Ind. Eng. Chem. Res. 2007, 46, 6375
6375
CORRESPONDENCE Comments on “The Second Virial Coefficient and the Redlich-Kwong Equation” Jianxiang Tian*,†,‡ and Yuanxing Gui‡ Department of Physics, Department of Applied Mathematics, Dalian UniVersity of Technology, Dalian 116024, People’s Republic of China, and Department of Physics, Qufu Normal UniVersity, Qufu 273165, People’s Republic of China Sir: Mathias recently proposed a two-parameter corresponding-states correlation for the second virial coefficient at relatively high temperatures,1 based on the Redlich-Kwong equation. There, the Berthelot equation,2
(
p+
)
a (V - b) ) RT TV2
(1a)
1 4ay 1 - 4y bRT2
(1b)
z)
with critical parameters
a)
27bRTc2 8
(7)
RTc 8pc
(8)
b)
Substituting eqs 7 and 8 into the second virial coefficient that is predicted by the Berthelot equation,1,3
B2 ) b -
a RT2
(9)
one obtains the following corresponding-states correlation for the second virial coefficient:
pc )
x
aR 216b3
Vc ) 3b Tc )
8a 27bR
(4)
3 8
(5)
was included. Mathias cited the work of Hirschfelder et al.3 to denote the corresponding-states correlation for the second virial coefficient, which is predicted by the Berthelot equation as1,3
B2pc 54/128 9 ) RTc 128 T 2
(6)
R
However, we repeated the calculations and determined that eq 6 is incorrect. Combining eqs 2 and 4, one obtains
* To whom correspondence should be addressed. Tel.: 086-41184706203. E-mail:
[email protected]. † Department of Physics, Department of Applied Mathematics, Dalian University of Technology. ‡ Department of Physics, Qufu Normal University.
(10)
R
(3)
x
zc )
B2pc 1 27/64 ) RTc 8 T 2
(2)
In the main text, R is the molar universal gas constant, p the pressure, V the molar volume, T the temperature, b the so-called “co-volume”, a the van der Waals attraction constant, y the packing fraction (y ) b/(4V)), z the compressibility factor (z ) pV/(RT)), B2 the second virial coefficient, and TR the reduced temperature (TR ) T/Tc). The subscript “c” denotes values at the critical point. Acknowledgment The authors acknowledge the support of the National Natural Science Foundation of China (under Grant No. 10573004), the China Postdoctoral Foundation, the Natural Science Foundation of Shandong Province (under Grant No. Y2006A06), and the foundation from Qufu Normal University and Dalian University of Technology. Literature Cited (1) Mathias, P. M. The Second Virial Coefficient and the RedlichKwong Equation. Ind. Eng. Chem. Res. 2003, 42, 7037. (2) Berthelot, D. J. Berthelot’s Equation of State. J. Phys. 1899, 8, 263. (3) Hirschfelder, J. O.; Curtis, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1964; p 252.
IE070291L
10.1021/ie070291l CCC: $37.00 © 2007 American Chemical Society Published on Web 08/21/2007
