# Acentric factor

The acentric factor ω is a conceptual number introduced by Kenneth Pitzer in 1955, proven to be very useful in the description of matter.[1] 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.[2] As it increases, the vapor curve is "pulled" down, resulting in higher boiling points.

It is defined as:

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

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

For many monatomic fluids

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

is close to 0.1, therefore ${\displaystyle \omega \to 0}$. In many cases, ${\displaystyle T_{r}=0.7}$ 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. ${\displaystyle \omega }$ is very close to zero for other spherical molecules.[2] 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[3] Acetone 0.304[4] Acetylene 0.187 Ammonia 0.253 Argon 0.000 Carbon Dioxide 0.228 Decane 0.484 Ethanol 0.644[4] Helium -0.390 Hydrogen -0.220 Krypton 0.000 Methanol 0.556[4] Neon 0.000 Nitrogen 0.040 Nitrous Oxide 0.142 Oxygen 0.022 Xenon 0.000

## References

1. Adewumi, Michael. "Acentric Factor and Corresponding States". Pennsylvania State University. Retrieved 2013-11-06.
2. 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.
3. Yaws, Carl L. (2001). Matheson Gas Data Book. McGraw-Hill.
4. 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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