# The Virial EOS

The Virial EOS is
based on the Ideal Gas EOS:
Since Z is not always equal to 1, the Ideal Gas EOS is expanded as an infinite power series in terms of 1/ :
The Virial Equation of State !
B, C, D, E and so on are the Virial Coefficients.
Virial Coefficients :
• Are functions of temperature only
• Can be determined experimentally
• Can also be determined theoretically for simple molecules using the principles of statistical mechanics.
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### Ch 2, Lesson F, Page 2 - The Virial EOS

• The Virial EOS is based on the Ideal Gas EOS and has a sound theoretical basis.
• The Ideal Gas EOS insists that the compressibility factor, Z, is always equal to one.
• We know that for real gases this just isn’t true.
• The Virial EOS uses a power series expansion in 1 over V-wiggle to describe the way in which Z deviates from 1.
• The coefficients of the terms in the power series are called the Virial Coefficients.
• B is called the First Virial Coefficient.  C is called the 2nd Virial Coefficient and so on.
• The Virial Coefficients are functions of temperature ONLY.
• The drawbacks of the Virial EOS are that the power series has an infinite number of terms and that the coefficients are not easy to determine.
• The strength of the Virial EOS is that it has a strong theoretical basis.  As a result, the 1st and 2nd Coefficients can often be determined from experimental data.  For simple molecules, the 1st and 2nd Virial Coefficients can be predicted using statistical mechanics.  Unfortunately, the prediction of the Virial Coefficients from a theoretical basis has not yet proven to be entirely accurate.
• As a result, a simplified form of the Virial EOS is generally used.
• Flip the page to learn how it is done.