PSRK

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PSRK

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← Previous revision Revision as of 23:06, 19 April 2026
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: \alpha(T_r) = \left[1 + c_1 \left(1 - \sqrt{T_r}\right) + c_2 \left(1 - \sqrt{T_r}\right)^2 + c_3 \left(1 - \sqrt{T_r}\right)^3 \right]^2.
: \alpha(T_r) = \left[1 + c_1 \left(1 - \sqrt{T_r}\right) + c_2 \left(1 - \sqrt{T_r}\right)^2 + c_3 \left(1 - \sqrt{T_r}\right)^3 \right]^2.


The parameters of the Mathias–Copeman equation are fitted to experimental vapor-pressure data of pure components and provide a better description of the vapor pressure than the original relation. The form of the equation is chosen as it can be reduced to the original Soave form by setting the parameters ''c''2 and ''c''3 to zero. Additionally, the parameter ''c''1 can be obtained from the [[acentric factor]], using the relation
The parameters of the Mathias–Copeman equation are fitted to experimental vapor-pressure data of pure components and provide a better description of the [[vapor pressure]] than the original relation. The form of the equation is chosen as it can be reduced to the original Soave form by setting the parameters ''c''2 and ''c''3 to zero. Additionally, the parameter ''c''1 can be obtained from the [[acentric factor]], using the relation


: c_1 = 0.48 + 1.574 \, \omega - 0.176 \, \omega^2.
: c_1 = 0.48 + 1.574 \, \omega - 0.176 \, \omega^2.
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[[Image:PSRK VLE Prediction Cyclohexane and Carbon Dioxide.png|300px|thumb|Vapor–liquid equilibrium of [[cyclohexane]] and [[carbon dioxide]]]]
[[Image:PSRK VLE Prediction Cyclohexane and Carbon Dioxide.png|300px|thumb|Vapor–liquid equilibrium of [[cyclohexane]] and [[carbon dioxide]]]]


The prediction of a vapor–liquid equilibrium is successful even in mixtures containing supercritical components. However, the mixture has to be subcritical. In the given example carbon dioxide is the supercritical component with ''T''c = 304.19 KAmbrose D., Trans. Faraday Soc., 52, 772-781, 1956. {{ISSN|0014-7672}}, {{doi|10.1039/TF9565200772}}. and ''P''c = 7475 kPa.Schmidt E., Thomas W., Forsch. Geb. Ingenieurwes. Ausg. A, 20, 161–170, 1954. The critical point of the mixture lies at ''T'' = 411 K and ''P'' ≈ 15000 kPa. The composition of the mixture is near 78 mole% carbon dioxide and 22 mole% cyclohexane.
The prediction of a [[vapor–liquid equilibrium]] is successful even in mixtures containing supercritical components. However, the mixture has to be subcritical. In the given example carbon dioxide is the supercritical component with ''T''c = 304.19 KAmbrose D., Trans. Faraday Soc., 52, 772-781, 1956. {{ISSN|0014-7672}}, {{doi|10.1039/TF9565200772}}. and ''P''c = 7475 kPa.Schmidt E., Thomas W., Forsch. Geb. Ingenieurwes. Ausg. A, 20, 161–170, 1954. The critical point of the mixture lies at ''T'' = 411 K and ''P'' ≈ 15000 kPa. The composition of the mixture is near 78 mole% carbon dioxide and 22 mole% cyclohexane.


PSRK describes this binary mixture quite well, the [[dew point]] curve, as well as the [[bubble point]] curve and the critical point of the mixture.
PSRK describes this binary mixture quite well, the [[dew point]] curve, as well as the [[bubble point]] curve and the critical point of the mixture.
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