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Principle of Corresponding States

Many properties of a fluid, including the

compressibility factor

, Z, depend primarily on how close the temperature and pressure of the fluid are to the critical temperature and critical pressure of that chemical species.

The

critical point

is the point at which the saturated liquid and saturated vapor phases are identical.

At the

critical point

, the temperature, pressure, and molar volume are called the critical temperature, Tc, the critical pressure Pc, and the critical molar volume,

Critical properties are tabulated in a variety of publications, including the NIST website.

Unfortunately, is not generally tabulated, so the ideal critical molar volume, , is used instead.

Lesson 2E: page 8 of 13

Ch2, Lesson E, Page 8 - Principle of Corresponding States

The principle of corresponding states tells us that many properties, including Z, are the same for ALL gases at their individual critical points.
This is an enormously powerful statement ! ALL gases. Water, methanol, hydrogen, air…whatever have the same value of Z at their individual critical points.
This principle goes even further. Properties like Z can be determined for ANY gas just by knowing HOW close the actual temperature and pressure are to the critical temperature and pressure ! Wow !
I’m sure you recall that the critical point is the temperature and pressure at which the saturated liquid and saturated vapor become identical.
The molar volume at the critical temperature and pressure is called the critical molar volume.
The good news is that the critical temperature and pressure can be found in almost any chemical reference source.
We will use the NIST website as our resource for almost ALL physical property and thermochemical data. This is the kind of stuff that ordinarily appears at the end of a textbook, but the NIST website holds more information than any textbook ever could. In the next chapter, you will learn all about how to use the NIST website to quickly find and retrieve tons of useful data.
OK, but the bad news is that the critical molar volume is seldom tabulated. It is tabulated on the NIST website, but in general, it isn’t available.
So, instead, the volume of a hypothetical ideal gas existing at the critical temperature and pressure is used.
Solving the ideal gas EOS for the molar volume gives us the nice simple formula, shown here, for calculating the ideal critical molar volume.
OK, now we need to figure out how we are going to USE these properties of the critical state to obtain a good estimate of the real molar volume at some other temperature and pressure.
Flip the page and you’ll see how we are going to do it.

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