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
For mixtures one replaces 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)