# 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 pressure saturation of vapors.

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 gases at atmosphere pressure.

Values of $\omega$ can be determined for any fluid from $\{T_r, p_r\}$, and a vapor measurement from $T_r = 0.7$, and for many liquid state matter is tabulated into many thermodynamical tables.

The definition of $\omega$ gives zero-value for the noble gases argon, krypton, and xenon. $\omega$ is almost exactly zero for other spherical molecules.[2] Experimental data yields compressibility factors for all fluids that are correlated by the same curves when $Z$ (compressibility factor) is represented as a function of $T_r$ and $p_r$. This is the basis premises of three-parameter theorem of corresponding states:

All fluids at any $\omega$-value, in $\{T_r, p_r\}=const.$ conditions, have about the same $Z$-value, and same degree of convergence.[citation needed][dubious ]

## 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