11.8 p–y–T Relations for Gas Mixtures
Many systems of interest involve mixtures of two or more components. The principles
of thermodynamics introduced thus far are applicable to systems involving mixtures,
but to apply such principles requires that mixture properties be evaluated.
Since an unlimited variety of mixtures can be formed from a given set of pure
components by varying the relative amounts present, the properties of mixtures are
available in tabular, graphical, or equation forms only in particular cases such as air.
Generally, special means are required for determining mixture properties.
In this section, methods for evaluating the p–y–T relations for pure components
introduced in previous sections of the book are adapted to obtain plausible estimates
for gas mixtures. In Sec. 11.9 some general aspects of property evaluation for multi-
component systems are introduced.
To evaluate the properties of a mixture requires knowledge of the composition.
The composition can be described by giving the number of moles (kmol or lbmol) of
each component present. The total number of moles, n, is the sum of the number of
moles of each of the components
n 5 n
1
1 n
2
1
. . .
1 n
j
5
a
j
51
n
i
(11.93)
The relative amounts of the components present can be described in terms of mole
fractions. The mole fraction y
i
of component i is defined as
y
i
5
n
i
(11.94)
Dividing each term of Eq. 11.93 by the total number of moles and using Eq. 11.94
1 5
a
j
51
y
i
(11.95)
That is, the sum of the mole fractions of all components present is equal to unity.
Most techniques for estimating mixture properties are empirical in character and
are not derived from fundamental principles. The realm of validity of any particular
technique can be established only by comparing predicted property values with
empirical data. The brief discussion to follow is intended only to show how certain
of the procedures for evaluating the p–y–T relations of pure components introduced
previously can be extended to gas mixtures.
MIXTURE EQUATION OF STATE. One way the p–y–T relation for a gas mix-
ture can be estimated is by applying to the overall mixture an equation of state such
as introduced in Sec. 11.1. The constants appearing in the equation selected would be
mixture values determined with empirical combining rules developed for the equa-
tion. For example, mixture values of the constants a and b for use in the van der
Waals and Redlich–Kwong equations would be obtained using relations of the form
a 5 a
a
j
51
y
i
a
i
1
/
2
b
2
,
b 5 a
a
j
51
y
i
b
i
b
(11.96)
where a
i
and b
i
are the values of the constants for component i and y
i
is the mole
fraction. Combination rules for obtaining mixture values for the constants in other
equations of state also have been suggested.
KAY’S RULE. The principle of corresponding states method for single components
introduced in Sec. 3.11.3 can be extended to mixtures by regarding the mixture as if
it were a single pure component having critical properties calculated by one of several
mixture rules. Perhaps the simplest of these, requiring only the determination of a
mole fraction averaged critical temperature T
c
and critical pressure p
c
, is Kay’s rule
TAKE NOTE...
The special case of ideal gas
mixtures is considered in
Secs. 12.1–12.4, with
applications to psychromet-
rics in the second part of
Chap. 12 and reacting mix-
tures in Chaps. 13 and 14.
Kay’s rule
11.8 p–y–T Relations for Gas Mixtures 675
c11ThermodynamicRelations.indd Page 675 6/21/10 9:36:14 PM user-s146 c11ThermodynamicRelations.indd Page 675 6/21/10 9:36:14 PM user-s146 /Users/user-s146/Desktop/Merry_X-Mas/New/Users/user-s146/Desktop/Merry_X-Mas/New