Download Mechanisms of Oxidation

Henry Taube
Stanford University
Stanford, California
Mechanisms of
Oxidation-Reduction Reactions
W i t h i n the last 20 years, rapid progress
has been made in understanding the mechanisms of
oxidation-reduction reactions. For a sub-class of these
reactions, namely those in which the net change in
oxidation state for the oxidizing agent matches that for
the reducing agent, the observations are simple and
understandable, yet interesting and important enough
to deserve mention at the undergraduate level. The
role of the electron in chemical binding is, of course,
already emphasized in the chemistry curriculum. The
field of the reactions to be described has special appeal
because in it we can trace the effect of changes in the
state of binding of each reaction partner when electron
transfer takes place, and a close relationship between
structural and dynamical aspects of chemical behavior is
revealed.
To appreciate the subject some preparation on the
relation between electron structure on the one hand and
molecular structure and lability on the other is neeessary.
The former of these subjects is dealt with at the undergraduate level; the second deserves to be. I have, in
the following, considered both of these introductory
aspects so as to indicate the kind of background which
is required for an appreciation of the proper subject of
this article. The treatment is, of necessity, sketchy
and, at most, is intended to encourage those interested
in making pedagogical use of the recent advances in
understanding how oxidation-reduction takcs place to
devote some time and energy to the subject matter
which is basic to understanding it. The leading references among the general ones cited at the end of the
article will be found to provide the neeessary background.
Oxidation Number and State of Coordination
The relation between substitution aud redox1 reactions is by no means symmetrical. Substitution can be
discussed without concern for redox processes, but the
reverse is by no means truc. Many, if not most, redox
reactions involve substitutional changes as an integral
part of the overall process. It is the interplay between
change in oxidation state and in the coordination state,
This paper by Professor Taube completes the series res~dtingfrom the Advisory Corincil on College Chemistry
Conference on Chemical 1)ynarnics held a t San Clernerrte,
California dliring Ikcember, 1066. The first nine papers
appeared in the June issue of ~ s rJOTJRN.AL.
s
The advisory
Co,~ncilon College Chemistry (ACs) is supported by the
National Science Foundation. Proiessor L. Carroll King
of Northwestern University is the cliairrnan.
The collection of ton papers will be bound in a reprint
volume and distrihnted by the ACJ to all individr~slson its
mailing list. This will be Serial Pnblication No. 37 of the
Advisory Council.
ranging from systems in which on change in oxidation
number the state of coordination remains unchanged,
through those in which the identity, but not the number,
of ligands in the first coordination sphere changes, to
those in which the coordination number changes that
gives the field much of its special interest. More than
this, as will be explained, progress in understanding the
mechanisms of redox reactions depends, and still continues t o depend, on understanding the relation between
state of coordination and oxidation state, as well as
between substitution lability and oxidation state.
To illustrate and emphasize the dependence of state
of coordination on oxidation number, let us consider the
common oxidatiou states of chromium in the aquo
system. For acidic solutions, a t ordinary concentration, say 0.01-0.1 M ,the dominant forms of chromium
in the 0, +2, +3, and +6 oxidation states are
Cr
Cr(H20)s2+
Cr(H%O).a+
CrxO7
These species feature striking changes in the state of
coordination as the oxidation number changes, but the
differences which will be described are just as great for
many other elements.
Chromium in the elementary state is a metal, and in
common with other metals, each atom is strongly
bonded to others of the same kind. In elementary
chromium, each atom has eight others as nearest
neighbors; the strength of this interaction can be
gauged from the heat of vaporization which is 80.5
Bcal/mole. Despite the great affinity of chromium
atoms for others of the same Bind, even mild oxidizing
agents can disrupt the solid. The removal of 2e- for
each Cr atom suffices to sever the Cr-Cr bonds completely by forming chromium in the oxidation state +2.
It must be emphasized that an essential part of the
oxidation process is the interaction of the +2 ions with
negative charges derived from the environment, as is
the case when water is the solvent, or from the oxidizing
agent as would be the case if chromium were to react
with dry chlorine. Except for the stabilization of the
+2 state by such interactions, the oxidatiou would not
occur.
Though in Cr(HzO)s2+,chromium is shown bound to
six water molecules in the first coordination sphere,
these are uot equivalent, and the structure of the aquo
complex is considered to be that of an octahedron elongated along one axis. The complex Cr(H20)6" (or
Cr(HzO)r(Hz0')22+)is extremely labile (I), the halftime for water exchange between the aquo complex and
the solvent being less than
sec. When an electron
is removed from Cr(H20)62+to produce Cr(Hz0)63+,
the aquo complex changes in structure. The ion Cr(HzO)2+has the structure of a regular octahedron, and
The term "redox" will be wed for "oxidation-reduction."
452
/
Journal o f Chemical Education
the Cr-0 bond distance is probably a little less t h a r ~the
lesser of the Cr-0 distances in the aquo chromium(I1)
complex.
The oxidation of Cr(Hz0)62+to C T ( H ~ O ) brings
~~+
about a dramatic change in lability in addition to a
change in geometry. The half-time for water exchange
between Cr(Hz0)63+and solvent (2) is -106 sec. It is
remarkable that chauging the electron couut by one
unit is this system changes the rate of substitution by a
factor of more than 10'6.
In the next higher stable oxidation state of chromium,
the +6 state, the coordination number of chromium to
oxygen is only four, but the intensity of the interaction
of the +6 ion with the solvent is so great that the protons are almost completely stripped from the water
molecules.
Cre+
+ 4H.O + HCr04- + 7HC
(1)
Thus Cr(V1) in acidic solution is an oxy rather than an
aquo or hydroxy ion. An additioual complication
which must be allowed for is the labile equilibrium
HnO
+ Cr201P- = 2HCrO.i
(2)
and in the reduction of Cr(V1) it is important to learn
whether the mononuclear or binuclear ion is present in
the activated complex for the reaction.
The species represented for the various oxidation
states are the dominant forms under the couditions
specified. For each state other species can be con~ i d e r e d - C r ( H ~ O ) ~as~ +
an aqua ion form for Cr(II1)but a t equilibrium these are in low concentration compared t o the ones represented. Such unstable species
may, however, be formed as the primary products of
redox processes, and it can't be taken as a foregone
conclusion that Cr(Hz0)63+in its equilibrium state is
the first product of the oxidation of Cr(H20)sZ+
or of the
reduction of Cr(V1). A central problem in the mechanism of redox reactions is learning how, during the
reaction, the changes in state of coordination are
coupled to the changes in oxidation state. As will
he shown, the changes in coordination state in question
are not only a matter of shape and size of the coordination sphere but also of the identity of the groups in the
sphere of coordination.
standing the mechanisms of reactions; and to the extent
that it is imperfectly understood for the net changes, the
mechanisms of redox reactions, though they may be
well described, will be imperfectly understood. It is
impossible in a short article to discuss the influeuce of
electron structure on configuration a t all completely,
and we will need to be content with illustrating the
connection with a few examples.
Though the principles govenring the influences of s or
p valence electrons on the configurations of molecules
are the same as those ford (or f ) electrons, owing to the
differences in uumbcr, interrelation, and energies of the
orbitals, striking differenccs can he noted between
the categories, justifying the separate discussion of the
classes of nonmetals and transition metals (and rare
earths and actinides).
A simple example to begin with is the partial process
H
H
Apoint to note is that in CHxX, all the low-lying orbitals
of C are fully occupied and, as a consequcnce, no ordinary reducing agent has the capacity to transfer an
electron to the molecule uuless a reduction in the
coordiuation number takes place. The change in
coordination depicted in reaction (3) is brought about
by stretching the -C+. . . X- bond. As the negatively charged ligand is removed, this lowers the energy
of the autibonding orbital (in CH3Xthe bonding orbital
can be taken as occupied by the electron pair shared
between C and X and, complementary to this, there
will be an antibonding orbital at higher energy), and
when the -C+. . . X- bond is stretched sufficiently,
electron transfer from a reducing agcnt can takc place.
The reduction of CIO1CIOn-
+ 2A+ + 2
e = H*O
+ ClOs-
(4)
can be discussed in a like fashion, but in this case the
discussion is even less satisfactory. A difficulty here
is that the electron structure of CIOn- is probably not
well represented by the electron-dot formula
Electronic Structure and Coordination State
The changes in geometrical structure with oxidation
number which has been illustrated for the chromium
oxidation states takes place in response to the changes
in electron count. As a result of this, ion radii and
charges change, and these alone demand a response in
the coordiuation spheres of the complexes. But
differenccs in electronic structure a t approximately
constant ionic radius and charge can themselves produce
changes in state of coordination, and this connection
can most successfully be illustrated for transition metal
complexes. Rlost of this section will be devoted to a
number of transition metal complexes which have been
studied extensively in redox reactions, but to suggest
the generality of the effects and to maintain unity of
the subject it seems desirable to consider also some
examples from among nonmetal complexes. The
relation between electronic and molecular structure is,
of course, one of the important basic problems of
chemical theory. It is very important also in under-
There is good reason to believe that the C1-0 bonds
have considerable double bond character as is indicated
for two of the oxygens in the electron dot formula
which is one of several equivalent structures which can
be written. To the extent that the CI-0 bond has
double bond character, it would be expected that ClOawould absorb electrons quite readily at the expense of
partially opening the double bonds. This expectation
is by no means realized, for it is known that ClOn- is
Volume 45, Number 7, July 1968
/ 453
not affected even by a reducing agent as strong as
alkali metal dissolved in liquid ammonia. The experimental observations force us t o consider an
additional factor to understand the behavior of Clod-.
The ion is negatively charged and can, therefore, be
expected to absorb electrons only if compensating
positive charge is introduced. But the oxygens of Clodare extremely weak bases, and effectivc interaction
with positive charge is achieved only by increasing the
0aC1+-02- separation. Increasing the separation not
only increases the basicity of 0 2 - but it also lowers the
energy of an unoccupied chlorine orbital. Thus, by
considering electronic structure and acid-base interactions, we have finally arrived at a rationalization, if not
explanation, of what is a fact: Clod- cau usually be
reduced only if the coordination number of chlorine is
at the same time decreased. This statement holds
true even for a l e - reduction: chlorine in the +6
state is known to have the formula C103, not C10a2-.
In each of the foregoing examples, adding even a
single electron to the oxidant results in a decrease in
coordination number for the central atom, and this
situation obtains fairly generally when the orbitals of
the valence shell have the same principal quantum
number. In a fcw instances among the nonmetallic
elements, on reduction the coordination number remains the same (NOa reduced to KO2-, or CIOl to
C102-), but in few does the coordination number increase on r e d ~ c t i o n . ~But when we turn to elements
for which the electron count in d orbitals of lower
quantum number changes, we encounter numerous
examples (among them one already considered,
HCr04--tCr(H20)63+), in which the coordination
number of the central atom increases on reduction.
The reason for the difference in behavior between Cr as
representative of a Group VI B element, and S as
representative of Group VI A, is worthy of some reflection, but will not be gone into here.
I n Figure 1 the electronic structures of the d orbitals
of the oxidized and reduced forms of couples we shall
consider in detail are shown. The present discussion of
the relation of electronic to geometric structure for
transition metal couples will be focused on octahedral
or approximately octahedral species. Since the substitution labilities of the species arc important for their
redox chemistry, and since there is a connection between electronic structure and s bstitution lability, it
seems economical of space to inclu e mention of substitution labilities a t this point. The selection of systems for detailed discussion was made with an eye to
showing a variety of structural and kinetic effccts, for
couples the redox reactions of which have been rather
intensively investigated. ,
The energies of the d orbitals are affected by the
ligands. Of the five d orbitals, the two of u symmetry
with respect to the octahedral bond axes interact
particularly strongly with the ligand orbitals. The
interaction gives rise t o a bonding set of levels and an
antibonding set. The six bonding orbitals, which are
largely ligand orbitals modified by a small admixture of
metal-centered orbitals and are occupied by six pairs
of electrons introduced by six ligands, are not shown.
The two u d orbitals shown in Figure 1 for each ion
(together with an s and three p orbitals not shown) and
which are largely metal centered, are the antibonding
levels complementary t o the occupied bonding levels
just described. The lower lying set of three d orbitals
shown for each couple in Figure 1 has a symmetry
with respect t o the bond axes. They are not affected
by u interactions, and thus lie lower in energy than the
two u d orbitals which, as has been pointed out, are
antibonding. With suitablc ligands, namely those
with low-lying, unoccupied T orbitals, the a d orbitals
of the metal can become bonding in character. I n
\
Exceptions do occur for carbon, owing to the fact that structures in which two OH groups are on a single carbon readily
dehydrate.
-
H
I
R-COH
I
OH
=
/H
R -C
\o
454 / Journal of Chemicol Education
+ H,O
tl tl ti
Figure 1.
COYP~~..
ti t i t i
---
Electronic structures of the complexes comprising some redo*
H-N-H
I
I H
Figure 2. Possible gometries of activated complexes for the reduction
of (NHslaCoNCS2+ b y CrP%ql.
(a) ond (b): models for outer-sphere
activated complexes; (4:model for an inner-sphere activated complex.
Each Co has additional NHs molecules above and below the plane of the
poper and each Cr has mdditionol HnO rnoleculer above and below tho
plane of the paper.
effect, a d electrons contributed by the metal ion are
accepted into the ligand orbitals. This kind of interaction has been called "bacB-bonding." Ligands
which can accept electron density in this way are called
"back-bonding" ligands; ligands which do not have
low-lying orbitals of symmetry suitable for back-bonding will be called "saturated ligands."
The splitting in energy in the a d orbitals as the
symmetry of the complex is reduced are represented
in Figure 1,but the splitting in energies in the a orbitals
when the symmetry is reduced from octahedral is
disregarded because the effects on the a orbitals arising
from the reduction in symmetry are smaller and, moreover, have thus far not been traced to the particular
phenomena we will be dealing with.
Chromium(II1) complexes have each of the a d
orbitals singly occupied and have a regular octahedral
structure. When an electron is added (that is, when
Cr(II1) is reduced), at least when the associated ligands
are saturated, the resulting chromium(I1) is high-spin
and the electron enters an antibonding orbital. Because
only one of the two antibonding orbitals is occupied, a
stabilization of the ion with respect to electronic energy
is possible if the ion becomes distorted so as to lower the
energy of one of the a orbitals relative to the other (the
centcr of gravity of the levels is undisturbed, and with
one electron, it occupies the lower lying level without
a compensatory promotion of another electron). The
distortion is, of course, limited by the interaction between the positive charge of the metal ion and the negative charge on the ligands, but it is, nevertheless, large
for Cr(I1). The inertia to substitution shown by Cr(111) complexes can be related to thefact that only nonbonding d orbitals are occupied, and they are fully
occupied. Nolow lying orbitals are available to engage
an entering ligand by an S Nmechanism;
~
an S Nmech~
anism is costly in energy because there are no electronic
effects to compensate for the energy required to remove
a ligand in an S N lprocess. The great lability of Cr(I1)
compared to Cr(II1) arises from the fact that an antibonding electron is added and also from the fact that the
charge on Cr2+isless than on Cr3+.
The amminecobalt(III) complexes, except for the
obvious effects on symmetry of the presence of heteroligands, are octahedral; Co(1II) is something of an
anomaly for first-row transition elements because it
assumes a low-spin electronic configuration, even for
saturated ligands such as NH3. I n most reduction reactions of Co(II1) the final Co(I1) product does, however,
assume a high-spin form. It is possible that a low-spin
form of Co(I1) is the first product of the reduction of a
Co(II1) complex and the electronic structure of an
intermediate low-spin form is shown in Figure 1. The
amminecobalt(II1) complexes undergo substitution so
slowly that they can maintain their molecular integrity
while being reduced; again because the charge is lower
and because antibonding orbitals become occupied, the
final cobalt(I1) complexes are very substitution-labile
compared t o cohalt(II1). The assumed intermediate
low-spin form of Co(I1) is expected to be very labile
in respect to substitution, at least in one of the positions.
The VZ+,3 + couple provides an interesting contrast
with Cr2+*a+. For the former couple only a d electrons
are in question and, as a result, the change in shape or
dimensions of the ions during the redox process is less
than for the latter. Furthermore, in contrast to the
situation for Cr(I1)-Cr(III), V(II), and V(II1) complexes are quite similar in lability, the higher charge on
V(II1) compensating for the change in electronic structure, that of V(I1) being more favorable to preserving
the octahedral against other configurations. The
half-time for the exchange of HzO between V(H20)a2+
sec.
(5) or V(Hz0)2+ and watera is
As is true generally of second and third row transition
elements, Ru(II)(da) and Ru(II1) (ds) assume low-spin
configurations even with saturated ligands. The
electron which is added in reducing Ru(II1) to Ru(I1)
goes into the a orbitals. Again there is little distortion
accompanying the reduction of Ru(III), but a slight
expansion of the coordination shell is expected because
of the decrease in the electrostatic interaction between
the central ion and the ligands. Because only, and
all, of the a d orbitals are occupied, Rn(II1) and Ru(I1)
are expected to undergo substitution relatively slowly,
and this expectation is borne out by experience. The
ruthenium(I1) complexes are much more labile than
those of ruthenium(III), however, and replacement of
halide by water, for example, in Ru(I1) must be reckoned with in studying the redox chemistry of ruthenium.
I n common with Ru(I1)-Ru(III), the couple Fe(I1)a
Estimated from rates of substitution of V(II1).
Volume 45, Number 7, July 1968
/
455
Pe(II1) is of the d6-d5 electronic type, hut there is an
important difference in the arrangement of the electrons.
With saturated ligands, Fe(I1) and Fe(II1) tend to
assume high-spin arrangements, and for both ions the
antibonding r d orbitals are occupied as well as the a d
orbitals. There is no significant distortion accompanying the reduction of Fe(III), but some expansion of the
coordination sphere does take place. Both Fe(I1) and
Fe(II1) complexes undergo substitution readily, those
of Fe(I1) being in general much more labile than those
of Fe(II1).
The Pt(I1)-Pt(1V) couple is a very important one to
consider in the present context because it is the only
one of the group which features a 2e- change. I n
terms of electronic structure Pt(I1)-Pt(1V) is very
similar to Cr(I1)-Cr(III), the difference being that the
orhitali are doubly occupied rather than singly occupied. Pt(IV) complexes are regular octahedra, at
least when the ligands are all identical, and undergo
substitution very slowly. The single electron entering
the antibonding orbital of chromium in the change
Cr(II1) Cr(I1) was seen to cause a strong distortion
in Cr(H20)62+. The pair of electrons added t o Pt(1V)
in reducing i t to Pt(I1) cause an even more severe distortion, weakening the bonds betweeu Pt(I1) and ligands
along a n axis of the octahedron to such an extent that
Pt(I1) complexes are ordinarily considered as square
planar in stmcture. The groups along the extended
axis are found to he extremely labile, but those in equatorial positions may undergo substitution quite slowly.
-
The Activated Complexes for Electron Transfer
Mechanisms, whatever be the type of reaction under
consideration, are discussed in terms of geometries and
properties of activated complexes, and for the purposes
of eomparing mcchanisrns for different systems it is
helpful t o classify the activated complexes. A classification which has been found useful for dealing with the
mechanisms of redox reactions is that of inner-sphere
versus outer-sphere activated complexes. These are
illustrated in kigure 2 for c ~ ( H ~ o ) reacting
~ ~ + with
(NH8)&oNCS2+.
I n the outer-sphere activated complexes the coordination sphere of the reaction partners remain intact, and
the electron given up by the reducing agent must transfer from the primary bond system of one complex to
that of the other. In an inner-sphere activated complex a molecule is shared between the coordination
spheres of both metal ions, so that, in effect, in the
activated complex the metal ions are part of a single
primary bond system. The definitions themselves
suggest important differences in the chemistries of the
two kinds of processes, primary bonds being broken and
formed in the course of the electron transfer for the
latter hut not the former, and it can reasonably be
expected that the electron transfer act itself may differ
in some respects for the two kinds of mechanisms.
Electron transfer by both kinds of mechanisms is
subject to the restrictions of the Franck-Condon Principle (4). The electron is much lighter than the nuclei
and therefore moves rapidly compared to them so that
clectron transfer takes place with the nuclei effectively
remaining stationary. Before electron transfer from
one ccriter to another can take place, the coordination
spheres must adjust so that the energy of the system is
456
/
Journol of Chemical Education
unaltered on the electron transfer. The configurations
which are appropriate for electron transfer represent a
very small fraction of the total configurations which
are accessible to the system, arid thus the rates of
electron transfer can he very low. Where the adjustments required involve only small changes from the
equilibrium dimensions, the probability of reaching a
suitable configuration is high and rates tend to be
rapid. It is clear, therefore, that the net changes in
the dimensions of the reaction partners on electron
transfer, as considered earlier, can have important
influences on rates and must be considered in discussing
mechanisms.
The classification of the activated complexes offered
is, of course, no better than the definition of coordination sphere on which it depends. The concept of
coordination sphere becomes indistinct in certain cases,
and it is expected that the classification of activated
complexes proposed will also become indistinct in some
cases. Nevertheless, it does cover a large number of
systems, and is useful everywhere if the limitations of
the classification are appreciated.
Reactions Proceeding by Outedphere
Activated Complexes
For many reactant mixtures, electron transfer takes
place more rapidly than does substitutiori in the coordination sphere of either partner. I n the absence of
an effect of one reagent labiliziug another for substitution, and such an effect has not yet been demonstrated,
we can conclude that in such systems electron transfer
takes place via outer-sphere activated complexes. This
kind of mechanism operates for all redox reactions, both
selfexchange and cross reaction^,^ among the complexes
given in Table 1.
Table 1 . Electron Transfer Process in
Outer Sphere Complexes
For every reactant pair chosen from the set in Table l
when the reactant concentrations are
M or above,
electron transfer is more rapid than substitution. All
of the reaction partners are recognized as being relatively inert to substitution, but this alone cannot lead
to a prediction of the reaction mechanisms. We need,
in addition, some idea of how rapidly electron transfer
can take place through the intact coordination spheres,
and here we must rely on experience.
Outer-sphere mechanisms operate even when one
reaction partner is substitution labile, if the other does
not provide a suitable site for coordination to the labile
partner. This is the case when Cr(HzO)aa+reduces
T h e term selfexchange refers to an electron transfer reaction
in which at most, the only net change is a redistribution of isotopes, eg.,
+
Ru(NH#+ + Ru (ND3hH = Ru(NHa)e8+ Ru(NDdea+
In a cross-reaction, electron transfer results in a net chemical
change, e.g.,
Ru(NIIs)2+ Ru(ophen)sa+ = R I I ( N H $ ) ~ + R ~ ( o p h e n ) ~ ~ +
+
+
Co(NHJ63+. The electronic structure of the coordinated ammonia is shown below and it is clear that it
does not provide an unoccupied electron pair t o interact
with Cr2+,no matter how substitution-labile Cr2+is.
Outer-sphere activated complexes may, of course,
operate even when both partners are relatively labile
to substitution and the ligands have suitable sites to
provide the bridging groups characteristic of innersphere mechanisms. However, in such systems it is
often difficult to discover what the reaction mechanism
is. Self-exchange between Fe(Hz0)62+,3 + has been
much studied, particularly since the first successful
attempt to measure the rate of the reaction (6). But,
owing to the lability of both partners, the nature of the
activated complex for this important reaction is not
known.
A powerful method for correlating information
obtained for outer-sphere mechanisms has been introduced by R. A. Marcus (6). This correlation in approximate form is expressed by the equation
kll =
l/kn&Km
Here lcll and lczz are the self-exchange rates for the
reaction partners and ICI2 is the equilibrium constant
for the cross reaction (in the complete theory KIP
needs to be modified when it becomes very large), and
lc12 is the specific rate for the cross reaction.
If the correlation were generally valid, the subject
would be reduced to studying self-exchange processes
and measuring equilibrium constants.
I n Table 2 are presented some examples testing the
correlation. I t is seen to be rcmarkably good for a
number of cases, but it fails in individual instances,
notably in most cases involving the Co(I1)-Co(II1)
couple. Idiosyncracies of other combinations will
undoubtedly appear as the data become more refined.
Nevertheless the Marcus correlation is a powerful one,
leading as it does to a calculation in most instances of a
specific rate to an order of magnitude or so.
Though the kinetics of the reactions being discussed
are usually simple-the rate has so far without exception been found t o he first-order in each respect-much
remains to he understood about this class of reactions.
A question which is unanswered for any system is the
distance of approach of the reaction partners on electron
transfer. Another is concerned with the influence of
the electronic structure of the ligands and of the central
Table 2.
Tests of the "Relative" Marcus Theory
ion on the reaction rates. Expressed in terms of selfexchange rates, the range covered is from a specific rate
a + (10) to >lo7
of <lo-" M-' sec-' for CO(NH&~+,
M-1 sec-I Fe(phen)a2+, a + (If). Just what the influence of the ligands is and what the interaction of
central ion with ligand is to produce such a large range
in specific rate is still a matter of conjecture. Particularly interesting is the possibility that the delocalization of the d electrons into the ligands (when these have
the capacity for back-bonding) plays an important role
in affecting the rates. Even greater contrasts in rate
can be expected as the factors influencing them are
better understood and a conscious effort is made to
change rates by modifying the ligands.
The Inner-Sphere Activated Complex
The conclusion that an inner-sphere mechanism
operates usually takes the form of proof that a group is
transferred from one reactant partner to another immediately accompanying the change in oxidation
number. To support the conclusion, it is not enough
t o show that net transfer of a group takes place, but the
possibility must also be covered that the group in
question may be first lost to the medium and then be
incorporated into the products. Proof that a hinuclear
intermediate is generated as the immediate product
of the electron transfer process can also be an adequate
basis for the conclusion that an inner-sphere mechanism operates, and such proof has been advanced in a
large number of systems.
Nonmetol Complexes
The inner-sphere activated complex is exemplified by
numerous reactions involving abstraction of a hydrogen
or halogen atom from carbon by means of a radical, as,
for example, in:
Even though in most such cases the conclusion that the
mechanism is as indicat,ed is based on examination of
the products of the net change, there is no strong reason
for questioning it because oft,en it is the only chemically
reasonable course for the reaction to take. Conclusions
about mechanism based on "chemical reasonableness"
become more and more secure as more is understood,
and so are particularly secure in many areas of organic
chemist,ry.
An inner-sphere activated complex is demonstrated
for the reaction
+ C10,- + H,O
SO2
=
+ H + + C102-
RS04-
by the observation (1g) t,hat each sulfate formed contains one atom of oxygen derived from C103- (the
reaction shown is the probable first step of a sequence
leading t o C1- as the final ehlorine-containing product).
I t seems likely that most reactions of this type-that is,
involving nonmetal centers undergoing 2e- changestake place by way of inner-sphere activated complexes.
By transfer of the entity:O from oxidant to reductant,
"The self-exchange rate for W(CN)s4-,5is not known but a
single value correlat,es the two mdependent rates measured for
this couple.
the coordinational changes a t each center demanded
by the changes in oxidat,ion state are simultaneously,
and a t least partially, met.
Even in reactions of oxy ions, it is by no means
mandatory that the entity t,ransferred t,o the reducing
Volume 45, Number 7, July 1968
/
457
agent be :O (or its equivalent H:O+). Thus there
is evidence that when HOCl reacts with SO2 (aq), only
part of the reaction rcsults in transfer of oxygen from
HOCl to sulfur. The remainder of the reaction may
well take a course in which C1+ is transferred from
HOCl
and virtually all of the product chromium is shown to be
in the form (H20)sCrC12+. It has also been shown that
if free radioactive chloride is present in the solution;
very little is found in the product (H20)5CrC12+. Thus
we can conclude that chlorine is transferred directly
from Co to Cr in the redox process and, furthermore,
that it is not first released to solution and then incorporated into a Cr(II1) complex. Thus the sequence of
events in the overall reaction can be represented as
follows
(NH8),CoC12++ Cr(H,O)?+
[(NH,)jCo"rCICr11(H20)i14+
-
0
I
CI-S-OH
I
+ H,O
-
H+
+ Cl- + HSo,-
(rapid equil.) (8)
(7)
0
Whether the reducing agent will attack an oxidant such
as HOCl a t an oxygen or the other nonmetal center is a
question that must still be settled by experiment.
Since Co(I1) undergoes substitution readily while
Cr(II1) does not, I1 is expected to dissociate a t the
Co-C1 position, and in acid solution the decomposition
of I1 according to the net change
Metal Complexes
The complexes featured in the preceding section are
held together by strongly covalent bonds, and conclusions about mechanism based on experience with these
are not necessarily applicable to the kind of metal
complex which will he considered in this section. We
will deal here with the other extreme of behavior in
which the central ions are strongly electropositive and
the oxidation state is low enough so that the complexes
exist as aquo rather than as oxy or hydroxy ions. I n a
complex such as Fe(H20)62+,or even (NH&COOHZ~+,
the bonds are highly ionic and there is no basis, short of
that provided by experiment, for holding that in a particular system an inner-sphere mechanism can operate
for reaction in such a system. Experiment has, however, demonstrated that inner-sphere mechanisms do in
fact also provide a path for electron transfer for complexes having highly ionic interactions between central
atoms and ligands.
The first system (IS) involving metal complexes in
which this kind of mechanism was demonstrated is quite
suitable for introducing the subject. Just as the experimental demonstration that the oxidation of SO? by
C103- proceeds by an inner-sphere mechanism depended on the fact that the reactant ClOa- and the
product Sod2- undergo oxygen exchange relatively
slowly, while SOz is substitution labile, so in the proof
of mechanism to be offered for the reaction of
Cr(Hz0)62+with (NH3)&oCl2+ advantage has been
taken of substitution characteristics of reactants and
products. The ion (NH3)&oC12+ persists intact in
acidic solution for many hours with essentially no release
of NH3 and with only a slight release of C1- to solution.
Substitution in Cr(H20)62+takes place very readily
(the half-time for the exchange of coordinated water
with the solvent is < l o - 9 sec). I n the products of the
reaction, the substitution labilities a t the two centers
are reversed, the Co(I1) center being very labile, while
substitution of C1- by H 2 0 on Cra+is about as slow as
it is for the cobaltammine complex. On the basis of
these considerations, we know that chromium can
readily make a bond to chloride when it (the chromium,
that is) is in the +2 state but not after it has heen
oxidized to the + 3 state. Now the reaction of
Cr(H20)s2+
with (iYH3)&oC12+takes place very rapidly,
458
/
Journal of Chemical Education
is expected and is realized.
This kind of mechanism seems to be general for the
reaction of Cr(H20)ti2+with Cr(II1) and Co(II1)
complexes when these oxidants have ligands which
provide suitable bridging groups (as will be shown, to
insure an inner-sphere mechanism for complex ligands
it is not enough that one of the ligands has a polar
group which Cr2+ can attach to). It has also been
demonstrated for the reaction of Cr2+with FeC12+(lh),
with V ( H 9 0 ) F (15), for the reduction by V(Hz0)o2+
of VOZ+(lo), and of some Co(II1) (17,18) and Cr(II1)
(19) complexes, for the reduction of Co(II1) complexes
by Fe(I1) (SO),and for a large number of reductions by
the ion C O ( C N ) ~ ~(21,
- 22). All of these foregoing
systems involve le- changes. It is, therefore, especially
important to note that inner-sphere mechanisms have
also been demonstrated (25) for 2e- redox reactions
involving metal complexes. A single rate law
k(C1F) (PtLbB+)
(t-PtL'ClgZt)
accounts for three different processes (1, represents a
neutral ligand)
( 1 ) C1-exchange between CI- in solution and 1-PtL4'Cl?+ as
catalysed by PtL2+ (L
=
L').
(2) Pt exchange between PtLda+and t-PtL+'CI?+ (L = L').
(3) The
reaction PtL2'
+
t-PtLKWC
=
+
P~LA'~'
The structure of the activated complex is presumably
The labile axial positions of PtLp2- are used to make
bonds to the bridging Cl- and to another brought in
from solution.
The possibility of electron transfer through a doubly
bridged activated complcx will come to mind, and this
possibility has led to attempts to find evidence for it.
The most definitive demonstration (24) has been made
for the reaction
The reaction was followed by isotopic labelling of
chromium, and it was found that the diazido complex
is conserved though the isotopically labelled chromium
becomes distributed over both Cr species. Furthermore, it is known that if N3- were once lost from
Cr(III), it would be reduced under the conditions of the
experiment, and thus the conclusion follows that the
azide groups are transferred in pairs.
Electronic Structure and Mechanisms
Of the reactions of the ions which comprise the particular couples displayed in Figure 1, those between
Cr(I1) as reducing agent and Co(II1) or Cr(II1) complexes as oxidizing agents show the greatest rate contrast
between inner and outer-sphere mechanisms, the innersphere mechanisms being strongly favored. A reason
for this preference can be advanced in terms of the electronic structures of the complexes. Structures 111,IV,
and V below show a hinuclear complex between (NH&
CoC12+and Cr2+in an initial state, in an intermediate
state, and in a state which then leads to Co-C1 rupture
and thus formation of the products
L(NII~)jCol"C1.. CrIr(H10).1'+
111
The electron to be transferred from Cr(I1) to Co(II1)
is in a a antibonding orbital and on transfer it enters a
a antibonding orhital for Co(II1). As C1- moves from
Co(II1) to Cr(II), the energy of the chromium a
orhital is raised and that of the cobalt a orhital is
simultaneously lowered. At somc intermediate configuration, suggested by the structure IV above, the
energy of the system is independent of whether the
electron is on Co or Cr, and if the interaction between
Co and Cr orbitals is great enough it can he found on
either center. As the motion of C1- continues to the
right, the relative changes in energy of the orbitals
continue, whereupon the electron is trapped on the
cobalt center, and reaction is then completed by dissociation of the now labile Co-Cl hond. It is clear that
the electronic structure type dealt with is especially
suited to the inner-sphere mechanism, because the needs
at the two centers required for electron transfer are
reciprocal and are met by the simple motion of a
bridging atom from oxidant to reductant. A similar
description can be given for the reaction in the 2ecase, as in Pt(I1) reacting with I't(IV), except that
here the problem is made even more interesting by the
very severe dislocations in the position trans to the
bridging group.
When V2+ acts as reducing agent, outer-sphere and
inner-sphere mechanisms are much more closely balanced than for Cr2+. Thus. a good case has been mesented for the conclusion tha<v2+ reacts with Goth
Co(NH&"
and (NH3)&oOHz3+ by outer-sphere
mechanisms (25). A strong case also has been presented (18) for the conclusion that the reaction of
r(NH&Co-0 \
I
(where Y is H, CHs, OH, NH,) is of the inner-sphere
type. The change in mechanism for H 2 0 in place of
carhoxylate as the heteroligand may be a consequence
of the fact that the latter but not the former has a
rather low-lying n orbital to engage the donor orbital
of V2+ (note that this has a symmetry) in an innersphere activated complex.
A new rate-determining situation arises for V2+ as
reductant by virtue of the fact that substitution on
V(Hz0)62+
is relatively slow, and with suitable hridging
groups electron transfer is rapid. In the reaction of
V2+with the complex (18)
r(NHACo-0,
77+
IL
\
c-c'
I1
I/
sii
1
_I
and with CrSCN2+ (19), the formation of the binuclear
complex appears to be rate-determining-that is, the
rate of substitution on V(HZO)B'+determines the rate
of the redox process. When substitution on V(H20)62+
is rate-determining, the redox reaction rates are rather
insensitive to the nature of the oxidizing agent. For
both CrCNZ+and the ar carbonyl cobalt(II1) complexes,
the second-order specificrates a t 25'C are about 10 A P 1
sec-l.
Ru(III), it will be remembered, has the electron
vacancy in the n d levels, while for Co(II1) it is in the
a d levels. This differenceexplains an important difference between the chemistry of the reduction of the two
kinds of complexes. When a Co(II1) complex is reduced by an inner-sphere mechanism, in no case thus
far encountered has a binuclear product been observed
as the product of the reduction with Cr2+; on the other
hand, with Ru(II1) complexes as oxidants, hinuclear
intermediate products are often observed, specifically
thus far with OH-, HC02-, and CH3C02- as bridging
groups (ZG). This differencein chemical behavior can
be traced to the fact that the a antibonding electron
absorbed by Co(II1) labilizes the Co-(bridging ligand)
bond much more than the n electron absorbed by Ru
lahilizes the Ru-(bridging ligand) hond. Co(II1) and
Ru(II1) differ in another respect; it seems to be rather
general that there is much less contrast in rates between
inner- and outer-sphere mechanisms for Ru(II1) ( a d
electron acceptor) than for Co(III), (a d donor).
Finally, just as with V2+compared to Cr2+as electron
donor, so for Ru(II1) compared to Co(II1) as acceptor
in mediating electron transfer a carhoxylate ion is relatively more efficient than a group such as OH-, which
does not have low-lying unoccupied s orbitals.
These few examples perhaps suffice to indicate that
there is a strong interplay between reaction rates by the
two mechanisms and the electronic structure. This
relationship has so far been only partially explored, and
it promises to become an extremely interesting facet of
this subject as we learn more about it.
Electron Transfer by Remote Attack
I n most of the systems discussed thus far a single
atom mediates in the electron transfer process. But in
comparing Cr2+ with V2+ or Co(II1) with Ru(II1) in
respect to the efficiencywith which a carboxylate serves
to mediate in electron transfer, the possibility of remote
attack has already been alluded to. Remote attack in
this context implies a redox process brought about by
electron transfer not merely through a single atom, hut
Volume 45, Number 7, July 1968
/
459
through a more extended bond system. Thus, V2+in
reacting with (NH8)sCoOzCH2+and making use of an
activated complex of the geometry shown below
would be described as reduction of the Co(II1) complex
by remote attack.
In the particular instance described above there is no
proof that V2+attacks a t the site indicated. The conclusion that it does is based on rather indirect arguments. By assuming remote attack for V2+we find a
reasonable e~planat~ion
for the fact that V2+compared
to Cr2+ find a carboxylate ion unusually effective in
mediating electron transfer. Direct proof for remote
attack has been obtained for other systems and the
proof is outlined for a system selected because it has
been rather thoroughly studied (27).
In the reaction of
with Cr2+when the oxidant is in excess and the acidity
is high, the major chromium-containing product of the
reaction bas the structure
This product cannot arise from the interaction of
Cr(H20)2+with
even catalysed by Cr2+,because it is in fact unstable
with respect to the free amide and hexaaquochromium(111). The rate a t which the intermediate aquates is,
however, slow enough so that it has been possible to
characterize the intermediate.
It is clear that where remote attack takes place there
are numerous opportunities for varying the nature of
the mediating group, and the effect of these changes on
the rate of reaction is a matter of interest. The rates
of reaction, even if they could be expressed in terms of
the concentration of some binuclear intermediate such
as
do not measure the rate a t which the electron traverses
the bridging molecule. Bond readjustments need to
take place prior to electron transfer and it is likely that
these, rather than the speed a t which the electron moves
through the bridging group, determine the rate of transfer in a binuclear intermediate.
460
/
Journol o f Chemical Educotion
A fund:menr:d problcm, which providcs a xrcat deal
of incentive for the research in this srea is that of lcorning the mechanism of electron transfer through extended
bond systems. A significant distinction in respect to
mechanism is the following: on the one hand a group
such as
may be involved by being converted to a radical ion
the electron then being passed on to the oxidant; on
the other, the bridging group may act by increasing the
probability of transfer by '' tunnelling." For a bridging
group such asF- mediating between Co(II1) and Cr(II),
it is certain that the latter kind of mechanism operates.
The intermediate state Co(III).F2-.Cr(III) (or the
alternative Co(I1) .F. Cr(II1) if an electroil were first
to transfer from bridging group to oxidant) is so high
in energy that it cannot provide a path for electron
transfer as facile as is observed. For the more complex
ligand, the situation is not nearly so clear and, in fact,
the evidence suggests (27) that in mediating in electron
transfer between Cr2+and Co(II1) or Cr(III), Cr2+ first
converts the bridging group to a radical ion. Even if
this conclusion is correct for the particular system mentioned, it would not necessarily apply to other cases.
The mechanism of electron transfer is expected to depend on the interrelation between the properties of the
electron donor, electron acceptor, and bridging group.
In the example mentioned, the possibilities may be
limited because the donor and acceptor orbitals have u
symmetry, whereas the lowest unoccupied orbitals for
the ligand have r symmetry. When the acceptor and
donor orbitals have a symmetry as well, i t may develop
that electron transfer does take place by resonance
transfer from reductant to oxidant.
The study of the mechanism of oxidation-reduction
reactions, even as limited to systems of simple chemistry, has only begun, but the chemistry involved
already has been shown to be astonishingly rich. Only
a few of the important aspects of the field have been
dealt with in this article; others which are recognized
and are the subject of current investigation are the
influence on the reaction rates of ligands which are not
direct carriers of the charge transferred, exploiting redox
reactions for preparative purposes, influencing the reactions by changing the solvent, learning the mechanism
of electron transfer at electrodes. Progress in understanding the basic chemistry of these processes also
represents progress in understanding and controlling
reactions of direct utility or of significance for other
areas of science, among them electrode processes, reactions involving oxygen (this includes corrosion as well
as the beneficiation of carbon compounds by oxidation),
metabolic reactions, and other catalytic processes.
There is also a relation between the phenomenon encountered in the study of redox reactions in solution and
electronic phenomena in solids; both subjects will benefit as this relationship is understood and developed.
General References
BASOLO,F., A N D PEARSON,R. G., ",Mechanisms of Inorganic
Reactionu" (Snd Ed.), John Wiley & Sons, Inc., New York,
1967.
GRAY,11. B., "Electrons and Chemical Bonding," W. A. Benjamin Inc., New York, 1964.
T n u n ~ ,H., Adu. in Inorganic Chemislrjl and Radio Chenrisl~l,
Academic Press Inc.. 1959. Vol. 1., Chanter 1.
HALPERN,
J., &uaTterlZ;~edievl(London), 15,207 (1961).
SUTIN,N., Annual Reuim, Physical Chemistql, 12, 28.5 (1962).
~
~.
~~
Literature Cited
(1) MERIDETH,C. W., A N D CONNICK,
R. E., UCRL-11704
(1965).
s.,
(1951);
(2) HUNT,J. P., A N D TAUBE,IT., J . Chen~.P ~ ~ I 19,602
PLANE,R. A., A N D HUNT,J. P., J . Am. Chem. Soc., 76,
5960 (19.54).
Y., J. Chem. Phys., bo be
(3) OLSON,M., A N D KANAZAW,
rn!hlished.
A~
~~---~.
(4) L I R ~ YW.
, F., J . Phys. Chem., 56,863 (1952).
(5) DODSON,
R. W., J. Am. Chem. Sac., 72, 3315 (1950).
(6) MARCUS,
It. A,, J . Phys. Chem., 67,853 (1963).
R. J., PUEDIE,N., AND SUTIN,N. Inorg. Chem., 3,
(7) CAMPION,
1091 (1964).
(8) MEYER,T. E:, AND TAUBE,H., Im~norg.Chem., 7 (1968).
(9)
J. F.. AND TAUBE.
, , ENDICOTT.
, H.., J. Am. Chem. Soe.. 86.
1686 (1964). '
(10) STRANKS,
D. R., Dise. Faraday Soc., 29, 73 (1960).
~~~~
(11) LARSEN,D. W., A N D WAHL,A. C., J . Chem. Phys., 43, 3765
(1965).
J., and TnuaE, IT., J . Am. Chem. Soe., 74, 37.5
(12) FIA~,PER~N,
11952).
(1964).
(15) ESPENSON,
J. H., Inorg. Chem., 4, 102.5 (196.5).
(16) NE\+TON,T. W., A N D B.~xER,F. B., Inorg. Chem. 3, ,569
11964).
(17) ESPENSON,J. H., J. Am. Chem. Soe., 89, 1276 (1967).
(18) PRICE,H. J., AND TAUDE,H., Inorg. Chem., 7, 1 (1968).
(19) R K E R ,B. R., ORHANOVIC,
M., A N D SUTIN,N., J. Am. Chem.
Sac., 89, 722 (1967).
(20) HAIM,A,, A N D SUTIN,N., J . Am. Chem. Sac., 88, 5343
(1966).
HAIM,A,, A N D WILMARTH,
W. K., J . Am. Chem. Soe., 83,
'
509 (1961).
CANDLIN.
3. P.. HALPERN.
J.. A N D NAKAMURA.
, S.., J. Am.
Chem. SOC., 85, 2517 (1963j.
BASOLO,F., MORRIS,M. L., A N D PEARSON,
R. G., Dise.
Fa~odmlSoe., 29,42 (1960).
SNELLGROVE,
R., A N D KING,E. L., J . Am. Chem. Soe., 84,
4609 (1962).
DoDE~,,P. IT., A N D TAUBE,H., Z. fur Phwzk. Chem., 44,
92 (1966).
I STRITAR,
J. A., Ph.D. Thesis, Stanford University, 1967.
NORDMEYER,
F.,A N D TAUHE,
H., J . Am. Chem. Sac., 90,
1162 (1968).
Volume 45, Number
7,July 1968 / 461