Geology Reference
In-Depth Information
sometimes called the activation enthalpy because of a formal similarity to an
enthalpy. Only in connection with a particular model in which the process is
specified in thermodynamic terms, as in the transition state theory, can Q be
properly identified with a thermodynamic energy function or potential. If tem-
perature and pressure are the independent variables, the appropriate quantity to use
is the molar Gibbs energy, in which case the specification of Q as an activation
enthalpy presumes that the entropy term in the Gibbs energy has been subsumed in
the pre-exponential constant. In any case, in the determination of Q from an
''Arrhenius plot'' of ln rat
ð Þ
versus 1
=
T
;
the slope gives only the enthalpy part.
When the concept of activation energy is used in describing experimental situa-
tions where no single activated process has been identified or where it is possible
that several are involved, it is appropriate that the term be qualified as the
empirical, experimental, and/or apparent activation energy. In this case, it is
simply a measure of the sensitivity of the measured macroscopic rate to change in
temperature.
3.2 Reaction Kinetics
3.2.1 Thermodynamic Approach
A reaction can be represented in general in the form
m
A
A
þ
m
B
B
þ!
m
P
P
þ
m
Q
Q
þ
ð
3
:
3a
Þ
where A, B,… are the reactants and P, Q,… are the products. The symbols A, B,…
and P, Q,… serve first to identify the components involved in the reaction, and
second to represent a unit amount of the component that is consumed or produced
when the reaction occurs. The dimensionless quantities m
i
are termed the stoi-
chiometric coefficients, which normally will be integers without a common divi-
sor. It is conventional to take the m
i
to be negative for reactants and positive for
products, in which case we have the following algebraic balance:
0
¼
m
A
A
þ
m
B
B
þþ
m
P
P
þ
m
Q
Q
þ
ð
3
:
3b
Þ
A simple phase transformation or similar change can also be represented by the
form (
3.3
), with only one ''reactant'' and one ''product'', both m
i
being of unit
magnitude.
In a thermodynamic approach, one can consider a time interval dt during which
dn
i
¼
m
i
dn of each reactant is consumed and dn
i
¼
m
i
dn of each product pro-
duced, where n is a quantity termed the advancement or extent of reaction;
thus dn
i
=
dt
¼
m
i
dn
=
dt is the rate of increase in the amount of each component
i during the reaction and is a measure of the rate of reaction (in mol s
-1
in SI.
