### The acentric factor ω is a conceptual number introduced by Kenneth Pitzer in 1955, proven to be very useful in the description of matter. It has become a standard for the phase characterization of single & pure components. The other state description parameters are molecular weight, critical temperature, critical pressure, and critical volume (or critical compressibility). The acentric factor is said to be a measure of the non-sphericity (centricity) of molecules. As it increases, the vapor curve is "pulled" down, resulting in higher boiling points.

It is defined as:

$$\omega =-\log _{{10}}(p_{r}^{{{\rm {{sat}}}}})-1,{{\rm {\ at\ }}}T_{r}=0.7.$$

where $$T_r = \frac{T}{T_c}$$ is the reduced temperature, $$p_{r}^{{{\rm {{sat}}}}}={\frac {p^{{{\rm {{sat}}}}}}{p_{c}}}$$ is the reduced saturation vapor pressure.

For many monatomic fluids

$$p_{r}^{{{\rm {{sat}}}}}{{\rm {\ at\ }}}T_{r}=0.7,$$

is close to 0.1, therefore $$\omega \to 0$$. In many cases, $$T_{r}=0.7$$ lies above the boiling temperature of liquids at atmosphere pressure.

Values of ω can be determined for any fluid from accurate experimental vapor pressure data. Preferably, these data should first be regressed against a vapor pressure equation, like ln(P) = A + B/T +C*ln(T) + D*T^6. (In this regression, a careful check for erroneous vapor pressure measurements must be made, preferably using a log(P) vs. 1/T graph, and any obviously incorrect or dubious values should be discarded. The regression should then be re-run with the remaining good values until a good fit is obtained.) Using the known critical temperature, Tc, vapor pressure at Tr=0.7 can then be used in the defining equation, above, to estimate acentric factor.

The definition of ω gives essentially zero for the noble gases argon, krypton, and xenon. $$\omega$$ is very close to zero for other spherical molecules. Values of ω ≤ -1 correspond to vapor pressures above the critical pressure, and are non-physical.

By definition, a van der Waals fluid has a critical compressibility of 3/8 and an acentric factor of about −0.302024, indicating a small ultra-spherical molecule. A Redlich-Kwong fluid has a critical compressibility of 1/3 and an acentric factor of about 0.058280, close to nitrogen; without the temperature dependence of its attractive term, its acentric factor would be only -0.293572.
Values of some common gases
Molecule Acentric Factor
Acetone 0.304
Acetylene 0.187
Ammonia 0.253
Argon 0.000
Carbon Dioxide 0.228
Decane 0.484
Ethanol 0.644
Helium -0.390
Hydrogen -0.220
Krypton 0.000
Methanol 0.556
Neon 0.000
Nitrogen 0.040
Nitrous Oxide 0.142
Oxygen 0.022
Xenon 0.000

Equation of state
Reduced pressure
Reduced temperature

References

Adewumi, Michael. "Acentric Factor and Corresponding States". Pennsylvania State University. Retrieved 2013-11-06.
Saville, G. (2006). "ACENTRIC FACTOR". A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering. doi:10.1615/AtoZ.a.acentric_factor.
Yaws, Carl L. (2001). Matheson Gas Data Book. McGraw-Hill.
Reid, R.C.; Prausnitz, J.M.; Poling, B.E. The Properties of Gases and Liquids (4th ed.). McGraw-Hill. ISBN 0070517991.

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