Demerits of Van Der Waals Equation

After Boyle’s and Charle’s law failed to describe the behaviour of real gases, the Van Der Waals equation came into existence. This equation establishes the true behaviour of all gases, and sometimes the fluids, at different temperatures, pressure, and volumes. Furthermore, the theory has proven to explain the behaviour of gases at critical points where the state changes from gaseous to liquid. The equation is now widely used in areas where liquid and gaseous states are involved at once, like in the PEM electrolyzer, polymeric solvents, and more. 

What does the Van Der Waals entail? 

According to the Van Der Waals theory, the following two points need to be considered: 

1. There exists a force of attraction between the gaseous molecules. This is a weak force, also termed the Van Der Waals force. 

2. When a gas occupies any space, the volume of the real gas at any given temperature and pressure is considered the difference in the total volume of space and the volume occupied by n moles of gas molecules. 

Evaluation of the Van Der Waals equation and the terms 

The ideal gas equation for n moles of gas can be represented as: 

PV = nRT 

Here, P represents the total pressure of an ideal gas, V represents the volume of the ideal gas, R is a constant, and T is the temperature measured in the absolute scale or Kelvin. 

According to this theory, the pressure of the gas doesn’t involve the electrostatic force of attraction between the gaseous molecules. Therefore, a new term is introduced to represent this entity, also known as ‘a a’. Similarly, the real gas volume is represented by ‘b’. If there are n moles of gas, then the ideal gas equation can be modified as: 

(P + an²/V²)(V – nb) = nRT

This equation considers the electrostatic force of attraction between the molecules in the gaseous state and the real gas volumes. The values of b and a aren’t the same for different elements. Rather, these values are derived from different types of experimentations to be used in practical applications like the PEM electrolyzer. 

Are there any limitations of the Van Der Waals equation? 

Nothing is accurate or perfect. Therefore, the Van Der Waals equation also has come with multiple constraints, which helps set the critical points for several physical applications like the electrolysis of different materials through the alkaline solution. 

The limitations of the Van Der Waals equation arise from a wide range of factors. Studying each factor helps identify the solutions to apply this theory and get the most accurate results. 

What are the limitations/ demerits of the Van Der Waals equation?

In this following section, the limitations of the Van Der Waals equation have been discussed. 

Varying values of the constants

There are two critical constants used in the Van Der Waals equation. These are: 

1. ‘a’ represents the electrostatic force of attraction between the gaseous molecules 

2. ‘b’ represents the volume of a real gas, which is equivalent to the space minus the volume of n moles of gas molecules

Since the atomic radius and the number of electrons and protons are different with each element, the values of both these constants also differ. Therefore, when multiple gases are examined simultaneously, new values need to be fed into the equation, introducing discrepancy. 

Disparity of carbon dioxide graphs 

One of the major limitations of the Van Der Waals equation is in the form of a CO2 curve. All the isotherms at the critical point and above it (the point at which CO2 exists in both liquid and gaseous states) are similar in the case of both the Van Der Waals graph and the tested graph from Andrews. 

However, below the critical point, the isotherms from Andrews sit higher than those representing the Van Der Waals equation. Besides, the Van Der Waals equation isotherm has one minima and maxima, which isn’t described in Andrew’s experimental isotherms. 

Incorrect valuation of real gas volume at a critical point

After solving the Van Der Waals equation, it can be known that the volume of a gas at the critical point, Vc, is said to be 3b. However, from the studies, it is found that the value of Vc is 2b. Hence, a huge discrepancy will be introduced between the critical volume values if the Van Der Waals equation is solved in either way only. 

Conclusion 

The Van Der Waals equation is used in several real-time applications, from being used in the PEM electrolyzer to polymeric preparations in solutions. However, it isn’t easy to assess the accurate results due to the constraints. If proper measurements are not taken, differences will creep between the expected valuation and the experimental data. Apart from this, the Van Der Waals equation has several other discrepancies that need to be addressed before being used in any real-life application.