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Related Concept Videos

The Van der Waals Equation01:26

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
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Mean free path and Mean free time01:22

Mean free path and Mean free time

Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path."
Deriving the Speed of Sound in a Liquid01:09

Deriving the Speed of Sound in a Liquid

As with waves on a string, the speed of sound or a mechanical wave in a fluid depends on the fluid's elastic modulus and inertia. The two relevant physical quantities are the bulk modulus and the density of the material. Indeed, it turns out that the relationship between speed and the bulk modulus and density in fluids is the same as that between the speed and the Young's modulus and density in solids.
The speed of sound in fluids can be derived by considering a mechanical wave propagating...

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Related Experiment Video

Updated: Jun 24, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Improved method for the self-diffusion coefficient in the modified free volume theory: simple fluids.

Yuan Qin1, Byung Chan Eu

  • 1Department of Chemistry, McGill University, 801 Sherbrooke Street West, Montreal, Qc H3A 2K6, Canada.

The Journal of Physical Chemistry. B
|April 3, 2009
PubMed
Summary
This summary is machine-generated.

This study enhances the modified free volume (MFV) theory for calculating diffusion. Replacing the hard sphere coefficient with the Chapman-Enskog formula significantly improves self-diffusion coefficient accuracy for Lennard-Jones fluids.

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Area of Science:

  • Physical Chemistry
  • Chemical Engineering
  • Thermodynamics

Background:

  • The modified free volume (MFV) theory is a theoretical framework used to model diffusion processes.
  • Accurate calculation of self-diffusion coefficients is crucial for understanding fluid behavior and transport phenomena.
  • Previous applications of MFV theory utilized hard sphere models, leading to limitations in accuracy.

Purpose of the Study:

  • To improve the accuracy of self-diffusion coefficients calculated using the modified free volume (MFV) theory.
  • To investigate the impact of different pre-exponential factors on MFV theory predictions.
  • To refine the application of the van der Waals equation of state within diffusion models.

Main Methods:

  • The study employs the modified free volume (MFV) theory, incorporating the van der Waals equation of state.
  • A key methodological change involves replacing the hard sphere self-diffusion coefficient with the Chapman-Enskog formula for the pre-exponential factor.
  • Simulations and theoretical calculations were performed for Lennard-Jones (LJ) fluids across various temperatures and liquid densities.

Main Results:

  • The revised MFV theory, using the Chapman-Enskog formula, demonstrates a significant improvement in the accuracy of self-diffusion coefficients for Lennard-Jones fluids.
  • The enhanced method provides more reliable predictions compared to the previous approach that relied on hard sphere models.
  • Improved accuracy was observed across a wide range of temperatures at liquid densities.

Conclusions:

  • The modified free volume (MFV) theory, when augmented with the Chapman-Enskog formula for the pre-exponential factor, offers a more accurate prediction of self-diffusion coefficients.
  • This refinement is particularly effective for Lennard-Jones fluids in the liquid state.
  • The study highlights the importance of selecting appropriate pre-exponential factors for enhancing the predictive power of diffusion theories.