Deviation of Real Gases and Van der Waals Equation

Answer: The Kinetic Theory of Gases, from which ideal gas laws are mathematically derived, contains two fundamentally faulty assumptions that cause real gases to deviate from ideal behavior. Dutch physicist J.D. Van der Waals corrected these two postulates to formulate a modified equation of state for real gases. According to his theory, by applying specific volume and pressure corrections to the ideal gas equation PV = nRT, the equation becomes perfectly applicable to real gases. This modified relation is widely recognized as the Van der Waals equation.

Causes of Deviation of Real Gases from Ideal Behavior:

Real gases do not strictly follow two core postulates of the kinetic theory. The underlying reasons for this deviation are classified into two major corrections:

1. Volume Correction
2. Pressure Correction

1. Volume Correction

One of the key postulates of the kinetic theory states that the actual volume occupied by gas molecules is completely negligible compared to the total volume of the container. However, under conditions of high pressure and low temperature, this assumption proves to be entirely invalid because:

• (i) At high pressures and low temperatures, a massive number of gas molecules are confined within a very restricted space. Under these circumstances, the actual volume of the gas molecules cannot be neglected relative to the total volume of the container.
• (ii) Under high pressure and low temperature, real gases can be liquefied and eventually solidified. Since substances possess a definite volume in their liquid and solid states, their molecules must inherently possess a definite intrinsic volume in the gaseous state as well.
• (iii) According to Avogadro’s hypothesis, the molar volume of any gas at STP is universally established as 22.4 L, which has been experimentally proven accurate. This structurally confirms that gas molecules possess a definite personal volume.

Consequently, while the free space available for the continuous movement of an ideal gas molecule is considered to be the total volume (V), the actual effective free volume for a real gas will be slightly less than V.

2. Pressure Correction

Another prominent postulate of the kinetic theory suggests that there are no mutual forces of attraction or repulsion operating between gas molecules. However, under high pressure and low temperature conditions, this assumption fails. Under these states, the kinetic energy of gas molecules decreases substantially, allowing intermolecular attraction to grow stronger, eventually transforming the gas into a liquid or solid phase. Since phase transitions would be impossible without molecular attraction, it proves that real gas molecules exert mutual attraction.

Because of these intermolecular forces, a real gas molecule approaching the container wall experiences an inward pull from the bulk molecules behind it. Consequently, it strikes the wall with less impact, exerting a lower pressure (P) than it would in an attraction-free ideal state.

According to Van der Waals, this internal correction pressure (pa) is directly proportional to the square of the density of the gas, which makes it inversely proportional to the square of its molar volume.

Here, a represents the Van der Waals constant, which serves as a quantitative measure of the intermolecular attractive forces of the gas.

Final Van der Waals Equation for Real Gases:

Substituting the corrected pressure and volume terms into the ideal gas equation PV = nRT, we get—