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:

\[\omega = - \log_{10} (p^{\rm{sat}}_r) - 1, {\rm \ at \ } T_r = 0.7\].

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 monoatomic, 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. 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]}

See also

• Equation of state
• Reduced pressure
• Reduced temperature