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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