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 & pure components, along with other state description parameters such as molecular weight, critical temperature, critical pressure, and critical volume (or critical compressibility).

Pitzer defined ω from the relationship

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

where ${\displaystyle p_{r}^{\rm {sat}}={\frac {p^{\rm {sat}}}{p_{c}}}}$ is the reduced saturation vapor pressure and ${\displaystyle T_{r}={\frac {T}{T_{c}}}}$ is the reduced temperature.

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. For many monatomic fluids, ${\displaystyle p_{r}^{\rm {sat}}{\rm {\ at\ }}T_{r}=0.7}$ is close to 0.1, which leads to ${\displaystyle \omega \to 0}$. In many cases, ${\displaystyle T_{r}=0.7}$ 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 which are 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.[3]