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chapter 16 Kinetics of Homogeneous electron transfer
16.1 Introduction…………………………………………………………………………….1
16.2 Types of Homogeneous Electron Transfer Processes……………………………….. 2
16.3 Reactions Between Metal Complexes………………………………………………… 3
16.3.1 Stable Oxidation States……………………………………………………….. 3
16.3.2 Complementary and Noncomplementary Reactions………………………….. 4
16.3.3 1:1 Electron Transfer Reactions………………………………………………. 8
16.3.4 2:1 Reactions………………………………………………………………….. 8
16.4 Reactions Between Metal Complexes and Nonmetallic Species…………………... 10
16.4.1 General Features…………………………………………………………….. 10
16.4.2 Reactions of Molecular Oxygen…………………………………………….. 18
16.4.3 Reactions of Aqueous Halogens and Hypohalous Acids……………………. 22
16.4.4 Reactions of Hydrogen Peroxide……………………………………………. 26
16.4.5 Reactions of Molecular Hydrogen…………………………………………... 28
16.4.6 Reactions of Sulfurous Acid………………………………………………… 32
16.5 Reactions Between Nonmetallic Species……………………………………………. 33
16.5.1 General Features…………………………………………………………….. 33
16.5.2 Reactions of Oxyanions……………………………………………………... 35
16.5.3 Peroxide Reactions………………………………………………………….. 39
16.5.4 Oxidation of Cyanide……………………………………………………….. 40
16.5.5 Oxidation of Sulfide…………………………………………………………. 42
16.1 Introduction
In the previous chapters we encountered two main categories of charged entities: electronic charge carriers (i.e., electrons and holes) and ionic charge carriers (i.e., cations and anions). In this chapter we examine the unique contributions of these charge carriers to the kinetics and mechanisms of chemical reactions in aqueous systems. As noted in Chapter 15, in general the rates of a given chemical reaction may be dependent on both chemical processes (i.e., the making and breaking of bonds, and changes in oxidation states) and physical processes (i.e., transport of reactants and products). In this chapter we turn our attention to the chemical aspects of electron transfer.
We distinguish between those reactions in which electron transfer requires collision of the reactants (this chapter) and those in which the respective reactants undergo oxidation and reduction steps at spatially separated sites on an electrode surface (Chapter 19). The first type of reaction, i.e., homogeneous redox reaction, may be represented as:
A+ (aq) + B(aq) Û A+ • B(aq) (16.1a)
A+ • B(aq) Û A(aq) + B+(aq) (16.1b)
On the other hand, the second type of reaction, termed an electrode or electrochemical reaction, takes the form:
A+ (aq) + e- (electrode) Û A (aq) (16.2a)
B (aq) Û B+ (aq) + e- (electrode) (16.2b)
Combination of Equations 16.2a and 16.2b gives an overall reaction which is the same as that described by Equations 16.1a and 16.1b:
A+(aq) + B(aq) Û A(aq) + B+(aq) (16.3)
In view of our discussion in Chapters 8 and 9, we expect that in general a solid/aqueous interface will carry an electrical potential. This potential is an important factor in interfacial rate processes (see Chapter 19).
16.2 Types of Homogeneous Electron Transfer Processes
In this section we are concerned with three main types of redox reactions: (a) Redox reactions between metal ions (e.g., Equation 16.45), (b) redox reactions between metal ions and nonmetallic species (e.g., Equations 16.46 - 16.48), and (c) redox reactions among non-metallic species (e.g., Equations 16.49 and 16.50).
Cr(II) + Co(III) ® Cr(III) + Co(II) (16.45)
4 Fe(II) + O2 + 4H+ ® 4Fe(III) + 2H2O (16.46)
Cu(II) + H2 ® Cu + 2H+ (16.47)
8V(III) + ClO4- + 8H+ ® 8V(IV) + Cl- + 4H2O (16.48)
H2SO3 + H2O2 ® H2SO4 + H2O (16.49)
S2O82- + 2I- ® 2SO42- + I2 (16.50)
All these reactions involve changes in oxidation states. However the reactions may also be accompanied by changes in molecular geometries and coordination numbers. For example, on going from Cr(H2O)62+ to Cr(H2O)63+ to HCrO4-, there is a change from a tetragonally distorted octahedral complex to an undistorted octahedral complex, to a tetrahedral structure.
The elementary reactions of homogeneous electron transfer processes between metal ions are of two types, involving inner-sphere (bridged) activated complexes, or outer-sphere activated complexes. In the case of the inner-sphere mechanism a ligand forms a bridge linking the two reacting metal ions. On the other hand in the case of the outer-sphere pathway, the coordination spheres of the reductant and the oxidant are preserved. In this case electron transfer occurs by tunneling between the two metal centers. The relative importance of one or the other mechanism is in part related to the ease with which the resulting complexes undergo ligand exchange reactions. It is to be noted that where redox reactions are coupled with changes in the composition and structure of the coordination spheres of the reactants, the rate-determining step may be an electron-transfer step in some cases, and a ligand substitution step in others.
An important aspect of redox reactions is the role played by reactive intermediates. In the case of redox reactions involving metal ions these intermediates take the form of metal ions with unstable oxidation states. On the other hand, reactions of nonmetallic species often involve bond-breaking processes and the reactive intermediates occur as free radicals, which are atoms or molecules with one or more unpaired electrons.
16.3 Reactions Between Metal Complexes
16.3.1 Stable Oxidation States
Since redox reactions involve the transfer of electrons leading to changes in oxidation states, it is helpful to begin our discussion by recalling the characteristic valencies of aqueous metal ions. A variety of oxidation states are encountered among metal ions present in aqueous solution; Table 16.3 presents a summary. Some metal ions have only one stable oxidation state in aqueous solution, e.g., the alkali metal ions (monovalent, M(I)) and the alkali earth metal ions (divalent, M(II)). Others have two stable oxidation states, e.g., Cu(I)/Cu(II), Au(I)/Au(III), Fe(II)/Fe(III). A number of metals exhibit more than two stable oxidation states, e.g., Cr(II), Cr(III), Cr(VI); V(II), V(III), V(IV), V(V). Not all the valence states indicated in Table 16.5 occur in noncomplexing aqueous solutions. Thus Cu(I) and Au(I) require stabilization by complexing ligands (e.g., Cu(I)-Cl-, Au(I) - CN-, Mo(IV) - CN-).
If only two stable oxidation states are accessible to a particular metal, and these differ by one, we refer to the metal as a one-electron reagent. On the other hand if the two available oxidation states differ by two (e.g., Tl(I)/Tl(III), Au(I)/ Au(III), Pt(II)/ Pt(IV)), we have a two-electron reagent. Similarly we have the three-electron reagent Cr (III)/ Cr (VI). It should be noted that a multi-valent metal ion can act as a one-electron reagent if it possesses two consecutive stable oxidation states differing by one (e.g., V(II)/V(III), V(III)/V(IV), V(IV)/V(V)).
Table 16.3 Stable oxidation states of metal ions in aqueous solution
Oxidation State Examples
M(-I) Re
M(0) Hg
M(I) Li, Na, K, Rb, Cs, Re, Cu, Ag, Au, Hg, Tl
M(II) Be, Mg, Ca, Sr, Ba, V, Cr, Mn, Fe, Ru, Os, Co, Rh, Ir, Ni, Pd,
Pt, Cu, Ag, Zn, Cd, Hg, Ge, Sn, Pb, Sb
M(III) Sc, Y, La, Eu, Ce, Ti, V, Nb, Cr, Mo, W, Mn, Re, Fe, Ru, Os,
Co, Rh, Ir, (Ag), Au, Ga, In, Tl, Bi
M(IV) Ce, Ti, Zr, Hf, Th, V, Mo, W, U, Ru, Os, Rh, Ir, Pd, Pt. Ge,
Sn, Pb
M(V) V, Nb, Ta, Mo, W, (U), Sb
M(VI) Cr, Mo, W, U, Mn, Ru, Os, Rh, Ir
M(VII) Mn, Re, Ru
M(VIII) Ru, Os
16.3.2 Complementary and Noncomplementary Reactions
Redox reactions between metal complexes in aqueous solution may be classified in terms of the number of electrons that are transferred between the reactants. Thus we can distinguish, for example, between one-, two-, and three-, electron transfer reactions. In a one-electron transfer reaction, the oxidation states of the respective reactants and products differ by only one. Thus the overall stoichiometric reaction involves the transfer of a single electron from one reactant to the other:
M(III) + N(II) = M(II) + N(III) (16.51)
M(II) + N(I) = M(I) + N(II) (16.52)
In a two-electron transfer the oxidation state of at least one of the reactants changes by two:
M(III) + N(II) = M(I) + N(IV) (16.53)
M(III) + 2N(II) = M(I) + 2N(III) (16.54)
Equation 16.53 represents a complementary reaction in that the changes in the oxidation states of the oxidant (M(III)) and the reductant (N(II)) involve the same number of electrons (i.e., 2 electrons: M(III)/M(I), N(II)/N(IV)). In contrast Equation 16.54 describes a noncomplementary reaction; in this case the oxidant and reductant experience different changes in oxidation state (i.e., 2 electrons: M(III)/M(I); 1 electron: N(II)/N(III)).
A reaction between an n-electron reagent and an m-electron reagent is termed an n : m electron transfer reaction. Thus Equations 16.51 and 16.52 describe 1:1 electron transfer reactions. On the other hand Equation 16.53 depicts a 2:2 electron transfer reaction while Equation 16.54 represents a 2:1 electron transfer reaction. Table 16.4 presents a summary of kinetic data for redox reactions between selected metal ions.
EXAMPLE 16.15 One- and two-electron reagents
Indicate whether the following are one- or two- electron reagents: (a) Fe(II), (b) Ce (IV), (c) Sn(II), (d) Cr(II), (e) U(IV).
Solution
(a) It can be seen from Table 16.5 that Fe has only two stable oxidation states in aqueous solution, i.e. Fe(II) and Fe(III). Since these oxidation states differ by one, we consider Fe(II) a one-electron reagent.
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Table 16.4 Rate laws for redox reactions between metal complexes
Reaction / Rate Law / Rate constantsCr(II) + Co(III) = Cr(III) + Co(II) / -d[Cr(II)]/dt = k1[Cr(II)][Co(III)] / Cr2+/ct(NH3)5X2+, k1(M-1s-1) = 0.5(X = H2O),
1.5 x 106(X = OH-), > 103(X = Cl-) at 25°C
Cr(II) + Fe(III) = Cr(III) + Fe(II) / k1[Cr2+] + k2[Cr2+][FeOH2+]
+ k3[Cr2+][FeCl2+] + k4[Cr2+][Fe3+][Cl-] / k1 = 2.3 x 103 M-1s-1, k2 = 3.3 x 106 M-1s-1,
k3 = 2.0 x 107 M-1s-1, k4 = 2.0 x 104 M-2s-2
Fe(II) + Co(III) = Fe(III) + Co(II) / k1[Fe2+][Co3+] + k2[Fe2+][CoOH2+] / k1 = 10 M-1s-1, k2 = 6500 M-1s-1 at 0°C
(I = 1.0)
Ti(III) + Fe(III) = Ti(IV) + Fe(II) / (k1 + k2[H+]-1 + k3[Cl-])[Ti(III)][Fe(III)]
Ti(III) + Hg(II) = Ti(IV) + ½(Hg(II))2 / (k1[H+]-1 + k2[H+]-2)[Ti(III)][Hg(II)]
Ti(III) + Pu(IV) = Ti(IV) + Pu(III) / k[Ti(III)][Pu(IV)][H+]-1
Np4+ + Fe3+ + 2H2O = NpO2 + Fe2+ + 4H+ / k[Np(IV)][Fe(III)][H+]3
U4+ + 2Fe3+ + 2H2O = UO22+ + 2Fe2+ + 4H+ / (k1[H+]-1 + k2[H+]-2)[U(IV)][Fe(III)]
U4+ + 2Ce4+ + 2H2O = UO22+ + 2Ce3+ + 4H+ / (k1[H+]-2 + k2[H+]-3)[U(IV)][Ce(IV)]
2Fe(II) + Tl(III) = 2Fe(III) + Tl(I) / 2k1k2[Fe(II)]2[Tl(III)]/k-1[Fe(III)] + k2[Fe(II)]
Tl(I) + 2Co(III) = Tl(III) + 2Co(II)
Tl(I) + 2Ce(IV) = Tl(III) + 2Ce(III)
(Hg(I))2 + 2Co(II) = 2Hg(II) + 2Co(II)
(Hg(I))2 + 2Ag(II) = 2Hg(II) + 2Ag(I)
(Hg(I))2 + Tl(III) = 2Hg(II) + Tl(I) / k[Hg(I))2][Ti(III)]/[Hg(II)]
(Hg(I))2 + 2Mn(III) = 2Hg(II) + 2Mn(I)
Cr(III) + 3Ce(IV) = Cr(VI) + 3Ce(III) / k[Cr(III)][Ce(IV)]2/[Ce(III)] / k =
3V(IV) + Cr(VI) = 3V(V) + Cr(III) / k[V(IV)][Cr(VI)]/[V/(V)] / k = 0.62 M-1s-1
2Fe(II) + Cr(VI) = 2Fe(III) + Cr(III) / k[Fe(II)][Cr(VI)]/Fe[Fe(III)]
V(III) + Fe(III) = V(IV) + Fe(II) / k1[V(III)][Fe(III)] + k2k3[Fe(III)][V(III)]/
k-2[Fe(II)] + k3[V(III)][V(CIV)]
Table 16.4 Continued
Fe(II) + V(V) = Fe(III) + V(IV) / (k1[H+]-1 + k2 + k3[H+])[Fe(II)][V(V)] / k1 = 17s-1, k2 = 240 M-1s-1, k3 = 4610 M-2s-1
at 55°C (I = 1.0)
V(III) + Co(III) = V(IV) + Co(II) / k1[V(III)[Co(III)] + k2[V(IV)][Co(III)] / k1 = 0.192 M-1s-1 at 0°C (I = 1.0)
V(III) + Np(V) = V(IV) + Np(IV) / k1 + k2[Np(IV)]/[V(IV)])[V(III)][Np(V)] / k1 = 0.3 M-1s-1, k2 = 0.16 M-1s-1
U(IV) + Tl(III) = U(VI) + Tl(I) / k[U(IV)][Ti(III)]
2Cr(II) + Tl(III) = (Cr(III))2 + Tl(I)
2V(III) + Tl(III) = 2V(IV) + Tl(I)
Sn(II) + V(V) =
Cr(II) + U(VI) =
Cr(II) + Np(VI) =
Co(II)(CN)53- + Fe(III)(CN)63- =
Fe(II) + Pu(VI) = Fe(III) + Pu(V) / [k1 + 1/(k2 + k3[H+])][Fe(II)][Pu(VI)]
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(b) Cerium has two stable oxidation states: Ce(IV) and Ce(III). Thus Ce(IV is a one-electron reagent.
(c) The two stable oxidation states of Sn are Sn(II) and Sn(IV), which differ by two. Thus Sn(II) is a two-electron reagent.
(d) Chromium has three stable oxidation states, i.e. Cr(II), Cr(III), and Cr(VI). However since the two successive oxidation states Cr(II) and Cr(III) differ by one, Cr(III) may be considered as a one-electron reagent in reactions in which the oxidation potential changes are sufficiently low to prevent the stabilization of the Cr(VI) state.
(e) According to Table 16.5, in aqueous solution uranium is capable of assuming the following oxidation states: U(IV), U(V), and U(VI). One would therefore expect that the U(IV)/U(V) couple makes U(IV) a one-electron reagent. It turns out, however, that U(V) is relatively unstable with respect to disproportion to U(IV) and U(VI):
2U(V) = U(IV) + U(VI)
In effect therefore U(IV) must be considered a two-electron reagent, in acknowledgement of the preference of the U(IV)/U(VI) couple over the U(IV)/U(V) couple.
EXAMPLE 16.16 Complementary and Noncomplementary reactions
For each pair of ions given below, write down the appropriate stoichiometric equation (similar to Equations 16.51 - 16.54), indicate the type of n : m reaction, and state whether the reaction is complementary or noncomplementary:
(a) Tl(III)/Cr(II) (b) Tl(III)/V(III)
(c) Pu(VI)/Ti(III) (d) Sn(IV)/Fe(II)
(e) Cr(VI)/Ag(I) (f) V(V)/Sn(II)
(g) Pt(IV)/Pt(II) (h) Co(III)/Fe(II)
16.3.3 1:1 Electron Transfer Reactions
The most common reaction between metal ions is that in which both reactants are one-electron reagents. A representative reaction may be written as:
M+ + N = M + N+ (16.55)
Typically the rate process involves a bimolecular mechanism, i.e.,
(16.56)
where the second order rate equation is given by:
- d [M+] / dt = k [M+] [N] (16.57)
Where M+ and N are aquo species, it is found that the rate constant k is pH-dependent:
k = ka + kb[H+]-1 (16.58)
The reaction mechanism accounting for Equation 16.58 consists of the following steps:
M+ + H2O MOH + H+ (16.59)
M+ + N M + N+ (16.60)
MOH + N M + NOH (16.61)