# Acentric factor

The acentric factor ${\displaystyle \omega }$ 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:

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

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 ${\displaystyle \omega }$ 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 ${\displaystyle \omega }$ gives a zero-value for the noble gases argon, krypton, and xenon. ${\displaystyle \omega }$ 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