Editing Redlich-Kwong equation of state

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>.

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>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 

:<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.

==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>):

:<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.  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>

or equivalently:

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

==References==
<references/>
[[category: equations of state]]