Diffusion Control and Pre-association in Nitrosation, Nitration and Halogenation

Diffusion Control and Pre-association in Nitrosation, Nitration and Halogenation JOHN H. RIDD Department of Chemistry, University College, London, England 1 Introduction 1 2 Generaltheory 4 Diffusion-controlled stage 4 The overall reaction 9 3 Nitrosation 13 Nitrosation by nitrosyl halides 14 Nitrosation by positive nitrosating agents 18 4 Nitration 23 Substrates not involved in prototropic equilibria 24 Substrates involved in prototropic equilibria 29 5 Halogenation 32 Halogenation by molecular halogens 33 Halogenation by positive halogens 40 6 Conclusion 43 Acknowledgements 46 References 46

1

Introduction

The subject of diffusion is important in many areas of chemistry. It provides one application of the theory of rate processes (Glasstone et al., 1941). It enters into polarography, electrochemistry and into many aspects of industrial chemistry, particularly in reactions involving heterogeneous catalysis (A.C.S. Advances in Chemistry, Series nos 109, 133). In homogeneous solutions, the rate of proton transfer is often subject to diffusion control (Eigen, 1964; Caldin, 1964; Hague, 1971). These aspects have been well covered in the literature. The present review is concerned with a different aspect of diffusion control. It has been recognized in recent years that a number of the common reactions of organic chemistry involve small concentrations of highly reactive inter1

2

JOHN H. RIDD

mediates and that, in principle, the reactions of these intermediates can be subject to diffusion control even though the overall reaction is relatively slow. However, the description of these reaction paths is complicated by the very short lifetime of some of the reactive intermediates for there may be insufficient time to permit the intermediates to come together by diffusion. This has implications concerning the mechanisms that can be written for these processes and for the products and relative reactivities that are observed. The purpose of the present review is to bring together the results for a number of reactions that raise questions concerning diffusion control, to consider the mechanistic points that arise thereby, and to formulate some generalizations concerning the implications of diffusion control on mechanistic pathways and relative reactivities. The restriction to nitrosation, nitration and halogenation reflects to some extent the interests of the author. These reactions are worth considering together, however, because they involve similar substrates and provide a number of related problems concerning diffusion control in electrophilic aromatic substitution. For reactions in solution, the mathematical analysis of diffusion control is usually based on the concept of a molecular encounter. In the gas phase, the amount of free space is sufficient to ensure that molecules normally separate rapidly after a collision; the probability of repeated collisions involving the same pair of molecules is slight. However, as the amount of free space in the system is reduced, it is possible to show by models (cf. Rabinowitch and Wood, 1936) that the number of repeated collisions (originally termed the number of collisions per set) increases rapidly. When two solute molecules come together in a solution, they are effectively held within a cage of solvent molecules and normally make a number of collisions with each other within this cage. Such a set of repeated collisions is termed an encounter (Fowler and Guggenheim, 1939). The walls of the cage are impermanent because of the diffusion of solvent molecules and so the lifetime of each encounter is very short, 10-’o-10-8 s (North, 1964). However, this lifetime is sufficient to ensure that the distribution in time of collisions between a pair of molecules is very different in solution from that in the gas phase. In solution the total number of collisions between solute molecules is much the same as when the same number of solute molecules occupy the same volume as a gas. The collisions in solution are bunched into sets or encounters, however, and the encounters themselves tend to occur in sets (Fowler and Guggenheim, 1939). If a reaction has a significant activation energy, so that the probability of reaction at a given collision is low, this distinction between collisions and encounters is unimportant as far as the overall reaction rate is concerned. The distinction becomes important as the probability of reaction at each collision approaches unity. In the limit, when reaction occurs at every collision, the limiting rate is the rate of encounter not the calculated rate of collision. since

3

DIFFUSION CONTROL A N D PRE-ASSOCIATION

only the first collision of every encounter contributes to the reaction rate. This is an important point, since the rate of encounter of solute molecules is a function of the viscosity of the medium whereas, to a first approximation, the rate of collision between solute molecules is independent of the viscosity of the medium. The last result arises because an increase in the viscosity of the medium decreases the frequency of encounters but increases the number of collisions per encounter (Fowler and Guggenheim, 1939). In considering the influence of the encounter rate on chemical reactivity, it is helpful to distinguish between microscopic and macroscopic diffusion control. In microscopic diffusion control, the reactants exist together in a homogeneous solution and reaction occurs on every encounter between them. It is obviously necessary that at least one of the reactants must be produced from an inactive precursor within the solution for otherwise the homogeneous solution could not have been formed; reaction would have been essentially completed in the process of mixing. Thus one scheme for an electrophilic substitution of this type is for an inactive precursor (A) to give rise to a low concentration of the electrophile (X) (usually by the elimination of a solvent molecule) in a preequilibrium step followed by the diffusion-controlled reaction of X (rate coefficient ken)with the substrate (B) to form the encounter pair (X.B) and then the products (Scheme 1). The nitration of mesitylene in 68.3% sulphuric acid appears to be a reaction of this type (Coombes et al., 1968), the initial reaction being the formation of the nitronium ion by the heterolysis of the nitric acidium ion (H,ONO:).

B

+X

- k,,,

X.B

Products

Scheme 1

Another type of electrophilic substitution subject to microscopic diffusion control occurs when a highly reactive form of the substrate is produced in a pre-equilibrium step (e.g. by proton loss) and when this form reacts on encounter with the electrophile. The nitration of p-nitroaniline in 90% sulphuric acid appears to be a reaction of this type (Hartshorn and Ridd, 1968), although the short lifetime of the free amine complicates the mechanistic interpretation. The formulation in Scheme 1 fits this type of reaction provided A is taken to represent the protonated amine, X the free amine, and B the nitronium ion. In 90% sulphuric acid, the nitronium ion is the bulk component of the NO:-HNO, equilibrium mixture. Many of the reactions in this review can be represented by Scheme k with some reservations concerning the lifetime of the intermediate X.

4

JOHN H . RIDD

The term macroscopic diffusion control has been used to describe processes in which the rate of reaction is determined essentially by the rate of mixing of the reactant solutions. The nitration of toluene in sulpholane by the addition of a solution of nitronium fluoroborate in sulpholane appears to fall into this class (Ridd, 1971a). Obviously, if a reaction is subject to microscopic diffusion control when the reactants meet in a homogeneous solution, it must also be subject to macroscopic diffusion control when preformed solutions of the same reactants are mixed. However, the converse is not true. The difficulty of obtaining complete mixing of solutions in very short time intervals implies that a reaction may still be subject to macroscopic diffusion control when the rate coefficient is considerably below that for reaction on encounter. The mathematical treatment and macroscopic diffusion control has been discussed by Rys (Ott and Rys, 1975; Rys, 1976), and has been further developed recently (Rys, 1977; Nabholtz et al., 1977; Nabholtz and Rys, 1977; Bourne et al., 1977). It will not be considered further in this chapter. For a number of the reactions considered here, the second stage of Scheme 1 is rate-determining. This does, however, require a delicate balance between the rates of the individual reaction stages. Thus, in Scheme 1, if the concentration of B is too high, the rate-determining stage will shift to the rate of formation of the reactive intermediate and the overall reaction rate will no longer be limited by diffusion. If the back reaction of X to form A is too great the lifetime of the reactive intermediate will be so short that reaction with B will not occur unless B is present as an encounter pair with A at the time of formation of X. Following Jencks (Jencks and Sayer, 1975) such a reaction path is said to involve pre-association. The importance of pre-association is best appreciated after the outline of the theory of diffusion in the following section. 2

General theory

In considering the type of reaction outlined in Scheme 1, it is helpful to deal first with the diffusion-controlled stage by itself, ignoring the continual formation of the reactive intermediate from its inactive precursor. DIFFUSION-CONTROLLED STAGE

The classical treatment of such processes derives from the consideration of the coagulation of colloids (Smoluchowski, 19 17), but many accounts have been given of how the same approach can be used for diffusion-controlled reactions (Noyes, 1961; North, 1964; Moelwyn-Hughes, 1971). The starting point is the assumption of a random distribution of the two reactants (here given the symbols X and B) in the solution. Then, if B is capable of reacting on encounter with a number of molecules of X, it follows that such reactions deplete the concentration of X in the neighbourhood of B and therefore set up a

DIFFUSION CONTROL A N D PRE-ASSOCIATION

5

concentration gradient between the region about a B molecule and the bulk of the solution. After a very short time interval (ca. lo-' s), a steady state is reached in which the diffusion of molecules of X towards B under the influence of this concentration gradient provides a reaction rate that maintains the concentration gradient. The rate coefficient (ken)for the reaction of X with B in this steady state is then given approximately by equation (1)' (Noyes, 1961; North, 1964). In this equation r, and rB are the radii of X and B (here considered as uniformly reactive spheres), D,, is the diffusion coefficient for the relative motion of X and B, and L is the Avogadro constant. ken= 4nLDxB(r,+ rB) (1) The use of the Stokes-Einstein equation (2) relating the diffusion coefficient (0)of a spherical solute molecule to its radius (r), the viscosity of the medium (q) and the Boltzmann constant (A) permits the rate coefficient (ken) to be expressed in (3) in terms of the viscosity of the medium. In this derivation, the

D

= kTI6nq-r

(2)

diffusion coefficient for the relative motion of X and B is taken as the sum of the separate diffusion coefficients. The value of kengiven by (3) is relatively insensitive to the ratio rx/rB (Debye, 1942) and so a further approximation is to put this ratio equal to unity, giving (4). Values of ken calculated from this equation are listed in Table I for some common solvents: the majority of the values lie in the range 109-1010 mol-I s-l dm3. In view of the many reactions carried out in aqueous sulphuric acid, the results for this solvent are also given (Table 2). In 98% sulphuric acid the value of ken drops to 3 x lo8 mol-' s-l dm3. ken= 2RT(rx + rB)z/3q-rxrB

(3) The application of diffusion theory leading to equation (4) is usually based on the assumption that one molecule of B is capable of reacting with a number ken= 8 R T 1 3 ~

(4)

of molecules of X; the concentration of X in the neighbourhood of a molecule of B is therefore less than that in the bulk of the solution. However, it is much more common for one molecule of B to react with only one molecule of X. It is then by no means obvious that the analysis in terms of concentration gradients is applicable, since the reaction of X with B that establishes the concentration gradient also prevents that molecule of B from having any further influence on the reaction rate. It appears, however, that (4) is still appropriate (Collins and Kimball, 1949) essentially because the continued existence of a molecule of B 1 The equations in this review are written to give the rate coefficients in units of concentration instead of in terms of the number of reacting molecules per ml. This convention and the use of S.I. quantities and units causes some of the equations to differ from those in the listed references.

6

J O H N H. RIDD

TABLEI Viscosities (t#'.h of some pure solvents. the temperature coefficients ( B y . and the corresponding rate coefficients (ken.eqn 4) for reaction on encounter Solvent Acetic acid Acetic anhydride Acetone Acetonitrile Benzene Carbon disulphide Carbon tetrachloride Ether Ethyl alcohol Formic acid Methyl alcohol Nitrobenzene Nitromethane Water

Temp./'C

15 25.2 0 18 0 25 0 25 0 20 0 20 0 20 0 25 0 20 7.59 20 0 25 2.95 20 0 25 0 4 19

Deuterium oxide"

25 4 19

lo4 q/N m-I s 13.1 11.5 12.4 9.0 3.99 3.16 4.42 3.45 9.12 6.52 4.36 3.63 13.3 9.69 2.84 2.22 17.7 12.0 23.9 18.0 8.2 5.47 29.1 20.3 8.53 6.20 10.3 8.90 22.5 12.5

BlkJ mol-' 9.13 11.77 6.32 6.71 11.17 6.10 10.54 6.67 12.94 15.63 10.96 14.21 8.64

18.9 26.4

hen/

mol-' s-' d m 2 4.9 5.7 4.9 7.2 15.2 20.9 13.7 19.1 6.6 10.0 13.9 17.9 4.5 6.7 21.3 29.8 3.4 5.4 2.6 3.6 7.4 12.1 2.1 3.2 7. I 10.7 3.4

1::; 7.4 2.7 5.2

' The viscosity is usually given in poise;

1 poise = 0.1 N m2s Taken from the "Handbook of Chemistry and Physics". Chemical Rubber Co.. 1976. p. F-32 except where noted Calculated for the temperature range listed Lemond. 194 I

I'

in the solution is itself evidence that the probability of finding a molecule of X in the neighbourhood is less than that in the bulk of the solution; this is sufficient for diffusion theory to be used. Equations (I), (3) and (4) can therefore be used when B reacts with only one molecule of X.

7

DIFFUSION CONTROL AND PRE-ASSOCIATION

TABLE2 Viscosities (q)" of aqueous solutions of sulphuric acid. the temperature coefficients ( B ) and the corresponding rate coefficients (k,,, eqn 4) for reactions on encounter

Wt/Oi,

0°C

25°C

Bh/kJ mol-'

10 20 30 40 50 60 70 80

2 1.5 26.0 34.0 46.5 64.4 107 197

10.8 13.7 18.0 23.9 34.2 5 1.8 89.4 181 210 207 270"

18.6 17.3 17.2 18.0 17.1 19.6 2 1.4

90

465 5 19 560

98

100 ~

~~

~

2 1.5 24.9 24.3

kenc/ mol-'s-' dm3 6.1 4.8 3.7 2.8 1.9 I .3 0.74 0.36 0.3 1 0.32 0.24d

~~

Taken from "International Critical Tables". 1929. Vol. 5 , p. 12, and "Tables of Physical and Chemical Constants", C. W. Kaye and T. H. Laby, eds.. 1973. 14th edn, p. 36 Calculated for the given range of temperatures ''At 25°C At 2OoC

One obvious weakness in the derivation of (4) is that the reacting molecules are represented by spheres with surfaces of uniform reactivity: the question of molecular orientation during reaction does not then arise. This is obviously a very crude approximation for the reaction of many complex molecules. Some recent studies (Solc and Stockmayer, 1971, 1973) have employed a more realistic model in which the representation as spheres is retained but with the assumption that only part of the area of the sphere is reactive. The contact of two spheres involving both reactive areas is then taken as a necessary and sufficient condition for reaction. With this model, a certain fraction of the encounters will occur through an initial collision involving both reactive areas and will thus lead to immediate reaction. Another fraction of the encounters will occur through an initial collision involving one or both unreactive areas but will lead to reaction as a consequence of rotation during the encounter. A third fraction of the encounters will not lead to reaction. The calculated rate coefficient for such a diffusion-controlled reaction is less than that given by (4) by a factor which depends on the relative radii of the reactants and on the fractions of the total areas that are considered reactive: this factor may be one or more powers of ten. A similar consequence is found when one of the reactants is taken as a plane carrying a single reactive site, but the reduction in the calculated rate coefficient for a diffusion-controlled reaction can then be even more marked

8

JOHN H. RIDD

(Schmitz and Schurr, 1972). The mathematical treatment of diffusioncontrolled reactions in terms of these newer models is complex' and so, for the purposes of the present chapter, the value of kengiven by (4) will be taken as the first approximation and probable upper limit of the rate coefficient for a diffusion-controlled reaction. If the species X and B are to react on every encounter, it is obvious that no significant activation energy can be required. This does not imply that the experimental activation energy (E,) will be zero, even for the diffusioncontrolled step, because of the temperature dependence of the viscosity of the medium. The variation of the viscosity of liquids with temperature normally follows equation (5) where b and B are constants. Even where this equation is not well obeyed (e.g. water), it is still convenient to define a mean value of B for a particular range of temperature. From (4) and (9,the variation of kenwith temperature is as shown in (6). When this expression for kenis substituted in q = b $/RT

(5)

equation (7) defining the experimental activation energy, the result is (8). The values of B for common solvents over the range 0-25OC are given in Tables 1 and 2. From these results and the value of RT(2.48 kJ molk' at 25'), the E,=--

Rdlnk

d T-'

E,=RT+B

(7)

(8)

experimental activation energy for the diffusion-controlled step can be seen to be about 10-20 kJ mol-' at room temperature. When the overall reaction of Scheme 1 is considered, E , also includes the value of A H o for the preequilibrium step. The above calculations refer to the formation of encounter pairs from neutral reactants. If the reactants are charged, the electrostatic interaction between them modifies the frequency of the encounters. Debye has shown that the effect of the electrostatic interaction can be usefully discussed in terms of the distance ( I ) at which this interaction is equal to kT (Debye, 1942). In §.I. units, this distance is given by (9) where q x and qg are the charges on the 1 = qXqB/4z&kT

(9)

reactants, k is Boltzmann's constant and E is the permittivity of the medium mk3 kg-I s4 A2). The effect of the (for water at 25O, E = 6.932 x electrostatic interaction is then to modify the frequency of the encounters (and hence the rate coefficient ken)by the factor f given by (10).

* A simplified treatment has now appeared (Schurr and Schmitz, 1976).

DIFFUSION CONTROL A N D PRE~ASSOCIATION

9

For reactions between univalent ions in water, the value of 1 from equation (9) is 7.16 A. If the values of rx and rg are each taken as 5 A, then from (10) the values of f for aqueous solutions are 0.45 and 1.9 depending on whether the electrostatic interaction is repulsive or attractive. If the values of rx and rB are each taken as 3 A,the corresponding values o f f are 0.24 and 2.6. The electrostatic interaction is more effective in reducing the frequency of encounters between reactants with charges of the same sign than in increasing the frequency of encounters between reactants with charges of opposite signs. The equations above provide only a first approximation to the consequences of electrostatic interaction because the effect of the ionic atmospheres is ignored. When a correction is made for this (Debye, 1942), the result is to bring the f values (eqn 10) nearer to unity. Other factors have been considered in more recent treatments (Sarfare, 1975). T H E O V E R A L L REACTION

The conventional treatment of the overall reaction of Scheme 1 in terms of a low steady-state concentration of X leads to (1 l), and the condition that the

rate-determining step should be the diffusion-controlled formation of the encounter pair requires that k - , & ken[Bl.The observed rate coefficient (kobs) is then given by (12) where K is the equilibrium constant for the first stage of Scheme 1. A number of reactions including nitration and nitrosation have been discussed on these lines.

There is however a possible inconsistency in the above approach. The calculated value of kenfor the solvents commonly used is about lo9 mol-' s-l dm3 (Tables 1 and 2). If we take a typical reactant concentration of lo-' mol dmP3, the inequality k-, 3 k,,[BI implies that k - , 9 lo7 s-I. This gives a halflife for the intermediate of < lo-' s. This half-life is short enough to require some reconsideration of the treatment in terms of diffusion. One problem arises because the rate coefficient ken does not refer to a uniform distribution of X and B in the solution but to a steady state after the fast initial reaction has abated. The shorter the lifetime of the intermediate, the more effective is the initial equilibrium in maintaining a uniform distribution of X in the solution. The consequence of this can be seen by considering the

10

JOHN H. RIDD

values of the corresponding time-dependent rate coefficient (k&)for the time ( t ) immediately after the establishment of a uniform distribution of X and B ‘in the solution. This rate coefficient is related to the steady-state rate coefficient (ken) by (13).3 If, as a guide to the values of kQ,, we take the values rx + rB = 10 A, m 2 s-l then the variation of kQ,lken with time is as follows: D,, = 2 x

tls

10-7

10-8

k:,k

1.04

1.13

10-9 1.40

lO-’O

2.26

When the lifetime of X is very low the reacting system is nearer to a uniform distribution of the reactants and the value of the rate-coefficient for encounter pair formation is greater than that given by (1). This is understandable because, when the lifetime of X is very short, reaction can occur only with those molecules of X that are formed in the immediate neighbourhood of B and these therefore have only a short distance to travel. As the lifetime of X becomes less, it becomes increasingly difficult to visualize the reactions as a diffusion-controlled process and pre-association mechanisms have to be considered in which X is formed from A within an already existing encounter pair containing the other reactant B. Such a process is shown in Scheme 2. A i B A.B X.B

k,,!

S A.B ---+

X.B Products

Scheme 2

The relative importance of the pre-association and diffusion-controlled mechanisms does not appear to have been considered in detail for the reactions discussed in this chapter. In order to do so, it is necessary to combine the reaction paths of Schemes 1 and 2 as shown in Scheme 3. In this and the previous Schemes, the species A . 3 and X .B are considered as encounter pairs without specific interaction between the components. It is, of course, possible to set up rate expressions for the formation of X .B by the upper (diffusion-controlled) and the lower (pre-association) paths in Scheme 3, but for our present purpose it is sufficient to consider only the three This equation is an approximation to the relationship given by Noyes (1961).

11

DIFFUSION CONTROL AND PRE-ASSOCIATION

X X.B

A

k5

Products

A.B Scheme 3

possible reactions of the encounter pair X.B. From the principle of microscopic reversibility, the ratio of the rate coefficients k-, and k - , is a measure of the relative rates of formation of X . B by the diffusion-controlled and pre-association paths. Also, the ratio of k, to (k-, + k-,) determines whether or not the formation of the encounter pair X . B is rate-determining. It is helpful therefore to consider each of these rate coefficients in turn. The rate coefficient k - , (Scheme 3) is that for the dissociation of an encounter pair. This is obviously given by the rate coefficient for the formation of an encounter pair (ken)divided by the equilibrium constant for encounter pair formation ( K ) .The value of kenhas been discussed above and for water at 2 5 O is 7.4 x lo9 mol-' s-I dm3. The value of K can be estimated from the number of possible sites about a given molecule and for aqueous solutions of small molecules comes to be ca. 0.5 mol-' drn3., Thus, for these systems, k-, is ca. 1.5 x 10'O s-I. The value of k-, should decrease with an increase in the size of the molecules and the viscosity of the medium (cf. North, 1964). The values of k - , obviously depend on the particular system being considered but, since chemical interaction between X and B is assumed to be absent in the encounter pair, these values, to a first approximation, may be put equal to those for the same reaction outside the encounter pair (k-]). One example, that occurs repeatedly in this chapter, is when X is an aromatic amine, A is the protonated amine, and B is a relatively long-lived electrophile. Then, since the protonation of such aromatic amines as N,N-dimethylaniline and p-nitro-N,N-dimethylaniline appears to occur on encounter in aqueous solution (Kresge, 1975; Kresge and Capen, 1975), the value of k-, at 25OC is given approximately by 4 x IO'O[H+] mol-' s-' dm3. Thus, as the hydrogen ion concentration ([H+])approaches 1 mol dmP3the breakdown of the encounter pair X . B by protonation becomes more probable than that by dissociation, When both components of the encounter pair are charged, the resulting electrostatic interaction will modify the equilibrium constant. On the simplest approximation, and using the quantities defined for equation (lo), this electrostatic interaction should change the equilibrium constant by a factor exp [-l(rx + rJ1. For uni-univalent ions of like charge in water at 2 5 O , this factor equals 0.30 when rx + rB = 6 A. A detailed discussion is available elsewhere (North, 1964).

12

JOHN H. RIDD

implying that pre-association rather than diffusion control becomes the main reaction path for formation of the encounter pair. This should happen, in general, when the half-life of the intermediate is < 10-lo s. The value of k, for the reaction of the encounter pair X. B to products also obviously depends on the system involved, but it is interesting to consider the maximum possible value of this rate coefficient when the activation energy for the reaction is zero. Since the collision frequency of a molecule with its neighbours in solution is ca. lo’* s-’ (cf. North 1964), the collision frequency with one specific neighbour will be less than this by a factor of ca. 10 leading to a maximum rate coefficient for reaction within the encounter pair of ca. 10” s-l. If the species X and B are considered to be in contact within the encounter pair, the maximum rate coefficient becomes that predicted by transition state theory for a unimolecular reaction (ca. 1013 s-l). These limiting values are greater than that for the dissociation of the encounter pair (k-J and are, in general, greater than that expected for the back reaction of X to form A. However, even when the activation energy for the reaction of B with X within the encounter pair is zero, it does not follow that reaction will occur at every collision for the relative orientation and positions of the reacting species may be important; the value of k, may then be one or more powers of ten below the limiting value (see p. 7). Thus, even if there is no activation energy for the reaction of X with B within the encounter pair, it does not follow that the encounter pair formation will necessarily be rate-determining, especially if the back reaction is the protonation of X in a highly acidic medium. In one respect, the representation in Scheme 3 oversimplifies the situation since it implies that the composition of the transition state of stage 5 is independent of the method of forming the encounter pair X . B. In general this is not true, since when the reactive species X is formed from A by the preassociation path, any other species formed at the same time as X will also be present when X reacts with B. However, such a species should then be present as a “spectator” (cf. Jencks and Sayer, 1975) and for present purposes can be ignored. In conclusion, it may be useful to summarize the kind of experimental observations that can be used as evidence that a given reactive intermediate X, considered here as an electrophile, reacts on encounter with a series of substrates B (cf. Scheme 1). Such an encounter reaction can be suspected when the reaction rate is proportional to the concentration of each substrate but almost independent of the nature of the substrates (provided that the substrates It is necessary to stipulate that the reaction rate should be proportional to the concentration

of the substrates because the condition k - , < k,,[B] in (11) leads to a reaction rate that is independent of both the concentration and the nature of the substrates. The observation of this zeroth order rate does not, however, imply that the reaction between X and B necessarily occurs on encounter.

13

DIFFUSION CONTROL AND PRE-ASSOCIATION

would be expected to be of very different reactivity). Such results are an obvious consequence of the condition k - , % k,,[Bl in (11) but do not in themselves distinguish between the reaction paths in Scheme 1 and Scheme 2. If the equilibrium constant for the formation of the elzctrophile is known then the true coefficient for the reaction of the electrophile with the substrate can be calculated and this can be compared with that given by (4). If the value of AHo for the formation of the electrophile is known, the true activation energy for the reaction of the electrophile and the substrate can be calculated and that should accord with (8). Finally, if the half-life of the electrophile is known, this should pe consistent with its participation in a diffusion-controlled step.

3

Nitrosation

Kinetic studies of nitrosation by aqueous nitrous acid have been carried out for reaction at nitrogen, carbon, oxygen, and sulphur. There are many similarities between the kinetic forms observed for reaction at the different centres: it appears that nitrosation can involve the nitrosonium ion or a number of carriers of the nitrosonium ion depending on the acidity and the other species present. Some of the nitrosating agents that have been suggested are shown below in the expected order of reactivity: NO+ > NO. OH,

> NOCl

- NOBr > NO. NO, - NO. OAc

The number of intermediates involved and the number of possible ratedetermining stages together make nitrosation a reaction of unusual kinetic complexity, but, for many nitrosation reactions, the contributions of the separate reaction paths have been clearly established and the corresponding rate-determining stages have been identified. The early work on the kinetics of nitrosation was carried out mainly on the N-nitrosation of primary aromatic amines leading to diazotization. Some of the stages for diazotization via an intermediate nitrosating agent NOX are shown in Scheme 4. The exact rate-determining stage in a given reaction depends on the experimental conditions but, in feebly acidic aqueous solutions, the stages X-

-

+ H+ + HNO, G

ArNH,

+ NOX

ArAH,NO ArNHNO

NOX

+

+ H,O

ArNH,NO

+ X-

ArNHNO+H+ ArN,OH

Scheme 4

ArN:

14

J O H N H. KIDD

subsequent to the N-nitrosation are usually fast and so do not affect the kinetic form (Ridd, 1961; Kalatzis and Ridd, 1966). Unless otherwise specified, the kinetic studies of diazotization described below refer to conditions for which the N-nitrosation stage is rate-determining. The other main source of evidence on the mechanisms of nitrosation comes from the C-nitrosation of aromatic compounds but, for this reaction, the final proton loss from the o-complex is usually rate-determining (Challis and Higgins, 1972). Under these conditions, the overall rate and kinetic form of the reaction provide no evidence on the rate and mechanism of the nitrosation stage. Fortunately the work of Challis and his co-workers (Challis and Higgins, 1973; Challis and Higgins, 1975; Challis and Lawson, 1973) has shown that the C-nitrosation stage is rate-determining for the nitrosation of some reactive aromatic substrates (2-naphthol, azulene, 1,2-dimethylindole) in feebly acidic media and these are the reactions referred to below. In considering the series of possible nitrosating agents, it is convenient to start with those that are the weakest electrophiles. In principle, nitrous acid itself is a potential nitrosating agent but no evidence has been found for its involvement in N or C-nitrosation. Nitrous anhydride (dinitrogen trioxide) is more reactive and is effective in the nitrosation of aromatic amines (Hughes et af., 1958a; Larkworthy, 1959a) and some indoles (Challis and Lawson, 1973). However, these reactions d o not appear to occur on encounter, since the reaction rate (under conditions where the attack on the substrate is ratedetermining) depends markedly on the reactivity of the substrate.6 The reaction rate is also several powers of ten less than that expected for an encounter reaction between the amine and nitrous anhydride (Ridd, 1961). As the reactivity of the nitrosating agent is increased, the evidence for encounter control comes in first with the reactions of the nitrosyl halides.

NITROSATION B Y N I T R O S Y L H A L I D E S

Solutions of nitrous acid in aqueous hydrochloric acid or hydrobromic acid give rise to an equilibrium concentration of the corresponding nitrosyl halides, as indicated in (14). At 25OC, the equilibrium constants for the formation of HNO,

+ H+ + X-

= NOX

+ H,O

(14)

these nitrosyl halides (taking the activity of water as unity) are X = C1, K = 1.14 x lop3mol-2 dm6; X = Br, K = 5.1 x mol-2 dm6. Extrapolation of A recent review of the reactivity of aliphatic amines towards nitrous anhydride (Mirvish, 1975), provides evidence that these reaction rates are curiously insensitive to the basicity of the substrate even though the overall reaction rate is much less than the encounter rate. The reason for this is not clear.

15

DIFFUSION CONTROL AND PRE-ASSOCIATION

the results to 0°C gives X = C1, K = 5.5 x mol-2 dm6; X = Br, K = 2.2 x lo-* mol-* dm6 (Schmid and Hallaba, 1956; Schmid and Fouad, 1957).

I

I 4

I

3

2

I

5

PK,

FIG. 1. Diazotization of aromatic amines through the intermediate formation of nitrosyl halides (NOX). The variation of the rate coefficient k (eqn 16) with the pK,-value of the amine. The broken line indicates the expected limit for a diffusion-controlled reaction. + ... X = C1; 0 ... X=Br

The first evidence for the involvement of these nitrosyl halides in nitrosation came from kinetic studies of diazotization. The rate equation for diazotization in aqueous hydrochloric and hydrobromic acids includes the kinetic term given in (15) where S stands for the free amine (Schmid, 1937; Schmid and Muhr, 1937). It was later recognized that this can be interpreted as the attack of the nitrosyl halides on the free amine (Hammett, 1940) and the kinetic term was rewritten as (16).' The corresponding rate coefficients and activation energies calculated from the equilibrium concentration of the nitrosyl halides are given in Tables 3 and 4 together with later results (Williams, 1977). Rate = k[SJ[HNO,I[H+JLX-l

(15)

Rate

(16)

= k[SI[NOXI

The extent to which the rate coefficients in Tables 3 and 4 approach that expected for a diffusion-controlled process is illustrated in Fig. 1. For the less reactive amines, nitrosyl chloride reacts significantly faster than nitrosyl

' Because of the number of rate equations in this chapter, the symbol k without subscripts or superscripts is used to designate any rate coefficient. A particular rate coeficient is then specified by reference to the equation by which it is defined.

16

JOHN H . RIDD

TABLE3 Rate coefficients (k, eqn 16) and activation energies for nitrosation by nitrosyl chloride in aqueous solution Substrate

Temp./'C

Aniline

25

o-Methylaniline m-Methylaniline

25 25

p-Methylaniline

25

0-Chloroaniline m-Chloroaniline

25 25

p-C hloroaniiine

25

m-Methoxyaniline p-Methoxyaniline p-Carboxyaniline p-Nitroaniline Ammonia Glycine Hydroxylamine O-Methylhydroxylamine Hydrazinium Ion Azulene 1,2-Dimethylindole 2-Phen ylindole

25 25 25 25 25 25 0 0 0 21.1 3 3

Schmid and Essler, 1957, and references quoted therein *Williams, 1977 Schmid, 1954

klmol-' s-' dm'

AH-/kJ mol-'

Ref.

19.1

a b a

2.44 2.70

{:::; 1.16 1.63

a 20.7

a

{ 3.03 ;:;;

5.86 1.09 0.2 1 0.05 0.0 17 0.035 0.0 16 0.00075 5.48 0.99 0.77

a b a

a b b b b b C C

d d e

33

f f f

Morgan et al., 1968 Perrott et al., 1976 /Challis and Higgins, 1975

bromide but the difference decreases as the basicity of the amine is increased and as the values of the rate coefficients approach that expected for reaction on encounter. The rate coefficients of the most reactive amines are below this limit (7.4 x lo9 mol-' s-' dm3) by about a factor of 2 (cf. Table 1). The activation energies (6-21 kJ mol-') are reasonably near that expected for a diffusioncontrolled process in water Ica. 20 kJ mol-', cf. eqn (8) and Table 11. In assessing these results, it should be remembered that there are a number of approximations in the calculation of both the theoretical and experimental quantities and so exact agreement cannot be expected. The complete set of results supports the earlier conclusion that these reactions approach closely the diffusion-controlled limiting rate (Ridd, 196 1). With the bromide-catalysed reaction, the first step of Scheme 4 can be made rate-determining by an increase in the concentration of the amine; the rate of

17

DIFFUSION CONTROL AND PRE-ASSOCIATION

TABLE4 Rate coefficients ( k , eqn 16) and activation energies for nitrosation by nitrosyl bromide in aqueous solution Substrate Aniline Aniline p-Meth ylaniline m-Methoxyaniline p-Methoxy aniline p-Chloroaniline p-Carboxyaniline m-Nitroaniline p-Nitroaniline Hydroxylamine 0-Methylhydroxylamine Hydrazinium ion Schmid and Fouad, 1957 *Williams, 1977

Temp./OC

klmol-'

25 25 25 25 25 25 25 25 25

dm3

SKI

3.2 1.69 2.69 2.24 3.02 2.46 0.43 0.106 0.043 0.037 0.0 I8 0.0000019

0 0 0

I'

AHllkJ mol-I

Ref.

6.15

CJ

b b b b b b b b c c

d

Morgan et al., 1968 Perrott et al., 1976

formation of nitrosyl bromide can then be measured. The reaction has the kinetic form of (17) and the value of k is 1170 mol-2 sP2dm6 at 0" (Hughes Rate = k[X-l[HNO,I[H+l

(1 7)

and Ridd, 1958). In the same way the rate of formation of nitrosyl chloride can be made rate-determining in the nitrosation of azide ions; this reaction also follows (17) and the value of k is 975 mol-* sP1 dm6 at 0" (Stedman 1959b). From these rate coefficients and the equilibrium constants for the formation of the nitrosyl halides, it is possible to calculate approximate rate coefficients for the hydrolysis of these halides at 0°C according to equation (18); the values Rate = k[NOXI

(18)

are 1.8 x lo6 s-l for nitrosyl chloride and 5.3 x lo4 s-' for nitrosyl bromide. The half-lives for the nitrosyl halides are therefore ca. 4 x lo-' s for nitrosyl chloride and 1.3 x lo-' s for nitrosyl bromide. These half-lives are consistent with the intervention of the species in a diffusion-controlled reaction. Consideration of the half-life of the free amine slightly complicates this interpretation. Most of the work listed in Tables 3 and 4 was carried out in 0.20.4 M hydrochloric acid (Schmid and Essler, 1957) or 0.2 M sulphuric acid (Williams, 1977). The amines used are sufficiently basic to react on encounter with the hydronium ion (cf. Kresge, 1975) so the second-order rate coefficient for protonation can be taken as 4 x 1Olo rno1-l dm3 (Kresge and Capen, 1975)

18

JOHN H. RIDD

and the half-life of the free amine in 0.2 M acid as ca. lo-'' s. The corresponding first-order rate coefficient for the protonation of the amine in the NOX. ArNH, encounter pair (ca. 1O'O s-I) is then very similar to that for the diffusion apart of the components. Hence, from the arguments on p. 11, the encounter pair should be formed in part from the pre-association of the nitrosyl halide with the protonated amine. In principle, therefore, the diffusioncontrolled limit could be exceeded (see Section 6). The results in Tables 3 and 4 include also the rate coefficients for the nitrosation of a number of inorganic species. I n reactions with aqueous solutions of nitrous acid, ammonia gives molecular nitrogen, hydroxylamine gives nitrous oxide, and hydrazine gives both ammonia and hydrazoic acid. In all these reactions, the nitrosation stage is considered to be rate-determining and the kinetic form of the halide ion catalysis is given by (1 5) with S as the appropriate substrate. However, the rate coefficients for these reactions, when expressed in terms of the concentrations of nitrosyl halides, are below the value expected for reaction on encounter. This is consistent with lower reactivity of nitrosyl bromide relative to nitrosyl chloride in reaction with the hydrazinium ion (NH,N+H,) (Perrott et af., 1976). It is, however, surprising that these halides should have the same reactivity towards hydroxylamine and its 0methyl derivative (Tables 3 and 4). The rate coefficient for the reaction of nitrosyl chloride with azulene (Table 3) suggests that this reaction occurs on encounter although the activation energy is somewhat higher than expected. The result is significant because it indicates that C-nitrosation by nitrosyl halides can be diffusion-controlled. This reaction was studied at much lower acidities ([H+] = 4 x M) than those with the aromatic amines and so the above arguments concerning the half-life of the aromatic substrate d o not apply. Azulene is an exceptionally reactive aromatic compound [in hydrogen-isotope exchange it is more reactive than benzene by a factor > 10" (Taylor, 1972)l and it is uncertain how far diffusion-controlled C-nitrosation persists down the scale of aromatic reactivity. This cannot, unfortunately, be tested since, with the less reactive aromatic compounds, the final proton loss is rate-determining (cf. p. 14). The related C-nitrosations of indoles in Table 3 could in principle occur by Nnitrosation followed by rearrangement. NITROSATION B Y POSITIVE N I T R O S A T I N G A G E N T S

For nitrosation by aqueous nitrous acid, one of the more important kinetic terms has the form of equation (19) where S can stand for a wide range of substrates. This term with S as the free amine, was first found in the Rate = k[SI[HNO,I[H+l

(19)

DIFFUSION CONTROL AND PRE ASSOCIATION

19

diazotization of o-chloroaniline in dilute perchloric acid (Hughes et al., 1958b) and the studies were then extended to the nitroanilines (Larkworthy, 1959b).8 The term occurs in the N-nitrosation of a number of inorganic species including hydrazoic acid, azide ions, thiocyanate ions (Stedman, 1959a, b), hydroxylamines (Morgan et al., 1968) and the conjugate acid of hydrazine (Perrott et al., 1976). Rate-determining C-nitrosation with the kinetic form (19) is represented by the 1-nitrosation of azulene (Challis and Higgins, 1975) and 2-naphthol (Challis and Higgins, 1973) and by the 3-nitrosation of certain indoles (Challis and Lawson, 1973). Reaction at oxygen is represented by the nitrosation of acetate ions (Stedman, 1960), hydrogen peroxide (Benton and Moore, 1970), ascorbic acid and ascorbate ions (Dahn et al., 1960). Nitrosation of the co-ordinated water molecules of some inorganic complexes also appears to involve this kinetic form9 (Matts and Moore, 1971). Nitrosation at sulphur is represented by the S-nitrosation of thioureas (Collings et al., 1975). The reaction of chloride and bromide ions according to (19) has already been discussed, and reaction also occurs with iodide ions (Hughes and Ridd, 1958). Many of the above nitrosations are followed by subsequent reactions but, except for the nitrosation of co-ordinated water molecules, there is evidence that the nitrosation stage is the rate-determining step in the reaction being followed. Unfortunately, in spite of the importance of this kinetic form, the identity of the electrophile is not yet clearly established. The kinetic form (1 9) is consistent with nitrosation by either the nitrous acidium ion [eqn (20)l or the nitrosonium ion [eqn (21)l. HNO,+H+ HNO,+H+

GXIII~

H,ONO+

(20)

NO++H,O

(21)

The nitrosonium ion is a well-known chemical species and the equilibrium constant for its formation has been determined spectrophotometrically as 3 x lo-' mol-' dm' (Bayliss et al., 1963).1° There is no spectroscopic evidence for the existence of the nitrous acidium ion. A number of the conjugate acids of aromatic amines also undergo diazotization with the kinetic form of equation (19) but these species are much less reactive than the free amines and are therefore excluded from the present discussion. In these reactions, the interaction of NO+ with the protonated amine appears to facilitate the proton loss. Since 0-nitrosation is not the rate-determining step in these reactions, the observed order with respect to nitrous acid is not necessarily the order with respect to nitrous acid in the nitrosation stage. l o This value is derived from measurements of acidity functions at 25OC and measurements of the concentration of NO+ at several lower temperatures. The equilibrium concentration of NO+ is not a marked function of temperature and so this value can probably be used for the range @ 25 "C without introducing greater errors than are implicit in the other approximations involved.

20

JOHN H. RIDD

The formation of the nitrosonium ion follows the acidity function H , and the conversion of nitrous acid to nitrosonium bisulphate is essentially complete in ca. 65% sulphuric acid. At these high acidities, there is no reason to doubt that the nitrosonium ion is the effective electrophile. The problem arises with studies at lower acidities for most of the kinetic evidence for equation (19) relates to feebly acidic media. For a number of years, there has been one strong argument against nitrosation by the nitrosonium ion in feebly acidic media. The reactions with anions appear to give a limiting value of k (eqn 19) of ca. 2500 mol-* s-l dm6 (see below). These reactions are first order with respect to the substrate and hence the substrate must be reacting with an equilibrium concentration of the electrophile. The actual rate of formation of the electrophile must therefore be faster than this rate of reaction with anions. If the nitrosonium ion were the electrophile, it would appear from (21) that each formation and rehydration of the electrophile should involve the exchange of one oxygen atom between nitrous acid and the solvent; such exchange should therefore be necessarily faster than the nitrosation of anions. The kinetics of the first-order "0exchange between nitrous acid and water at 0°C are given by (22) with k = 230 mol-' s-l dm3 and, at the same temperature, the kinetics of the nitrosation of azide ions are given by (23), with k = 2340 mo1k2 s-' dm6; hence, at I"; > 0.1 mol dmP3, the latter rate should be faster than the former (Bunton and Stedman, 1959)." This appears to rule out the free nitrosonium ion as an intermediate. Rate

= k[HNO,][H+]

(22)

Rate = k[Nil[HNO,] [H+1

(23)

There is, however, one possible weakness in the above argument for it assumes that the lifetime of the nitrosoniurn ion is long enough for exchange to occur among the surrounding water molecules. There is some evidence that this may not be so. The kinetics of nitrosation of hydrogen peroxide show evidence of a transition to the zeroth-order formation of the electrophile as the concentration of hydrogen peroxide is increased to 1 mol dmP3.l2The kinetics of the formation of the electrophile appear to follow (22) and at 0°C k = 617 mol-I s-' dm3 (Benton and Moore, 1970). The authors identify this electrophile ' I The order with respect to azide ions does not appear to have been determined for IN71 >

0.1 mol dm-3 but experiments with greater concentrations of azide ions have been carried out in H, and accord with the concurrent reactions of (22) and (23) (Bunton and Stedman, 1959).

This evidence is not compelling partly because the transition to a zeroth-order form is not complete and partly because high concentrations of substrates have, in other reactions, produced a spurious transition to a zeroth-order form as a result of medium effects (Marziano et al., 1974). However, if the zeroth-order kinetics arise from medium effects, the rate coefficient for the formation of the electrophile must be even greater than the value of 617 mol-' s-' dm3 quoted above.

DIFFUSION CONTROL AND PRE ASSOCIATION

21

with the nitrosonium ion but, if so, comparison with the equilibrium constant for the reaction indicates that, in dilute acids, the half-life of the nitrosonium ion would be only ca. 3 x s. A species with such a fleeting life could well react with the same water molecule on rehydration. Thus the present evidence does not exclude the nitrosonium ion as the electrophile responsible for the kinetic form of equation (19) provided it is recognized that the half-life of the electrophile must then be extremely short. The nitrous acidium ion remains a possible electrophile but the complete absence of spectroscopic evidence for this ion weakens the case for its consideration (cf. Bayliss et al., 1963). Rate coefficients for the nitrosation of a wide range of substrates according to equation (19) are collected in Table 5. The list is not comprehensive but it includes those substrates whose reactivity is great enough to have a bearing on possible diffusion control in the reaction. In this connection, it is helpful to look first at the reactivity of the anions. There is no generally acceptable measure of nucleophilic reactivity since both the scale and order of relative reactivities depend on the electrophilic centre being attacked (Ritchie, 1972). However, in the present reaction, the similarity in the reactivity of the different anions is remarkable. Thus, the Swain and Scott n-values (cf. Hine, 1962) indicate that the iodide ion should be 100 times more reactive than the chloride ion in nucleophilic attack on methyl bromide in aqueous acetone. In the present reaction, the ratio of the rate coefficients for iodide ions and chloride ions is 1.4. This similarity led to the suggestion that these reactions are near the diffusion-controlled limit (Ridd, 1961). If, from the results in Table 5, we take this limit to correspond to a rate coefficient (eqn 19) of 2500 mol-' s-' dm6 then, from the value of kenfor aqueous solutions at Oo (3.4 x lo9 mol-' s-' dm3; Table l), it follows that the equilibrium constant for the formation of the electrophile must be ca. 7.3 x mol-I dm3. This is very similar to the equilibrium constant reported for the formation of the nitrosonium ion (p. 19). The agreement is improved if allowance is made for the electrostatic enhancement of the diffusion-controlled reaction by a factor of ca. 3 (p. 8); the equilibrium constant for the electrophile then comes to be ca. 2.4 x 10-7. The above agreement is based as the assumption that the encounter pair NO+. X- is formed only by diffusion together of the components. From the equilibrium constant for the formation of the nitrosonium ion [3 x lop7mol-' dm3 (Bayliss el al., 1963)l and the suggested rate coefficient for the formation of the nitrosonium ion according to equation (22) [617 mol-I s-l dm3 (Benton and Moore, 1970)1, it follows that the first-order rate coefficient for the reaction of the nitrosonium ion with water in feebly acidic media should be ca. 2 x lo9 s-l. This is rather similar to the first-order rate coefficient for the separation of the encounter pair by diffusion, and hence, by the argument on p.

22

JOHN H. RIDD

TABLE5 Rate coefficients ( k , eqn 19) for nitrosation by the acid-catalysed reaction Substrate

Neutral molecules 0-C hloroaniline p-Nitroaniline o-Nitroaniline 2,4-Dinitroaniline Hydrazoic acid 0-Methylhydroxylarnine 0,N-Dimethylhydroxylamine Azulene Azulene 2-Methylindole 1,2-Dimethylindole 2-Phen ylindole Hydrogen peroxide Ascorbic acid Thiourea N-Meth ylthiourea N,N'-Dimethylthiourea N,N-Dimethylthiourea N,N,N'-Trimeth ylthiourea

Ions Chloride ion Bromide ion Iodide ion Thiocyanate ion Nitrite ion Ascorbate ion Acetate ion Azide ion Hydrazinium ion

Temp./OC

klmol-* s-' dm6

Ref.

0 0

175 16 1 145 3.7 33.7 184 225 3000 23000 484 530 650 143 1 63 6960 5620 66 10 5790 4340

a

0 0 0 0 0

0 25.3 3 3 3 0.5 0 25 25 25 25 25 0

0 0 0 0 0 0 0 25

6 b b C

d d e e ef ef ef g

h i i 1

I

i

975 1170 1370 1460 1893 2000 2200 2340 611

.i k k

.i 1 h

m

.i n ~

"Hughes etal., 1958b Larkworthy, 1959b Stedman, 1959a Morgan el al., 1968 'Challis and Higgins, 1975 fChallis and Lawson, 1973 Benton and Moore, 1970

Dahn et al., 1960 Collings ef al., 1975 'Stedman, 1959b Hughes and Ridd, 1958 Hughes ef al., 1958a Stedman, 1960 " Perrott et al., 1976

'

11, there may be some encounter pair formation by pre-association. However, this argument does not require the pre-association path to be dominant and so does not invalidate the agreement of the experimental results with those calculated for the diffusion-controlled process.

DIFFUSION CONTROL A N D PRE-ASSOCIATION

23

The pattern of results involving the neutral molecules listed in Table 5 is more difficult to interpret. The variation of k (eqn 19), with the basicity of the amines was originally interpreted as an approach to a diffusion-controlled limiting rate; the limit would correspond to a value of k of ca. 200 mol-2 ssl dm6, and the difference between this limit and that observed with the anions was attributed to electrostatic enhancement of the latter reaction (Ridd, 196 1). The results with the 0-alkylhydroxylamines are obviously consistent with the same limit, but the much faster reactions of azulene and the indoles pose problems. One possibility is that the reactions of the amines and hydroxylamines reach a limiting rate which is below the true encounter rate because of orientational constraints or hindrance to the reaction by hydrogen bonding to the lone pair at the nitrogen. Hydrogen bonding would not occur at the reaction centre in the C-nitrosations of azulene and the indoles. This role of hydrogen bonding in reducing the rate of reaction of nucleophiles with cations has been stressed by Ritchie although in other respects the systems he has studied have little in common with those discussed above (Ritchie, 1972). On that basis, nitrosation at sulphur should occur at a similar limiting rate to nitrosation at carbon. The results for the thioureas refer to 2 5 O , but, from the activation energy for the nitrosation of thiourea, the rate coefficient at 0' should be 637 mol-* s-l dm6, a value similar to those of the indoles. Taking this value for sulphur, it is interesting that the variation in the maximum rate coefficients for nitrosation at carbon, nitrogen (as NT), oxygen (as H,O,), sulphur, chlorine (as Cl-), bromine (as Br-) and iodine (as I-) is by a factor of 4.7. This remarkable insensitivity to the nature of the reaction site is perhaps the best evidence for microscopic diffusion control of the limiting reaction rate. 4

Nitration

In two respects, the discussion of diffusion control in nitration is simpler than that in nitrosation. First there are fewer problems over the identity of the electrophile since, in nitration, the effective electrophile is the nitronium ion over a wide range of conditions. Secondly, there is less difficulty over the ratedetermining stage because, in nitration, the rate-determining stage is normally either the formation of the nitronium ion or the attack of the nitronium ion on the substrate; later stages in the reaction (e.g. the proton loss) are rarely ratedetermining (Myhre et d , 1968a). The above statement concerning the effectiveness of the nitronium ion over a wide range of conditions has not always been accepted and, until recently, some workers held that the nitronium ion was not the effective electrophile in solutions of nitric acid in aqueous acids and organic solvents. It is unnecessary now to go into these arguments since the subject has been covered in a number of recent reviews (Ridd, 1971a; Hoggett et al., 1971; Stock, 1976), and the

24

JOHN H. RIDD

authors are essentially in complete agreement. The nitronium ion is now accepted a s the nitrating agent in nitration by nitric acid itself and by solutions of nitric acid in concentrated sulphuric acid, aqueous sulphuric acid, other aqueous mineral acids and such organic solvents as acetic acid, nitromethane, and sulpholan. The only solvent for which there is still some uncertainty is acetic anhydride and so the results for nitration in this solvent are discussed separately below. As outlined above (p. 3), a reaction can be subject to microscopic diffusion control only if one of the reactive intermediates is formed from an inactive precursor in the reaction mixture. There are two sets of conditions which have provided evidence for microscopic diffusion control in nitration. One concerns solutions of nitric acid in aqueous mineral acids or organic solvents for, in most of these solutions, the stoicheiometric nitric acid is mainly present as the molecular species in equilibrium with a very small concentration of nitronium ions. A reaction between a substrate and a nitronium ion from this equilibrium concentration can, in principle, be subject to microscopic diffusion control. The other set of conditions is when the substrate is mainly present as the protonated form SH+ but when reaction occurs through a very small concentration of the neutral base S. A reaction between the neutral base and a nitronium ion can then, in principle, be subject to microscopic diffusion control even if the nitronium ions are the bulk component of the HNO,/NO: equilibrium. In considering the evidence for microscopic diffusion control it is convenient to consider separately the reactions of those species involved in prototopic equilibria. SUBSTRATES NOT I N V O L V E D I N PROTOTROPIC EQUILIBRIA

The clearest evidence for microscopic diffusion control in nitration comes from the kinetic studies of Coombes et al. (1968), with low concentrations of nitric acid in 68.3% sulphuric acid as solvent. In this medium, the concentration of nitronium ions is proportional to the concentration of molecular nitric acid as required by (24) and, since the concentration of nitronium ions is very small, the concentration of molecular nitric acid is effectively equal to the stoicheiometric concentration of nitric acid. At a given acidity, the reactions have the kinetic form (25). Nitric acid is written out in full in this equation to show that the rate coefficient is calculated with reference to the stoicheiometric concentration of the acid. This convention assists the comparison of reaction rates over a wide range of acidity. HNO,+H+

NO:+H,O

Rate = k[ArHl[NitricAcid]

(24) (25)

DIFFUSION CONTROL AND PRE-ASSOClATION

25

Relative rate coefficients from (25) are listed in Table 6, taking that for benzene as unity. The most interesting feature of these results is the apparent limiting reaction rate at about forty times the reactivity of benzene. This limit is quite inconsistent with the predictions of the additivity principle. Thus, from the additivity principle and the partial rate factors for the nitration of toluene, the reactivities of rn-xylene and mesitylene would be expected to exceed that of benzene by factors of 400 and 16 000 respectively (Coombes et al., 1968). The limiting reaction rate does not arise from the rate of formation of the electrophile since the reactions remain first-order with respect to the aromatic substrate. The limiting rate does not arise from a general breakdown in the additivity principle, e.g. as a result of the saturation of substituent effects, since the limiting rate is not found in some related reactions in which the substituent effects in deactivated systems are similar to those in nitration. This is illustrated by the results for bromination by positive bromine discussed in Section 5 . Coombes et a/. suggest that the limit arises from rate-determining formation of an encounter pair (ArH.NO:) between the nitronium ion and the aromatic substrate (Scheme 5). HNO,+H+ NOZ+ArH

-

NO:+H,O ArH.NO:

Scheme 5

One test of this approach is to calculate the rate coefficient under the limiting conditions in terms of the concentrations of the aromatic substrate and the nitronium ion as in (26). The concentration of nitronium ions in the reaction medium cannot be measured directly, but an indirect estimation is possible from the fact that nitric acid is entirely converted to nitronium bisulphate in 90% sulphuric acid and the assumption that the change in reaction rate with the concentration of sulphuric acid comes essentially from the change in the position of the nitric acid-nitronium ion equilibrium. Then, from the rate coefficient for the nitration of mesitylene in 68.3% sulphuric acid (2.1 mol-' s-' dm3) (Coombes et al., 1968), the rate coefficient for the nitration of the phenyltrimethylammonium ion in 90.1% sulphuric acid (3.5 x mol-' s-' dm3) (Gillespie and Norton, 1953), and the relative reactivity of mesitylene and the phenyltrimethylammonium ion (a factor of 1.0 x lo9) (Table 6; see also Gastaminza et al., 1969); it is possible to calculate that the concentration of nitronium ions in 68.3% sulphuric acid is less than the stoichiometric concentration of nitric acid by a factor of ca. 6 x The value of the rate coefficient for mesitylene in (26) then becomes 3.5 x lo7mol-' s-l dm3. This is

TABLE6 Relative rates of nitration at 25 O by nitric acid in various media

N o\

Sulphuric acid Substrate Substrate Benzene Toluene o-Xylene m-Xylene p-Xylene Mesitylene 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene Bromomesitylene Anisole p-Methylanisole o-Methylanisole Phenol m-Cresol Biphenyl Naphthalene I -Methylnaphthalene 2-Methylnaphthalene 1,6-Dimethylnaphthalene I -Naphthol 1 -Methoxynaphthalene Thiophene

' Hartshorn er a/.. 197 I Coombes er a/.. 1968 Hoggett el a/., 1969 Barnett et al., 1975

57.2%"

(1)

(17) 95 I50

68.3%b

(1)

17 38 38 38 36 ca. 36d ca. 36d

Perchloric acid 6 l.05%*

(1)

19

85 78

16 28

(1)

20 61 100

I14

350

Nitromethane 15% aq.'

(1)

25 139 146 I30 400

Acetic acid 8-1996 aq."

(1)

23

136 355

30 175

13'

20' 23' 24

Sulpholan 7.5% aq.'

31 59 27

28

56

35

85 88 52

Trifluoroacetic acid 1 mol dm-? HLOg

(1)

30 82 100 106 88 98 I26

700 15.5 33 450-500' 230 700

-66

L

0

-150

' Barnett el a/.. 1977 (calculated from the rate coefficients given in this paper) 'Evidence for nitrous acid catalysis Moodie er al., 1977

z z

P

0 0

DIFFUSION CONTROL AND PRE-ASSOCIATION

27

less than the value expected for an encounter reaction in this medium (ca. 8 x los mol-' s-' dm3; Table 1) but, in view of the many approximations involved, the discrepancy is not such as to invalidate the argument. Rate = k[ArHl[NO;j

(26)

A further test of this interpretation is provided by the activation energies of the reactions that occur at the limiting rate. The observed activation energies for the nitration of mesitylene and naphthalene in 67.1% sulphuric acid are 75.3 and 64.8 kJ mol-' respectively (Coombes et al., 1968). On the interpretation in terms of reaction on encounter the activation energy should be the sum of the AH" term for the formation of the nitronium ion (43 kJ mol-' in 68.3% sulphuric acid) (Hartshorn et af., 1972), and the term derived from the temperature dependence of the viscosity of the solvent (24 kJ mol-'; see (8) and Table 2). Thus, the expected activation energy is ca. 67 kJ mol-', a value in reasonable agreement with the experimental results. A final point concerns the lifetime of the nitronium ion. By using higher concentrations of the aromatic compound and somewhat greater acidities the rate of formation of the nitronium ion has been made rate-determining (Chapman and Strachan, 1974). Extrapolation of these results to 68% sulphuric acid gives a value of between 0.02 and 0.08 s-' for the rate coefficient k in (27) at 25". When these values are combined with the estimate of 6 x lo-* Rate = k[HNO,I

(2 7)

for the [NO:J/[HNO,l ratio (see above), the corresponding first-order rate coefficient for the reaction of the nitronium ion with water becomes 3.3 x los - 1.3 x lo6 s-' giving a half-life of ca. s. This is consistent with the involvement of the nitronium ion in a diffusion-controlled reaction. Thus, all the characteristics of the reaction are consistent with the representation of Scheme 5 and with the interpretation of the limiting reaction rate as the formation of the ArH. NO: encounter pairs. Moodie, Schofield and their co-workers have extended their studies to the other media listed in Table 6, but the evidence for a limiting reaction rate is then less clear cut. This is, however, to be expected since the other media are less viscous than 68% sulphuric acid and so the influence of diffusion control in reducing the apparent reactivity of the more reactive compounds should be less marked. It is possible also that nitration through nitrosation is significant with some of the most reactive compounds, although Moodie, Schofield and their co-workers took care to minimize the interference by this reaction. The reactivity of mesitylene is far less than that expected from the additivity principle in all of the media listed in Table 6; thus, on the above interpretation, this compound should be sufficiently reactive to react on encounter in all of these conditions. Since the nitrating agent is considered to be the nitronium ion

28

JOHN H. RIDD

in all of these media, the rate of reaction of mesitylene can be written as (28). In the same way, the rate of nitration of benzene can be written as (29) where ke,/kB = R (the relative reactivity of mesitylene to benzene). Rate = k,,[C,H,Me,l[NO~]

(28)

Rate = k,[C,H,][NO~]

(29)

The equation k , = k,,/R provides a way of checking the self-consistency of the above arguments for it provides values of the true rate coefficient for the reaction of benzene with the electrophile in the various media listed in Table 6. If the electrophile remains constant, then the values of k, should also be approximately constant (apart from medium effects). Values of kenat 25O have been taken from Tables 1 and 2 or calculated using (4) from the viscosities TABLE7 True rate coefficients for reaction of the electrophile with benzene in various nitrating media at 25OC Solvent

HPO,

k, rnol--' s-I dm3

57.2%

68.396

HC10, 61.05%

C,H,SO, 7.596 aq.

1.0

2.3

2.8

0.46

CHINO, CH,CO,H 15% aq. 8-1996 aq. 2.7

1.6

CF,CO,H 1 M H,O 8.8

given in the literature (Moodie et al., 1977). The results are in Table 7. The range of values is considerable but it is worth noting that the results for aqueous sulphuric acid are approximately in the middle. Since the nitronium ion is known to be the electrophile for reaction in aqueous sulphuric acid, the range of values above is consistent with appreciable medium effects on the reaction of the nitronium ion with the benzene molecule. The results for nitration by solutions of nitric acid in acetic anhydride were omitted from the above discussion since this reaction has several special features. Unlike the other solvents, acetic anhydride reacts with nitric acid with the result that the stoichiometric nitric acid is actually present as acetyl nitrate as shown in (30). However, the marked retardation of the reaction by trace amounts of ionized nitrates shows that the actual electrophile is a positive ion present in very low concentration (Paul, 1958; Ridd, 1966). HNO,

+ Ac,O

W

AcONO,

+ AcOH

(30)

As with the other solvents, a limiting rate of nitration appears to be reached with mesitylene (Hartshorn et al., 1971), and the most recent investigation of this has indicated that mesitylene is 650 times as reactive as benzene

DIFFUSION CONTROL A N D PRE-ASSOCIATION

29

(Marziano et al., 1977). The use of this value and a value of kenof 7.7 x lo9 mol-' s-' dm3 at 25°C (cf. Table 1) gives the rate coefficient for the reaction of benzene with the electrophile as 1.2 x lo7 mol-' s-' dm3. This is within the range of values found for reaction with the nitronium ion (see above). The assumption that the nitronium ion is the electrophile is also consistent with the relative reactivities and isomer proportions found in compounds that react at rates below the encounter rate (Ridd, 1966; Baas and Wepster, 1972). There is, however, one difficulty with this interpretation. One of the unusual features of nitration in acetic anhydride is that the rate of formation of the electrophile cannot be made rate-determining even when the concentration of the aromatic substrate is as large as 0.5 mol dm-3 and when the substrate (mesitylene) appears to react at the limiting rate (Marziano et al., 1974). This implies that the rate coefficient for the back reaction of the electrophile (considered as a first-order reaction) must be > lo'* s-' for otherwise the rate of the back reaction would not markedly exceed the rate of encounter of the electrophile with this concentration of the substrate. It follows therefore that the half-life of the electrophile must be below lo-'* s. This is the condition that leads to predominant reaction via pre-association (p. 11). Since the characteristics of the reaction accord with nitration by the nitronium ion, the simplest interpretation is to assume that this ion is formed within an encounter pair consisting of the aromatic substrate and an inactive precursor of the nitronium ion (e.g., CH,CO. ONO,H+). The limiting rate of such a reaction can exceed the diffusion-controlled limit (Sections 2 and 6). For the nitration of a species such as benzene, this distinction between the formation of the encounter pair by diffusion and preiassociation is irrelevant, since the encounter pair formation is not rate-determining. Hence, it may be significant that the relative reactivity of mesitylene to benzene is greater in acetic anhydride (a factor of 650) than in the other solvents (Table 6). However, this can also be explained by the greater viscosity of most of the other media. S U B S T R A T E S INVOLVED I N PROTOTROPIC EQUILIBRIA

The nitration of many aromatic and heteroaromatic substrates, e.g., amines, azines, azoles and their derivatives, can in principle occur through either the neutral substrate S or the conjugate acid SH+. With some substrates, the mechanistic distinctions concerning the reactive form are more complex; thus, electrophilic substitution in aminopyridines can in principle occur in either the neutral substrate, the conjugate acid formed by protonation at the ring nitrogen atom, the conjugate acid formed by protonation at the amino-group or the diconjugate acid. Such mechanistic distinctions are important in interpreting the products and relative rates of substitution. A great deal of work has been

30

JOHN H. RIDD

done on this subject, much of it by Katritzky and his co-workers (Katritzky, et al., 1975; cf. Hoggett et al., 1971; Ridd, 1971b). The present discussion is concerned only with those reactions in which the reacting species is the minority component of the equilibrium and in which this species appears to react with the nitronium ion on encounter (Scheme 6). The number of such reactions is small but their characteristics are important in that this type of reaction is often taken in mechanistic discussions as providing the limiting rate for reaction through the neutral substrate. SH+ S+NOl S . NO;

-

S+H+ S.NOt

Products

Scheme 6

If, for simplicity, we consider reactions according to Scheme 6 in > 90% sulphuric acid, then the concentration of nitronium ions is equal to the stoichiometric concentration of nitric acid. Under these conditions the observed rate coefficient k [defined by (31)l should have the value given by (32) where h, is the appropriate acidity function for the protonation of S and K,,, is the thermodynamic dissociation constant for the dissociation of SH+. The Arrhenius activation energy for such a reaction should then be given by (33) where A H o is the heat of dissociation of SH+ [cf. (8), and Hartshorn and Ridd, 19681. Rate = k[SH+l[nitric acid]

k = K,,Jc,,/h,

E, =AH"

+ RT + B - R[d(-In h,)/dT-'l

(3 1)

(32) (33)

The comparison of the observed values of k and E, with those calculated from (32) and (33) therefore provides evidence on whether or not the reaction occurs on encounter. At lower acidities, allowance has to be made for the extent of conversion of nitric acid to nitronium salts. Several pieces of evidence can be used to determine whether the nitration of a given substrate occurs through the conjugate acid (SH+) or through the small amount of neutral substrate in equilibrium with it; these approaches include the determination of the rate profile and comparisons with the reactivities of model compounds (Ridd, 1971b). From such evidence, it appears that a number of nitration reactions involve the small amount of neutral substrate in equilibrium with the conjugate acid; the substrates include 2,6-dichloropyridine, pyridine1-oxide, l-methylpyrazole-2-oxide, 3-methyl-2-pyridone, acetophenone and p nitroaniline. These reactions have been reviewed recently (Hoggett et al., 197 1; see especially Chap. 8). However, for the majority of these substrates, the

31

DIFFUSION CONTROL AND PRE-ASSOCIATION

observed rate coefficients are below the values expected for reaction on encounter. The clearest exceptions are p-nitroaniline and 2-chlor0-4-nitroaniline'~ (Hartshorn and Ridd, 1968). The rate profiles and positions of nitration (ortho to the amino-group) show that these molecules react through the small amount of free amine present, and the values of k in (31) are in close agreement with those calculated from (32) using ken values obtained from (4). For pnitroaniline, the heat of dissociation of the conjugate acid is known and the observed activation energy (76.1 kJ mol-I, 98% H,SO,) can therefore be compared with that calculated from (33) (80.0 kJ mol-')14 (Johnson et al., 1969). The agreement between these values together with the overall rate of reaction provide support for the reaction path shown in Scheme 6. Unfortunately, evidence from proton transfer reactions suggest that this agreement may be misleading and that the true reaction path is more complex. Nmr studies based on the analysis of line shapes indicate that the protonation of N,N-dimethylaniline in aqueous acids occurs on encounter with the solvated hydrogen ion, the second-order rate coefficient being 4 x 10*Omol-' s-I dm3 (Kresge and Capen, 1975). There is evidence that the same is true for the protonation of p-nitro-N,N-dimethylaniline (Kresge, 1975). Thus, for solutions more acidic than [H+l = 1 M, the half-life of these free amines should be < lO-'O s. Under these conditions, as outlined on p. 11, the encounter pair NO:. ArNH, should be formed predominantly by the pre-association of the nitronium ion with the protonated amine. This conclusion is reached also by considering directly the dependence of the rate of proton transfer on the acidity function for the protonation of the amine. The unit slope indicates that these reactions occur through the stages shown in (34),15 where S . H30+ and SH+.H,O represent encounter pairs in the correct S H + + H,O

SH+.OH,

S.HOH:

-

S +H,O+

(34)

orientation to react and where the proton transfer to S in S.H,O+ is fast in comparison with the separation of the encounter pair. Thus, the half-life of the S . H,O+ encounter pair should be less than that of a normal encounter pair. l 3 The nitration of 1,4,5-trimethylimidazole-3-oxide and 1-methylpyrazole-2-oxidemay also occur at about the encounter rate (Ferguson et al., 1977). I4In the original paper (Hartshorn and Ridd, 1968), the calculated activation energy was given as ca. 54 kJ mol-' but this was based on the earlier work on the temperature dependence of H , (Gel'bshtein et al., 1956). The revised values for this temperature dependence (Johnson et al., 1969) give the value in the text. l 5 An additional pair of intermediates are often shown in such proton transfer reactions representing those encounter pairs before and after proton transfer that are not in the correct orientation to react (Hassid et al., 1975; Burfoot and Caldin, 1976). However, the consideration of such intermediates is not required in the present discussion.

32

JOHN H. RIDD

The half-life of a base hydrogen-bonded to a strong acid can be very short indeed since proton transfer can occur by tunnelling; thus the rate coefficient for proton transfer to water hydrogen-bonded to H,O+ has been estimated at lo1, s-’ (Crooks, 1977). For the nitrations in concentrated sulphuric acid as solvent, H,SO, and HSO; should take the place of H,O+ and H,O in (34) (cf. Cox, 1974). A number of mechanistic problems remain, after accepting that the encounter pair ArNH,. NO: is formed by pre-association. One such problem concerns whether the rate-determining step is the proton transfer or the reaction of the nitronium ion with the free amine formed within the encounter pair. It seems likely that the latter view is true from consideration of the rate profile, the very short half-life of the free amine, and the fact that these reactions do not show a marked primary hydrogen isotope effect when the rates in H,SO, and D,SO, are compared; the reduction in rate by a factor of 2-3 in the deuterated solvent (Hartshorn and a d d , 1968) is consistent with the lower concentration of the free amine. The reaction path can then be written as shown in Scheme 7 where NO:.ArNH:. B is an encounter “triplet”. + NO: + ArNH,

+B G

NO:. ArNH,. B NOz.ArNH,.HB+

G

+ NO:. ArNH,. B NO:. ArNH,. HB+

Products

Scheme 7

One remaining problem is why this reaction path should so closely simulate the characteristics of a diffusion-controlled reaction between the free amine and the nitronium ion. This probably arises in part because the concentration of encounter pairs involving the nitronium ion and the hydrogen-bonded free amine follows the concentration of free amine as calculated from the appropriate acidity function. Also, as outlined in Section 2, the rate coefficient for reaction within the encounter pair may be near itslimiting value. However, in this example, it may be unrealistic to consider the nitronium ion and free amine as separate species within the encounter pair. This point is considered further in Section 6. 5

Halogenation

The experimental evidence for microscopic diffusion control in chlorination, bromination, and iodination is complicated by the number of possible electrophilic species which may be involved and, with some substrates, by uncertainty over the exact rate-determining stage. The mechanistic picture therefore resembles that for nitrosation rather than that for nitration. As usual,

DIFFUSION

CONTROL A N D PRE-ASSOCIATION

33

it is convenient to divide the experimental studies into those which start with the molecular halogens and those which start with positive halogens, e.g., hypohalous acids in aqueous mineral acids. The mechanisms of both types of reaction have been reviewed in a recent monograph (de la Mare, 1976). HALOGENATION B Y MOLECULAR HALOGE NS

The reactions described below refer to halogenation in aqueous solution under conditions where the halogenating agent is the molecular halogen with a possible contribution from the trihalide ion. Almost all the work comes from the research groups of Bell and Dubois. The majority of the studies refer t o bromination, but comparisons are made with the other halogenation reactions where the results are available.

QO

/I

H

-c-c-

I I

II OH

I

-c=c

/

2

\

Scheme 8

The rate of bromination of ethylene in aqueous solution is below the encounter rate (Atkinson and Bell, 1963) and so studies on the limiting rate of bromination require the use of activated substrates. Much of the work has therefore been carried out using enols and enolate ions (Scheme 8). Where the ketone is the bulk component of the keto-enol equilibrium, the rate of bromination according to Scheme 8 is normally governed by the rate of formation of the enol or enolate ion, but by using very low concentrations of bromine (ca. lo-’ mol dm-3) the rate of bromination can be made partly or wholly rate-determining. The observed rate coefficient is then given by (35) and the rate coefficients for the actual reacting species by (36). Where the ketone is the bulk component and the enol is the main reacting species, the rate O H Rate

I1

I

= k[-C-C-l[X,J

(35)

I

OH I

0I

34

J O H N H. RIDD

coefficients of (35) and (36) are related by (37) where Keno,is the equilibrium constant for the formation of the enol. The value of Keno,has to be known in order to calculate k in (36) from the observed rate coefficient [k(eqn 35)l. k (eqn 35)/k (eqn 36) = K,,,,

(37)

The fact that the formation of the reactive enol or enolate ion can be made to occur in the slow step shows that the lifetime of these species must be long enough for them to participate in a diffusion-controlled step since, under zeroth-order conditions, the reaction obviously occurs in two distinct stages. There are, however, difficulties in determining whether or not the value of the rate coefficient accords with a diffusion-controlled reaction. These difficulties can be illustrated with reference to the aqueous halogenation of acetone at 25 '. The chlorination of acetone with [Cl,] = ca. lop6 mol dmP3 in aqueous perchloric acid (0.05-0.20 mol dmP3) gives k (eqn. 36) = 7.3 x lo5 mol-' s-' dm3 assuming that Keno,= 2.5 x (Bell and Yates, 1962a). The value of k (eqn 36) does not vary with the concentration of chloride ions, suggesting that C1, and C1; react at similar rates with the enol. In the same way, the insensitivity of the reaction rate to the acidity shows that the enolate ion is not involved or that the enol and enolate ion react at the same rate. Similar experiments on the bromination of acetone give k (eqn 36) = 1.03 x lo7mol-' s-' dm3 (Bell and Davis, 1964; cf. Yates and Wright, 1963). The rate coefficient for bromination is sensitive to the concentration of bromide ions, and the analysis of this variation yields a value of k (eqn 38) = 2.8 x lo6mol-' OH

I

Rate = k[-C=C
s-' dm3 for the reaction of the tribromide ion. Both the rate coefficients for bromination are based on a slightly different value for Ken,, (2.0 x from that used in calculating the rate coefficients for chlorination. Unfortunately it now seems that these values of Keno,are too high and that the true value may be as low as 9 x lop7 (Bell and Smith, 1966) or 1.5 x (Toullec and Dubois, 1973).16 This uncertainty over the value of Keno,makes it difficult to know how close the halogenation of the enol is to a diffusion-controlled reaction. Another approach to this problem is to compare the rate coefficients for reaction with the different molecular halogens. The latest results, in Table 8 (Dubois and Toullec, 1973), indicate that the reactivity of a given enol to the three halogens is remarkably similar, suggesting that all three reactions occur on encounter. With less reactive compounds, the reactivities of the three l 6 The lowest value is based on the assumption that the halogenation of acetone occurs on encounter with the molecular halogens.

35

DIFFUSION CONTROL A N D PRE-ASSOCIATION

halogens are very different. The same explanation can be used to account for the similar reactivity of a given enol towards molecular chlorine and trichloride ions. From the earlier results, the reaction of acetone with chlorine appeared to be slower than that with bromine (see above) and Dubois and Toullec suggest that the previous work is in error because of the use of unnecessarily high concentrations of chlorine. However, it may be significant that chlorine is also less reactive than bromine (by a factor of ca. 6) towards the enol of 2butanone17 (Deno and Fishbein, 1973). TABLE8 Rate coefficients ( k , eqn 35) for the halogenation by molecular halogens (X,) of ketones in aqueous acids ([H+l 1 mol dm-') at 25"

-

klmol-' s-* dm3 Substrate Acetone Diethylketone Di-isopropylketone

x, = Cl,h 14.5 100 -

Br2e

I,e

18.7 105 44

16.5 109 49

The values are calculated with respect to the stoichiometric concentration of the ketone but refer to conditions where the attack of the halogen on the small equilibrium concentration of the enol is rate-determining (Dubois and Toullec, 1973) For ICl-1 = 1 mol dm-': the rate does not depend significantly on the concentration of chloride ions Extrapolated to [X-I = 0 a

The problems arising from the uncertainty in the values of Ken,, can be avoided by changing to compounds for which the enol is the bulk component of the keto-enol equilibrium. This is true for the compounds [ 11441 for which the enol content in aqueous solution and the pK,-value is also given (Bell and Davis, 1965). The corresponding rate coefficients for bromination by molecular bromine are given in Table 9. The values of k (eqn 36) show little variation with the reactivity of the enol and are similar (106-107 mol-' s-I dm3) to that reported above for acetone. These values appear curiously low for reaction on encounter. The most curious feature of the results for compounds [1]-[4] is that the reaction rate is insensitive to the acidity over the range p H 1-3. For [31, the p H was increased to 4.9 but with no significant change in the reaction rate. This implies that the rate of bromination is independent of whether the bulk of the substrate exists as the enol or the enolate ion. The simplest interpretation of I' In these studies, the halogenation stage of Scheme 8 is made rate-determining by the use of a strongly acidic medium (concentrated sulphuric acid).

36

JOHN H. RIDD

OH

,3,

Me Me 2-Bromodimedone, 98% enol, pK, = 3.2

Me Me

Dimedone, 93% enol, p K ,

= 5.27

[11

[21

u:

u:

OH

OH

3-Methyltetronic acid, 98% enol, pK, = 4.15

3-Bromotetronic acid, 98% enol. pK, = 2.23

131

[41

TABLE 9 Rate coefficients (eqn 36) for the halogenation of enols, enol ethers and enolate ions in aqueous media at 25OC

Substrate Diethyl maIonate'I Dimedoneb" 2-Br~modimedone~" 3-Methyltetronic acidbc 3-Bromotetronic acid Meth ylacetylacetone' 2-Acetylcy~lohexanone~ Methylmethanetricarboxylateb 2-Eth~xypropene~ Dimedone enol methyl ether'

Halogen

k (eqn 36)/ mol-' s-' dm3 (enol)

3 x 105

8 x lo6 4 x 106 2.2 x 107 8.5 x lo6 6.9 x lo6 7.2 x lo6 5.0 x lo6 8.3 x lo6 ca. 1.4 x lo4

1.5 x lo8 2.8 x lo5 (at 0')

k' (eqn 36)/ mol-' s-' dm3 (enolate) 1 x 10" 4 x 10'' 1 x 10'2

3.0 x 109

~~

Bell and Yates, 1962b

* For [H+] = 0.1 mol d t r 3 , [Br-1 = 0.1 mol dm-3, Bell and Davis 1965

CThe reaction rate does not vary significantly with the acidity indicating that the enols and enolate ions have about the same reactivity Average velocity constants for the reactions of Br, and Br; Toullec and Dubois, 1973 fMarshall and Roberts, 1971

"

DIFFUSION CONTROL AND PRE-ASSOCIATION

31

these results is that both the enol and the enolate ion react on encounter with molecular bromine. However, as Bell and Davis point out, there are some difficulties with this interpretation, notably that the rate coefficient is below the value expected for reaction on encounter and that certain other enolate ions react with bromine at what appear to be much faster rates (Table 9). The rate coefficient for the iodination of 2-ethoxypropene is also appreciably greater than those found for the bromination of compounds [ 1]-[4].Thus, although these studies of enols and enolate ions provide some evidence for reaction on encounter, they provide also a number of unexpected observations that are not yet fully explained. The halogenation of phenols and aromatic amines in aqueous solution also provides evidence for diffusion control, but the interpretation is complicated by the fact that either the formation of the a-complex or the proton loss from the a-complex can be rate-determining. The reaction path for the halogenation of aromatic amines in aqueous acids is believed to be that shown for N,N-dialkyl anilines in Scheme 9. Where the formation of the a-complex is ratedetermining, the kinetic form for attack by the molecular halogen is given by (39). In this equation, the observed rate coefficient (k') is related to the rate coefficient for the reaction of the amine molecule ( k ) by (40), where K,,, is the + Rate = k'lArNR,HI[X,] = kLArNR21[X,l (39) k = k'hs/KsH+

(40)

dissociation constant of the anilinium ion and h, is the appropriate acidity function. +

C,H,NR,H

C,H,NR, + HS

Scheme 9

For chlorination, the formation of the a-complex would be expected to be the rate-determining step since the aromatic chlorination of other substrates does not appear to give rise to deuterium isotope effects (Baciocchi et al., 1960; de la Mare and Lomas, 1967). The effect of the experimental conditions on the rate-determining step in the aqueous bromination of aromatic amines has been investigated in detail by Dubois and his co-workers (Dubois et al., 1968a, b, c; Dubois and Uzan, 1968). This work suggests that, for tertiary aromatic amines, the proton loss is fast for para-bromination but partly or wholly rate-determining for ortho-bromination. There is however some

38

JOHN H. RlDD

evidence that proton loss may be partly rate-determining in the parabromination of 2,6-dichloroaniline (Bell and D e Maria, 1969). In the iodination of aromatic amines, the proton loss from the a-complex is usually, but not always, rate-determining (Vainshtein and Shilov, 1960). Most of the rate comparisons in the halogenation of aromatic amines refer to bromination; rate coefficients for para-substitution are collected in Table 10. Further results for ortha-substitution are provided in the cited references. Some of the early calculation based on (39) and (40) may be in error, because it was not then realized that the appropriate acidity function in (40) depends on the structure of the substrate (cf. Bell and Ramsden., 1958; Bell and Ninkov, 1966). The appropriate acidity function was used for the results listed in Table 10 but it is still advisable for rate comparisons to be based on experiments carried out under the same conditions. The values of the rate coefficients in Table 10 approach that expected for a diffusion-controlled reaction (cf. k = 3.4 x lo9 mol-‘ s-I dm’ for 3,5,N,Ntetramethylaniline). However, it is worth noting that most of these results refer to hydrogen-ion concentrations 20.5 mol dm-3 and that the basicity of the amines is such that protonation probably occurs on encounter. Thus, the halflife of the free amine is likely to be < s and, under these conditions, the TABLE10 Rate coefficients ( k , eqn 39) for the para-bromination of aromatic amines in aqueous acids at 25O Substrate

Conditions

N.N-Dimethylaniline

a

3-Methyl-N,N-dimethylaniline 3-Bromo-N.N-dimethylaniline 2.3-Dimethyl-N.N-dimethylaniline 2,5-Dimethyl-N,N-dimethylaniline

a a a a a a d d

2.6-Dimethyl-N.N-dimethylaniline 3,5-Dimethyl-N.N-dimethylaniline 2,6-Diethylaniline 2,6-Dichloroaniline

k (eqn 39)/ mol-I s-I dm’ 2.17 x loWb 2.41 x lo6 1.2 x 10J 9.83 x lo* 5.91 x 10J 2.70 x 10’ 2.72 x 107 7.61 x los 3.40 x lo9 9.7 x 108 3.4 x 106

“ Sulphuric acid (0.5 mol dm-’). sodium bromide (0.2 mol dm-’) (Uzan and Dubois, 1971) Some orfho-substitution also occurs with k = 1.39 x lo8 rnol-’ s-’ dm3 ‘Perchloric acid (0.00-5.14 mol dm-’), sodium bromide (0.025 mol dm-’) (Bell and Ninkov, 1966) Perchloric acid (up to ca. 8 mol dm-’), sodium bromide (0.025 mol dm-’) (Bell and De Maria, 1969)

DIFFUSION CONTROL AND PRE-ASSOCIATION

39

formation of the ArNMe,. Br, encounter pair should occur by pre-association rather than by diffusion (p. 11). It is doubtful therefore whether a diffusioncontrolled limiting rate should be expected. The rate coefficients do in fact provide evidence for structural effects on reactivity; thus, the rate coefficients for the 3-substituted N,N-dimethylanilines (3-Me; 3,5-Me2 3-Br) correspond to a p-value (based on Za+) of -2.19 (Uzan and Dubois, 1971). This is, of course, much less negative than that normally found for aromatic bromination by molecular bromine (-12.1) (Stock and Brown, 1963). The low value of p could derive from the necessary curvature of a linear free-energy relationship as a limiting rate is approached or it could be a consequence of the reduced substituent effects expected from the Hammond principle for highly reactive substrates. The accuracy of the values of k is probably insufficient to distinguish between these alternatives. The results in Table 10 also provide evidence for the expected secondary steric effect of ortho-groups in the orthosubstituted N,N-dimethylanilines. The bromination of anisoles and phenols has been studied in similar detail. The rate coefficients for reaction with molecular bromine is aqueous solution at 25O are less than that for reaction on encounter for anisole (kortho = 5.2 x lo2 mol-' s-' dm3; kparo= 3.0 x lo4 mol-' s-' dm3) (Aaron and Dubois, 1971) and phenol ( k = 1.8 x los mol-' s-l dm3) (Bell and Rawlinson, 1961), but for 3,5-dimethylanisole (kortho = 1.2 x lo6 mol-'s-' dm3; kpRm = 2.2 x lo7mol-' s-l dm3) (Aaron and Dubois, 1971) the reactivity approaches that of some enols. Reactions with substituted anisoles give bromination by molecular bromine a p-value of -5.6: the reaction is therefore more selective than the bromination of substituted dimethylanilines. Deuterium substitution in the ring gives no significant isotope effects for the bromination of phenol (Zollinger, 1964), anisole and the methylanisoles (Joseph and Gnanapragasam, 1972; Aaron and Dubois, 1971), and so the above results should refer to the formation of the a-complex. It is worth noting, however, that the bromination of phenol in acetic acid gives a marked solvent isotope effect (kHOAJkDOAc = 1.8) (de la Mare and El-Dusouqui, 1967); attack at the para-position appears then to be facilitated by the breaking of the 0-H bond. The reaction of molecular bromine with the more acidic phenols gives rise to two kinetic terms (41) corresponding to attack on the neutral phenol molecule Rate = k[ArOHI[Br,]

+ k'[ArO-l[Br,l

(4 1)

and the phenoxide ion.18 The rate coefficients for these two reactions are listed in Table 11. The values of the rate coefficients for the more reactive phenoxide ions are close to those expected for a diffusion-controlled reaction, and the '!'For simplicity, the contribution of the iess reactive tribromide ion is omitted from this account, but details are given in the cited references.

40

JOHN H. RIDD

small difference in the reactivity of the 4-bromo and 3-nitro derivatives supports the view that the rates of these reactions are near a limiting value. These experiments were carried out at lower acidities ([H+] = 0.02-0.15 mol dm-3) and so the importance of the reaction path involving pre-association should be less. Unfortunately there are too few substituents to provide clear evidence for a limiting reaction rate. TABLE11 Rate coefficients (k, k‘ eqn 41) for the reaction of molecular bromine with phenols and phenoxide ions in dilute perchloric acid (ca. 0.1 mol dm-3) at 25”

-

klmo1-l s-’ dm3 (ArOH)

Substrate Phenol 4-Bromophenol 2,3-Dibromophenol 3-Nitrophenol 2,6-Dinitrophenol 2,4-D initrophenol

1.8 x 3.2 x 5.5 x 1.0 x

105 109 102 102

-

k’/mol-’s-‘ dm3 (ArO-) -

7.8 x 1.5 x 1.3 x 5.4 x 1.0 x

loy 109 109 106 106

Bell and Rawlinson. 1961 H A L O G E N A T I O N B Y POSITIVE H A L O G E N S

There are several sets of conditions that lead to halogenation by what appears

to be a highly reactive electrophile; these include halogenation by the halogens

in sulphuric acid in the presence of silver sulphate and halogenation by the hypohalous acids of chlorine and bromine in aqueous mineral acids. These reactions are often referred to as “positive halogenations” but without the implication that the halogen cations are necessarily involved as intermediates. The present account is limited to the reactions of hypochlorous acid and hypobromous acid in aqueous mineral acids since these “positive halogenations” are the most suitable for kinetic studies. The relevance of the work to the subject of the present chapter comes from the fact that these reactions appear to occur faster than would be expected even if the substrate and the electrophile reacted on every encounter. Halogenation by aqueous solutions of hypochlorous acid and hypobromous acid in dilute mineral acids has the kinetic form (42).19 As with the analogous Rate = k[SI[HOXI[H+]

(42)

l9 Other kinetic terms are present in chlorination by hypochlorous acid but are less important than that given above (de la Mare and Ridd, 1959a).

41

DIFFUSION CONTROL AND PRE-ASSOCIATION

kinetic form in nitrosation (Section 3), the most obvious mechanistic interpretation involves the intermediate formation of the protonated hypohalous acids or the halogen cations as shown in (43) and (44). However, in halogenation, there is reason to believe that these intermediates are not necessarily involved. HOX+H+

+ H,OX

(43)

HOX+H+

X++H,O

(44)

The evidence on this matter is complicated, but the main points are as follows. (a) There is no spectroscopic or other physical evidence for the species X+ and H,OX+ in the reaction mixtures. (b) Thermodynamic calculations (Bell and Gelles, 195 1;Mishchenko and Flis, 1957) suggest that the concentrations of X+ and H,OX+ in the reaction mixtures are far too low for them to be effective intermediates. (c) If the acid catalysis of the brominations is ascribed to the increasing concentrations of H,OBr+ or Br+ with acidity then, at the highest acidities, there would have to be more than 100% conversion of HOBr to H,OBr+ or Br+ to account for the rate of halogenation (Gilow and Ridd, 1973). Conversely, from the fact that hypobromous acid is not fully converted into positive ions at the highest acidities, the concentration of the positive electrophiles at the lowest acidities must be too low to account for the observed reaction rate even if reaction occurred at every encounter. (d) There is no evidence for a limiting rate of reaction as the reactivity of the substrate is increased. This last point is particularly unexpected since the effective electrophile in positive bromination appears to be more reactive than the nitronium ion; thus, it will even brominate the 4-methylpyridinium ion (Gilow and Ridd, 1974). However, it apparently fails to react on encounter with compounds a thousand times more reactive than benzene. This is illustrated by the rates of bromination of the ions [51-[71 relative to that of benzene as unity (Gilow and Ridd, 1973). A similar lack of evidence for a limiting reaction rate occurs with positive chlorination (Burton et al., 1972). It is difficult to reconcile these observations with the prior formation of a single positive halogenating agent in the reaction mixture. One suggestion (De

Relative rates 24

[51

1500

520 000

[61

[71

42

JOHN

n.

RIDD

la Mare, 1976) is that two or more positive halogenating agents are effective (e.g. X+ and H,OX+) depending upon the acidity, so that part of the acidity dependence of the reaction rate comes from a change in the mean reactivity of the halogenating agent and part from a change in the concentration of the halogenating agent. This overcomes the difficulty raised in point (c) above. One problem with this interpretation is that there is no clear evidence that the discrimination of the electrophile depends significantly on the acidity used; relative rates of bromination of a series of substrates studied over the range 0.14-9.0 mol dm-3 perchloric acid give a conventional logarithmic plot against o+ with a slope of -6.2 (de la Mare and Hilton, 1962). Related evidence on the discrimination of the electrophile in positive bromination comes from the comparison of relative rates of bromination with relative rates of nitration. Both reactions were studied over a wide range of acidity but the logarithmic plot of one set of relative rates against the other is linear up to the point at which nitration becomes a reaction on encounter (Gilow and Ridd, 1973). Another difficulty with this interpretation is that it does not meet the criticism based on thermodynamic arguments concerning the possible concentrations of X+ and H,OX+ in the reaction mixtures (see above). Another suggestion is that the Wheland structure or a-complex exemplified by [S] is in equilibrium with the reactants and that this equilibrium is maintained by the protonation of a n-complex of the aromatic substrate and hypobromous acid followed by the elimination of water (Shilov et al., 1961). The rate-determining step is then the proton loss from this a-complex. This suggestion meets the difficulties raised by points (a)-(c) above since there is no longer any need for the prior formation of the positive halogenating agent in the solution. However, there is no isotope effect for the proton loss stage in the positive bromination of benzene (de la Mare et al., 1957), and so it is unlikely that this interpretation is correct in general.,O

[Sl

The most recent suggestion is a development of that of Shilov et al. and uses the dual pathways illustrated in Scheme 10 with stage 5 as the rate-determining stage (Gilow and Ridd, 1973). This is an example of the two pathways represented generally in Scheme 3. From the principle of microscopic reversibility, the relative importance of the upper and lower pathways in the formation of the encounter pair A r H .H,OBr+ should be determined by 2o The proton loss stage of positive bromination can become rate-determining when the ucomplex is very stable as in the bromination of 7-hydroxynaphthalene-1,3-disulphonicacid (Christen and Zollinger, 1962), or when steric interactions are present as in the bromination of 1,3,5-tri-t-butylbenzene(Myhre et al., 1968b).

43

DIFFUSION CONTROL AND PRE-ASSOCIATION

whether this encounter pair returns to the reactants mainly by dissociation into ArH and H,OBr+ or mainly by an initial proton loss. Since H,OBr+ is believed to be a strong acid, the lower pathway is the more probable, except perhaps in strongly acidic media. The rate-determining step in this mechanism is the reaction of H,OBr+ with the aromatic compound. This is the same as that suggested by the majority of previous workers. The presence of H,OBr+ rather than Br+ in the transition state has recently received support from studies of nitro-debromination (Moodie et al., 1976). The solvent isotope effect (k,201k,, = 2.2) provides evidence for the pre-equilibrium protonation of the hypobromous acid before the rate-determining stage (Gilow and Ridd, 1973).

Scheme 10

ArBr

On this mechanism, the pre-association of HOBr and ArH provides a way of forming the encounter pair A r H . H,OBr+. This meets the points (a), (b) and (c) on p. 41. Thus the reactions of hypobromous acid, and also hypochlorous acid, provide some of the clearest evidence for the pre-association pathway. However, some problems remain including the absence of any limiting rate with the most reactive substrates. This may be a consequence of interaction between the components in the encounter pair A r H . HOBr (cf. Section 6). 6

Conclusion

The previous sections have been largely concerned with classifying reactions involving highly reactive intermediates into those that provide evidence for diffusion control and those that appear to occur through pre-association. I n conclusion, it is useful to look at the pattern that emerges and at some possibly unjustified simplifications in the arguments used. Classijication of reactions. Before considering the individual reactions it is helpful to look at the factors that determine the balance between the diffusioncontrolled and pre-association mechanisms. Consider first a diffusioncontrolled reaction according to Scheme 3 in which the rate of formation of the encounter pair B . X is rate-determining. These conditions require that k-, > k,[B] so that the reaction rate is given by (45).*' The corresponding rate of

z1 In these equations, the formation of the intermediate is treated as a first-order reaction of the precursor A since the other species involved is usually the solvent or a proton transfer involving the solvent.

44

J O H N H.

RlDD

formation of B .X through the pre-association path is given by (46). This equation is based on the assumption that k-, s k,, but this should be justified since Rate,,

=kcn k,lAl

[Bl

k-3

k-, relates to the diffusion apart of a n encounter pair and k , to the formation of a highly reactive intermediate. Since the equilibrium constant for encounter pair formation is near unity in the units mol dm-, (North, 1964) k,,/k-,1 mol-’ dm3. Also, since no chemical interaction has been assumed within an encounter pair, k , -k,. Hence the relative rates of formation of X . B along the diffusion-controlled and pre-association paths is determined by the ratio kenlkThus, for a reaction for which ke,/k-, > 1 mol-I dm3, it follows that the limiting rate for the pre-association mechanism will normally be less than the limiting rate by the diffusion-controlled mechanism. One simple indication of whether ke n / k- ,> 1 mol-I dm3 is whether the overall reaction becomes zerothorder with respect to B for [B] < 1 mol dmP3. If this is so, the above inequality must hold. For nitration by nitric acid in nitromethane, acetic acid, or ca. 70% sulphuric acid, the reaction rate becomes zeroth-order with respect to the aromatic compound for [ArHl < 1 mol dm-,. Hence, under these conditions the nitration reaction cannot “take advantage” of the pre-association pathway to exceed significantly the limiting rate imposed by the diffusion-controlled pathway since the fo:mer limit is necessarily much less than the latter. This does not apply to nitration in acetic anhydride. To see what happens when the lifetime of the intermediate is decreased, it is helpful to imagine t’iat the rate coefficients k , and k - , increase together so that the lifetime of X falls but the equilibrium concentration of X stays constant. For half-lives > lo-’ s, the diffusion-controlled rate should be constant but for shorter half-lives the value of kenshould increase according to (13). At the same time, the contribution of reaction through pre-association should increase and become dominant when k - , > ken,corresponding to halflives of ca. s. In itself, this would lead to a steady increase in the overall reaction rate as k - , increases. However, at some point during the increase in k-, the rate-determining stage may also change since the formation of B .X will remain rate-determining only while (k-2 + k-,) < k , and k-, is probably about equal to k-,. Not much is known about rate coefficients for reaction within encounter pairs but the calculated rate coefficients for proton transfers within hydrogen-bonded systems make it probable that k-, > k, for some reactions in strongly acidic media. The most important criterion in classifying the reactions discussed in this

,.

DIFFUSION CONTROL A N D PRE-ASSOCIATION

45

chapter is the lifetime of the intermediate X. The long-lived intermediates (t,,2 > lo-' s) include NO: (under most conditions) and NOCl as electrophiles, and enols and aromatic amines (at pH > 2) as substrates. These should form the encounter pair B.X by the diffusion-controlled route and then the ratedetermining step depends on the relative values of k-, and k, in Scheme 3. For nitration, there is clear evidence that the overall reaction rate can be determined by diffusion control (p. 27); for nitrosation by NOX (X = C1, Br), there is evidence for a close approach to the diffusion-controlled rate (p. 16); and, for the halogenation of enols, there is considerable evidence for diffusion control although some uncertainty over the rate coefficients involved. The short-lived intermediates (tl,2 < 1O-Io s) include aromatic amines in strongly acidic media, strongly acidic species (H,OBr+) in less acidic media and, apparently, NO: in acetic anhydride. These intermediates should form the encounter pair B .X by the pre-association route. For nitration in acetic anhydride there is evidence of a limiting reaction rate suggesting that the formation of the encounter pair ArH.NOz is rate-determining but, for the intermediates formed by proton transfers, the evidence suggests that the proton transfers are not rate-determining (p. 32). In a hydrogen-bonded system, it is reasonable that exothermic proton transfers should compete even with extremely rapid reactions within encounter pairs. Interaction within encounter pairs. The above arguments have assumed that there is no interaction between the components in the encounter pairs A . B and B.X (Scheme 3) but this is probably unrealistic. Stabilization of the encounter pair A . B by charge-transfer interaction should favour the pre-association path by reducing the value of k - , and possibly also increasing that of k, [cf. equation (46)].22 Thus, in the nitration of neutral amine molecules (X) by nitronium ions (B) in concentrated sulphuric acid, interaction between the components in the encounter pair ArNH:.NOl should increase the acidity of the N-H hydrogens and facilitate the formation of the free amine. In the bromination of aromatic compounds (B) by HOBr(A), interaction between the components should increase the concentration of the encounter pair ArH. HOBr and facilitate the protonation of the hypobromous acid. Interaction between the components in the encounter pair B.X does not necessarily favour either the diffusion-controlled or the pre-association mechanism but, by prolonging the lifetime of the encounter pair, may help to make the formation of this encounter pair the rate-determining stage of the overall reaction.22Thus, charge-transfer interaction between the components in the encounter pair ArH .NO: may be one factor leading to the easily observed 22 These arguments assume that the interaction stabilizing the encounter pair operates also to stabilize the transition state of the subsequent reaction. If this were not so, the effect of an increase in the stability of the encounter pair would be compensated by a decrease in the rate coefficient of the subsequent reaction (cf. de la Mare and Ridd, 1959b).

46

J O H N El.

RIDD

encounter limit in nitration. Indeed one recent suggestion attributes many of the characteristics of these reactions to complete electron transfer within the encounter pair leading to the cation radical ArH'+ and NO, (Perrin, 1977). However, such electron transfers should not be necessary for the encounter limit to be observed in electrophilic aromatic substitution since, in principle, the lifetime of the encounter pair can also be increased by an increase in the viscosity of the medium. Final comments. The above discussion has shown that some difficulties in the interpretation of these reactions involving highly reactive intermediates can be resolved by recognizing that reaction can occur through the pre-association path and that the importance of this mechanism depends on the lifetime of the intermediate involved. However, a number of problems remain, some general, others applying to particular reactions. One general problem concerns the nature and extent of the interaction between the components of encounter pairs. On the pre-association pathway, such interaction within the encounter pair A.B (Scheme 3) could in principle lead to the direct formation of the reaction products by a concerted reaction by-passing the encounter pair X. B. Another general problem concerns whether the electrophile in a given encounter pair should be restricted to a particular part of the substrate molecule. If so, an encounter pair of a given stoichiometry should exist in a number of forms with the rate of interconversion dependent on the viscosity of the medium. Some theoretical treatments of this type have been developed (p. 7) but they have not been widely applied although the viscosity dependence of the product composition in the nitramine rearrangement has recently been shown to accord with a model of this type (White et al., 1976). It is possible that some of the problems discussed above in connection with the individual reactions derive from the oversimplified model used, in which the above complications are ignored. This appears to be an area in which further work is needed on the more exact delineation of reaction paths. Acknowledgements

The author thanks Dr B. C. Challis, Dr R. B. Moodie, Professor K. Schofield, Dr G. Stedman and Dr D. L. H. Williams for the provision of unpublished material and for their helpful comments on the manuscript. He acknowledges also some very useful discussions with Professors M. M Kreevoy and A. J. Kresge. References

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47

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