Physical Chemistry Third Edition

1.3 Real Gases 23

Table 1.1 displays several additional equations of state, and values of parameters for

several gases are found in Table A.3. The parameters for a given gas do not necessarily

have the same values in different equations even if the same letters are used. The

accuracy of several of the equations of state has been evaluated.^2 TheRedlich–Kwong

equation of stateseemed to perform better than the other two-parameter equations, with

the van der Waals equation coming in second best. The Gibbons–Laughton modification

of the Redlich–Kwong equation (with four parameters) is more accurate than the two-

parameter equations.

Table 1.1 Some Equations of State

The lettersaandbstand for constant parameters that have different values for different

substances. These parameters do not necessarily have the values for the same substance

in different equations of state.

The Berthelot Equation of State

(

P+

a

TVm^2

)

(Vm−b)RT

The Dieterici Equation of State

Pea/VmRT(Vm−b)RT

The Redlich–Kwong Equation of State

P

RT

Vm−b

−

a

T^1 /^2 Vm(Vm+b)

The Soave Modification of the Redlich–Kwong Equation of State

P

RT

Vm−b

−

aα(T)

Vm(Vm+b)

whereα(T){ 1 +m 1 −(T/Tc)^1 /^2 }^2 , wheremis a constant parameter and where

Tcis the critical temperature. See the article by Soave for values of the parameterm.

The Gibbons–Laughton Modification of the Redlich–Kwong-Soave Equation

of State

The equation is the same as the Soave modification, butα(T) is given by

α(T) 1 +X(T/Tc)− 1 +Y(T/Tc)^1 /^2 − 1

whereXandYare constant parameters. See the article by Gibbons and Laughton for

values of these parameters.

Other equations of state can be found in the book by Hirschfelder, Curtiss, and Bird,

including the Beattie–Bridgeman equation, with five parameters, and the Benedict–

Webb–Rubin equation, with eight parameters.

(^2) J. B. Ott, J. R. Goates, and H. T. Hall, Jr.,J. Chem. Educ., 48 , 515 (1971); M. W. Kemp, R. E. Thompson,
and D. J. Zigrang,J. Chem. Educ., 52 , 802 (1975).