Concise Physical Chemistry

c02 JWBS043-Rogers September 13, 2010 11:23 Printer Name: Yet to Come

28 REAL GASES: EMPIRICAL EQUATIONS

pR

0 2 4 6 8 10

Z 1.0

2.0

0.0

TR = 1.2

TR = 1.5

TR = 2.0

FIGURE 2.7 Compressibility factors calculated from the van der Waals constants.

The van der Waals constants, which are characteristic of individual gases, have been

eliminated in the more general equation, which holds for any gas.Zcan be calculated

as a function ofpRfrom the equation of corresponding states as shown in Fig. 2.7.

Portrayal of extensive families of curves like those in Fig 2.7 can be found in the

chemical engineering literature. The equation of corresponding states is approximate

and holds only insofar as the van der Waals equation, on which it is based, holds.

2.7 DETERMINING THE MOLAR MASS OF A NONIDEAL GAS

A nonideal gas, even if it is pure, will generally not occupy a molar volume of 24.789

dm^3 atp=1.000 bar andT=298.15 K; hence any molar mass computed on the

basis of this molar volume will be wrong. Depending on the temperature, the error

may be 50% or more. If, however, the weight and the volume of a pure gas sample

are known along with the pressure and temperature, the (incorrect) molar mass, often

called theeffective molecular weight(EMW), can be calculated from the ideal gas

law. Historically, EMWs were measured at several different pressures, treating a real

gas as though it were ideal. The EMWs were then extrapolated as a function ofpto

p=0 to obtain the true molecular weight. It is fruitless to ask about the meaning of

the properties of a gas at zero pressure; one has simply “extrapolated out” the error

due to nonideality. Extrapolating out is a common applied mathematical device. A

number of more accurate methods for determining molar mass now exist.

PROBLEMS AND EXERCISES

Exercise 2.1 The van der Waals Cubic

Show that the van der Waals equation is a cubic.