# More Sophisticated EOS's

Equations of State that we studied in the previous lesson:

1. Ideal Gas

2. Generalized Compressibility Factor

More sophisticated Equations of State that we will study in this lesson:

1. Virial EOS

2. Van der Waals EOS

3. Redlich-Kwong EOS

4. Soave-Redlich-Kwong (SRK) EOS

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### Ch 2, Lesson F, Page 1 - More Sophisticated EOS's

• In the previous lesson, we learned a method to help us decide whether the Ideal Gas EOS is accurate for a given state.
• We also learned to use the Generalized Compressibility Factor EOS when the Ideal Gas EOS was not applicable.
• The problem is that the Generalized Compressibility Factor EOS is not well suited to iterative or computer aided calculations.
• Other more sophisticated EOS’s have been developed that are NOT graphical in nature.
• These more sophisticated EOS’s allow us to take advantage of the power of computer programs such as Excel to solve involved problems that require repeated use of an EOS.
• Some of these equations of state can be used to describe vapor-liquid equilibrium and to predict a variety of thermodynamic properties of liquids and gases.  But these applications of the EOS’s are beyond the scope of this course.
• In this lesson, we will consider 4 EOS’s.
• We begin with the Virial EOS because it is based on the Ideal Gas EOS and it was one of the first EOS’s to improve on the Ideal Gas EOS.
• Next we will study the Van der Waal’s EOS.  This was the first cubic EOS and it the set the stage for many cubic EOS’s that followed.
• One of best cubic EOS’s is the Redlich-Kwong EOS.  It is commonly used to predict the PVT of a wide variety of non-polar gases.
• We will wrap up with the Soave-Redlich-Kwong EOS.  This EOS is a slight modification of the RK EOS that yields better accuracy for hydrocarbon systems.
• It is important to note that none of these EOS’s are very accurate for polar molecules, especially at smaller molar volumes.
• Water is the perfect example.  Specialized EOS’s have been developed just for water !  These specialized EOS’s are beyond the scope of this course.  When you need to know the thermodynamic properties of water, I recommend that you access the NIST website.
• OK, now we are ready to dive into the Virial EOS.