PHYSICAL CHEMISTRY IN BRIEF

CHAP. 2: STATE BEHAVIOUR [CONTENTS] 53

Note:The constants of the Redlich-Kwong’s equation of state are not identical with the

identically denoted constants of the van der Waals equation.

For the second virial coefficient, the Redlich-Kwong equation yields

B= 0. 08664

RTc

pc

[

1 − 4. 93398

(

Tc

T

) 3 / 2 ]

. (2.30)

For the Boyle temperature, the Redlich-Kwong equation gives

TB= 2. 898 Tc. (2.31)

2.2.8 Benedict, Webb and Rubin equation of state

p =

RT

Vm

+

RT B

Vm^2

+

RT C

Vm^3

+

aα

Vm^6

+

c(1 +γ/Vm^2 )

T^2 Vm^3

exp(−γ/Vm^2 ),

z = 1 +

B

Vm

+

C

Vm^2

+

aα

Vm^5

+

c(1 +γ/Vm^2 )

RT^3 Vm^2

exp(−γ/Vm^2 ), (2.32)

where
B=B 0 −A 0 /(RT)−C 0 /(RT^3 ), C=b−a/(RT).

The equation contains eight adjustable constantsA 0 ,B 0 ,C 0 ,a,b,c,α,γ, which are obtained
from experimental data on state behaviour.

2.2.9 Theorem of corresponding states

The theorem of corresponding states says that the compressibility factor is a function of reduced
quantitiesTr, prorTr, Vrwhich is independent of the substance

z=f(Tr, pr) or z=f(Tr, Vr). (2.33)

Based on experimental data on state behaviour of gases, a diagram of the compressibility
factor dependence on reduced variables has been drawn allowing for convenient and generalized
(i.e. independent of the substance) estimation of state behaviour. The theorem of corresponding