Van der Waals equation is an equation of state that describes the behavior of real gases, taking into account the finite size of gas molecules and the attractive forces between them. Van Der Waals equation is written like this: [P + a (n²/V²)] (V-nb) = nRT. The Van der Waals equation stands as a crucial development in understanding the behavior of real gases. It is very similar to the Ideal Gas Law PV = nRT except that for attraction between gas molecules with ‘a’ and volume of those molecules with ‘b’.

In this article, we will learn about, Van Der Waals Equation, Van Der Waals Equation Formula, Van Der Waals constants, Van Der Waals Equation Derivation, and others in detail.

What is Van Der Waals Equation?

Van der Waals equation, proposed by Dutch physicist Johannes Diderik van der Waals in 1873, addresses the limitations of the ideal gas law.

Ideal Gas Law

Ideal gas law states that,

PV = n × R × T

where,

• P is Pressure
• V is Volume
• n is Number of Moles
• R is Gas Constant
• T is Temperature

Assuming that gas molecules have no volume and do not exert attractive forces on each other. However, real gases deviate from this ideal behavior, especially at high pressures and low temperatures.

Van Der Waals Equation Formula

Van Der Waals equation adjusts ideal gas law to account for volume occupied by gas molecules and attractive forces between them. The equation is given by:

[P + a (n²/V²)] (V – nb) = nRT

where,

• P is Pressure
• V is Volume
• n is Number of Moles
• T is Temperature
• a is Correction Factor for Attractive Forces Between Molecules
• b is Correction Factor for Volume Occupied by Gas Molecules

Term a(n²/V²) corrects for Attractive Forces, and nb corrects for Volume Occupied by Gas Molecules. Van Der Waals equation is particularly useful in describing behavior of real gases under conditions where deviations from ideal behavior are significant.

Van Der Waals Constants

Van Der Waal’s constant are,

• ‘a’ Parameter: Reflects the attractive forces between gas molecules. Higher values of ‘a’ indicate stronger intermolecular forces.
• ‘b’ Parameter: Accounts for the volume occupied by gas molecules. It represents the correction for the finite size of gas particles.

Units of Van Der Waals Constant

• a: Measured in (Pa⋅m⁶)/mol².
• b: Measured in m³/mol.

Need for Van Der Waals Equation

Real gases deviate from ideal behavior under conditions where the assumptions of the ideal gas law break down. This occurs notably at high pressures and low temperatures. In these scenarios, intermolecular forces and the finite volume of gas particles become significant. Unlike ideal gases, real gases experience attractive and repulsive forces between molecules, leading to deviations in their behavior. The Van der Waals equation accounts for these deviations by introducing correction terms (‘a’ for attractive forces and ‘b’ for volume occupied) and provides a more accurate representation of real gas behavior under diverse conditions.

Van Waal Theory of Gas

Van der Waals equation, proposed by Johannes Diderik Van Der Waals in 1873, addresses the limitations of the ideal gas law. This theory acknowledges that real gas molecules occupy space and experience attractive forces between them, aspects overlooked in the ideal gas model.
The equation introduces correction terms a and b to account for molecular interactions and the finite volume occupied by gas particles. a represents the strength of attractive forces, while b adjusts for volume occupied by gas molecules.
Van der Waals theory provides a more accurate depiction of gas behavior under non-ideal conditions, contributing to a deeper comprehension of the intricacies of gas interactions.

Van Der Waals Equation Derivation

Using ideal gas equation,

PV = nRT

This equation assumes that gas molecules have negligible volume and do not experience attractive or repulsive forces.

However, real gases deviate from these idealized conditions, particularly at high pressures and low temperatures.

Correcting for Volume

First correction factor, nb, is introduced to account for the volume occupied by gas molecules.

Corrected volume becomes (V – nb). Thus, final equation will be:

P(V – nb) = nRT

Correcting for Attractive Forces

To correct for attractive forces between gas molecules, a term proportional to is added. This term reflects the reduction in pressure due to attractive forces, making the pressure term in the equation

((P + a(n²)/V²)⋅(V) = nRT

Here, a is a constant that represents the strength of attractive forces between molecules. Term a(n²)/V² can be seen as an adjustment to the pressure term to account for the reduction caused by attractive forces.

Combining Corrections

Combining these corrections with the ideal gas law yields the Van der Waals equation:

((P + a(n²)/V²) ⋅ (V-nb) = nRT

Equation is more accurate for describing the behavior of real gases, especially under conditions where deviations from ideal behavior are significant.

Van Der Waals equation is a crucial advancement over Ideal Gas Law, providing a more realistic representation of gas behavior by considering both molecular volume and intermolecular forces.

Advantages and Disadvantages of Van Der Waals Equation

There are several advantages and disadvantages of Van Der Waals equations some of these are listed below:

Advantages of Van Der Waals Equation

• Realistic Representation: Corrects ideal gas law assumptions.
• Precision: Applicable under various conditions.
• Industrial Applicability: Crucial in industries like chemical manufacturing.

Disadvantages of Van Der Waals Equation

• Limited Accuracy: Faces challenges in extreme conditions.
• Complex Molecular Interactions: May struggle with highly complex molecular scenarios.
• Phase Transition Prediction: Difficulty in accurately predicting phase transitions.

Applications of Van der Waals Equation

1. Drug Design and Pharmaceutical Industry: Predicting drug solubility and optimizing drug-receptor interactions.
2. Materials Science and Engineering: Employed to forecast and control material properties.
3. Environmental Chemistry: Assists in studying gas behavior in the atmosphere for pollution control.
4. Chemical Engineering Processes: Ensures precision in reactions under various conditions.
5. Biological Systems and Biomolecular Interactions: Contributes to understanding biomolecular interactions in life processes.
6. Astrophysics and Gas Behavior in Space: Predicts gas behavior in space, aiding our understanding of celestial bodies.

Ideal Gas Equation vs Van der Waals Equation: A Comparative Analysis

Ideal Gas Equation

Ideal gas equation,

PV = nRT

It provides a simplified model for the behavior of gases by assuming that gas molecules have negligible volume and do not exert attractive or repulsive forces on each other. While it serves as a useful approximation under many conditions, real gases deviate from ideal behavior, especially at high pressures and low temperatures.

Van der Waals Equation

Van der Waals equation, proposed by Johannes Diderik van der Waals in 1873, offers a more comprehensive description of real gas behavior. It introduces corrections to the ideal gas equation to account for the finite size of gas molecules and the attractive forces between them. The equation is given by:

((P + a(n²)/V²)⋅(V – nb) = nRT

Here, a corrects for attractive forces, and b corrects for the volume occupied by gas molecules.