Acentric factor

The acentric factor ω is a conceptual number introduced by Kenneth Pitzer in 1955, proven to be useful in the description of fluids.^[1] It has become a standard for the phase characterization of single and pure components, along with other state description parameters such as molecular weight, critical temperature, critical pressure, and critical volume (or critical compressibility). The acentric factor is also said to be a measure of the non-sphericity (centricity) of molecules.^[2]

Pitzer defined ω from the relationship

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

where ${\displaystyle p_{\text{r}}^{\text{sat}}=p^{\text{sat}}/p_{c}}$ is the reduced saturation vapor pressure, and ${\displaystyle T_{\text{r}}=T/T_{c}}$ is the reduced temperature.^[3]

Pitzer developed this factor by studying the vapor-pressure curves of various pure substances. Thermodynamically, the vapor-pressure curve for pure components can be mathematically described using the Clausius–Clapeyron equation.

The integrated form of equation is mainly used for obtaining vapor-pressure data mathematically. This integrated version shows that the relationship between the logarithm of vapor pressure and the reciprocal of absolute temperature is approximately linear.^[1]

For a series of fluids, as the acentric factor increases the vapor curve is "pulled" down, resulting in higher boiling points. For many monatomic fluids, ${\displaystyle p_{\text{r}}^{\text{sat}}\approx 0.1}$ at ${\displaystyle T_{\text{r}}=0.7,}$ which leads to ${\displaystyle \omega \to 0}$. In many cases, ${\displaystyle T_{\text{r}}=0.7}$ 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. The definition of ω gives values close to zero for the noble gases argon, krypton, and xenon. ${\displaystyle \omega }$ is also very close to zero for molecules which are nearly spherical.^[2] Values of ω ≤ −1 correspond to vapor pressures above the critical pressure and are non-physical.

The acentric factor can be predicted analytically from some equations of state. For example, it can be easily shown from the above definition that a van der Waals fluid has an acentric factor of about −0.302024, which if applied to a real system would indicate a small, ultra-spherical molecule.^[4]

Values of some common gases

Molecule	Acentric factor[5]
Acetone	−0.304[6]
Acetylene	−0.187
Ammonia	−0.253
Argon	−0.000
Carbon dioxide	−0.228
Decane	−0.484
Ethanol	−0.644[6]
Helium	−0.390
Hydrogen	−0.220
Krypton	−0.000
Methanol	−0.556[6]
Neon	−0.000
Nitrogen	−0.040
Nitrous oxide	−0.142
Oxygen	−0.022
Xenon	−0.000

See also

• Equation of state
• Reduced pressure
• Reduced temperature

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. "Acentric Factor Calculator". www.calculatoratoz.com. Retrieved 2024-05-17.
4. Shamsundar, N.; Lienhard, J. H. (December 1983). "Saturation and metastable properties of the van der waals fluid". Canadian Journal of Chemical Engineering. 61 (6): 876–880. doi:10.1002/cjce.5450610617. Retrieved 10 August 2022.
5. Yaws, Carl L. (2001). Matheson Gas Data Book. McGraw-Hill.
6. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. (1987). The Properties of Gases and Liquids (4th ed.). McGraw-Hill. ISBN 0070517991.