Redlich-Kwong equation of state - Revision history

Carl McBride: /* Soave Modification */ Fixed the link

2011-11-07T16:14:44Z

Soave Modification: Fixed the link

← Older revision		Revision as of 18:14, 7 November 2011
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	==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 [[Law of corresponding states#~~acentric~~ factor \| acentric factor]] (<math>\omega</math>):		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(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>		:<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>

Carl McBride: /* Soave Modification */ Added an internal link to the acentric factor

2011-11-07T16:13:55Z

Soave Modification: Added an internal link to the acentric factor

← Older revision		Revision as of 18:13, 7 November 2011
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	==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 ~~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 [[Law of corresponding states#acentric factor \| acentric factor]] (<math>\omega</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>		:<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. This leads to an equation of state of the form:

	:<math> \left[p+\frac{a\alpha(T)}{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>
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	:<math> p=\frac{RT}{v-b}-\frac{a\alpha(T)}{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]]

Carl McBride: Corrected pre-factor for b

2011-11-07T16:09:40Z

Corrected pre-factor for b

← Older revision		Revision as of 18:09, 7 November 2011
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	and		and

	:<math>b = \frac{9(2^{1/3}-1)}{3} \frac{RT_c}{p_c} \approx 0.08664034995 \frac{RT_c}{p_c}</math>		:<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.

Carl McBride: Added critical point compressibility factor

2011-11-07T16:07:04Z

Added critical point compressibility factor

← Older revision		Revision as of 18:07, 7 November 2011
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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>.

	~~where~~		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>		:<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.~~0867~~ \frac{RT_c}{~~P_c~~}</math>		:<math>b = \frac{9(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.

Josephrpeterson at 02:59, 7 November 2011

2011-11-07T02:59:40Z

← Older revision		Revision as of 04:59, 7 November 2011
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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>

Josephrpeterson at 02:57, 7 November 2011

2011-11-07T02:57:53Z

@@ Line 1: / Line 1: @@
 :<math>\left[ p + \frac{a}{T^{1/2}v(v+b)} \right] (v-b) = RT</math>
@@ Line 10: / Line 12: @@
 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.
 ==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)]
+<references/>
 [[category: equations of state]]

Nice and Tidy at 16:32, 6 February 2008

2008-02-06T16:32:28Z

← Older revision		Revision as of 18:32, 6 February 2008
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	:<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>

	where		where
Line 8:		Line 8:

	:<math>b= 0.0867 \frac{RT_c}{P_c}</math>		:<math>b= 0.0867 \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.
	==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)]		#[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)]
	#[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)]		#[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)]
	[[category: equations of state]]		[[category: equations of state]]

Carl McBride: /* References */

2007-10-31T12:13:08Z

References

← Older revision		Revision as of 14:13, 31 October 2007
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	==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)]		#[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)]
			#[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)]
	[[category: equations of state]]		[[category: equations of state]]

Carl McBride: New page: : $\left[ P + \frac{a}{T^{1/2}v(v+b)} \right] (v-b) = RT$ where : $a= 0.4278 \frac{R^2T_c^{2.5}}{P_c}$ and : $b= 0.0867 \frac{RT_c}{P_c}$ ==References== ...

2007-06-08T11:10:26Z

New page: :<math>\left[ P + \frac{a}{T^{1/2}v(v+b)} \right] (v-b) = RT</math> where :<math>a= 0.4278 \frac{R^2T_c^{2.5}}{P_c}</math> and :<math>b= 0.0867 \frac{RT_c}{P_c}</math> ==References== ...

New page

:<math>\left[ P + \frac{a}{T^{1/2}v(v+b)} \right] (v-b) = RT</math>

where

:<math>a= 0.4278 \frac{R^2T_c^{2.5}}{P_c}</math>

and

:<math>b= 0.0867 \frac{RT_c}{P_c}</math>
==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]]