Van der Waals equation of state revisited: importance of the dispersion correction
Related Experiment Video
Updated: Jun 3, 2026

Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup
Published on: October 7, 2025
1Manchester Interdisciplinary Biocentre and School of Chemical Engineering and Analytical Science, University of Manchester, Manchester, United Kingdom. sam.devisser@manchester.ac.uk
Abstract:
One of the most basic equations of state describing nonideal gases and liquids is the van der Waals equation of state, and as a consequence, it is generally taught in most first year undergraduate chemistry courses. In this work, we show that the constants a and b in the van der Waals equation of state are linearly proportional to the polarizability volume of the molecules in a gas or liquid. Using this information, a new thermodynamic one-parameter equation of state is derived that contains experimentally measurable variables and physics constants only. This is the first equation of state apart from the Ideal Gas Law that contains experimentally measurable variables and physics constants only, and as such, it may be a very useful and practical equation for the description of dilute gases and liquids. The modified van der Waals equation of state describes pV as the sum of repulsive and attractive intermolecular interaction energies that are represented by an exponential repulsion function between the electron clouds of the molecules and a London dispersion component, respectively. The newly derived equation of state is tested against experimental data for several gas and liquid examples, and the agreement is satisfactory. The description of the equation of state as a one-parameter function also has implications on other thermodynamic functions, such as critical parameters, virial coefficients, and isothermal compressibilities. Using our modified van der Waals equation of state, we show that all of these properties are a function of the molecular polarizability volume. Correlations of experimental data confirm the derived proportionalities.
Related Concept Videos
Van der Waals Equation
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
Van der Waals Interactions
The Van der Waals Equation
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
The de Broglie Wavelength
Deviation from Ideal Behaviour

