Mixing rules

Mixing rules (see also Combining rules).

van der Waals mixing rules

The van der Waals equation of state can be written as

$\left(p+{\frac {an^{2}}{V^{2}}}\right)\left(V-nb\right)=nRT$

For mixtures one replaces $a$ and $b$ with expressions that depend on the composition:

$a\rightarrow \sum _{i}^{n}\sum _{j}^{n}x_{i}x_{j}a_{ij}$

and

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b \rightarrow \sum_i^n \sum_j^n x_i x_j b_{ij}}

where

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{ij} = (1-k_{ij}) \sqrt{(a_{ii} a_{jj})} ~~~~~~~~ i\neq j}

and

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_{ij} = \frac{(b_{ii} b_{jj})}{2} ~~~~~~~~ i\neq j}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_{ij}} is obtained from a fit.

See also

References

Related reading

• T. Y. Kwak and G. A. Mansoori "Van der waals mixing rules for cubic equations of state. Applications for supercritical fluid extraction modelling", Chemical Engineering Science 41 pp. 1303-1309 (1986)
• Kenneth R. Hall, Gustavo A. Iglesias-Silva, and G. Ali Mansoori "Quadratic mixing rules for equations of state: Origins and relationships to the virial expansion", Fluid Phase Equilibria 91 pp. 67-76 (1993)