# 16: The Properties of Gases

- Page ID
- 11811

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- 16.1: All Dilute Gases Behave Ideally
- Gases behave according to the ideal gas law when interactions between the gas molecules and the container as well as the size of the particles can be ignored. At low pressures and high temperatures since the gas occupies a large volume, the volume occupied by the constituents of the gas become even more insignificant in comparison. Thus real gases approach ideal behavior at low \(P\) and high \(T\).

- 16.2: van der Waals and Redlich-Kwong Equations of State
- 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 equations of state, but many others have been developed.

- 16.4: The Law of Corresponding States
- An additional assumption about real gases made by van der Waals was that all gases at corresponding states should behave similarly. The corresponding state that van der Waals choose to use is called the reduced state, which is based on the deviation of the conditions of a substance from its own critical conditions.

- 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
- Proposed by Sir John Edward Lennard-Jones, the Lennard-Jones potential describes the potential energy of interaction between two non-bonding atoms or molecules based on their distance of separation. The potential equation accounts for the difference between attractive forces (dipole-dipole, dipole-induced dipole, and London interactions) and repulsive forces.

- 16.7: Van der Waals Constants in Terms of Molecular Parameters
- The van der Waals equation of state assumes the hard sphere model at close distances and weak intermolecular attractions at larger distances. These are represented by the van der Waals coefficients \(a\) for intermolecular attractions and \(b\) for finite volume of particles (hard sphere model).

- 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.

Thumbnail: Motion of gas molecules. (CC BY-SA 3.0; Greg L via Wikipedia)