Selected Geochemical Processes - Contaminant Geochemistry - page 38

H þ þ HCO 3 H þ þ CO 2 3 : ð 2 : 32 Þ

Thus, at the molecular level, the reactions that actually take place and their
associated chemical pathways can be completely different from the cerussite
precipitation scheme presented in Eq. ( 2.27 ).
In addition to a number of solution species and a solid, species adsorbed to and
desorbed from the surface can be included and described using elementary reac-
tions. As discussed previously, to determine the reaction order, rate-determining
steps, or other kinetic parameters, one must choose the kinetic species to be
included in the elementary reactions that make up the overall process. Ideally,
molecular or chemical information is available to guide this choice. Therefore, the
set of kinetic species for any overall chemical reaction is generally larger (and
usually more complicated) than the set of equilibrium species. The only constraints
on overall reactions are that they proceed in the same direction as DG 0 and that the
overall reaction rate approaches zero at equilibrium. This connection between the
rate of an overall reaction and the driving force supplied by thermodynamics can
be expressed by including a free energy term in a rate equation.
The change in free energy of a reaction not at equilibrium (DG r ) is given by

Q
KE ;

DG r ¼ RT ln ð 2 : 33 Þ

where R, T, and K eq have the same meaning as in Eq. ( 2.29 ) and Q is the measured
ion activity product for the reaction. By comparing the activity product of a species
observed in the system with the expected concentration product at equilibrium
(K eq ), the ratio Q/K eq provides a measure of how far from equilibrium the reaction
is and in which direction it is going (note that Q = K eq , and therefore DG r = 0, at
equilibrium). In general, rate equations derived from experiments have many terms
that account explicitly for variables such as concentrations of species in solution,
pH, ionic strength, possible catalytic or inhibitory effects, and different forms of
expression for f(DG r ). Rate expressions should be able to account for the differ-
ence in reaction rate far from and close to equilibrium. However, it cannot be
assumed that the reaction mechanism is the same for both dissolution and pre-
cipitation. In the context of environmental systems, the first, and sometimes the
most difficult, task is determining the species and stoichiometry of reactions that
govern the fate of the elements of interest, then deciding whether they can be
treated as equilibrium reactions for the time scale of interest. Reactions that occur
at surfaces and the molecular species involved are inherently difficult to charac-
terize because their concentrations usually are lower than those of bulk species and
they often are transitory.