Acentric factor

The acentric factor $\omega$ is a conceptual number introduced by 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.The a-centric factor is said to be a measure of the non-sphericity (centricity) of molecules.

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 pressure saturation of vapors.

For many monoatomic, fluids

$p_{r}^{\rm {sat}}$ at T_r = 0.7,

is close to 0.1, therefore $\omega \to 0$. In many cases, $T_{r}=0.7$ lies abovew 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 $T_{r}=0.7K$, and for many liquid state matteris tabulated into many thermodynamical tables.

The definition of $\omega$ gives zero-value for the noble gases argon, krypton, and xenon. 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.

See also

• Equation of state
• Reduced pressure
• Reduced temperature