Geoscience Reference
In-Depth Information
soil science, or aquatic chemistry (e.g., Stumm and Morgan
1995
; Sposito
1981
),
and the reader is directed to such sources for ample information on this topic.
In a closed system when temperature and pressure are constant, the sum of
chemical potentials of all components is fixed; in contrast, in an open system, the
chemical potential of all components is influenced by both the thermodynamic
parameters of the phases and various parameters outside the system. The main
relationship among phases, components, and physical conditions is given by the
phase rule.
The phase rule states that when equilibrium conditions are sustained, a minimum
number of intensive properties of the (subsurface) system can be used to calculate its
remaining properties. An intensive property is a property that is independent of the
amount of substance in the domain. Examples of intensive properties include tem-
perature (T), pressure (P), density (q), and chemical potential (l), which is a relative
measure of the potential energy of a chemical compound. The phase rule specifies
the minimum number of intensive properties that must be determined to obtain a
comprehensive thermodynamic depiction of a system.
A phase is defined as a state of matter that is uniform throughout in terms of its
chemical composition and physical state; in other words, a phase may be con-
sidered a pure substance or a mixture of pure substances wherein intensive
properties do not vary with position. Accordingly, a gaseous mixture is a single
phase, and a mixture of completely miscible liquids yields a single liquid phase; in
contrast, a mixture of several solids remains as a system with multiple solid
phases. A phase rule, therefore, states that, if a limited number of macroscopic
properties are known, it is possible to predict additional properties.
A system is homogeneous when the intensive properties are not a function of
position, while a system is heterogeneous when the composition of a given mixture
varies as a function of position. For example, the subsurface liquid phase usually
comprises an aqueous solution incorporating a number of solutes; in contaminated
subsurface environments, nonaqueous phase liquids also may be present. The air
phase of the subsurface includes gases with various partial pressures, and the solid
phases comprise a mixture of minerals and organic compounds.
A phase diagram describes how a system reacts to changing conditions of
pressure and temperature and consists of a field in which only one phase is stable,
separated by boundary curves along which a combination of phases coexist in
equilibrium.
2.1.3 Solubility, Chemical Potential, and Ion Activities
The chemical potential of species i, l
i
, is expressed in terms of the Gibbs free
energy added to a system at constant T and P, as well as relative to the mole
fraction of each added increment of i. When adding an incremental number of
molecules of i, free energy is introduced in the form of internal energies of i as
well as by the interaction of i with other molecules in the system. As i increases,
