Acentric factor

The acentric factor $\omega$ 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:

$\omega = - \log_{10} (p^{\rm{sat}}_r) - 1, {\rm \ at \ } T_r = 0.7$.

where $T_r = \frac{T}{T_c}$ is the reduced temperature, $p^{\rm{sat}}_r = \frac{p^{\rm{sat}}}{p_c}$ 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 $\omega$ can be determined for any fluid from accurate experimental vapor pressure data. Preferably, these data should first be regressed against a reliable vapor pressure equation such as the following:

ln(P) = A + B/T +C*ln(T) + D*T^6

(This equation fits vapor pressure over a very wide range of temperature for most components, but is by no means the only one that should be considered.) 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. The vapor pressure at Tr=0.7 can then be used in the defining equation, above, to estimate acentric factor.

Then, using the known critical temperature, Tc, find the temperature at Tr = 0.7. At this temperature, calculate the vapor pressure, Psat, from the regressed equation.

The definition of $\omega$ gives a zero-value for the noble gases argon, krypton, and xenon. $\omega$ is very close to zero for other spherical molecules.^[2]

Values of some common gases

Molecule	Acentric Factor[3]
Acetylene	0.187
Ammonia	0.253
Argon	0.000
Carbon Dioxide	0.228
Decane	0.484
Helium	-0.390
Hydrogen	-0.220
Krypton	0.000
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. Yaws, Carl L. (2001). Matheson Gas Data Book. McGraw-Hill.