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…………………………………………………316.3.1 Stable Oxidation States………………………………………………………..316.3.2 Complementary and Noncomplementary Reactions…………………………..416.3.3 1:1 Electron Transfer Reactions……………………………………………….816.3.4 2:1 Reactions…………………………………………………………………..8

16.4 Reactions Between Metal Complexes and Nonmetallic Species…………………... 1016.4.1 General Features…………………………………………………………….. 1016.4.2 Reactions of Molecular Oxygen…………………………………………….. 1816.4.3 Reactions of Aqueous Halogens and Hypohalous Acids…………………….2216.4.4 Reactions of Hydrogen Peroxide……………………………………………. 2616.4.5 Reactions of Molecular Hydrogen…………………………………………...2816.4.6 Reactions of Sulfurous Acid………………………………………………… 32

16.5 Reactions Between Nonmetallic Species……………………………………………. 3316.5.1 General Features…………………………………………………………….. 3316.5.2 Reactions of Oxyanions……………………………………………………... 3516.5.3 Peroxide Reactions………………………………………………………….. 3916.5.4 Oxidation of Cyanide……………………………………………………….. 4016.5.5 Oxidation of Sulfide………………………………………………………….42

16.1 IntroductionIn 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

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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) A+ • B(aq) (16.1a)A+ • B(aq) 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) A (aq) (16.2a)

B (aq) 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) 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).

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16.2 Types of Homogeneous Electron Transfer ProcessesIn 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.

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16.3 Reactions Between Metal Complexes16.3.1 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 solutionOxidation State Examples M(-I) ReM(0) HgM(I) Li, Na, K, Rb, Cs, Re, Cu, Ag, Au, Hg, TlM(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, SbM(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, BiM(IV) Ce, Ti, Zr, Hf, Th, V, Mo, W, U, Ru, Os, Rh, Ir, Pd, Pt. Ge,

Sn, PbM(V) V, Nb, Ta, Mo, W, (U), SbM(VI) Cr, Mo, W, U, Mn, Ru, Os, Rh, IrM(VII) Mn, Re, RuM(VIII) Ru, Os

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16.3.2 Complementary and Noncomplementary ReactionsRedox 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 25CCr(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 0C(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)]

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Table 16.4 Continued

Reaction Rate Law Rate constantsFe(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 55C (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 0C (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)5

3- + 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 ReactionsThe 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.,

k

M + N+(16.56)

where the second order rate equation is given by:

- d [M+] / dt = k [M+] [N] (16.57)

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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)

16.3.4 2:1 ReactionsConsider the reaction between a two-electron oxidant and a one-electron reductant:

M2+ + 2N = M + 2N+ (16.62)The rate process can be rationalized in terms of two alternative mechanisms involving either (a) a one-electron first step or (b) a two-electron first step.

Mechanism (a) is based on the following steps:

M2+ + N M+ + N+ (16.63)

M+ + N M + N+ (16.64)

The resulting rate equation is:

- d [M2+] / dt = ka1 ka2 [M2+] [N]2 / {k -a1 [N+] + ka2 [N]} (16.65)

Two important limiting forms of Equation 16.65 may be derived. When k-a1 [N+] << ka2 [N], Equation 16.65 simplifies to:

- d [M2+] / dt = ka1 [M2+] [N] (16.66)

On the other hand, when k-a1 [N+] >> ka2 [N], Equation 16.65 becomes:

- d [M2+] / dt = Ka1 ka2 [M2+] [N]2 / [N+] (16.67)

where Ka1 = ka1/k-a1.

Kd

ka1

k-a1

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Mechanism (b) consists of the following steps:

M2+ + N M + N2+ (16.68)

N2+ + N )The corresponding rate equation is given by:

- d [M2+]/dt = kb1 kb2 [M2+] [N]2/{k-b1 [M] + kb2 [N]} (16.70)

In this case too, we can obtain two useful limiting forms of the rate equation.

When k-b1[M] << kb2 [N], Equation 16.70 reduces to:

- d [M2+]/dt = kb1 [M2+] [N] (16.71)

On the other hand when k-b1 [M] >> kb2 [N], Equation 16.70 becomes:

- d [M2+]/dt = Kb1 kb2 [M2+] [N]/[M] (16.72)

where Kb1 = kb1/k-b1.

kb1

k-b1

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16.4 Reactions Between Metal Complexes and Nonmetallic Species16.4.1 General Features

In the reactions considered in this section, the nonmetallic species may be ionic species (e.g., I-, SO32-, S22-, S2O82-, ClO4-) or molecular species (e.g., Cl2, O2, H2O2, H2O, H2) .

Depending on the reaction, the metal ion may serve as the oxidant (e.g., Ce(IV), Co(III), Fe(III)) or the reductant (e.g. Cu(I), Cr(II), Ti(III), V(IV)). In the previous section we encountered unstable oxidation states as reaction intermediates in multi-step electron transfer reactions between metal complexes. An unstable oxidation state intermediate, i.e., the free radical, is frequently encountered in the reactions of metal complexes with nonmetallic species. Reactions of nonmetallic species often involve bond-breaking steps which give rise to free radicals, which are atoms or molecules with unpaired electrons and which are therefore very reactive. Table 16.5 presents a collection of free radicals frequently found in aqueous systems. As can be seen, free radicals may be neutral species (e.g. OH, HO2) or ionic species (e.g., O2-, SO3-, C2O4-).

Table 16.6 presents rate mechanisms and rate laws for selected redox systems where metal ions are oxidized by nonmentallic reagents. Corresponding mechanisms and rate laws for reductions by nonmetallic species are presented in Table 16.7.

Nonmetallic oxidants and reductants, like metal complexes, may be one-, two-, or multi-electron reagents. Redox reactions of metal complexes with two- and multi-electron nonmetallic reagents typically involve unstable oxidation states of the metal or the nonmetallic species. For example, the oxidation of a one-electron divalent metal ion (M(II)) by a two-electron nonmetallic reagent (B2) may occur via one-electron steps, involving the slow formation

of a radical nonmetallic intermediate (B•) followed by a rapid reaction of this intermediate:

M(II) + B2 M(III) + B- + B• (16.60)

M(II) + B• M(III) + B- (16.61)

Alternatively, a two-electron step in which an unstable M(IV) intermediate forms is also possible:

M(II) + B2 M(IV) + 2B- (16.62)

M(IV) + M(II) 2M(III) (16.63)

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Table 16.5 Free Radicals of Nonmetallic Reagents

Nonmetallic Reagent Free Radical Nonmetallic Reagent Free Radical

Halogen (X2, X = Cl, Br, I) X Hydrogen (H2) H

Halide (X-, X = Cl ,Br, I) X Hydroxylamine (H2NOH) NH2, OHOxygen (O2) O Hydrazine (H2N - NH2) NH2Hydrogen Peroxide (H2O2) OH, HO2 CN- CNOxalate (C2O) C2O Sulfite (SO) SOOxalate (C2O) C2O Peroxodisulfate (S2O) SO___________________________________________________________________________________________

EXAMPLE 16.17 Two-electron versus one-electron mechanism in the oxidation of metal ions by nonmetallic species.

It has been suggested that the tendency to form a dimeric immediate product should be greater for the two-electron mechanism, since the second step (Equation 16.63) produces two M(III) ions. (Conocchioli et al., J. Amer. Chem. Soc., 87, 926-927 (1965)). The immediate products formed in the fraction of Fe2+ with chlorine, hypochlorous acid, hydrogen peroxide, and ozone were determined by Conocchioli et al. Table E16.17 presents the results obtained with Fe2+ concentrations ranging from 10-4 to 10-1 M and oxidant concentrations between 5x10-5

and 5x10-4 M. Perchloric acid concentration was in the range of 0.1 to 3.0 M. Speculate on the likelihood that the reaction of a particular oxidant involves a two- or a one-electron mechanism.

SolutionAccording to Table E16.17, the ozone reaction shows ~40% yield of the dimer (FeOH)24+. This

suggests a two electron mechanism. The next likely candidate for a two-electron mechanism is the hypochlorons acid reaction.

It was found by Conocchioli et al. that the yield of the dimer in the Fe2+ - HOCl reaction decreased with increase in acidity and this led to the proposal that the dimer has a chloro bridge at intermediate acidities:

OH Fe Fe

4+

Cl

Table E16.17 Rate constants and products of Fe2+ oxidation

Yields %

Oxidant [HClO4] (M) k (M-1s-1) Fe3+ + FeOH2+ FeCl2+ (FeOH)24+

H2O2 0.2 65 5 >99 <1Cl2 3.0 80 5 <30 >70 <5

HOCl 0.1 (3.2 0.4) x 103 ~ 80 5 ~ 15O3 1.0 (1.7 0.4) x 105 ~ 60 ~ 40

This dimer converts to the dihydroxy-bridged species at low acidities, but it dissociates to give Fe3+ and FeCl2+ with increase in acidity. Under the given experimental conditions, the dissociation of (FeOH)was found to have the rate constant kd:

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kd = k1 +k2 [H+]

where k1 = 0.35 s-1 and k2 = 3.5 M-1 s-1 at 25°C.

The fact that the H2O2 reaction yields less than 1% of dimer points to a one-electron mechanism. In the

case of the Cl2 reaction, there is some ambiguity. The high yield (>70%) of FeCl2+ could result from a 2-electron reaction involving "a short-lived, dichloro-bridged dimer". On the other hand, referring to Equations 16.60 and 16.61 the presence of FeCl2+ is compatible with a 1-electron reaction:

Fe(II) + Cl2 FeCl2+ + Cl.

Fe(II) + Cl. FeCl2+____________________________________________________________________________________________

Tables 16.6 and 16.7 respectively present kinetic data for the oxidation and reduction of selected metal ions by nonmetallic reagents. The oxidation of metal complexes via the ion-radical mechanism is exemplified by the following systems: U(IV)/O2; X2(halogen)/Fe(II), V(II); HOX/V(IV); Fe2+/H2O2; Fe2+/S2O ; Cu+/S2O . The Ag+ - S2O reaction involves both metal and nonmetal unstable oxidation states, i.e., Ag3+ and SO . Direct electron transfers (i.e., redox reactions involving no unstable oxidation states) are also observed in some special cases, e.g. the oxidation of U(IV) to U(VI) with two-electron oxidizing agents such as Cl2 and

HOCl. In some ion-radical systems, the electron transfer is preceded by a fast hydroxylation of the metal ion. Examples of systems exhibiting this behavior are: U(IV)/O2, V(III)/X2, V(IV)/X2

(halogen), U(IV)/HOCl. All these cases involve situations where the final metallic species acquires at least one extra oxygen atom in its first coordination sphere (i.e., U4+ UO , V3+

VO2+, VO2+ VO ). Thus the hydroxyl ion transferred to the metal ion in the hydrolysis step facilitates the formation of the final product.

There are a number of redox reactions (e.g. the systems P2O /FeL , L=phen, bipy)

where a necessary condition for electron transfer is inner-sphere ligand substitution. The relevant reaction mechanisms can be summarized in general terms as:

MLn MLn-1 + L (16.64)

MLn-1 + X MLn-1X (16.65)

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Table 16.6 Oxidation of Metal Complexes by Nonmetallic Reagents

Nonmetallic Reagent Metal Ion Overall Reaction Mechanism Rate Law

Oxygen (O2) Fe2+

U(IV)

2Fe2+ + O2 + 2H+ = 2Fe3+ + H2O2

2U4+ + O2 + 2H2O = 2UO22+ + 4H+

See Ex. 16.19

See Ex. 16.18

-d[Fe(II)]/dt = k[Fe2+]x[O2], x = 1, 2

-d[U(IV)]/dt = k[U(IV)][O2]/[H+]

Halogen (X2, X = Cl, Br, I) Fe(II), V(II)

V(III), Ti(III)

V(IV)

2M2+ + X2 = 2M3+ + 2X-

2M3+ + X2 + 2H2O = 2MO2+ + 2X- + 4H+

2VO2+ + Cl2 = 2VO2+ + 2Cl- + 4H+

M2+ + X2 M3+ + X2- (slow)

M2+ + X2- M3+ + 2X- (fast)

M3+ + H2O MOH2+ + H+ (fast)

MOH2+ + X2 MOH3+ + X2- (slow)

MOH2+ + X2- MOH3+ + 2X- (fast)

MOH3+ MO2+ + H+ (fast)

VO2+ + H2O + Cl2 VO2. . .Cl2 + 2H+

VO2 . . .Cl2 VO2+ + Cl2

-

VO2+ + Cl2- VO2

+ + 2Cl- + 2H+

-d[X2]/dt = k[M2+][X2]

-d[X2]/dt = k[M3+][X2]/[H+]

-1/2 d[V(IV)]/dt = k[V(IV)][Cl2]/[H+]2

k = 0.7 x 10-2 Ms-1 at 25C and I = 1.0 M

Halogen (X2, X = Cl, Br, I U(IV) U4+ + X2 + 2H2O = UO22+ + 2X- + 4H+ U4+ + 2H2O = U(OH)2

2+ + 2H+ (fast)

U(OH)22+ + X2 U(OH)2

4+ + 2X- (slow)

U(OH)24+ = UO2

2+ + 2H+ (fast)

-d[X2]/dt = k[U4+][X2]/[H+]2

Hypochlorous Acid (HOCl) FeL32+

V(IV)

2FeL32+ + HOCl = 2FeL2

3+ + OH- + 2L + Cl-

2VO2+ + HOCl = 2VO2+ + Cl- + 3H+

FeL32+ FeL2

2+ + L (slow)

2FeL22+ + HOCl 2FeL2

3+ + OH- + Cl- (fast)

VO2+ + HOCl VOOCl+ + H+ (slow)

VOOCl+ VO2+ + Cl (slow)

VO2+ + Cl VO2+ + Cl- + 2H+ (fast)

-d[FeL32+]/dt = k[FeL3

2+]

K1

K

k1

k-1

13

Hypochlorous Acid (HOCl) U(IV) U4+ + 2HOCl = UO22+ + Cl2 (aq) + 3H+ U4+ + H2O UOH3+ + H+ (fast)

UOH3+ + HOCl UO22+ + Cl- + 2H+ (slow)

HOCl + H+ + Cl- Cl2 (aq) + H2O (fast)

-d[U4+]/dt = k[U4+][HOCl]/[H+]

k = 1.1s-1

14

Table 16.6 (cont’d) Oxidation of Metal Complexes by Nonmetallic Reagents

Nonmetallic Reagent Metal Ion Overall Reaction Mechanism Rate Law

Hydrogen Peroxide

(H2O2)

Fe2+ 2Fe2+ + H2O2 + 2H+ = 2Fe3+ + 2H2O Fe2+ + H2O2 FeOH2+ + OH (slow)

Fe2+ + OH FeOH2+ (fast)

FeOH2+ + H+ Fe3+ + H2O (very fast)

-d[Fe2+]/dt = k[Fe2+][H2O2]

Peroxodisulfate (S2O82-) Ag+

Fe2+

2Ag+ + S2O82- = 2Ag2+ + 2SO4

2-

2Fe2+ + S2O82- = 2Fe3+ + 2SO4

2-

S2O82- 2SO4

- (fast)

2SO4- + Ag+ 2SO4

2- + Ag3+ (slow)

Ag+ + Ag3+ 2Ag2+ (fast)

Fe2+ + S2O82- Fe3+ + SO4

2- + SO4- (slow)

Fe2+ + SO4- Fe3+ + SO4

2- (fast)

-d[S2O82-]/dt = k[Ag+][S2O8

2-]

-d[S2O82-]/dt = k[Fe2+][S2O8

2-]

Peroxydisulfate (S2O82-)

Cu+ 2Cu+ + S2O82- = 2Cu2+ + 2SO4

2- Cu+ + S2O82- CuS2O8

-

CuS2O8- Cu2+ + SO4

2- + SO4-

Cu+ + SO4- Cu2+ + SO4

2-

-d[S2O82-]/dt = k[Cu+][S2O8

2-]

Peroxodiphosphate (P2O84-) FeL3

2+

(L = Phen, bipy)

FeL32+ + P2O8

4- = FeL32+ FeL2

2+ + L

FeL22+ + P2O8

4- Products

-d[FeL22+]/dt = k[FeL3

2+]

15

Table 16.7 Reduction of Metal Complexes by Nonmetallic Reagents

Nonmetallic Reagent Metal IonOverall Reaction Mechanism Rate Law

Hydrogen Peroxide (H2O2) Co3+

Mn3+

2Co3+ + H2O2 = 2Co2+ + O2 + 2H+

2Mn(III) + H2O2 = 2Mn(II) + O2 + 2H+

Co3+ + H2O = CoOH2+ + H+ (fast)

CoOH2+ + H2O2 Co2+ + H2O + HO2 (slow)

CoOH2+ + HO2 Co2+ + H2O + O2 (fast)

Mn3+ + H2O2 Mn2+ + H2O2+

MnOH2+ + H2O2 Mn2+ + HO2 + H2O

Mn3+ + H2O2 Mn2+ + 2H+ + O2

MnOH2+ + H2O2+ Mn2+ + H3O+ + O2

H2O2 + H2O2+ OH + H3O+ + O2

Mn2+ + OH Mn(III) + OH-

-d[Co(III)]/dt = k[Co(III)][H2O2]/[H+]

k = 1540 M-1 min-1 at 25C and I = 2.0 M,

[HClO4]o = 0.5 – 2.0 M

-½d[Mn(III)]/dt = k[Mn(III)][H2O2]

1/k = A + B[Mn(II)]/[Mn(III)]o

+ C[H2O2]o/[Mn(III)]o

A = 1.4 x 10-5 Ms,

B = 4.14 x 10-8 Ms,

C = 1.32 x 10-5 Ms at 25C,

[HClO4]o = 2.0 M

Iodine (I-) Fe3+ Fe3+ + 2I- = Fe2+ + I2 Fe3+ + I- FeI2+

FeI2+ + I- Fe2+ + I2-

Fe3+I2- Fe3+ + I2

-d[Fe3+]/dt = k[Fe3+][I-]2/(1 + k[Fe2+]/[Fe3+])

CN- MnO4- 2MnO4

- + CN- + 2OH- = 2MnO42- + CNO- + H2O MnO4

- + CN- [O3Mn – O – CN]2-

[O3MN – O – CN]2- MnO3- + NCO-

2OH- + MnO3- + MnO4

- 2MnO42- + H2O

-d[MnO4-]/dt = k[MnO4

-][CN-]

k = 6.4 x 107 exp (-9000/RT) M-1s-1

H2O Ag2+ 2Ag2+ + H2O = 2Ag+ + 2H+ + ½O2 2Ag2+ Ag+ + Ag3+ (fast)

Ag3+ + H2O AgO+ + 2H+ (fast)

AgO+ Ag+ + ½O2 (slow)

-d[Ag2+] = k[Ag2+]2/[Ag+][H+]2

16

Table 16.7 (cont’d) Reduction of Metal Complexes by Nonmetallic Reagents

H2O Co3+ 4Co3+ + 2H2O = 4Co2+ + 4H+ + O2 Co3+ + H2O CoOH2+ + H+ (fast)

2CoOH2+ [Co-O-Co]4+ + H2O (fast)

[Co–O–Co]4+ + 2H2O [HOCo–O–

CoOH]2+ + 2H+ (fast)

CoOH2+ + [HOCo–O–CoOH]2+ 3Co2+ +

2OH- + HO2 (slow)

CoOH2+ + HO2 Co2+ + H2O + O2 (fast)

-d[Co(III)]/dt = k[Co(III)]3/2/[H+]2

17

MLn-1X Products (16.66)

Different rate equations may be derived from the above mechanism, depending on the rate-determining step. If the forward reaction of the first step (Equation 16.64) is rate-determining, the resulting rate equation is:

-d[MLn]/dt = k1[MLn] (16.67)

If the forward reaction of the second step (Equation 16.65) is rate-determining, the corresponding rate equation is:

-d[MLn]/dt = (k1k2/k-1)[MLn][X]/[L] (16.68)

Finally, if the forward reaction of the third step (Equation 16.66) is rate-determining, the corresponding rate equation is obtained as:

-d[MLn]/dt = (k1k2k3/k-1k-2)[MLn][X]/[L] (16.69)

In some cases, e.g. the redox reactions of metal oxyanions, (HMO) the ligand displacement step (Equation 16.64) is facilitated by protonation. The redox reactions of oxyanions are often pH- dependent; the rate laws are consistent with an acid-catalyzed mechanism involving an initial rapid protonation, followed by the slow substitution of the coordinated water by the incoming ligand (i.e. the nonmetallic reagent):

MO3OH- + H+ MO3OH2 (16.70)MO3OH2 + B MO3B + H2O (16.71)MO3B Products (16.72)

The corresponding rate law is:

-d[HMO]/dt = k[HMO][B][H+] (16.73)

K1

18

16.4.2 Reactions of Molecular OxygenIn its reactions as an oxidant, molecular oxygen itself undergoes a reduction reaction

which may be represented by the overall reaction:

O2 + 4H+ + 4e- = 2H2O Eh˚ = 1.23V (16.74)

The magnitude and sign of the standard reduction potential (+1.23V) indicate that molecular oxygen is a strong oxidizing agent.

Equation 16.74 also indicates that the reduction of molecular oxygen involves the transfer of four electrons, i.e., di-oxygen is a four-electron oxidant. We learned above (Section 16.3.1) that two-electron transfers are unusual. Thus we can take it for granted that the simultaneous transfer of four electrons is out of the question. If we consider the oxygen reduction process (Equation 16.74) in terms of a set of consecutive one-electron transfers, we must invoke as reaction intermediates two free radicals (HO2, OH) and hydrogen peroxide (H2O2):

O2 + H+ + e- = HO2 Eh˚ = -0.32V (16.75)HO2 + H+ + e- = H2O2 Eh˚ = 1.68V (16.76)H2O2 + H+ + e- = OH + H2O Eh˚ = 0.80V (16.77)OH + H+ + e- = H2O Eh˚ = 2.74V (16.78)

It can be seen by inspection that the combination of Equations 16.75 - 16.78 gives Equation 16.74. It can be seen further that the first electron transfer reaction (16.75) is associated with a negative standard reduction potential. This means that a strong reducing agent is needed in order to accomplish this step. It is likely that a factor contributing to make the first step so unfavorable, is the repulsive interaction between the incoming electron and the electrons already present in molecular oxygen.

In the case of a two-electron process the relevant reactions are:

O2 + 2H+ + 2e- = H2O2 Eh˚ = 0.68V (16.79a)H2O2 + 2H+ + 2e- = 2H2O Eh˚ = 1.77V (16.79b)

Here the standard reduction potential for the first two-electron step (Equation 16.79a) is favorable. However, in order for this transfer to take place the prospective electron donor must provide two orbitals that permit the simultaneous overlap of the two perpendicular di-oxygen π*

orbitals. Obviously only select donors can satisfy such symmetry and energy requirements.

19

The above considerations underlie the well-known chemical inertness of molecular oxygen. From a kinetic standpoint, di-oxygen may be activated by two approaches, involving the application of (a) brute force, e.g., use of elevated temperatures to cause the formation of free radicals, or (b) gentle persuasion, e.g., the use of photochemical processes to generated excited di-oxygen O2, and interaction of oxygen orbitals with the d orbitals of transition metal ions. Table 16.8 presents thermodynamic data for the hydrolytic reactions H2O2 and related radicals.

Table 16.8 Hydrolytic reactions of hydrogen peroxide and related radicals*

Reaction Equilibrium ConstantH3O2+ = H+ + H2O2 ~ 103, I = 1MH2O2 = H+ + HO2- 5.4 x 10-2 M, I=1MHO2- = H+ + O22- Extremely small, I = 1MH2O2+ = H+ + HO2 ~10-1 M, acidicHO2 = H+ + O2- 3.5 x 10-5 M, I = 10-2 M______________________________________________________________________________*Davies et al., Inorg. Chem., 7, 146 (1968)

EXAMPLE 16.18 Oxidation of uranium (IV) by molecular oxygen in aqueous perchloric acid solution

The overall reaction for the oxidation of uranium (IV) by molecular oxygen is given by:

2U4+ + O2 + 2H2O = 2UO22+ + 4H+ (1)

An experimental investigation by Halpern and Smith (Can. J. Chem., 34, 1419-1427 (1956)) gave the following rate law:

- d [U(IV)]/dt = k [U(IV)] [O2]/[H+] (2)

Show that the above experimental result is consistent with the following chain mechanism:Rapid pre-equilibrium:

U4+ + H2O UOH2+ + H+ (3)

Initiation:

UOH3+ + O2 + H2O UO2+ + HO2 + 2H+ (4)

Propagation:

UO2+ O2 + H2O UO22+ + HO2 + OH- (5)

HO2 + UOH3+ + H2O UO2+ + H2O2 + 2H+(6)

K

20

Termination:

UO2+ + HO2 + H2O UO22+ + H2O2 + OH- (7)

Fast reaction:U4+ + H2O2 UO22+ + 2H+ (8)

Solution (see Katakis, p. 28)

In the above mechanism UO2+ and HO2 are termed chain carriers; these species are responsible for propagating the chain reaction (Equations 5 and 6). The initiation step generates new carriers, while the termination step removes them. Therefore a steady-state is attained, given by:

d[UO2+]/dt = k1[UOH3+][O2] - k2[UO2+][O2] + k3[UOH3+][HO2]

- k4[UO2+][HO2] = 0 (9)

d[HO2]/dt = k1[UOH3+][O2] + k2[UO22+][O2] - k3[UOH3+][HO2]

- k4[UO2+][HO2] = 0 (10)

Addition of Equations 9 and 10 gives:

k1[UOH3+][O2] = k4[UO2+][HO2] (11)

On the other hand subtraction of Equation 9 from 10 gives:

k3[UOH3+][HO2] = k2[UO2+][O2] (12)

It follows from Equations 11 and 12 that:

[HO2] = (k1k2/k3k4)1/2 [O2] (13)

Also according to Equations 4 and 6,

- d[UOH3+]/dt = 2(k1[UOH3+][O2] + k3[UOH3+][HO2]) (14)

where "the factor 2 is included to account for the additional U(IV) oxidized by H2O2 according to Equation 8" (Katakis, p. 29). Combination of Equations 13 and 14 results in Equation 15:

- d[UOH3+]/dt = 2k{1 + (k2k3/k1k4)1/2} [UOH3+][O2] (15)

In view of the pre-equilibrium step (Equation 3), we can express [UOH2+] as:

[UOH2+] = K[U4+]/[H+] (16)

Substitution of Equation 16 in Equation 15 gives:

- d[U(IV)]/dt = 2k1K{1 + (k2k3/k1k4)1/2} [U4+][O2]/[H+] (17)

21

It can be seen by inspection that Equation 17 is in the form of Equation 2, where:

k = 2k1K{1 + (k2k3/k1k4)1/2} (18)

EXAMPLE 16.19 The oxidation of ferrous ion by molecular oxygen in aqueous solution

Experimental investigations indicate that the oxidation of Fe(II) by molecular oxygen follows a rate law of the general form: - d[Fe(II)]/dt = k[Fe2+]x [O2] (1)

Both first (x=1) and second (x=2) order rate dependence have been reported for the ferrous ion concentration.

(a) Show that these observations are consistent with the following reaction mechanism:

(i) Formation a ferrous ion-oxygen complex:

H...OFe(OH2)62+ + O2 [(H2O)5 Fe(II)...O ]2+ (2)

(A) (B) H...O

(ii) Formation of a bi-nuclear aquo-complex with an oxygen bridge: H…O H...O...H

[(H2O)5 Fe(II)..O ]2+ + Fe(OH2)62+

(B) H...O (C) H...O...H (3)

(iii) Intermolecular oxidation of Fe(II) in the bi-nuclear complex: H...O...H H

[(H2O)5Fe(II)...O O...Fe(II)(OH2)5]

(C) H...O...H (D) H + H2O2 (4)

Solution

The above elementary steps can be summarized as:k1

A + O2 B (5)k2

k3

B + A C (6)k4

C D + H2O2 (7)

Applying the steady-state assumption, the concentrations of the intermediates are obtained as:

[B] = k1 (k4 + k5)[A][O2]/{k2k4 + k2k5 + k3k5[A]} (8)

[C] = k1k3 [A]2 [O2]/(k4 + k5)(k2 + k3[A] - k3k4[A])} (9)The reaction product (D) is formed at a rate given by:

k2

k1

k4

k3

22

d[D]/dt = k5[C] (10)

Therefore substitution of Equation 9 in Equation 10 gives:d[D]/dt = k1k3k5[A]2[O2]/{k2k4 + k5(k2 + k3[A])} (11a)

= k1[A][O2] - k1k2[O2](k4 + k5)[A]/{k2(k4 + k5) + k3k5[A]} (11b)

When k2 >> k3 [A] and k2k4 >> k3k5 [A], Equation 11a reduces to:

d[D]/dt = (k1k3k5/k2k4) [A]2 [O2] (12a)

On the other hand when k2 << k3 [A] and k2k4 << k3k5 [A], Equation 11b becomes:

d[D]/dt = k1[O2][A] - {k1k2(k4 + k5)/k3k5} [O2] (12b)

Ref: A.N. Astanina and A.P. Rudenko, Russ. J. Phys. Chem., 45, 191-194 (1971). P. George, J. Chem., Soc., 4349-4359 (1954).

16.4.3 Reactions of Aqueous Halogens and Hypohalous Acids In aqueous solution the heavier halogens (X2 = Cl2, Br2, I2) undergo hydrolysis

reactions according to:kf

X2 + H2O HOX + H+ + X- Kh (16.80)kr

where HOX represents a hypohalous acid (e.g. hypochlorous acid, HOCl; hypobromous acid, HOBr; hypoiodous acid, HOI. In addition, in the presence of halide ions, the halogens form trihalide ions X3-:

X2 + X- = X3- Kx (16.81)

Table 16.9 presents the relevant thermodynamic and kinetic parameters.

23

Table 16.9 Thermodynamic and kinetic parameters for the hydrolysis of the heavier halogens*

Halogen Kh(M2), 25°C kf(s-1),20°C Kx(M-1), 25°CCl2 3.9 x 10-4 11.0 0.18Br2 5.8 x 10-9 110 17I2 5.4 x 10-13 3.0 769

*R. C. Thompson, Adv. Inorg. Bioinorg. Mech., 4, 65-106 (1986)

In view of the rapid hydrolysis reaction (Equation 16.80), aqueous solutions of halogens are expected to consist of equilibrium mixtures of X2 and HOX species. The fraction of X2 increases with increase in acidity, as indicated by Equation 16.80. Recalling that the halogen molecule is a two-electron reagent (X2 + 2e- 2X-), it is clear that both one-electron and two-

electron transfers are possible, in principle. Redox reactions in which the halogen is an active participant typically proceed via one-electron mechanisms where the hihalogen radical anion, X2- is the intermediate. As can be seen in Table 16.7, for the divalent metal ions the mechanism

involves two one-electron steps. For the trivalent ions the one-electron steps are preceded by hydroxylation. The quadrivalent ions V(IV) and U(IV) also require hydroxylation prior to electron transfer; however, whereas the V(IV) reaction involves one-electron transfers, U (IV) undergoes a two-electron transfer.

Reactions of hypohalous acids show some similarities as well as differences in comparison with the halogen reactions. Like Cl2, HOCl reactions with V (IV) and U (IV)

involve one-and two-electron transfers respectively. However, the proton dependence of the rate laws is different. For these M(IV) ions, the proton terms are [H+]-2 and [H+]-1 respectively for the Cl2 and HOCl reactions. The difference is related to the need to form the O-M-O structure

prior to electron transfer. The VO2+ and U4+ reactions require one and two oxygens respectively. These oxygens can be supplied by the oxidant and/or water molecules. The type of proton dependence is related to the number of water molecules that react with the metal ion in the pre-equilibrium step. With HOCl, the oxidant can provide an oxygen atom and therefore no hydrolysis step is needed for VO2+; on the other hand, one hydrolysis step is needed for U4+. In the case of Cl2, VO2+ requires one and U4+ two hydrolysis steps. The transfer of oxygen from

HOCl to VO2+ and U4+ suggests an inner-sphere mechanism for the corresponding electron transfer reactions.______________________________________________________________________________

24

EXAMPLE 16.20 The oxidation of iron (II) by aqueous chlorine in highly acidic chloride solution.

In highly acidic chloride solution the formation of hypochlorous acid is suppressed (Equation 16.80). Therefore Cl2 rather than HOCl is the active reactant. At the same time the presence of chloride ions favors the

formation of the trichloride ion Cl3-. Show that with both Cl3- and Cl2 redox active, it is reasonable to expect a rate law of the form:

d[Fe(III)]/dt = k[Fe(II)] [Cl2] (1)

Assume that the Cl3- reaction follows a mechanism similar to that shown in Table 16.6 for the Fe(II)X2 reaction.

Solution

Referring to the entry for Fe(II)/X2 in Table 16.6, we can write

Fe2+ + Cl2 Fe3+ + Cl2- (2)

Fe2+ + Cl3- Fe3+ + Cl2- + Cl- (3)

d[Fe3+] / dt = k1 [Fe2+] [Cl2] + k2 [Fe2+] [Cl3-] (4)

But from Equation 16.81,

[Cl3-] = Kcl [Cl-] [Cl2] (5)

Substitution of Equation 5 in Equation 4 gives:

d[Fe3+]/dt = k[Fe2+] [Cl2] (6)

wherek = k1 + k2Kcl [Cl-]

A mass balance on total chlorine can be written as:

[Cl2]T = [Cl2] + [Cl3-] (7a)

= [Cl2] (1 + Kcl [Cl-]) (7b)

Thus,[Cl2] = [Cl2]T/ (1 + Kcl [Cl-]) (8)

Substitution of Equation 8 into Equation 6 gives:

d[Fe3+]/dt = [Fe2+] [Cl2]T (9)

If k1 = k2, Equation 9 becomes:

d[Fe3+]/dt = k1[Fe2+] [Cl2]T (10)

25

EXAMPLE 16.21 Comparison of chlorine and hypochlorous acid as oxidants

The relative rates of chlorine and hypochlorous acid oxidations of metal ions can be predicted with the aid of reduction potential data (Cornelius and Gordon, Inorg. Chem., 15, 997-1002 (1976)). The first step in the chlorine reaction is the reduction of chlorine to the dichloride ion:

Cl2 + e- = Cl Eh˚ = 0.43V

It has been proposed that the rate of the chlorine reaction is greater than that of hypochlorous acid only if the metal ion is a sufficiently strong reductant relative to the first one-electron step.

For the oxidation of (a) Fe(II), (b) V(III), (c) V(IV), determine whether the chlorine or hypochlorous acid reaction is faster. Relevant thermodynamic data are presented below:

Fe(III) + e- = Fe(II) Eh˚ = 0.77VV(IV) + e- = V(III) Eh˚ = 0.36VV(V) + e- = V(IV) Eh˚ = 1.0V

Solution

Examination of the thermodynamic data provided indicates that Eh˚ for the V(IV)/V(III) couple is lower than that for the Cl2/Clcouple; however the Eh˚ values for the Fe(III)/Fe(II) and V(V)/V(IV) couples are higher. Thus only V(III) is capable of effecting the first one-electron step of the chlorine reaction. Accordingly one would expect that with V(III) as the reductant, the chlorine reaction would proceed more rapidly than the hypochlorous acid reaction. The opposite trend would be expected for Fe(II) and V(IV) as the reductants.

EXAMPLE 16.22 Inner-sphere vs. outer-sphere mechanisms in the reactions of Cl2 and HOCl with metal ions.

The following guidelines may be used to predict the relative reactivities of Cl2 and HOCl towards a given metal ion: (a) For inner-sphere reactions, HOCl tends to be a faster reactant than Cl2. This trends may be attributed to the greater ability oxygen (from HOCl) to serve as a ligand compared with the chloride atom of Cl2. (b) For outer-sphere reactions or substitutionally inert metal complexes, Cl2 tends to be the more reactive oxidant. This trend may be rationalized in terms of the smaller structural changes associated with one-electron reduction of Cl2 compared with HOCl.

With these principles in mind, speculate on the likelihood of inner-sphere vs. outer-sphere mechanisms for the U(IV)/Cl2 and U(IV)/HOCl reactions.

Solution

It can be seen from the rate data provided in Table 16.6 that for the U(IV)/Cl2 reaction,

-d[U4+]/dt = k[U4+] [Cl2]/[H+]2 (1)

where k = 0.01 Ms-1. Thus for [H+] = 1M,

-d[U4+]/dt = (0.01 M-1s-1) [U4+] [Cl2] (2)

Similarly, for the U(IV)/HOCl reaction,

26

-d[U4+]/dt = k[U4+] [HOCl]/[H+] (3)

where k = 1.1 s-1. Thus for [H=] = 1M,

-d[U4+]/dt = (1.1M-1s-1) [U4+] [HOCl] (4)

Comparison of the pseudo second-order rate constants shown in Equations 2 and 4 respectively for the Cl2 and HOCl reactions indicates that the rate of the U(IV)/HOCl reaction is faster than that of the U(IV)/Cl2 reaction.____________________________________________________________________________________________

In contrast to the halogen reactions indicated in Table 16.6, the oxidation of peroxotitanium (IV) and peroxovanadium (V) by chlorine follows an indirect mechanism. The overall reaction describing the oxidation of peroxotitanium (IV), TiO2

2+ by chlorine is given by:

TiO22+ + Cl2 + H2O = TiO2+ + O2 + 2Cl- + 2H+ (16.82)

In this reaction, the +4 oxidation state of titanium is preserved on both sides of the equation. Thus the oxidation reaction involves the oxidation of the peroxide ligand (O

22- O2- + ½ O2).

The following reaction mechanism has been proposed by Thompson (Inorg. Chem., 23, 1794-1798 (1984)):

TiO22+ + H2O TiO2+ + H2O2 (16.83)

H2O2 + Cl2 O2 + 2H+ + 2Cl- (16.84)

The corresponding rate equation is:

-d[TiO22+]/dt = k1k2[TiO2

2+] [Cl2]/(k-1[TiO2+] + k2 [Cl2]) (16.85)

16.4.4 Reactions of Hydrogen PeroxideWhen hydrogen peroxide (H2O2) acts as an oxidant, it undergoes an overall two-

electron reaction:

H2O2 + 2e- + 2H+ = 2H2O Eh°=1.77V (16.86)

This reaction generally proceeds via two consecutive one-electron steps:

k1k-1

27

H2O2 + e- OH. + OH- Eh°=0.8V (16.87)

OH + e- + H+ H2O Eh°=2.74V (16.88)

The rate-determining step is the disruption of the O-O bond. It should be noted that the strength of this bond is greater in O2 compared with H2O2; this difference is attributable to the fact that the antibonding orbitals of H2O2 contain two additional electrons. Thus H2O2 is more reactive than O2. The O-O bond can be broken by thermal or photochemical activation to give

hydroxyl radicals:

H2O2 2OH (16.89)

Alternatively, activation may be achieved by interaction with metal ions:

M2+ + H2O2 MOH2+ + OH. (16.90)

Hydrogen peroxide can also act as a reducing agent:

H2O2 O2 + 2H+ + 2e- Eh°=0.69V (16.91)

In this case the relevant one-electron steps are:

H2O2 HO2 + H+ + e- (16.92)

HO2 e- (16.93)

It can be seen from Equations 16.86 and 16.91 that the decomposition of hydrogen peroxide to H2O and O2 is thermodynamically feasible:

2H2O2 2H2O + O2 (16.94)

However the presence of a catalyst (typically a transition metal or its compound) is necessary before the reaction rate becomes appreciable.

The radicals OH and HO2 play an active role in the reactions of hydrogen peroxide

with metal ions. For example, the following mechanism has been proposed by Barb et.al (Trans. Farad. Soc., 47, 462-500 (1951)) for the Fe(II) - H2O2 reaction:

Fe2+ + H2O2 (16.95)

28

Fe2+ + OH Fe3+ + OH- (16.96)H2O2 + OH H2O + HO2 (16.97)Fe2+ + HO2 (16.98)Fe3+ + HO2 Fe2+ + O2 + H+ (16.99)

When the H2O2/Fe(II) ratio is relatively low, the only significant steps are 1, and 2.

The overall reaction is then:

2Fe2+ + H2O2 + 2H+ = 2Fe3+ + 2H2O (16.100)

Under these circumstances the reaction follows a second order rate law:

-d[Fe(II)]/dt = kobs [Fe(II)] [H2O2] (16.101)

In these case of the Fe(III)-H2O2 reaction, the relevant reaction steps have been proposed

as (Bart et al, Trans. Farad. Soc., 47, 591-616 (1951)):

Fe3+ + H2O2 HO2 + Fe2+ + H+ (16.102)Fe2+ + H2O2 OH + OH- + Fe3+ (16.103)OH + H2O2 HO2 + H2O (16.104)Fe3+ + HO2 O2 + H+ + Fe2+ (16.105)HO2 + Fe2+ OH- + Fe3+ (16.106)

HO2 + Fe2+ HO2- + Fe3+ (16.107)

It can be seen that the mechanism for the Fe(III)-H2O2 system consists of the reaction steps given previously for the Fe(II)-H2O2 system preceded by an initiation step (Equation 16.102). When

the hydrogen peroxide to ferric ion ratio is high, the above rate mechanism results in a second order rate law, in agreement with experiment:

-d[H2O2]/dt = k[Fe3+] [H2O2] (16.108)

16.4.5 Reactions of Molecular HydrogenAmong the stable molecules, molecular hydrogen counts as the simplest. This

molecule also tends to be kinetically inert. The relative chemical inertness of molecular hydrogen is attributable to the large dissociation energy (~103 kcal/mol) and the closed shell electronic configuration. In order for hydrogenation reactions to occur, splitting or activation of

29

the hydrogen molecule is necessary. The activation reaction can proceed in two different ways, i.e., heterolytic (Equation 16.109) and homolytic (Equation 16.110) splitting:

H2 H- + H+ (16.109)H2 2H (16.110)

Heterolytic splitting results in two kinds of atomic hydrogen, i.e., the hydride (H-) and proton (H+). On the other hand homolytic splitting yields only one kind of atomic hydrogen, i.e., the hydrogen atom with an unpaired electron (H).

In heterolytic splitting the rate-determining step involves only one metal ion, e.g.,

Cu2+ + H2 CuH+ + H+ (16.112)Ag+ + H2 AgH˚ + H+ (16.113)MnO4- + H2 HMnO42- + H+ (16.114)

In contrast the rate-determining step in homolytic splitting involves two metal ions:

2Ag+ + H2 2AgH+ (16.115)Hg22+ + H2 2HgH+ (16.116)Ag+ + MnO4- + H2 AgH+ + HMnO4- (16.117)

The intermediates CuH+, AgH+, etc. are unstable and undergo reverse reactions to regenerate H2,

or additional reactions involving reduction of the metal ion or a second available aqueous species.

30

EXAMPLE 16.23 Heterolytic activation of molecular hydrogen by cupric perchlorate

The homogeneous reaction between molecular hydrogen and cupric ions was investigated in perchloric acid solution by Peters and Halpern (J. Phys. Chem., 59, 793-796 (1955); J. Phys. Chem., 60, 1455-1456 (1956)). The experiments involved hydrogen reduction of dichromate ion with the cupric ion as a catalyst, the over all reaction being:

Cr2O72- + 3H2 + 8H+ = 2Cr3+ + 7H2O (1)

The reaction rate was found to be independent of dichromate concentration. The following rate law was obtained for experiments conducted at low acidities:

-d[H2]/dt = k [Cu2+][H2] (2)

It was observed, however, that at relatively high acidities, the reaction rate decreased with increase in HClO4 concentration.

Show that the above observations are consistent with the following reaction mechanism:

Cu2+ + H2 CuH+ + H+ (3)

CuH+ + Cu2+ 2Cu+ + H+ (4)

Cr2O72- + 6Cu+ + 14H+ 2Cr3+ + 6Cu2+ + 7H2O (5)

Solution

Application of the steady-state approximation to the reaction intermediate CuH+ gives:

-d [H2]/dt = k1[Cu2+]2[H2]/{[Cu2+] + (k-1/k2)[H+]} (6)

At low acidities Equation 6 reduces to Equation 2. On the other hand at high acidities, the resulting rate equation is:

-d[H2]/dt = (k1k2/k-1)[Cu2+]2[H2]/[H+] (7)

It can be seen from Equation 7 that the rate now shows a reciprocal dependence on hydrogen ion concentration, in agreement with experimental observation.

The silver ion exhibits both homolytic and heterolytic catalytic behavior. Experiments similar to those described in Ex. 16.23 were conducted by Webster and Halpern (J. Phys. Chem., 60, 280- (1956)) who used silver instead of copper perchlorate. In the temperature range of 30-70˚C, and Ag+ concentrations of 0.02 - 0.11 mol dm-3, the following rate law was obtained:

-d [H2] / dt = k [Ag+]2 [H2] (16.118)

31

The reaction rate had no dependence on dichromate or proton concentration. Equation 16.118 is consistent with a homolytic activation mechanism, with Equation 16.115 as the rate-determining step. On the other hand at higher temperatures the heterolytic pathway predominated.

For a given metal ion the nature of the complexing ligand has a profound effect on the rate of the heterolytic activation pathway. The transition state corresponding to the complex MLn2+ may be visualized thus:

Ln-1 M2+ L

H- H+

That is, the transition state involves stretching of the M-L and H-H bonds, with simultaneous formation of M-H and L-H bonds. Thus the reactivity of the complex increases with increase in the strength of the M-L bond. When a group of ligands form relatively weak metal-ligand bonds, then the L-H bond effect tends to predominate; accordingly it is found that the reactivity increases with the basicities of the ligands. On the other hand, if relatively strong metal-ligand complexes form, then the M-L bond effect determines the reactivity; that is, the weaker the complex, the greater the reactivity.

Investigations of homogenous hydrogenation kinetics have identified only a small group of ions (e.g. Cu2+, Ag+, Hg2+, MnO4-) which can activate molecular hydrogen. The

ability of these ions to activate hydrogen is attributable to their special electronic configuration. These ions are characterized by the presence of nearly filled or completely filled d-shells (d8-d10). In addition, the d- and s- energy levels of the d10 ions must not be too far apart. These electronic characteristics influence the reaction rate through their effects on the stability of the activated complex. If the activated complex does not have sufficient low-lying orbitals, then the extra electrons have to be assigned to higher energy level non-bonding orbitals and this results in an increase in the activation energy. Metal ions with nearly filled d-shells provide unoccupied d-energy levels which are sufficiently low to satisfy the needs of the activated complex. On the other hand d10 ions capable of promoting d- electrons into s- oribitals can contribute their now empty d-oribitals to the activated complex.

EXAMPLE 16.24 Effect of complexing on the catalytic activation of molecular hydrogen by metal ions.

Table E 16.24 presents kinetic data for the catalytic activation of molecular hydrogen by various cupric and silver complexes. Also given are the mean formation constants of M-L complexes and the first protonation constants of the respective ligands. (a) Rationalize the trend in the relative reaction rates of the cupric complexes. (b) Repeat (a) for the silver complexes.

32

Table E 16.24

Complex Relative Rate "Mean" ComplexationConstant

Ligand Protonation Constant

CuAc2(aq) 120 30 5.75 X 104CuSO4(aq) 6.5 100 97.7

CuCl42- 2.5 1 <<1

Cu(H2O)62+ 1.0 ------ ------

AgAc(aq) 80 3 5.75 x 104

Ag(en)2+ 25 x 103 8.74 x 109

Ag+ 1 ------ ------

Ag(CN)2- No reaction x 1.62 x 109

Solution

(a) For the copper complexes, the relative reaction rates decrease in the order Ac- > SO42- > Cl- > H2O. This trend shows no systematic correlation with the "mean" complexation constants. In contrast the ligand protonation constants decrease in the same order as the reactivity. Thus, it can be concluded that for these complexes it is the L-H bond strength that dictates the variations in reactivity. That is, the more basic the ligand (high ligand protonation constant), the higher the reaction rate.

(b) In the case of the silver complexes, the relative reaction rates decrease in the order Ac- > en > H2O >> CN-.

The corresponding complexation constants follow the reverse trend, i.e., Ac- < en < CN-. On the other hand there is no correlation between the reaction rate and the corresponding ligand protonation constants. It follows therefore that the relative reactivities of the silver complexes reflect the relative M-L bond strengths. The stronger the metal-ligand bond, the slower the reaction rate.

EXAMPLE 16.25 Effect of electron configuration on the catalytic activation of molecular hydrogen by metal ions.

Since the catalytic activity of d10 metal ions relies on the ability of these ions to promote their electrons from d- to s- energy levels, it follows that the smaller the energy gap between the d- and s- orbitals, the greater the reactivity. For a series of metal ions, the d-s energy gap decreases with increase in quantum number but it rises with increase in nuclear charge.

Given the above considerations speculate on the relative reactivities of the following metal ions: Cd2+, Cu+, Hg2+, Tl3+, and Zn2+.

Solution

The electronic configurations are: Cd2+ (4d10), Cu+ (3d10), Hg2+ (5d10),Tl3+ (5d10), Zn2+ (3d10). If we compare the 3d10 metal ions, i.e., Cu+, and Zn2+, the higher nuclear charge of Zn2+ implies a greater d-s energy gap and therefore a smaller catalytic activity compared with Cu+. Similarly for the 5d10 metal ions Hg2+ and Tl3+

we would expect Hg2+ to be the more active of the two. Finally, we can compare the divalent metal ions, i.e. Zn2+, Cd2+, and Hg2+. We would expect catalytic activity to follow the order Hg2+ > Cd2+ > Zn2+, which is the order

33

of decreasing quantum number. Note: It is known from experimental investigations that both Cu+ and Hg2+ are active but Cd2+, Tl3+, and Zn2+ are inactive (see Halpern).

16.4.6 Reactions of Sulfurous AcidA conventional name for acidic solutions of sulfur dioxide (SO2) is sulfurous acid

(H2SO3). This name suggests a reaction of the form

SO2 + H2O = H2SO3 (16.119)

The presence of significant amounts of H2SO3 in aqueous solution has, however, not been demonstrated. Therefore it is more appropriate to represent the solution of SO2 as:

SO2 + nH2O = SO2.nH2O (16.120)

The acidic behavior of 'sulfurous acid' can then be described as:

SO2.H2O H+ + HSO3- (16.121)HSO3- H+ + SO32- (16.122)

Dimerization of hydrogen sulfite gives metabisulfite (S2O52-):

2HSO3- = S2O52- + H2O (16.123)

The overall reaction of bisulfite with a transition metal ion, e.g., Cu2+, can be written as:

HS(IV)O3- + 2Cu(II) + H2O = 3H+ + 2Cu(I) + S(VI)O42- (16.124)

The following reaction mechanism has been proposed by Conklin and Hoffmann (Environ. Sci. Technol., 22, 891-898 (1988)):

HSO3- H+ + SO32- (16.125)

Cu2+ + SO32- CuSO3(aq) (16.126)

Cu2+ + CuSO3(aq) [Cu(II)S(IV)O3Cu(II)]2+ (16.127)

K1

K2

K3

34

[Cu(II) S(IV)O3Cu(II)]2+ [Cu(I)S(V)O3Cu(II)]2+ (16.128)

[Cu(I)S(V)O3Cu(II)]2+ [Cu(I)S(VI)O3Cu(I)]2+ (16.129)

[Cu(I)S(IV)O3Cu(I)2+ + H2O 2Cu(I) + SO42- + 2H+ (16.130)

According to the above mechanism, dimeric Cu(II) species constitute the redox-active species. The inner-sphere intramolecular electron transfer is slow because of the difference in stereochemistry and coordination number of the d9 electron configuration of Cu(II) compared with the d10 electron configuration of Cu(I).

35

16.5 Reactions Between Nonmetallic Species16.5.1 General Features

Redox reactions between nonmetallic species have many of the features encountered above for reaction systems of the type metal ion-metal ion and metal ion-nonmetallic species. Table 16.10 presents representative examples of redox reactions of nonmetallic species. There are two main types of reactions: (a) nucleophilic displacement, and (b) free radical reactions.

In a nucleophilic displacement an electron donor (A) attached to a given central atom (X) is replaced by another electron donor (B):

B + X-A X-B + A (16.131)

Regarding detailed mechanisms, the process may involve associative substitution (SN2) or dissociative substitution (SN1). In the associative mechanism, B binds to X while A is still

attached:

B + X-A B - X - A (slow) (16.132)

B - X - A X - B + A (16.133)

In the dissociative process, there is a bond-breaking step (Equation 16.134), followed by a bond-formation step (Equation 16.135):

X - A X + A (slow) (16.134)

X + B X - B (16.135)

In view of the above considerations, a key step in many of the reactions listed in Table 16.10 involves the formation of an intermediate species in which the oxidant and reductant are linked by a covalent bond. Examples of such intermediates are Cl-OOH (Cl2/H2O2), I-SCN (I2/SCN-), [O2ClO-SO2]- (ClO /H2SO3), HOO-SO2H (H2O2/H2SO3), and HOO-NO(H2O2/HNO2). These oxidant-reductant intermediate species are similar to the ligand-linked

binuclear intermediates found in the inner-sphere electron transfer reactions of transition metals. Thus reducing agents such as SO , SCN-, Cl- etc. may be viewed as Lewis bases while the

oxidants are Lewis acids. The formation of the intermediate then corresponds to a Lewis acid-base reaction.

36

Table 16.10 Redox Reactions Between Nonmetallic SpeciesOxidant Reductant Overall Reaction Mechanism Rate LawOxygen (O2) H2SO3

-

Chlorine (Cl2) H2O2 H2O2 + Cl2 = O2 + 2H+ + 2Cl- H2O2 + Cl2 HOOCl + H+ + Cl-

HOOCl O2 + H+ + Cl-

-d[H2O2]/dt = k[H2O2][Cl-]/[H+][Cl-]

Iodine (I2) SCN- SCN- + 4I2 + 4H2O = SO4

2- + ICN + 7 I- + 8 H+

SCN- + I2 ISCN + I-

ISCN + H2O + B HOSCN + I + HB+

HOSCN Products (fast)

-d[I2]/dt = k[SCN-][I3-][B]/[I-]2

Hypochlorous Acid(HOCl)

H2O2 H2O2 + HOCl = O2 + H2O + H+ + Cl- HOCl = ClO- + H+ (fast)ClO- + H2O2 O2 + H2O + Cl-

-d[H2O2]/dt = k[H2O2][HOCl]/[H+]

Chlorate (ClO3-) H2SO3 3H2SO3 + ClO3

- = 3SO42- + Cl- + 6H+ H2SO3 SO2 + H2O

SO2 + ClO3- (O2Cl-O-SO2)-

(O2Cl-O-SO2)- SO3 + ClO2-

SO3, ClO2- Products (fast)

-d[ClO3-]/dt = k[H2SO3][ClO3

-]

Hydrogen Peroxide(H2O2)

I-

H2SO3

HNO2

2I- + H2O2 + 2H+ = 2H2O + I2

H2SO3 + H2O2 = SO42- + 2H+ + H2O

NO2- + H2O2 = NO3

- + H2O

I- + H2O2 H2O + IO-

I- + H2O + H+ H2O + HIOIO-, HIO Products (fast)H2SO3 SO2 + H2OSO2 + H2O2 HO – S(O) – OOHHO – S(O) – OOH 2H+ + SO4

2-

NO2- + 2H+ = H2NO2

+ (fast)H2NO2

+ NO+ + H2ONO+ + H2O2 ONOOH + H+

ONOOH NO3- + H+

-d[I-]/dt = (k1 + k2[H+])[I-][H2O2]

-d[H2O2]/dt = k1[NO2-][H2O2][H+]2/

(k2 + k3[H2O2])

Ozone (O3) Cl- 2Cl- + 2H+ + O3 = Cl2 + O2 + H2O Cl- + O3 ClO- + O2 (slow)ClO- + Cl- + 2H+ Cl2 + H2O (fast)Cl- + O3 + H+ HClO + O2 (slow)Cl- + HClO + H+ Cl2 + H2O (fast)

Peroxodisulfate (S2O82-) H2O2

37

16.5.2 Reactions of OxyanionsIt will be recalled that an oxyanion is a complex in which oxide ions are bound to a

central atom which is in a positive oxidation state. Consider the following reaction of the oxyanion XOwith a nucleophile B:

XO+ B Products (16.136)

In general, it is found that in order for the desired electron transfer to occur, an intermediate species must form in which X and B are covalently bonded. Formation of this intermediate involves the replacement of an X-O bond by an X-B bond.

There is a well-established parallelism between the rates of oxyanion redox reactions and the rates of oxygen exchange. This is because both processes proceed via similar mechanisms, i.e., nucleophilic displacements.

Oxygen exchange. The oxygen exchange reaction is given by the following equation:

XO+ O*H2 XO*(Om-1)- + H2O (16.137)

It can be seen that this exchange involves the breaking of an X-O bond and the formation of an X-O* bond.

Hydrogen ions catalyze the oxygen exchange reaction. This catalysis has its origins in the ability of protonation to alter the basicity of the oxide ion. The strength of the X-O bond decreases in the order: X-O2- > X-OH- > X-OH2. That is, the successive addition of protons to

the oxide ion results in a systematic decrease in the basicity of the oxygen and therefore, the strength of the X-O bond. Accordingly, marked dependence of oxyanion reactions on acid concentration is often observed. This effect is similar to that discussed above in connection with redox reactions of oxo-metal ions.

The strength of the X-O bond is also influenced by the nature of the central atom, X. When the central atom is large and/or minimally charged, protonation to X-OH is sufficient to cause X-O bond breakage. The oxygen exchange process then involves the following steps:

38

(16.138)

(16.139)

(16.140)

The corresponding rate law is:

r = k[XO] [H+] (16.141)

Examples of oxyanions that follow this rate law are OCl-, OBr-, ReOand IO.When, on the other hand, the central atom is small and highly charged, the initial X-O

bond is very strong. Hence, it is necessary to protonate to X-OH2 before significant bond

breakage can occur:

XO O

OH

XO O

O*H2+

O

XO O

-

+ H+ XO O

OH

+ H+

+

XO O

2OH

+

XO O

2OH

O*H2 + H O2+

XO O

O*H2+ O

XO O

-

+ 2H+

(16.142)

(16.143)

(16.144)

(16.145)

O OH X + H+ X O O O O

OH O*H2

X + O*H2 X + OH-

O O O O

+

- O*H2 O* X X + 2H+

O O O O

+

39

These steps result in the following rate law:

r = k[XO] [H+]2 (16.146)

Oxyanions that obey this rate law include SO, NO, ClO, BrO, COand NO.

EXAMPLE 16.26 Effects of the central atom on the rate of oxygen exchange in oxyanions.

Speculate on the relative rates of exchange of oxygen atoms between water molecules and the following oxyanions:

(a) ClO, HPO, SO, H2SiO(b) OCl-, ClO, ClO, ClO(c) BrO, ClO, IO

Solution

(a) The central atoms Cl, P, S, Si occur in the same period (row) of the Periodic Table. The charge on the central atom increases in the order: Si4+ < P5+ < S6+ < Cl7+. Thus, we expect the X-O bond strength to increase in the same order. The stronger the X-O bond, the slower the rate of bond breakage and therefore, the lower the exchange rate. Thus, we expect the rate of exchange to follow the order: H2SiO > HPO > SO > ClO .

(b) The oxidation state of the chloride atom is different in the various chlorine oxyanions: OCl- (Cl+), ClO , ClO , ClO . As the charge (z) on Clz+ increases, we expect the strength of the Cl-O bond to increase and hence, the exchange rate to decrease. Thus, the exchange rate should follow the trend: OCl- > ClO > ClO > ClO .

(c) Since all three oxyanions have the charge and the central atoms come from the same group (column) of the Periodic Table, we expect size to be the determining factor. The sizes of the central atoms increase in the order: I > Br > Cl. The larger the size of X, the weaker the X-O bond. Thus, we expect the exchange rate to follow the order: IO > BrO > ClO .

Redox reactions. Parallel to the trends found in oxygen exchange reactions, redox reactions of oxyanions are catalyzed by protons. In general, the observed rate for the oxidation of a donor B by an oxyanion, XO, is of the form:

r = k[XO] [B] [H+]x (16.147)

where x = 1 or 2. The rate order of the proton is unity when only one protonation step is required before B-X bond formation:

40

XO+ H+ XOm-1 (OH) (16.148)

B + XOm-1 (OH) Products (16.149)

When two protonation steps are necessary, the rate is second order with respect to the proton and the relevant reaction steps are:

XO+ H+ XOm-1 (OH) (16.150)

XOm-1 (OH) + H+ XOm-1 (OH2)+ (16.151)

XOm-1 (OH2)+ + B XOm-1 (B)+ + H2O (slow) (16.152)

XOm-1 (B)+ Products (16.153)

16.5.3 Peroxide ReactionsPeroxides have the general formula ROOY. Examples are: hydrogen peroxide (H2O2)

and peroxymonosulfuric acid (Caro's acid, H2SO5). Many redox reactions of peroxides with

nucleophiles occur via the nucleophilic displacement mechanism:

ROOY + B RO—O....B RO- + BOY+ (16.154)|

YThe corresponding rate law has the form:

r = k[ROOY] [B] (16.155)

41

Table 16.11 Selected rate data for peroxide reactions.

ROOY B k1(L mol-1 s-1) k2(L2 mol-2 s-1)

H2O2 SO 2x10-1

S2O 2.5x10-2 1.7

I- 6.0x10-1 10.5

CN- 1.0x10-3

SCN- 5.2x10-4 2.5x10-2

NO 3x10-7

OH- 1x10-7

Br- x 1.4x10-2

Cl- x 5.0x10-5

HSO Br- 1.0

Cl- 1.8x10-3

It can be seen that one of the oxygen atoms of the peroxo group (O-O) serves as the "central" atom. It can also be seen that RO- represents the leaving group. Any factors that decrease the basicity of the leaving RO- group will decrease the strength of the RO-O bond, thereby increasing the rate of the oxidation reaction.

Peroxide decomposition. The overall reaction describing the decomposition of a peroxide may be expressed as:

2ROOH 2ROH + O2 (16.156)

The reaction mechanism can be viewed in terms of the nucleophilic attack of ROOH by the anion ROO-:

ROOH + ROO-

RO- + ROOOH 2RO- + H+ + O2 (16.157)

42

16.5.4 Oxidation of CyanideAmong the reagents that have been investigated in the oxidation of cyanide are chlorine

(and hypochlorous acid, HOCl), hydrogen peroxide, peroxymonosulfuric acid (H2SO5, Caro's

acid), and ozone.Oxidation with Chlorine. With chlorine and hypochlorous acid, there is an initial rapid

reaction to give cyanogen chloride (ClCN):

Cl2 + CN- ClCN + Cl- (fast) (16.160)

HOCl + CN- ClCN + OH- (fast) (16.161)

Cyanogen chloride has a relatively high vapor pressure and it is also toxic. This compound has a relatively high solubility in acidic solution (pH ~2). However, it undergoes hydrolytic decomposition in basic solutions:

ClCN + 2OH- NCO- + Cl- + H2O (slow) (16.162)

The following rate law has been established for this hydrolysis reaction:

d[ClCN]/dt = -k[ClCN] [OH-] (16.163)

Values of k range from 80 L mol-1 min-1 at 0°C to 530 L mol-1 min-1 at 25°C. The reaction mechanism involves nucleophilic displacement:

N N ||| |||

Cl — C : + OH- Cl — C . . . . OH- Cl- + NCOH (16.164)

NCOH NCO- + H+ (16.165)

Further reactions occur between chlorine and cyanogen chloride and with cyanate:

2ClCN + 3HOCl + H2O N2 + 2CO2 + 5HCl (16.166)

2NCO- + 3HOCl N2 + 2CO2 + H2O + HCl + 2Cl- (16.167)

43

NCO- + 4HOCl CO2 + NO+ 4HCl (16.168)

These reactions are relatively slow at high pH (e.g., pH ~11). At lower pH (e.g., pH ~6.5), the reactions proceed much more rapidly.

In the absence of chlorine or hypochlorite, cyanate undergoes rapid hydrolytic decomposition in acidic solution (pH <2.5):

NCO- + 2H+ + H2O CO2 + NH (16.169)

Oxidation with Peroxygen Reagents. The first stage of cyanide reaction with hydrogen peroxide and with peroxymonosulfuric acid involves oxidation to cyanate:

CN- + H2O2 OCN- + H2O (16.170)

CN- + H2SO5 OCN- + H+ + HSO (16.171)

The reaction mechanism can be viewed in terms of the nucleophilic attack by the cyanide carbanion:

HN∫C- : + HO-OH N∫C- … O-OH N∫C-OH + OH- NCO- + H2O (16.172)

HN∫C- : + HO-SO3OH N∫C- … O-SO3OH N∫C -OH + HSONCO- + H+ + HSO (16.173)

Oxidation by Ozone. The reaction of ozone with cyanide is very fast. The first product is cyanate:

CN- + O3 = CNO- + O2 (16.174)

2CNO- + 3O3 + H2O = N2 + 2HCO + 3O2 (16.175)

In basic solutions, cyanate hydrolyzes readily to give ammonia:

44

CNO- + OH- + H2O CO + NH3 (16.176)

Ammonia is rapidly oxidized by ozone to nitrate:

NH + 4O3 NO + H2O + 4O2 + 2H+ (16.177)

16.5.5 Oxidation of SulfideThe reaction between sulfide and oxygen is complicated by the pH-dependent

speciation of sulfide and by the variety of possible oxysulfur compounds. For example, with bisulfide (HS-) as the sulfide species, oxidation may produce elemental sulfur, thiosulfate (S2O

), or sulfate (SO ):

2HS- + O2 + 2H+ 2H2O + 2S (16.180)

2HS- + 2O2 H2O + S2O (16.181)

2HS- + 4O2 2SO + 2H+ (16.182)

It can be seen from the above chemical equations that elemental sulfur formation is proton-consuming. With thiosulfate formation protons are neither consumed nor produced. In the case of sulfate formation, oxidation is accompanied by proton generation.

The rate of the following reaction was investigated by Chen and Morris (Environ. Sci. Technol., 6, 529-537 (1972)):

HS- + O2 Products (16.183)

The resulting initial rate law was formulated as:

d[S(II)]T/dt = -k[S(II)] [O2] (16.184)

The apparent rate constant k has a complicated pH dependence, as illustrated schematically in Figure 16.1, with maxima at ~pH 8 and ~pH 11 and a minimum at ~pH 9.

45

6 8 10 1412

k

pH

Figure 16.1 Effect of pH on the apparent rate constant (k) for the HS-/O2 reaction(schematic).

The following observations were made:

1. The pH of the first maximum in k (~pH 8) coincides with the pH at which rapid

polysulfide (S ) formation is detected (via UV absorption at 285-290 µm).

2. Near neutral pH, elemental sulfur formation predominates when the HS-/O2 ratio is high.

With relatively low HS-/O2 ratio, thiosulfate (S2O ) and other oxyanions form

predominantly.

3. Above pH 8.5, the major product is thiosulfate, irrespective of the HS-/O2 ratio.

4. The decrease in oxidation rate observed below ~pH 7 may be related to the protonation of

HS- to H2S. Apparently H2S is not attacked as readily as HS-.

The following reaction pathways were proposed by Chen and Morris:

HS- + O2 HS + O (16.185)

HS + O2 HO2 + S (16.186)

HS + O S + HO (16.187)

HS- + (x-1) S H+ + Sx2- (x = 2 – 5) (16.188)

46

47

FURTHER READING

1. H. Taube, "Electron Transfer Between Metal Complexes: Retrospective," Science, 226, 1028-1036 (1984).

2. H. Taube, Electron Transfer Reactions of Complex Ions in Solution, Academic, New York, 1970.

3. A. G. Sykes, "Further Advances in the Study of Mechanisms of Redox Reactions," Adv. Inorg. Chem. Radiochem., 10, 153-245 (1967).

4. A. Haim, "Mechanisms of Electron Transfer Reactions: The Bridged Activated Complex," Prog. Inorg. Chem., 30, 273-357 (1983).

5. R. C. Thompson, "Reaction Mechanisms of the Halogens and Oxohalogen Species in Acidic, Aqueous Solution," Adv. Inorg. Bioinorg. Mechanisms, 4, 65-106 (1986).

6. A. G. Sykes, Kinetics of Inorganic Reactions, Pergamon, New York, 1966, Chapters 7, 8, 9, 10.

7. D. Katakis and G. Gordon, Mechanisms of Inorganic Reactions, Wiley, New York, 1986, Chapter 7.

8. N. Uri, "Inorganic Free Radicals in Solution," Chem. Rev., 50, 375-454 (1951).

9. R. D. Cannon, Electron Transfer Reactions, Butterworths, Boston, MA, 1980.

10. J. O. Edwards, "Rate Laws and Mechanisms of Oxyanion Reactions with Bases," Chem. Rev., 50, 455-482 (1952).

11. E. Chaffee and J. O. E. Edwards, "Replacement as a Prerequisite to Redox Processes," Prog. Inorg. Chem., 13, 205-242 (1970).

12. W. J. Eilbeck and G. Mattock, Chemical Processes in Waste Water Treatment, Wiley, New York, 1987.

13. J. O. Edwards, Inorganic Reaction Mechanisms. An Introduction. W. A. Benjamin, New York, 1964.

14. G. E. Eden, B. L. Hampson, and A. B. Wheatland, "Destruction of Cyanide in Waste Waters by Chlorination," J. Soc. Chem. Ind., 69, 244-249 (1950).

15. G. E. Eden and A. B. Wheatland, "Effect of Temperature and Presence of Hypochlorite on the Rate of Hydrolysis of Cyanogen Chloride in Alkaline Solution," J. Soc. Chem. Ind., 69, 166-169 (1950).

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16. C. C. Price, et al., "Hydrolysis and Chrorinolysis of Cyanogen Chloride," J. Amer. Chem. Soc., 69, 1640-1644 (1947).

17. G. E. Eden, A. M. Freke, and K. V. Melbourne, "Treatment of Waste Waters Containing Hydrogen Peroxide, Hydrazine, and Methyl Alcohol," Chem. Ind., 1104-1106 (1951).

18. P. L. Bailey and E. Bishop, "Hydrolysis of Cyanogen Chloride," J.C.S. Dalton, 912-916 (1973).

19. G. H. Wiegand and M. Tremelling, "The Kinetics and Mechanism of the Decomposition of Potassium Cyanide in Aqueous Alkaline Medium. Hydrolysis of the Simplest Nitrile, HCN," J. Org. Chem., 37, 914-916 (1972).

20. J. A. Zeevalkink, et al., "Mechanism and Kinetics of Cyanide Ozonation in Water," Water Res., 14, 1375-1385 (1980).

21. K. Y. Chen and J. C. Morris, "Kinetics of Oxidation of Aqueous Sulfide by O2," Environ. Sci. Technol., 6, 529-537 (1972).

22. D. J. O'Brien and F. B. Birkner, "Kinetics of Oxygenation of Reduced Sulfur Species in Aqueous Solution," Environ. Sci. Technol., 11, 1114-1120 (1977).

23. M. R. Hoffmann, "Kinetics and Mechanism of Oxidation of Hydrogen Sulfide by Hydrogen Peroxide in Acidic Solution," Environ. Sci. Technol., 11, 61-66 (1977).

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