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. 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 $\omega$ 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.

By definition, a van der Waals fluid has a critical compressibility of 3/8 and an acentric factor of about −0.302024, indicating a large spherical molecule.

Values of some common gases

Molecule	Acentric Factor
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