# 16: The Properties of Gases

• 16.1: All Dilute Gases Behave Ideally
For sufficiently low pressures (hence, low densities), each gas approaches ideal-gas behavior.
• 16.2: van der Waals and Redlich-Kwong Equations
The van der Waals Equation of State is an equation relating the density of gases and liquids to the pressure, volume, and temperature conditions. The Redlich–Kwong equation of state is an empirical, algebraic equation that relates temperature, pressure, and volume of gases. It is generally more accurate than the van der Waals equation and the ideal gas equation at temperatures above the critical temperature.
• 16.3: A Cubic Equation of State
Cubic equations of state are called such because they can be rewritten as a cubic function of molar volume. The Van der Waals equation of state is the most well known of cubic EOS, but many others have been developed.
• 16.4: The Law of Corresponding States
The theorem of corresponding states (or principle of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree.
• 16.5: The Second Virial Coefficient
Because the perfect gas law is an imperfect description of a real gas, we can combine the perfect gas law and the compressibility factors of real gases to develop an Equation to describe the isotherms of a real gas. This Equation is known as the virial Equation of state, which expresses the deviation from ideality in terms of a power series in the density. The second virial coefficient describes the contribution of the pair-wise potential to the pressure of the gas.
• 16.6: The Repulsive Term in the Lennard-Jones Potential
The Lennard-Jones intermolecular pair potential takes its name from Sir John Edward Lennard-Jones and consists of two 'parts'; a steep repulsive term, and smoother attractive term, representing the London dispersion forces. Apart from being an important model in itself, the Lennard-Jones potential frequently forms one of 'building blocks' of many force fields.
• 16.7: Van der Waals Constants in Terms of Molecular Parameters
• 16.E: The Properties of Gases (Exercises)
These are homework exercises to accompany Chapter 16 of McQuarrie and Simon's "Physical Chemistry: A Molecular Approach" Textmap.