Geology Reference
In-Depth Information
(a)
(b)
T /K
800
1200
1000
600
In k
k
0
0.8
1. 0 .2
1. 4 .6
10 3
( T /K)
500
1000
1300
T /K
Figure 3.2 Variation of the rate constant with temperature. (a) k plotted directly against T (in kelvins). (b) k plotted against
reciprocal temperature. T −1 has been multiplied by 10 3 to give a more convenient number scale. The reciprocal temperature
scale is graduated directly in kelvins along the top margin. (This axis shows the recognized way of writing 10 3 / T with T
expressed in kelvins).
algebraically by expressing the rate constant k for a
reaction in terms of an exponential equation:
G
E a
kA ERT
a /
=
e
(3.5)
G reactants
This has become known as the Arrhenius equation and it
has a number of important applications in geology. R is
the gas constant (8.314 J mo1 1 K 1 ) and T represents
temperature in kelvins . A and E a are constants for the
reaction to which the rate constant refers (varying from
one reaction to another). A is called the pre-exponen-
tial factor, and it has the same units as the rate constant
(which depend on the order of the reaction concerned).
The constant E a is called the activation energy of the
reaction and has the units J mol 1 .
Chapter  1 showed that physical and chemical pro-
cesses often encounter an energy 'hurdle' that impedes
progress from the initial, high-energy (less stable) state
to the lower-energy configuration in which the system is
stable (Figure 1.4). The hurdle is illustrated for a hypo-
thetical chemical reaction in Figure 3.3. It arises because
the only pathway leading from reactants to products
necessarily passes through a higher-energy transition
state. For a reaction involving the rupture of one bond
and the establishment of a new one, this involves the for-
mation of a less stable intermediate molecular species
Δ G
G products
Reactants
Activated
complex
A ... B ... C
Products
A-B
C
A
B-C
Progress of reaction
Figure 3.3 Energetics of a hypothetical reaction AB + C →
A + BC. The vertical axis represents the free energy of the
system. E a is the activation energy, which is released again
(except in the case of endothermic reaction, when only a
part is released) on completion of the molecular reaction.
(the activated complex in Figure 3.3). The activation energy
E a in the Arrhenius equation may be visualized as
the 'height' of the hurdle (in free energy units) relative to
the initial reactant assemblage. Box 3.4 explains how the
activation energy can be understood on the atomic scale.
 
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