Geology Reference
In-Depth Information
units). The quantity dn
=
dt is called the rate of reaction (Atkins
1986
, p. 651).
When the system is taken to be a unit volume, dn
i
=
dt becomes the rate of change
in the amount-of-substance concentration of the component i, designated dc
i
=
dt or
d
½=
dt
;
a measure that can be extended to continuous systems (SI. units
mol m
-3
s
-1
). When dn
i
=
dt or dc
i
=
dt is used to specify the rate of reaction care
must be taken to specify the component i to which it refers, an elaboration not
required when the ''true rate'' dn
=
dt or dc
i
=
d
ð Þ=
m
i
is used.
In a closed system, an equilibrium state will exist at certain proportions of
reactants and products, as determined thermodynamically by the equilibrium
constant K
¼
Q
i
a
ðÞ
m
i
;
where a
i
¼
c
i
c
i
is the activity of the ith component and c
i
its activity coefficient. At equilibrium the rate of reaction is zero. When the
departure from equilibrium is small, it may be expected that the rate of reaction
will be proportional to the degree of departure from equilibrium, giving the linear
thermodynamic relation
n
¼
L
k
A
ð
3
:
4
Þ
where n
¼
dn
=
dt is taken as the rate of reaction, L
k
is the phenomenological/
kinetic/thermodynamic coefficient, and A is a thermodynamic force (affinity)
driving the reaction, defined in chemical reactions at constant temperature and
pressure as A
¼
oG
=
o
ð Þ¼
P
i
m
i
l
i
;
where the l
i
are the chemical potentials
of the components. In transformations at constant temperature and pressure, A is
simply the difference in chemical potentials of the untransformed and transformed
phases. In SI units, A is in J mol
-1
and so L
k
is in mol J
-1
s
-1
; if the rate of
reaction is alternatively specified in terms of a rate of change of molar concen-
tration, then the phenomenological coefficient is in mol
2
m
-3
J
-1
s
-1
. ''Near to
equilibrium'' can be usefully defined by the condition A
RT
;
a condition that
can be rationalized on the basis of the theory of fluctuations or statistical ther-
modynamics using the approximation that exp A
=
RT
ð
Þ
is linear in A if A
RT
:
3.2.2 Kinetic Approach
In empirical kinetics, relations are sought between the rate of reaction and the
concentrations of the components rather than between the rate of reaction and a
quantity (affinity) based on the chemical potentials of the components. The
empirical kinetic relations are therefore of the form
rate
¼
kf c
ðÞ
ð
3
:
5
Þ
where the rate of reaction is specified by n or, more commonly, by the rate of
change in concentration of one of the reactants, k is a parameter called the
empirical or kinetic rate coefficient or rate constant (an optional suffix can be
added to distinguish it from the Boltzmann constant, if necessary), and fc
ðÞ
is a
