Redlich-Kwong equation of state

Critical isotherm ( T _r  = 1) according to the Redlich-Kwong model, compared to Van der Waals gas and ideal gas

The Redlich-Kwong equation of state is an equation of state for real gases that was found in 1949 by Otto Redlich and Joseph Neng Shun Kwong . It improves the Van der Waals equation only marginally, but is still of interest today due to its comparatively simple form.

Further developments are the Soave-Redlich-Kwong equation of state and the PSRK equation of state .

formulation

The Redlich-Kwong equation of state reads:

${\displaystyle {\begin{aligned}RT&=\left(p+{\frac {a}{{\sqrt {T}}V_{\mathrm {m} }(V_{\mathrm {m} }+b)}}\right)\cdot \left(V_{\mathrm {m} }-b\right)\\\Leftrightarrow p&={\frac {RT}{V_{\mathrm {m} }-b}}-{\frac {a}{{\sqrt {T}}V_{\mathrm {m} }\left(V_{\mathrm {m} }+b\right)}}\end{aligned}}}$

With

• Cohesive pressure ${\displaystyle a={\frac {0{,}42748R^{2}T_{\mathrm {c} }^{2{,}5}}{p_{\mathrm {c} }}}}$
• Co-volume ${\displaystyle b={\frac {0{,}08664RT_{\mathrm {c} }}{p_{\mathrm {c} }}}}$
• ${\displaystyle V_{\mathrm {m} }}$- molar volume
• ${\displaystyle T}$- temperature
• ${\displaystyle T_{\mathrm {c} }}$- critical temperature
• ${\displaystyle p}$- pressure
• ${\displaystyle p_{\mathrm {c} }}$- critical pressure
• ${\displaystyle R}$- universal gas constant .

With the reduced state variables , the equation of state can be written in the reduced form : ${\displaystyle \textstyle \ p_{\mathrm {r} }={\frac {p}{p_{\text{c}}}}\ ,\ V_{\mathrm {r} }={\frac {V_{\text{m}}}{V_{\text{m,c}}}}\ ,\ T_{\mathrm {r} }={\frac {T}{T_{\text{c}}}}}$

${\displaystyle p_{\mathrm {r} }={\frac {3T_{\mathrm {r} }}{V_{\mathrm {r} }-b'}}-{\frac {1}{b'{\sqrt {T_{\mathrm {r} }}}V_{\mathrm {r} }\left(V_{\mathrm {r} }+b'\right)}}}$

with . ${\displaystyle b'={\sqrt[{3}]{2}}-1\approx 0{,}26}$

scope of application

The Redlich-Kwong equation is suitable for the calculation in gas phases if the ratio of pressure to critical pressure is less than half the ratio of temperature to critical temperature .:

${\displaystyle {\frac {p}{p_{\mathrm {c} }}}<0{,}5\cdot {\frac {T}{T_{\mathrm {c} }}}}$

Equivalent: the reduced pressure may be a maximum of half the size of the reduced temperature : ${\displaystyle T_{\mathrm {r} }}$

${\displaystyle \Leftrightarrow p_{\mathrm {r} }<0{,}5\cdot T_{\mathrm {r} }}$

A poor approximation is shown for liquid phases, which is why the equation cannot be used for gas-liquid equilibria . However, this disadvantage can be compensated for by using better fitted equations separately.

literature

• Otto Redlich , JNS Kwong: On the Thermodynamics of Solutions. V. An Equation of State. Fugacities of Gaseous Solutions. In: Chemical Reviews . tape 44 , no. 1 , 1949, p. 233-244 , doi : 10.1021 / cr60137a013 .