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
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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
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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
