Geoscience Reference
In-Depth Information
30
20
10
0
T
(
°
C)
5
4
3
2
SO
2
−
⇒
S
2
−
1
4
0
3.2
3.3
3.4
3.5
3.6
3.7
1000/
T
(K)
Figure 5.9
An example of reaction kinetics: sulfates being reduced to sulfides in diagenetic solutions. A linear
relation is found in the semi-logarithmic Arrhenius plot (data from Westrich and Berner,
1984
).
the potential barrier
E
to be crossed so as to “activate” the reactants. This is therefore
written:
k
CH
2
O
2
SO
2
4
d
d
t
=
(5.23)
where it can be seen that the probabilities are multiplicative properties, with
exp
−
E
RT
=
k
0
ν
k
(5.24)
where
k
0
is a constant that includes many parameters, notably the specific surface area of
the reactants (a finely divided mineral is more reactive than a single large crystal). We rec-
ognize a Boltzmann law, which can be represented in an Arrhenius plot ln
k
T
(
Fig. 5.9
). A large number of kinetic constants were determined in the 1980s and 1990s. At
high temperatures, reaction kinetics is normally fast but, in the context of diagenesis and
weathering, dissolution is slow. With the advent of fast computers, the calculation of kinetic
constants using ab initio methods has made very substantial progress and kinetic modeling
of reaction paths has become a quantitative field to the point that reaction mechanisms can
be tested very accurately.
The last equation has particularly important consequences for kinetic isotope effects
(see
Section 3.1
). First, let us go back to
Fig. 3.2
and observe that a bond involving a
light isotope is higher up on the energy scale and therefore easier to break than the same
bond involving a heavy isotope. For example, proceeding along the reaction path there-
fore requires less energy for an O
H
bond than for an OD bond (
Fig. 5.10
). Second, the
frequency term
=
A
+
B
/
varies with 1/
√
μ
is the reduced mass of the oscillator: the
vibrational frequencies of bonds involving light isotopes therefore are higher than those
of bonds involving heavy isotopes. Light isotopes will go through more frequent attempts
to engage into the reaction pathway than heavy isotopes. Species of elements such as C,
S, and N have very different coordinations under different redox conditions, in particular
those prevailing during biological reactions. The term “kinetic isotope effect” is used to
ν
, where
μ
