Mixing rules: Difference between revisions
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'''Mixing rules''' | '''Mixing rules''' | ||
==van der Waals mixing rules== | ==van der Waals mixing rules== | ||
The [[van der Waals equation of state]] can be written as | |||
:<math>\left(p + \frac{an^2}{V^2}\right)\left(V-nb\right) = nRT</math> | |||
For mixtures one replaces <math>a</math> and <math>b</math> with expressions that depend on the composition: | |||
:<math>a \rightarrow \sum_i^n \sum_j^n x_i x_j a_{ij}</math> | |||
and | |||
:<math>b \rightarrow \sum_i^n \sum_j^n x_i x_j b_{ij}</math> | |||
where | |||
:<math>a_{ij} = (1-k_{ij}) \sqrt{(a_{ii} a_{jj})} ~~~~~~~~ i\neq j</math> | |||
and | |||
:<math>b_{ij} = \frac{(b_{ii} b_{jj})}{2} ~~~~~~~~ i\neq j</math> | |||
where <math>k_{ij}</math> is obtained from a fit. | |||
See also <ref>[http://dx.doi.org/10.1039/TF9696502034 T. W. Leland, J. S. Rowlinson, G. A. Sather and I. D. Watson "Statistical thermodynamics of two-fluid models of mixtures", Transactions of the Faraday Society '''65''' pp. 2034-2043 (1969)]</ref> | |||
==References== | ==References== | ||
<references/> | <references/> | ||
;Related reading | |||
*[http://dx.doi.org/10.1016/0009-2509(86)87103-2 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)] | |||
*[http://dx.doi.org/10.1016/0378-3812(93)85079-2 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)] | |||
[[category: classical thermodynamics]] | [[category: classical thermodynamics]] | ||
[[category: mixtures]] | [[category: mixtures]] | ||
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Mixing rules
van der Waals mixing rules
The van der Waals equation of state can be written as
- 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 \left(p + \frac{an^2}{V^2}\right)\left(V-nb\right) = nRT}
For mixtures one replaces 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} 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} with expressions that depend on the composition:
- 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 \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 [1]
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)