Geology Reference
In-Depth Information
If we double the initial concentrations of both NO and
O
3
, we find the initial rate is quadrupled. This suggests
that the rate is related to reactant concentrations:
rate of a heterogeneous reaction. This is one reason
why diesel fuel injected as a fine spray into an engine
reacts explosively with air, whereas the bulk liquid
burns much more slowly.
The condition of the interface is also a very import-
ant factor. The rate of inversion of aragonite to calcite,
for example, is greatly accelerated by the presence of
traces of water along the grain boundaries. Surface
chemistry has many important applications in the
chemical industry and in mineral processing (for
example, the use of a frothing agent to optimize the
separation of ore minerals by flotation).
Mechanical factors come into play as well. When
a solid dissolves in still water, the aqueous phase
surrounding it becomes locally saturated, and this
impedes further solution until diffusion has distrib-
uted the dissolved species more evenly. Dissolution of
sugar in coffee can therefore be accelerated by the use
of a teaspoon to promote homogenization, and natural
forms of agitation can be correspondingly effective in
the marine environment. Experiments show that the
rate at which calcite dissolves in water can be rep-
resented like this:
d
c
rate
=− =⋅ ⋅
NO
kc c
(3.3)
NO
O
d
t
3
Equation 3.3 is called the
rate equation
for this reaction.
Because it contains
two
concentration terms (
c
NO
and
c
O
3
), the reaction is said to have
second-order
kinetics.
The constant
k
, whose numerical value is specific to
this reaction (and to the temperature at which the
experiment is run), is called the
rate constant
. The equa-
tion predicts that as the reactants are used up the rate
will decline, which is consistent with the flattening out
of the slopes in Figure 3.1.
The process of radioactive decay can be analysed in
a similar manner (Boxes 3.2 and 3.3).
Heterogeneous reactions
Reactions like 3.1 that take place within a single
phase (in this case a homogeneous gas mixture) are
called
homogeneous reactions
. Nearly all reactions
of geological significance, on the other hand, are
het-
erogeneous reactions,
involving the participation of
two or more phases (minerals, melts, solutions …).
Because they require the migration of components
across the
interface
dividing one phase from another,
the formulation of rate equations for heterogeneous
reactions is much more complicated than for homo-
geneous reactions.
The most obvious consequence of involving two
phases in a reaction is that the surface area of their
interface becomes a variable in the rate equation.
Interfacial surface area is determined chiefly by parti-
cle size. The surface area of a cube 1 cm across is 6 cm
2
(six sides each of 1 cm
2
area). Cutting the cube in half in
each direction produces eight cubes, each 0.5 cm across
and each having a surface area of 6 × 0.5
2
= 1.5 cm
2
. The
total volume of all the cubes together is unchanged
(1 cm
3
) but the total surface area has increased from
6 cm
2
to 8 × 1.5 = 12 cm
2
. Dividing the original cube into
1000 cubelets each of 0.1 cm size would increase the
total area to 60 cm
2
, while reducing to particle sizes
equivalent to silt and clay sediments would increase
their surface area to 3000 and 60,000 cm
2
respectively.
Particle or crystal size, because it determines the area
of contact between phases, has a profound effect on the
)
(
)
1
2
−
(
1
2
α
3
0
Rate
=
kA Kc
c
(3.4)
CO
2
+
2
−
Ca
3
The
c
terms refer to concentrations of ions in solu-
tion,
K
0
and
k
are constants,
A
is the total surface area
of the calcite phase present, and
α
is the experimental
stirring rate (which appears as the cube root for reas-
ons that need not concern us). No doubt the effect of
natural wave-agitation is still more complicated. This
equation illustrates how rapidly the complexities mul-
tiply when even the simplest heterogeneous reactions
are studied kinetically.
Temperature-dependence of reaction rate
Everyday experience tells us that chemical reactions,
whether homogeneous or heterogeneous,
speed up
as
the temperature is raised. Epoxy adhesives cure more
quickly in a warm oven. Conversely, the very fact that
we use refrigerators and freezers to preserve food
indicates that biochemical reactions
slow down
at
lower temperatures. Quantitatively the temperature
effect which these examples illustrate is quite pro-
nounced: many laboratory reactions roughly double
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