Geoscience Reference
In-Depth Information
increasing ease of data retrieval and extrapolation and the availability of free
energy minimization algorithms, this information is accessible and useful,
allowing application of thermodynamics to a wide variety of geochemical systems.
Despite this usefulness, thermodynamic considerations have limitations, and
these most often are apparent in environmental systems at lower temperatures, in
biological systems, and in the description of reactions at phase boundaries.
Thermodynamics applies to chemical processes among large numbers (i.e.,
Avogadro's number) of molecules and deals with overall reactions among a set of
chemical
species.
Strictly
speaking,
equilibrium
thermodynamics
provide
no
information about how a chemical system reached its current state.
The earth's subsurface is not at complete thermodynamic equilibrium, but parts
of the system and many species are observed to be at local equilibrium or, at least,
at a ''dynamic'' steady state. For example, the release of a toxic contaminant into a
groundwater reservoir can be viewed as a perturbation of the local equilibrium,
and we can ask questions such as, What reactions will occur? How long will they
take? and Over what spatial scale will they occur? Addressing these questions
leads to a need to identify actual chemical species and reaction processes and
consider both the thermodynamics and kinetics of reactions.
For any chemical reaction, whether inorganic or organic, we must choose which
kinetic species to include in the elementary reactions that make up the overall
process; ideally, molecular or chemical information is available to guide this
choice. In general, for an elementary (irreversible) reaction among species A and
B, to give species C and D, in relative amounts a, b, c, and d, respectively,
aA
þ
bB
!
cC
þ
dD
;
ð
2
:
16
Þ
the rate of the reaction is
Rate ¼
1
a
d½A
dt
¼
1
d½B
dt
¼
1
d½C
dt
¼
1
d
d½D
dt
¼ k½A
a
½B
b
;
ð
2
:
17
Þ
b
c
where [ ] denotes concentration, a + b is the order of the reaction, and the
coefficient k is the rate constant for the reaction.
In a first-order reaction, the rate-determining step involves a transformation
where one reactant reacts to give one product, that is, A ? B. In first-order reactions,
there is an exponential decrease in the reactant concentration, so that at any given
time, the transformation rate is dependent on the corresponding concentration of the
reactant at the same time. This can be expressed in the following way:
Rate ¼
d½A
dt
¼
k½A
;
ð
2
:
18
Þ
½A
t
¼½A
0
e
kt
;
ð
2
:
19
Þ
where here k is the first-order rate constant with dimension [time
-1
] and the
subscripts t and 0 denote time and initial time, respectively. Plotting ln[A]
t
/[A]
0
