similarly, due to the remarkably large value of volume (V), the constant co-volume b becomes completely negligible compared to V and can be ignored.
(P + aV2) ≈ P and (V − b) ≈ V
Under these conditions, the modified form of the Van der Waals equation becomes: PV = RT. Since this is the standard ideal gas equation, real gases exhibit ideal behavior at very low pressures.
ii. At High Temperature
According to Charles’s Law, the volume of a gas increases extensively at high temperatures. Furthermore, at very high temperatures, the kinetic energy of the gas molecules increases rapidly. This heightened kinetic energy easily overcomes the weak intermolecular forces of attraction existing between the molecules.
As a result, at very high temperatures, the attraction correction term
P. Concurrently, due to the expanded volume (V), the value of b can also be ignored with respect to V.
(P + aV2) ≈ P and (V − b) ≈ V
Consequently, the Van der Waals equation reduces back to: PV = RT. Therefore, at very high temperatures, real gases tend to show ideal behavior.
