Equations oi State with Two Constants In a recent paper, Ott, Goates and Hall1 compared results from various two-constant (excluding R ) equations of state, including those of van der Waals, Berthelot, and Dieterici, to real gas behavior. They concluded that the van der Waals equation was superior hut inadequate. We wish to call your attention to an additional two-constant real gas model, the Redlich-Kwong2 equation. This equation of state is little more complex than the Berthelot equation, but is in relatively excellent agreement with real gas behavior except near the critical point. The equation, which is quite old (19491, is presented below
RT p = --V
-
b
-
a
PV(V
+ b)
a = 0.4278R2T,Z-5/P,
where:
b
=
0.0867RT,lPC
and where b also equals 0.264 V, resulting in a value for r,, the compressibility factor at the critical point, of 0.328. In reduced form the Redlich-Kwong equation becomes
where 1,r , and pare reduced pressure, temperature and volume, respectively, while the compressibility factor becomes
Note the similarity of the Redlich-Kwong equation to the Berthelot equation whieh suggests that "fine tuning" of the exponent on temperature in the second term might lead to further improvements. Additionally, several attempts have been made to modify the equation for better fit by the addition of coeffi~ients.~ For n-butane, Shah and Thodos4 found the Redlich-Kwong equation to he equal or superior to the Beattie-Bridgeman and Benediet-Webb, Rubin equations which have many more constants.
0.2 O
I
I
I'
2
I
1
I
REDUCED PRESSURE.
Figure 1. Comparison ol experimental values for z (bra-
imes) in the low pressure region with r values ealtulated from the Redlich-Kwong equation of state (solid ilnes) ken
1
1
I
6
II
Figure 2. Comparison of experimental values for r (braken lines) with z values calculated from the RedlichKwong equation of state (solid lines).
Figures I and ?compare the Hrdlich-Kwong gas to the real gas data of Reference ( 1 , . It is seen that there ir ex~.ellent agreement except in the critical region. The Redlich-Kwong gas is the bcsr two-constant real gas mudel knuwn to us.
' Ott, J. B., Goates, J. R., and Hall, H. T., Jr., J. CHEM. EDUC., 48,515 (i971). Redlich, O., and Kwang, J. N. S., Chem. Reu., 44,233 (1949). Redlich, 0..and Ngo, V. B. T., Ind. Eng. Chem. Fundom., 9.287 (1970). 'Shah, K. K., and Thodos, G., Ind. Eng. Chem., 57 (3),30 (1965). University of Tulsa Tulsa, Oklahoma 74104
802 / Journal of Chemical Education
Marwin K. Kemp Richard E. Thompson Dennis J. Zigrang
