Redlich-Kwong equation of state: Difference between revisions
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A modification of the the Redlich-Kwong equation of state was presented by Giorgio Soave in order to allow better representation of non-spherical molecules<ref>[http://dx.doi.org/10.1016/0009-2509(72)80096-4 Giorgio Soave "Equilibrium constants from a modified Redlich-Kwong equation of state", Chemical Engineering Science '''27''' pp. 1197-1203 (1972)]</ref>. In order to do this, the square root temperature dependence was replaced with a temperature dependent acentricity factor: | A modification of the the Redlich-Kwong equation of state was presented by Giorgio Soave in order to allow better representation of non-spherical molecules<ref>[http://dx.doi.org/10.1016/0009-2509(72)80096-4 Giorgio Soave "Equilibrium constants from a modified Redlich-Kwong equation of state", Chemical Engineering Science '''27''' pp. 1197-1203 (1972)]</ref>. In order to do this, the square root temperature dependence was replaced with a temperature dependent acentricity factor: | ||
:<math>\alpha=\left(1+\left(0.48508+1.55171\omega-0.15613\omega^2\right)\left(1-\sqrt\frac{T}{T_c}\right)\right)^2 </math> | :<math>\alpha(T)=\left(1+\left(0.48508+1.55171\omega-0.15613\omega^2\right)\left(1-\sqrt\frac{T}{T_c}\right)\right)^2 </math> | ||
where <math>T_c</math> is the critical temperature and <math>\omega</math> is the acentric factor for the gas. This leads to an equation of state of the form: | where <math>T_c</math> is the critical temperature and <math>\omega</math> is the acentric factor for the gas. This leads to an equation of state of the form: | ||
:<math> \left[p+\frac{a\alpha}{v(v+b)}\right]\left(v-b\right)=RT</math> | :<math> \left[p+\frac{a\alpha(T)}{v(v+b)}\right]\left(v-b\right)=RT</math> | ||
or equivalently: | or equivalently: | ||
:<math> p=\frac{RT}{v-b}-\frac{a\alpha}{v(v+b)}</math> | :<math> p=\frac{RT}{v-b}-\frac{a\alpha(T)}{v(v+b)}</math> | ||
Revision as of 03:59, 7 November 2011
The Redlich-Kwong equation of state is[1]:
- 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{a}{T^{1/2}v(v+b)} \right] (v-b) = RT}
where
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= 0.0867 \frac{RT_c}{P_c}}
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 p} is the pressure, 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 T} is the temperature 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 R} is the molar gas constant. 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 T_c} is the critical temperature 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 P_c} is the pressure at the critical point.
Soave Modification
A modification of the the Redlich-Kwong equation of state was presented by Giorgio Soave in order to allow better representation of non-spherical molecules[2]. In order to do this, the square root temperature dependence was replaced with a temperature dependent acentricity factor:
- 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 \alpha(T)=\left(1+\left(0.48508+1.55171\omega-0.15613\omega^2\right)\left(1-\sqrt\frac{T}{T_c}\right)\right)^2 }
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 T_c} is the critical temperature 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 \omega} is the acentric factor for the gas. This leads to an equation of state of the form:
- 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{a\alpha(T)}{v(v+b)}\right]\left(v-b\right)=RT}
or equivalently:
- 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 p=\frac{RT}{v-b}-\frac{a\alpha(T)}{v(v+b)}}
References
- ↑ Otto Redlich and J. N. S. Kwong "On the Thermodynamics of Solutions. V. An Equation of State. Fugacities of Gaseous Solutions", Chemical Reviews 44 pp. 233 - 244 (1949)
- ↑ Giorgio Soave "Equilibrium constants from a modified Redlich-Kwong equation of state", Chemical Engineering Science 27 pp. 1197-1203 (1972)