Chemistry Reference
In-Depth Information
Measurement of variation in rate constants with temperature allow determination of the
activation parameters (activation enthalpy,
H
=
, and activation entropy,
S
=
) applying in
the reaction, which assist in elucidating the mechanism.
In some reactions, the rate constant is seen to vary with concentration of one of the
reactants (say molecule X). If a plot of the measured rate constant (
k
obs
) determined under
particular defined conditions versus [X] present is made, where reaction with various
concentrations of X has been examined, and is found to increase linearly with increasing
[X], then the behaviour can be represented as (5.35)
k
obs
=
k
X
·
[X]
(5.35)
and
k
X
is then called a second-order rate constant and will have units of M
−
1
s
−
1
,theex-
perimentally observed rate constant (
k
obs
,s
−
1
) being dependent on the molar concentration
of X. This type of behaviour means that X is involved in the reaction in some way; it
may appear as part of the product, although it may alternatively participate only in the
transition state and not appear in the product. These are brief aspects of reactions that form
a background to our discussion of the mechanisms of reactions below.
5.2.3
Lability and Inertness in Octahedral Complexes
We have already introduced the concept of rate of change for complexes, expressed in terms
of the two extremes of
labile
(fast) and
inert
(slow), where charge and size are key factors.
Experimental observations of reactivity allow us to define, at least approximately, which
metal ions fall into which category. For transition metals, although size/charge effects
are important, they do not fully explain experimental observations. It was Henry Taube
who showed that the d-electron configuration played an important role, and that high-spin
complexes are generally labile. The following groupings were identified from experimental
observations of octahedral complexes:
labile
- all complexes where the metal ion has electrons in
e
g
∗
orbitals [e.g. Co
2
+
(d
7
:
t
2g
5
e
g
2
); high spin Fe
3
+
(d
5
:
t
2g
3
e
g
2
)], and all complexes with less than three d electrons
[e.g. Ti
3
+
(d
1
)];
inert
- octahedral d
3
complexes [e.g. Cr
3
+
(d
3
:
t
2g
3
e
g
0
)], and low spin d
4
,d
5
and d
6
complexes [e.g. Co
3
+
(d
6
:
t
2g
6
e
g
0
)].
An analysis in terms of the relative energies of the precursor and reaction intermedi-
ate predicts lability for octahedral complexes with populated
e
g
∗
levels, in line with the
experimental observations.
There are, of course, 'grey' areas. Even within a traditionally inert system, reactivity may
vary markedly with the type of ligand undergoing reaction. For [Co
III
(NH
3
)
5
X]
n
+
reacting
in water to replace the X-group by a water molecule, the rate constant varies by an order of
∼
10
10
from NH
3
(
k
=
5.8
×
10
−
12
s
−
1
at room temperature, a half-life of 3800 years) to
OClO
3
−
10
−
2
s
−
1
, a half-life of 7 seconds). Such variations reflect the nature
of the ligand more than the metal, since the ligand lability or capability as a good leaving
group tends to extend across a wide range of metal ions.
(
k
=
1.0
×
