# Acentric factor

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Measure of the non-sphericity of molecules

The **acentric factor** ω is a conceptual number introduced by [Kenneth Pitzer](/source/Kenneth_Pitzer) in 1955, proven to be useful in the description of [fluids](/source/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](/source/Molecular_weight), [critical temperature](/source/Critical_temperature), [critical pressure](/source/Critical_pressure), and [critical volume](/source/Critical_point_(thermodynamics)) (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

- ω = − log 10 ⁡ ( p r sat ) − 1 at T r = 0.7 , {\displaystyle \omega =-\log _{10}(p_{\text{r}}^{\text{sat}})-1{\text{ at }}T_{\text{r}}=0.7,}

where p r sat = p sat / p c {\displaystyle p_{\text{r}}^{\text{sat}}=p^{\text{sat}}/p_{c}} is the [reduced saturation vapor pressure](/source/Reduced_pressure), and T r = T / T c {\displaystyle T_{\text{r}}=T/T_{c}} is the [reduced temperature](/source/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](/source/Clausius%E2%80%93Clapeyron_relation).

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](/source/Vapor_pressure) and the reciprocal of [absolute temperature](/source/Absolute_temperature) is approximately linear.[1]

For a series of fluids, as the acentric factor increases the [vapor curve](/source/Vapor_pressure) is "pulled" down, resulting in higher [boiling points](/source/Boiling_point). For many monatomic fluids, p r sat ≈ 0.1 {\displaystyle p_{\text{r}}^{\text{sat}}\approx 0.1} at T r = 0.7 , {\displaystyle T_{\text{r}}=0.7,} which leads to ω → 0 {\displaystyle \omega \to 0} . In many cases, T r = 0.7 {\displaystyle T_{\text{r}}=0.7} lies above the [boiling temperature](/source/Normal_boiling_point) 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](/source/Noble_gas) [argon](/source/Argon), [krypton](/source/Krypton), and [xenon](/source/Xenon). ω {\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](/source/Critical_pressure) and are non-physical.

The acentric factor can be predicted analytically from some [equations of state](/source/Equations_of_state). For example, it can be easily shown from the above definition that a [van der Waals fluid](/source/Van_der_Waals_equation) 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](/source/Equation_of_state)

- [Reduced pressure](/source/Reduced_properties#Reduced_pressure)

- [Reduced temperature](/source/Reduced_properties#Reduced_temperature)

## References

1. ^ [***a***](#cite_ref-:0_1-0) [***b***](#cite_ref-:0_1-1) Adewumi, Michael. ["Acentric Factor and Corresponding States"](https://www.e-education.psu.edu/png520/m8_p3.html). Pennsylvania State University. Retrieved 2013-11-06.

1. ^ [***a***](#cite_ref-thermopedia_2-0) [***b***](#cite_ref-thermopedia_2-1) Saville, G. (2006). "ACENTRIC FACTOR". *A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering*. [doi](/source/Doi_(identifier)):[10.1615/AtoZ.a.acentric_factor](https://doi.org/10.1615%2FAtoZ.a.acentric_factor).

1. **[^](#cite_ref-3)** ["Acentric Factor Calculator"](https://www.calculatoratoz.com/en/acentric-factor-calculator/Calc-29475). *www.calculatoratoz.com*. Retrieved 2024-05-17.

1. **[^](#cite_ref-4)** Shamsundar, N.; Lienhard, J. H. (December 1983). ["Saturation and metastable properties of the van der waals fluid"](https://onlinelibrary.wiley.com/doi/pdf/10.1002/cjce.5450610617). *Canadian Journal of Chemical Engineering*. **61** (6): 876–880. [doi](/source/Doi_(identifier)):[10.1002/cjce.5450610617](https://doi.org/10.1002%2Fcjce.5450610617). Retrieved 10 August 2022.

1. **[^](#cite_ref-5)** Yaws, Carl L. (2001). *Matheson Gas Data Book*. McGraw-Hill.

1. ^ [***a***](#cite_ref-pgas4e_6-0) [***b***](#cite_ref-pgas4e_6-1) [***c***](#cite_ref-pgas4e_6-2) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. (1987). *The Properties of Gases and Liquids* (4th ed.). McGraw-Hill. [ISBN](/source/ISBN_(identifier)) [0070517991](https://en.wikipedia.org/wiki/Special:BookSources/0070517991).

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