Redlich-Kwong equation of state: Difference between revisions
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The Redlich-Kwong equation of state is<ref>[http://dx.doi.org/10.1021/cr60137a013 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)]</ref>: | The '''Redlich-Kwong equation of state''' is <ref>[http://dx.doi.org/10.1021/cr60137a013 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)]</ref>: | ||
:<math>\left[ p + \frac{a}{T^{1/2}v(v+b)} \right] (v-b) = RT</math> | :<math>\left[ p + \frac{a}{T^{1/2}v(v+b)} \right] (v-b) = RT</math>. | ||
The Redlich-Kwong equation of state has a critical point [[compressibility factor]] of <ref>[http://dx.doi.org/10.1021/ed062p110 Reino. W. Hakala "The value of the critical compressibility factor for the Redlich-Kwong equation of state of gases", Journal of Chemical Education '''62''' pp. 110-111 (1985)]</ref>: | |||
:<math>a= 0. | :<math>Z_c = \frac{p_c v_c}{RT_c}= \frac{1}{3} </math> | ||
leading to | |||
:<math>a = \frac{1}{9(2^{1/3}-1)} \frac{R^2T_c^{5/2}}{p_c} \approx 0.4274802336 \frac{R^2T_c^{5/2}}{p_c}</math> | |||
and | and | ||
:<math>b= 0. | :<math>b = \frac{(2^{1/3}-1)}{3} \frac{RT_c}{p_c} \approx 0.08664034995 \frac{RT_c}{p_c}</math> | ||
where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points | critical]] temperature and <math>P_c</math> is the pressure at the critical point. | where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points | critical]] temperature and <math>P_c</math> is the pressure at the critical point. | ||
==Soave Modification== | ==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<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 | 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 [[Law of corresponding states#Acentric factor | acentric factor]] (<math>\omega</math>): | ||
:<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 | where <math>T_c</math> is the critical temperature. 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> | ||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: equations of state]] | [[category: equations of state]] | ||
Latest revision as of 17:14, 7 November 2011
The Redlich-Kwong equation of state is [1]:
- .
=RT}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ada21aa6800f063a969940dd07f3ecd090c50f65)
The Redlich-Kwong equation of state has a critical point compressibility factor of [2]:
leading to
and
where is the pressure, is the temperature and is the molar gas constant. is the critical temperature and is the pressure at the critical point.
Soave Modification[edit]
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[3]. In order to do this, the square root temperature dependence was replaced with a temperature dependent acentric factor ():
where is the critical temperature. This leads to an equation of state of the form:
![{\displaystyle \left[p+{\frac {a\alpha (T)}{v(v+b)}}\right]\left(v-b\right)=RT}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ce50e4604ea8c62c8977f802ae245798b53e936d)
or equivalently:
References[edit]
- ↑ 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)
- ↑ Reino. W. Hakala "The value of the critical compressibility factor for the Redlich-Kwong equation of state of gases", Journal of Chemical Education 62 pp. 110-111 (1985)
- ↑ Giorgio Soave "Equilibrium constants from a modified Redlich-Kwong equation of state", Chemical Engineering Science 27 pp. 1197-1203 (1972)