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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>:
| | :<math>\left[ P + \frac{a}{T^{1/2}v(v+b)} \right] (v-b) = RT</math> |
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| :<math>\left[ p + \frac{a}{T^{1/2}v(v+b)} \right] (v-b) = RT</math>.
| | where |
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| 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= 0.4278 \frac{R^2T_c^{2.5}}{P_c}</math> |
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| :<math>Z_c = \frac{p_c v_c}{RT_c}= \frac{1}{3} </math>
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| leading to
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| :<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> | |
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| and | | and |
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| :<math>b = \frac{(2^{1/3}-1)}{3} \frac{RT_c}{p_c} \approx 0.08664034995 \frac{RT_c}{p_c}</math> | | :<math>b= 0.0867 \frac{RT_c}{P_c}</math> |
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| 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.
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| ==Soave Modification==
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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 [[Law of corresponding states#Acentric factor | acentric factor]] (<math>\omega</math>):
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| :<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>
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| where <math>T_c</math> is the critical temperature. This leads to an equation of state of the form:
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| :<math> \left[p+\frac{a\alpha(T)}{v(v+b)}\right]\left(v-b\right)=RT</math>
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| or equivalently:
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| :<math> p=\frac{RT}{v-b}-\frac{a\alpha(T)}{v(v+b)}</math>
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| ==References== | | ==References== |
| <references/>
| | #[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)] |
| [[category: equations of state]] | | [[category: equations of state]] |