Poynting factor

The Poynting factor (also: Poynting correction ) describes a quantity from chemical thermodynamics and can be understood as the correction of the standard pressure on the pressure of the mixture. ${\displaystyle \Pi _{0i}}$

definition

The Poynting factor results as an exponential term :

${\displaystyle \Pi _{0i}=\exp \left({\frac {1}{RT}}\int _{p_{0i}^{LV}}^{p}v_{0i}^{L}\,dp\right)}$

With

• universal gas constant  R
• absolute temperature  T
• Vapor pressure of the pure substance  i (index for liquid vapor ) ${\displaystyle p_{0i}^{LV}}$ ${\displaystyle ^{LV}}$
• System pressure p
• molar volume of the pure substance i in the liquid phase (index for liquid ). ${\displaystyle v_{0i}^{L}}$ ${\displaystyle ^{L}}$

If the distance from the critical point is sufficient , the equation can be written as follows:

${\displaystyle \Pi _{0i}=\exp \left({\frac {v_{0i}^{L}(p-p_{0i}^{LV})}{RT}}\right)}$

A rule of thumb states that the Poynting correction can be neglected if the difference between system pressure and steam pressure is less than 10 bar:

${\displaystyle p-p_{0i}^{LV}\leq 10\,\mathrm {bar} \Rightarrow \Pi _{0i}\approx 1}$

Poynting factor for the liquid phase

The fugacity of a pure, real substance i in the liquid phase is given by: ${\displaystyle f_{0i}^{L}}$

${\displaystyle f_{0i}^{L}=\varphi _{0i}^{LV}\cdot p_{0i}^{LV}\cdot \Pi _{0i}}$

With

• Fugacity coefficient of the pure liquid phase, consisting of substance i, based on the vapor pressure. ${\displaystyle \varphi _{0i}^{LV}}$

Using the isofugacity criterion, equating the fugacity of a component in the gas phase with its fugacity in the liquid phase, a phase equilibrium relationship can be established that must be fulfilled for every component of a system in phase equilibrium:

${\displaystyle y_{i}\cdot \varphi _{i}\cdot p=x_{i}\cdot \varphi _{0i}^{LV}\cdot p_{0i}^{LV}\cdot \Pi _{0i}\cdot \gamma _{i}}$

With

• Molar fraction of component i in the gas phase ${\displaystyle y_{i}}$
• Fugacity coefficient of component i in the gas phase ${\displaystyle \varphi _{i}}$
• Molar fraction of component i in the liquid phase ${\displaystyle x_{i}}$
• Activity coefficient of the component i. ${\displaystyle \gamma _{i}}$

Poynting factor for the solid phase

Analogous to the liquid phase, a Poynting factor can also be defined for the solid phase. This takes into account the influence on the fugacity of the component in the solid as a result of the deviation of the system pressure from the saturation pressure .

Individual evidence

1. ↑ ^{a b} Dorothea Lüdecke, Christa Lüdecke: Thermodynamics: Physico-chemical basics of thermal process engineering , 2000, ISBN 3-540-66805-5 .
2. ^ John M. Prausnitz, Rüdiger N. Lichtenthaler, Edmundo Gomes de Azevedo: Molecular Thermodynamics of Fluid-Phase Equilibria - Third Edition , New Jersey, 1999, ISBN 0-13-977745-8 .
3. ↑ Ralf Dohrn: Calculation of phase equilibria , Braunschweig / Wiesbaden, 1994, ISBN 3-528-06587-7 .