Page 14 - Partition & Adsorption of Organic Contaminants in Environmental Systems

SECOND LAW OF THERMODYNAMICS 5

becomes the criterion for any infinitesimal process within a closed system (i.e.,
where no mass transfer occurs across the system boundary) to take place at
equilibrium [i.e., (dG) T,P = 0] or spontaneously [i.e., (dG) T,P < 0] at constant
temperature and pressure. For a single-component system, dG is a function of
temperature and pressure (or volume). For a complex mixture, dG depends
also on the composition, as will be seen.
If a phase transition (e.g., from liquid to vapor) takes place in a closed
single-component system at constant T and P, the transition can thus be
carried out at equilibrium with any phase-mass ratio as long as both phases
coexist in finite amounts. In this case, dG/dl, or DG, is equal to 0, where DG
corresponds to a finite phase transition and l is the progress variable. In a
closed multicomponent system where a chemical reaction takes place or a
component distributes between phases at fixed T and P, usually only one com-
position can satisfy the condition for equilibrium (i.e., dG/dl=DG = 0).
For simple systems without mass and composition changes, one can thus
write

dE = T dS - P dV (1.8)

and

-
+
+
-
-
=
dG T dS P dV P dV V dP T dS SdT
or
dG = V dP - S dT (1.15)
In a closed system where a change in state or a chemical reaction takes
place at constant temperature, one finds from Eq. (1.12) an important relation
as follows:

DG = DH T DS (1.16)
-
Thus, the reduction in free energy of a closed system at constant temperature
is favored by a decrease in system enthalpy or by an increase in system
entropy. However, chemical processes seldom occur with emission of heat (i.e.,
DH < 0) coupled with an increase in DS. In some special cases, the process may
proceed with DH = 0 and TDS > 0, such as the expansion and mixing of ideal
gases or the formation of an ideal solution, or with DH < 0 and TDS 0, such
as chemical reactions in which the moles of reactants equal the moles of prod-
ucts. Frequently, chemical processes occur with opposing effects of DH and T
DS, in which one outweighs the other.
To illustrate how either DH or TDS may act as the main driving force for a
spontaneous process, let us consider two physical processes, vaporization and
adsorption, at constant temperature in a closed system. When a fraction of a
liquid in excess quantity is being evaporated into a fixed vacuum space, the