Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 43

3 Multicomponent

Equilibrium
Thermodynamics

Environmental systems are inherently complex and involve several phases, each
containing many components. It is a characteristic of nature, and amply demonstrated
through the science of thermodynamics, that when two or more phases are in contact
they tend to interact with each other via exchange of matter and/or energy. The phases
interact till a stateofequilibrium is reached. Two new concepts have to be introduced,
namely, fugacity and activity , to describe multi-component heterogeneous systems
that display varying degrees of nonideality.
There are three steps involved in understanding complex heterogeneous multi-
component systems: (i) translation of the real problem into an abstract world of
mathematics,(ii)solutiontothemathematicalproblem,and(iii)projectionofthesolu-
tion to the real world in terms of meaningful and measurable parameters (Prausnitz,
Lichtenthaler, and de Azevedo, 1999). The chemical potential discussed in Chapter
2 is the appropriate mathematical abstraction to the physical problem. The definition
of equilibrium in terms of chemical potential is the framework for the solution of the
physical problem in the abstract world of mathematics.
Knowledge of heterogeneous multi-component equilibrium is essential in design-
ing processes for environmental separations. Separation efficiency is driven by the
tendency of a system to move toward equilibrium from a state of disequilibrium.
As noted in Chapter 2, the property called chemical potential introduced by Gibbs
is a highly useful mathematical abstraction to physical reality. The chemical potential
is only measured indirectly. Hence, a new term was defined called fugacity . We begin
with a discussion of the fugacity (Lewis and Randall, 1961).

3.1 IDEAL AND NONIDEAL FLUIDS
The distinction between ideal and real gases is straightforward. If molecules in a gas
do not interact with one another, it is considered “ideal.”The molecules in an ideal gas
have no excluded volumes. The pressure-volume-temperature ( P - V - T ) relationship
for an ideal gas is given by the well-known “ideal gas law”:

PV = nRT . (3.1)

We know that most gases are not ideal since a gas cannot be cooled to zero volume
and, even at moderate densities, the molecules interact with one another. Molecules
in real gases have definite excluded volumes. The P - V - T relationship for a real gas

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