Acid-Base Catalysis and Molecular Structure

Acid-Base Catalysis and Molecular Structure R. P. BELL Balliol College, Oxjord, England

CONTENTS I. [ntroduction.

. . . .

Page

..................

11. The Empirical Law atalysis.. . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Salt Effects.. . . . . . . ....... 2. General and Specific ..................................... 3. Acid-Base Catalysis in Nonaqueous Solvents. . . . . . ......... 4. Relations between Acid-Base Strength and Catalyt 111. The Molecular Mechanism of Acid-Basc Catalysis 1. The General Nature of Acid-Base Catalysis.. . . . . . . . . . . . . . . . . . . . . . . . . 2. Examples of the Mechanism of Acid-Base Catalysis.. . . . . . . . . . . . . . . . . . a. Some Reactions of Enolisable Ketones and Similar Substances. . . . . . b. Nitro-Compounds and Nitramide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Reversible Addition of Hydroxy-Compounds to the Carbonyl Group.

153 153 157

164 165 165 169 171

d. Esterification and Hydrolysis of Carboxylic Esters, . . . . . . . . . . . . . . . . 173 3. Kinetic Steps in Acid-Base Catalysis., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 a. Reactions Involving a Single Proton Transfer.. . . . . . . . . . . . . . . . . . . . 174

.............

1. Pseudo-Acids and Pseudo-Bas

.............

V. The Importance of Molecular Structure.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. The Structure of t h e Substrate.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. The Structure of the Catalyst.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

201 201 204 207

I. INTRODUCTION The early study of catalysis by acids and bases was concerned chiefly with the use of catalyzed reactions for investigating general problems of physical chemistry. For example, the first correct formulation of the kinetic laws of a first order reaction was made by Wilhelmy in 1850 in connection with his measurements of the catalytic inversion of cane sugar by acids (Wilhelmy, 1). Catalytic reactions also played an important 1 F1

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R. P. BELL

part in the foundation of the classical theory of electrolytic dissociation toward the end of the nineteenth century. The parallelism between the electrolytic conductivity and the catalytic activity of solutions of acids received a ready explanation in terms of the high mobility and catalytic activity of the hydrogen ion (Ostwald, 2), and measurements on catalyzed reactions (notably the hydrolysis of esters) were used widely for investigating the state of solutions of electrolytes. The classical theory of acid-base catalysis assumed that hydrogen and hydroxyl ions were the only effective catalysts, that the reaction velocity was proportional to the concentration of the catalyzing ion, and that the degrees of dissociation of the electrolytes involved were given directly by their electrolytic conductivities. These assumptions, although giving a good general description of the facts, led to a number of discrepancies when applied quantitatively. The next phase in the study of acid-base catalysis, especially associated with the name of J. N. Bronsted, dealt mainly with the clearing up of these discrepancies, partly by the application of modern views on electrolytic solutions, and partly by the deduction from experiment of new laws governing catalytic phenomena. In this way the systematics of acid-base catalysis were largely established in the decade 1920-1930, and little has been added later to this aspect of the subject. This part of the story is well known l(see, for example, Bell, 3), and Sec. I1 of this review therefore contains only a brief summary of the empirical laws of acid-base catalysis, with few references. The aspect of acid-base catalysis which will be mainly dealt with in this article is its bearing on the molecular mechanisms of the reactions concerned and the structure of the molecules taking part. This side of the subject is of comparatively recent development. Most reactions catalyzed by acids and bases involve fairly complicated organic molecules, and although physical chemists used these reactions widely as tools for investigating their own problems, there was a general reluctance to speculate as to the detailed reaction mechanisms. Catalyzed reactions were of course included in some of the early attempts of organic chemists to devise reaction mechanisms, but the catalyst was often regarded only as an auxiliary influence which facilitated an uncataly zed mechanism, a view which is now known to be incorrect. Closer analysis shows that in most catalyzed reactions in solution the rate-determining step is chemically a simple one, though the overall reaction may be fairly complex. Catalyzed reactions are in fact often very suitable for studying general problems in the field of reactivity and structure, and much modern work on the effect of substitution on reactivity has in fact dealt with catalyzed reactions. Sections 111 and IV describe how the nature of the ratedetermining step can be ascertained in many reactions, and Sections

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153

V gives examples of how the reaction velocity depends on the molecular structure of the catalyst or substrate. 11. THE EMPIRICAL LAWS OF ACID-BASECATALYSIS 1. Salt Efects

The subject of salt effects in one which arises in all reaction-kinetic problems involving electrolytes and has no special relevance to acid-base catalysis. However, much of the early work on salt effects was in fact carried out with catalyzed reactions, and a neglect of these effects is still the commonest cause of misinterpretation of data on acid-base catalysis, so that a brief account will be given here. It is convenient to include under the heading of “salt effects” the various ways in which the assumptions of the classical theory have been modified by modern views on electrolytic solutions. Since the catalyst itself is commonly ionic, the same problems often arise even when no other electrolyte has been added to the system. The classical theory regarded all electrolytes as being incompletely dissociated in solutions of moderate concentration, the degree of dissociation being given by A/A,, the conductivity ratio. The present view is that those electrolytes commonly classed as strong (most salts, and a few acids such as HC1, HBr, HI, HC104, and sulfonic acids) are effectively completely dissociated in aqueous solution, even at concentrations where the conductivity ratio indicates a considerably smaller degree of dissociation. The decrease in equivalent conductivity with increasing concentration is attributed to the electrostatic forces between the ions rather than to a decrease in the degree of dissociation. This assumption of the complete dissociation of strong electrolytes (for which there is, of course, much evidence from various sources) simplifies considerably the interpretation of catalysis by strong acids or strong bases, since it is often found that the reaction velocity in such solutions is approximately proportional to the total concentration of acid or base rather than to the conductivity of the solutions. * The same is true in nonaqueous media such as methyl and ethyl alcohol, in spite of the more powerful interionic forces in these media. It is not strictly true to say that the velocity of a reaction catalyzed by a strong acid or a strong base is universally or exactly proportional to the catalyst concentration. In the first place, this statement ignores the primary salt effect (see below), though deviations attributable to this cause are unlikely to exceed a few per cent in 0.1 N solution. In the second place it is once more becoming fashionable to describe such salts

* For examples, see Bell, 3, Chapter 11.

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R. P. BELL

as “incompletely dissociated,” especially those containing multiply charged ions or the anions of certain organic acids, though the degrees of association attributed to them are much smaller. than those allotted by the classical treatment (Davies, 4). As far as acid-base catalysis goes, the most important examples are certain metallic hydroxides such as Ca(OH)2, Ba(OH)2, TlOH, whose aqueous solutions are supposed to contain appreciable concentrations of the species CaOH+, BaOH’, and TlOH. There has been some difference of opinion about the status and usefulness of the concept of incomplete dissociation in these cases (cf. Owen, 5 ) , but it is supported by kinetic measurements using solutions of the above hydroxides (Bell and Prue, 6; Bell and Waimd, 7). However, in spite of the above qualifications it still remains a good approximation to say that the catalytic effect of a strong acid or base is proportional to its total concentration, provided that high concentrations and certain types of catalyst are avoided. One of the main anomalies encountered in app1.ying the classical theory of catalysis was the large accelerating effect produced by the addition of neutral salts to catalyzing solutions containing weak electrolytes: for example, the addition of 0.1 M K N 0 3 to 0.05 M acetic acid increases by 30% its catalytic effect in the reaction of diazoacetic ester with water (Bronsted and Teeter, 8). Such an effect is now termed a secondary salt efect and is independeht of any kinetic considerations, being due to the increase in the degree of dissociation of the acetic acid caused by the increased ionic concentration. This; increase can be detected by other means (e.g., indicators, conductivity measurements) and its theoretical basis is now well understood. If the hydrogen ion concentration of a solution is controlled by a dissociation equilibrium of the type HA G H+ A-, then the concentration dissociation constant K , is given by the expression

+

where K is the thermodynamic dissociation constant, dependent only on the solvent and the temperature, and the f’s are activity coefficients. To a good approximation f H A is unity, independent of salt concentration, and the ionic activity coefficients can be predicted by the interionic attraction theory of electrolytes. For aqueous solutions at 25” a good approximation is (Guggenheim, 8a), where z is the valency of the ion and I the ionic strength defined by I = fZnLizi2

(3)

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ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

mibeing the molality of an ion of species i, and the summation being

taken over all the ions present in the solution. Applying this t o Eq. (1) we find log,, Kc = log,, K

+ Z$4/(1 + X W )

(4)

which shows that the Concentration dissociation constant (and hence the degree of dissociation) is increased by the addition of salt and serves t o estimate the magnitude of the effect. When a neutral salt is added t o a solution of a weak acid, the ions of the added salt are the main contributors t o the ionic strength. If, on the other hand, measurements are being made in a buffer solution (e.g., acetic acid sodium acetate), then the constituents of the buffer itself contribute largely t o the ionic strength, and there may be considerable secondary salt effects even without the addition of other salts to the system. For example, the classical dissociation theory predicts that the hydrogen ion concentration in a buffer solution of acetic acid sodium acetate should depend only on the ratio of the buffer constituents. Actually, because of the secondary salt effect, the hydrogen ion concentration depends also on the total buffer concentration, increasing with increasing salt concentration. These variations can be allowed for approximately by using Eq. (4),but it is usually simpler t o carry out kinetic experiments a t constant total salt concentration by adding appropriate amounts of a neutral salt. For example, the following series of solutions are to a good approximation “isohydric,” since the ionic strength is throughout 0.1 :

+

+

0 . 1 N acetic acid 0.075 N acetic acid 0 . 0 5 N acetic acid 0 . 0 2 5 N acetic acid

+ O . 1 N sodium acetate +O. 075 N sodium acetate +0.05 N sodium acetate +0.025 N sodium acetate

+O ,025 N NaCl + O . 05 N NaCl +0.075 N NaCl

This principle of maintaining a constant ionic strength is of great value in simplifying the comparison of kinetic data and should be followed whenever possible. Equations (l), (3), and (4) apply only when the hydrogen ion concentration is controlled by the dissociation of an uncharged acid molecule. I n many instances different types of equilibria are involved. For example, in a buffer solution of ammonia ammonium chloride the relevant equilibrium is NH4+ $ NH3 H+, while in a phosphate buffer it is HzP04HP04= H+. It is easy t o generalize the expressions for the secondary salt effect to cover all these cases. If the equilibrium is A B H+, where A bears z positive charges and B z - 1 (z can of course be a positive or negative number), then the application of Eq. 2 gives

+

+

+

+

156

H. P. BELL

Equation (4) is a special case of Eq. ( 5 ) with z = 0. I t may be noted that if z = +1 (as in a buffer of ammonia ammonium chloride), the secondary salt effect is to a first approximation zero, so that the hydrogen ion concentration of this type of buffer is relatively insensitive to changes in salt concentration. An analogous treatment applies to the hydroxyl ion concentration in solutions containing weak electrolytes, where it must be remembered that the value of the ionic product [H+][OH-] will increase with increasing ionic strength. The primary salt e$ect deals with the effect of salt concentration on reaction velocity when the reacting system involves no equilibria which can be displaced by a change in ionic environment. This effect can be very large when both the reacting species are ions, but it is of less importance in acid-base catalysis, where the substrate is almost always an uncharged molecule. To avoid complications due t o secondary salt effects, the primary effect is best studied in catalysis by solutions of strong acids and bases, and there exists a large body of experimental data. Some of the main conclusions are as follows: (i) For a given reaction and a given added salt the percentage change in velocity is a linear function of the salt concentration. (ii) The magnitude of the effect depends upon the individual nature of the reaction and of the added salt, but it rarely exceeds 4 to 5% in an 0.1 N solution of a uni-univalent salt. (iii) The addition of salt invariably causes an increase of velocity in reactions catalyzed by hydrogen ions, while for hydroxyl ion catalysis there is sometimes an increase and sometimes a decrease. It is possible to give a formal theoretical treatment of the primary salt effect, though it leads to little in the way of quantitative prediction. For a reaction involving the hydrogen ion and an uncharged substrate S, the theory gives for the effect of environment on the velocity of the reaction v ,

+

=

k[H+][S]fa+fs/fx+

(6)

where X+ represents the transition state (or critical complex) between the two reactants, and k depends only on the temperature. This expression was originally advanced by Bronsted (9) on not very clear theoretical grounds, but would now be regarded,as a special cas,e of the transition state theory of reaction velocities. It should be noted that it is never justifiable in a reaction of this type to introduce the factor fE+fB into the rate expression, omitting fx+, This assumption was made in the so-called activity rate theory, but it is correct only for reactiolns between ions of

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

157

equal and opposite charge. Unfortunately the ratio fH+/fx+ is not accessible experimentally (except from the kinetic measurements themselves), nor is it amenable to theoretical treatment, since theoretical expressions such as (2) predict the same value for the two activity coefficients. The most useful approach is that due to Hammett (lo), who pointed out that in the equilibrium of a simple basic indicator B, the ratio of the two forms is given by

where the activity factor has just the same form as in (6). This factor can be determined experimentally and is found to have approximately the same value for different indicators. Moreover, it gives a good account of the catalytic power of solutions of strong acids, with and without the addition of salts, in many cases up to high ionic concentrations. However, in view of the absence of any satisfactory theory of concentrated electrolytic solutions it would seem desirable t o confine kinetic measurements as far as possible to more dilute solutions, in which primary salt effects are small and secondary ones can be reliably estimated. 2. General and SpeciJic Catalysis The classical ,theory of catalysis supposed that the hydrogen and hydroxyl ions were the only effective catalysts in solutions of acids and bases. In a few instances early attempts were made to remedy some of the discrepancies encountered by attributing some catalytic power to undissociated acid molecules, but these attempts were mostly based on incorrect values for degrees of dissociation, and they did not take into account the possibility of primary or secondary salt effects. However, later work has shown definitely that species other than hydrogen and hydroxyl ions often can exert a catalytic effect, and the development of these ideas was closely linked with a closer understanding of the nature of the hydrogen ion in solution, and with the clarification of acid-base definitions (cf. Bell, 11). As long as the hydrogen ion was regarded as a bare proton, H+, it seemed reasonable to suppose that it had a unique catalytic power (perhaps in virtue of its powerful electrostatic field), and this idea seemed t o fit in with its abnormally high ionic mobility. However, evidence soon accumulated to show that there could be no significant concentration of free protons in any solvent, but that the “hydrogen ion” is H30+ in water, C2H,0H2+ in ethyl alcohol, NH,+ in liquid ammonia, etc. This realization destroyed the unique position of the hydrogen ion, and it was soon found (Lowry and Smith, 12; Bronsted and Guggenheim, 13) that

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R. P. BELL

both the ammonium ion and the hydrogen ion acted a s catalysts in the mutarotation of glucose. At about the same time the Bronsted-Lowry definition of acids was put forward, according to which a n acid i s a n y species which has a tendency to give u p a proton. This definition makes no mention of the charge in the species, and in fact we now regard H30+, NH4+,etc., as cation acids, completely analogous to uncharged acids like HC1 and CH,COOH. The first clear demonstration that uncharged acid molecules are catalytically active was given by the work of Dawson (14) on the reaction between acetone and iodine, though some of his quantitative conclusions need modification in the light of later work on electrolytes. Uncharged acids were also found to be catalysts in the mutarotation of glucose, and subsequently in many other reactions. The position is similar in basic catalysis. The hydroxyl ion has no strong claims to uniqueness, being merely the anion of a weak acid. According to the Bronsted-Lowry acid-base definition, a base i s a n y species which has a tendency to accept a proton. This obviously includes anions like OH-, CH3COO-, HPO,=, as well as uncharged basic molecules like ammonia and the amines. Catalysis by all these species was first found in the decomposition of nitramide (Bronsted and Pedersen, 15), and subsequently in many other reactions. General catalysis by acids and bases is now recognized as a very common phenomenon. Since a reaction may exhibit both acid and base catalysis, many different species may contribute to catalysis in the same solution. For example, in an acetate buffer the most general expression for the observed velocity would be 2,

=

Uo

+

f ~ H + [ H$ +.]~oH-[OH-] ~EAO[HAC] k ~ o - [ A c - ]

(8)

The term v o represents what is commonly described as the “spontaneous” reaction, though this is really a misnomer, since it it3 actually due to catalysis by solvent molecules, acting as acids or bases. It appears th a t all reactions catalyzed by acids or bases can be arrested completely in solvents having no acidic or basic properties (e.g., hydrocarbons), and an apparently uncatalyzed reaction of this type can usually be traced to the presence of some adventitious acidic or basic catalyst. I n aqueous solution it is not always easy to establish with certainty the existence of catalysis by species other than hydrogen or hydroxyl ions, and some of the early conclusions in this field werle based on insufficient evidence. The safest method is to use as catalysts a series of buffer solutions of equal ratios but varying concentrations, using the principle of constant ionic strength to eliminate secondary salt effects, as described in the last sub-section. If the observed reaction velocity increases with increasing buffer concentration in such a series, this is proof that one or

159

ACID-BASE CATALYSIS A N D MOLECULAR STRUCTURE

both of the buffer constituents is exerting a catalytic effect. The evaluation of the separate catalytic constants, e.g., kH+, kOH-, kHAo,and kr.- in Eq. (8), demands an extensive series of carefully planned experiments (see for example, Bell and Baughan, 16). Although many reactions exhibit general acid-base catalysis in the sense described above, there remain a few in which no catalysis by species other than hydrogen or hydroxyl ions can be detected. This behavior is known as specific catalysis. We shall see later that it is doubtful whether these reactions differ in principle from those exhibiting general catalysis. Most probably the failure to detect general catalysis is due to the quantitative relations between the catalytic effects of different species rather than to any pecularity in the reaction. However, specific catalysis is important in practice, since it provides a means of measuring the concentrations of hydrogen or hydroxyl ion in a solution without disturbance from catalysis by other species. Examples of specific catalysis by hydrogen ions in aqueous solution are the decomposition of diazoacetic ester, and the hydrolysis of acetals, while specific catalysis by hydroxyl ions is exhibited by the depolymerization of diacetone alcohol and the decomposition of nitrosotriacetonamine. 3. Acid-Base Catalysis in Nonaqueous Solvents

In general catalytic measurements in aqueous solutions are easier to interpret with certainty than those in other solvents, since our knowledge of the properties of solutions (especially of electrolytes) is very limited outside water. However, it is often necessary to use nonaqueous solvents for practical reasons e.g., solubility and chemical inertness, and the use of different solvents has elucidated a number of points of interest in the general theory of acid-base catalysis. The solvents which differ least from water are the lower alcohols. For example, in ethyl alcohol the analogues of the hydrogen and hydroxyl ions in water are C2HsOH2+ and C2H50- respectively. These ions cannot exist in appreciable concentration in aqueous solution, since the CzH50H H30+ and C2H50H2O reactions CzH50Hz+ HzO + C2H50H OH- go completely from left to right. This shows that C,H50H2+ is a stronger acid than H30+, and C2H50- a stronger base than OH-. Correspondingly, alcoholic solutions will often catalyze transformations which cannot be effected in water. Similarly, certain acids which are strong in water become weak in alcoholic solution. For example, nitric acid dissociates almost completely in water according to NOa-, while it is only slightly the scheme H N 0 3 H2O 3 &of dissociated in alcohol, so that catalysis by undissociated HNOl molecules can be studied in alcohol, but not in water. On the other hand, the

+

+

+

+

+

+

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R. P. BELL

quantitative interpretation of kinetic data is much more difficult in alcoholic than in aqueous solutions, partly because of the lower dielectric constant. For this reason salt effects (both primary and secondary) are much greater in magnitude and less well investigated. Thus in the activity coefficient expression (2), the numerical factor which is 0.5 in water would be about 2.8 in ethyl alcohol, and the concentration range over which such expressions are valid is much reduced. In solvents which differ more radically from water, the chief new feature is the range of catalytic species which can be effective. This may be illustrated by reference to the solvent anhydrous acetic acid, which is highly acidic, but which has very weak basic properties. For this reason, solutions of strong acids like HCl, HBr, and HClO, are very little dissociated in this solvent and differ considerably in their catalytic and other properties, whereas solutions of the same acids in water are converted completely into hydrogen ions, and therefore exhibit almost identical properties. Correspondingly, all bases which in water are stronger than aniline behave as “strong l 1 bases in anhydrous acetic acid, reacting completely with the solvent according to the equation B CH3COO- + BH+ CH3COO-, and thus: yielding solutions of identical basic properties. Special interest attaches to solvents such as the hydrocarbons, which exhibit neither acid nor basic properties, being unable t’o lose or to gain a proton. They are often described as aprotic and are typified by the hydrocarbons and their halogen derivatives. Although there are no analogues of the hydrogen and hydroxyl ions in these solvents, and even the strongest acids and bases remain undissociated, inevertheless their solutions possess catalytic activity, often exceeding that of any aqueous solution. This provides very direct evidence of the possibility of catalysis by undissociated acids and bases, and in principle the study of catalysis in aprotic solvents should be much simpler than in solvents of other types. For example, if acetic acid is dissolved in water, the sohtion contains the species HzO, H30+,OH-, CH3COOII, and CH3COO-, all of which may be catalytically active (cf. Eq. ( S ) ] , while in a solution of acetic acid in benzene the only active species is the acetic acid molecule itself. In practice this advantage is to some extent counterbalanced by complications which are found to arise in the kinetics of catalyzed reactions in these solvents. These are due to the low dielectric constants of the media concerned, which favor strong interactions between polar molecules, leading to association of reactants and catalysts and to kinetic abnormalities analogous to salt effects. Nevertheless, measurements in aprotic solvents often provide information of interest and have been increasingly used.

+

+

ACID-BASE CATALYSIS A N D MOLECULAR STRUCTURE

161

Since acid-base catalysis can take place in solvents which play no part (by promoting dissociation or otherwise) in the reaction, it is natural to inquire whether such catalysis can take place in the complete absence of a solvent, i.e., as a gas reaction. Practical difficulties connected with the instability or low volatility of the reactants often hinder an investigation of this point, but it has been shown in a few instances (Bell and Burnett, 17, 18; Wassermann, 19, 20) that catalysis by acids can certainly take place in the absence of a solvent, though in most cases the reaction takes place predominantly on the walls of the reaction vessel. Only for one reaction, the dimerization of cyclopentadiene, has homogeneous acid catalysis been observed in the gas phase. The preference for a heterogeneous reaction can be reasonably accounted for in terms of the type of reaction mechanism which we shall discuss later in this article. These mechanisms involve a considerable charge separation, which will be favored by the proximity of any polarizable material, such as the wall of the vessel (cf. Bell, 21). In this connection it may be of interest to mention that occasionally acid-base catalysis may be effected heterogeneously at the surface of a solid catalyst. For example, ion exchange resins have been used as acid catalysts in the esterification reaction (Haskell and Hammett, 22; Levesque and Craig, 22a), and it is possible that some of the oxide catalysts used industrially in various organic reactions may be functioning as acids or bases (Walling, 22b). However, little is yet known about acid-base catalysis of this type.

4. Relations between Acid-Base Strength and Catalytic Power Since there is a qualitative correlation between the acid-base properties of a species (ion or molecule) and its ability t o act as a catalyst, it is reasonable to expect that there may also be a quantitative relation between the acid-base strength of a species and its effectiveness as a catalyst for a given reaction. Such relations become still more likely when we consider (as in later sections of this article) the actual mechanism of catalysis, but they were in fact originally derived empirically from experimental data without reference to mechanism and will therefore be described briefly here. The catalytic power of a particular species is most conveniently specified by the catalytic constant (kA or kB), as shown in Eq. (8). The acid strength of a catalyst is usually described by its dissociation constant in water, K A . The basic strength of a catalyst may be measured by the conventional basic dissociation constant, but it is more convenient to use the reciprocal of the dissociation constant of the corresponding acid :thus = [HAc]/[H+][Ac-], and for the acetate ion we write KB = l/KHAD for ammonia, K , = 1/KNH4+= [NH4+]/[H+][NH3]. Strictly speaking,

162

R . P. BELL

these should be converted into thermodynamic constants by the inclusion of activity coefficients, but the distinction is often unimportant in the present context. The following equations are then found to hold approximately for acid and basic catalysis respectively kA =

G A K A ~ ,kB

=

GB(~/KA)O

(9)

where G A , G B , a,and p depend only on the solvent, the temperature, and the nature of the catalyzed reaction considered, a and p being always positive and less than unity. A different choice of constants for specifying the strength of acids or bases would not affect the -form of the equations or the values of a or p, but would of course modify the parameters G, or G,. This type of relation was first established by Bronsted and Pedersen (15) for the decomposition of nitramide and is usually known as the Bronsted relation. Later sections of this article will deal with the exact range of validity of the Bronsted relation and with its theoretical interpretation, and we shall give here only some of the salient facts. A relation of this kind has been found to hold, a t least approximately, for every reaction in which a series of related catalysts has been investigated, the range of k or K frequently covering several powers of ten. The values of G, a, and p vary from one reaction to another. G also varies markedly with solvent and temperature, a and p much less so. A drastic change in the nature of the catalyst (in particular a change in the charge which it bears) necessitates a change in the parameters of the equation. The same type of relation governs catalysis in nonaqueous solvents, even when these are aprotic. In the latter case it is not possible to specify the strengths of acids and bases by dissociation constants in the same solvent, but use may be made of equilibria with an added acid-base system, e.g., an indicator. Frequently such equilibrium measurements are not available, and dissociation constants in water are commonly used as a basis of comparison with catalytic measurements in other solvents. Since the relative strengths of acid-base systems of the same charge type vary little from one solvent to another, the use of aqueous dissociation constants will not alter the form of Eqs. (9), though it will of course change the value of G. If it can be assumed that the Bronsted relation remains approximately valid for the ions and moIecules of the solvent, it is possible to make some interesting deductions about the possibility of detecting general acid-base catalysis. The point is best illustrated by taking a particular example, e.g., acid catalysis in an aqueous solution 0.1 N with respect to both acetic acid and acetate ions. We assume that the catal.ytic effect of acids (without reference to charge or structure) is given ttpproximately by

ACID-BASE CATALYSIS A N D MOLECULAR STRUCTURE

163

Eqs. (9). In applying this to the species H30+and HzO we use the acid constants

The quantitative significance of these figures is doubtful, since they involve the concentration of water molecules in pure water (taken as 55.5 moles/liter), but experience shows that they give a roughly correct estimate. The following figures are then obtained for the proportion of catalysis due to the three acidic species in the solution, for different values of the exponent Exponent 01 = 0 . 1 01 = 0 . 5 a = 1.0

Proportion of Catalysis due to

H30+ 0.002y*

3.6% 99.8%

H,O

CHECOOH

0.01%

2% 96.4% 0.2%

98 % 5

x

10-’0%

When a = 0.1, most of the catalysis is due to the solvent, and the reaction would in practice be regarded as uncatalyzed, since the rate is but little increased even in solutions of strong acids. When a = 0.5, the rate in the buffer solution is largely due to the undissociated acetic acid, as could be verified by varying the buffer concentration and keeping its ratio constant. On the other hand, the catalytic effect of OH3+ could be measured independently in solutions of strong acids, and the “spontaneous” (H20-catalyzed) reaction in solutions sufficiently alkaline to repress the effect of the hydrogen ions. This case is thus a favorable one for the study of general acid catalysis. Finally, if a = 1, the catalytic effect of the buffer is almost entirely due to the hydrogen ions which it contains, and it is clear that no experiments could detect with certainty the small effect of the acetic acid molecules. Moreover, the watercatalyzed reaction is so slow that it would be impossible to detect it. The reaction would thus be classed experimentally as an instance of specific catalysis by hydrogen ions. This treatment is easily generalized and leads to the conclusion that in water or similar solvents general acid catalysis will be observable only for intermediate values of the exponent a. If a is too small, the catalytic effect of acids will be swamped by that of the solvent, while if a approaches unity, the effect of all other acids will be masked by that of the hydrogen ion. Similar conclusions apply to basic catalysis. It is possible, therefore, that those reactions in aqueous solution which appear to show specific catalysis by hydrogen or hydroxyl ions (cf. preceding sub-section) do not constitute a special class of reaction, but are actually

164

R. P. BELL

examples of general acid-base catalysis in which the exponent of the Bronsted relation approaches unity. These considerations do not, of course, affect the practical application of these reactions for measuring hydrogen and hydroxyl ion concentrations. In aprotic solvents, on the other hand, there are no limits to the value of a! observable in practice, and values as low as 0.2 and as high as unity have in fact been observed (Bell and Brown, 23).

111. THEMOLECULAR MECHANISM OF ACID-BASECATALYSIS I. T h e General Nature of Acid-Base Catalysis Early views on the nature of catalysis regarded it as an indefinite influence of some kind. Somewhat later a rather more definite picture was formed of catalysis by the hydrogen ion (regarded as a bare proton), which was supposed to attract the reactants together in virtue of its powerful electric field. This explanation did not seem especially appropriate to hydroxyl ion catalysis and obviously would not apply to catalysis by uncharged molecules. These early views envisaged reactions which could take place in the absence of a catalyst, but which were facilitated by itt3 presence. Evidence gradually accumulated to show that many of the reactions subject to acid-base catalysis could not take place at all in the complete absence of catalysts, apparently “spontaneous reactions” being often due to catalysis by acidic or basic solvent molecules, or by some adventitious acidic or basic impurity. This seemed to indicate that the catalyst took a fundamental part in the reaction, possibly in :a chemical sense. It was soon realized that the essential property of acilds and bases was their power respectively to lose and to add on a proton, and enquiry also showed that substrates involved in acid catalysis could always be supposed to have some basic properties, while those in base-catalyzed reactions could always in principle act as acids, though the acid-base properties of the substrates were often so weak as to elude detection by ordinary means. This led to the suggestion that acid-base catalysis always involves an acid-base reaction between the catalyst and the substrate. Such a reaction is also often termed a protolytic reaction, since it involves the transfer of a proton between the two reacting species. This view of acid-base catalysis is now generally accepted, and specific mechanisms have been proposed for a large number of types of reaction. For the purpose of illustration a few of these are given in the next subsection, but no attempt has been made at comple-teness. I n many instances the mechanism involves two successive proton transfers, and it may be a matter of some difficulty to decide the relative rates of the two successive steps. This question is considered in Sec. 111.3.

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

165

a. ExampEes of the Mechanism of Acid-Base Catalysis a. Some Reactions of Enolizable Ketones and Similar Substances. The earliest reaction in this class to be studied in any detail was the halogenation of ketones and allied compounds. It was found by Lapworth (24) that the rate of reaction of ketones with iodine is independent of the iodine concentration and was in fact the same for bromine as for iodine under the same conditions. This shows that the process being measured is not the halogenation reaction at all, but some change in the ketone itself. The rate of halogenation is increased by addition of strong acid, and halogenation also takes place rapidly under alkaline conditions, though further reactions often take place (e.g., the iodoform reaction with acetone and similar substances). These facts led Lapworth to suggest that the process being measured was in fact the enolization of the ketone, since enols are known to react very rapidly with halogens, and the interconversion of keto-enol isomers is catalyzed both by acids and by bases. The ordinary tests do not show any detectable amount of enol in simple ketones, and the supposed preparation of these enols by indirect means has been disputed (Kohler and Thompson, 25). These and other arguments have led some authors to reject the enolization mechanism for the halogenation of simple ketones (Arndt, 26). However, the presence of an appreciable amount of enol at equilibrium is not a necessary condition for the correctness of Lapworth’s mechanism, and in any case it has been shown recently that simple ketones do contain a very of enol (Schwarzenbach and Wittwer, 27). small proportion (Even before this demonstration the enolization mechanism was generally accepted, for example in the extensive work of Dawson (14) on the iodination of acetone. Dawson found that the reaction was catalyzed not only by hydrogen or hydroxyl ions, but also by undissociated acid molecules and by the anions of weak acids, and similar demonstrations of general acid-base catalysis were given later for the halogenation of other carbonyl compounds (Pedersen, 28, 29; Bell and Lidwell, 30). It is of interest to note that the same kind of kinetics can be observed for the acid-catalyzed halogenation of acetone in hydrocarbon solvents, though here it is necessary to use N-halogen compounds as halogenating agents rather than free halogens, so as t o avoid the formation of undissociated hydrogen halides, which have an enormous catalytic effect (Bell and Tantram, 31). We must now consider the mechanism by which acids and bases can effect the transformation of a keto to an enol form and in doing so shall have occasion to modify slightly the enolization view of halogenation. All compounds containing a carbonyl group have some basic properties.

166

R . P. BELL

These are too weak t o detect in aqueous solution, but ar’erevealed in very acid solvents such as concentrated sulfuric acid (e.g:., Hammett, 32; Flexser, Hammett, and Dingwall, 33). Similarly, every enolizable ketone containing the group

\

giving the ion

/

/

C:C.O-.

\

/

/

C H C : 0 can in principle act as an acid,

@-Diketones and similar substances are in

fact acids of measurable strength in aqueous solution, blut simple ketones are such weak acids that their acidic properties can o,nly be studied in inert solvents (Conant, 33a). Reasonable mechanisms for the formation of the enol are then as follows, where A represents any acid, and B any base : Acid catalysis

+A

‘CH.C
/

i +

\

/

/+ CHC:OH

\

/

C:C.OH

/

+A

(10)

(1)

Basic catalysis

\

+B

/

CH.C:O+B=

/

\

/

/

C:C.O-+A*

\

/

C:C.OH + B

/

(11)

Each mechanism involves a two-stage reaction, and there is no direct transfer of a hydrogen atom from the carbon atom t o the oxygen. I n fact, the hydrogen of the -OH will probably not be the same atom as Each mechanism also requires the participation of that of the -CH. both an acid and a base, though the order of attack is different. It is not, however, necessary deliberately to add both an acid and a base in order to bring about the change. In water or a similar medium the solvent molecules themselves can act either as acids or as bases, and even in an aprotic solvent the first stage of the reaction will convert an acid into a base, or vice versa, so that both types of molecule will be present although only one was added initially. This point will be considered further in the next sub-section in connection with tlhe kinetics of the successive steps. The above mechanism for the acid-catalyzed formation of the enol accords with Lapworth’s interpretation of the halogenation, but for basic catalysis some modification is necessary. The proposed mechanism involves the anion (11) as an intermediate in the formation of the enol,

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

167

and it would be anticipated that this anion will react very rapidly with halogens. This is in fact found to be the case for ketones which are sufficiently acidic to be converted completely into the enolate ion. This means that in presence of halogen no enol will be formed, and the measured rate of halogenation under conditions of basic catalysis is therefore the rate of ionization of the ketone, rather than its rate of enolization. No corresponding change is needed in the mechanism for acid catalysis, since the cation (I) will not be reactive toward halogens. The conversion of a ketone into its enol or enolate ion can be observed by other means than by reaction with halogens. For example, if the ketone is dissolved in water (or a similar solvent) containing a considerable proportion of deuterium, the formation of enol or enolate ion will lead to the exchange of hydrogen isotopes between the ketone and the solvent. We should therefore expect that this isotope exchange would be catalyzed by acids and by bases, and this is in fact found to be so. Similarly, if an optically active ketone R1R2CH*C0.Ris prepared, the formation of enol or enolate ion will lead to racemization, and correspondingly the racemization of such a substance is found to be catalyzed by acids and bases. The close relation between the mechanisms of halogenation, isotope exchange, and racemization is further confirmed by quantitative comparisons of the rates of these processes. Thus the rate of racemization of the ketone CsH&OCH(CH3)C2HS by sodium hydroxide in a dioxane-water mixture was found to be identical with its rate of interchange with sodium deuteroxide under the same conditions (Hsii, Ingold, and Wilson, 33b). Similarly, the rates of bromination and racemization of the ketone

were found to be identical when catalyzed by acetate ions in aqueous acetic acid solution (Hsii and Wilson, 34). These two comparisons refer to basic catalysis, but the position is similar for catalysis by acids. For example, the rates of acid-catalyzed halogenation and racemization have been found to be identical for both the optically active ketones mentioned above (Ingold and Wilson, 35; Bartlett and Stauffer, 36), and the acidcatalyzed bromination and isotope exchange of acetone also proceed at equal rates (Reitz, 37). It has just been assumed that the formation of an enol or enolate ion from an optically active ketone automatically leads to racemization, and this is clearly to be expected on the basis of the planar structures

168

R . P. BELL

Ri

\

7%

R2/c=c\K

R1 \

0-

/'

,c=c\,

R2

R

However, it is possible that the actual structures derive partly from the forms R,

\ - //

/c-c\R

R2

which would be nonplanar and might or might not racemize readily. For this reason some differences of opinion have been expressed about the optical stability of carbonium ions (cf. Hammett, 38). The rate correspondences mentioned above show that this stability is very small for monoketones, but it may well depend upon the actual compound concerned, and perhaps upon the ability of the solvent to solvate the ion. One piece of evidence is sometimes quoted which seems to conflict with the mechanism given above for the bromination and racemization of the cyclic ketone studied by Ingold and his collaborators-the observation of Leuchs (39) that this ketone can be brominated without complete loss of optical activity. However, this bromination was carried out in a solvent differing greatly from that employed by Ingold, and in any case it is doubtful whether the claim of Leuchs can be accepted, since he isolated only a small quantity of product of low optical activity and doubtful purity. The enols and enolate ions of ketones and similar substances will react not only with halogens but with many other substances, and in particular the many addition and condensation reactions undergone by carbonyl compounds in presence of basic catalysts can be referred t o an ionization of the type

\ / CHC:O /

---t

\ / C:C.O-. /

An example of such a

reaction is the reversible aldol condensation of aldehydes and ketones, for which the reaction scheme is:

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

169

Alternative mechanisms have been proposed (Nelson and Butler, 39a), but the above scheme seems the most probable (Walters and Bonhoeffer, 40). b. Nitro Compounds and Nitramide. Nitroparaflns which have at least one hydrogen atom on the carbon atom to which the nitro group is attached behave rather like enolizable ketones in their halogenation reactions. The reaction is of zero order with respect to halogen and is catalyzed by anion bases such as the acetate ion (Junell, 41; Pedersen, 42: Reitz, 43). This was originally interpreted in terms of conversion to the aci-nitro form, which is present at equilibrium only in minute concentrations (Turnbull and Maron, 44) ; however, the arguments already given for the halogenation of ketones indicate here also that the reactive species in halogenation is the ion I in the following scheme:

(a)

\ CH.N +/

/

\

0

0-

+ B e \ C:N +/

/

\

0-

+.)

0(13)

The nitroparaffins differ from the ketones in that their halogenation in aqueous solution is not catalyzed by acids: this is because the nitro group is much less basic than the carbonyl group, having in fact hardly any tendency to add on a proton. As would be expected, deuterium exchange between nitromethane and DzO is catalyzed by acetate ions, and the rate of exchange is equal t o the rate of bromination under the same conditions (Reitz, 43). Similar correspondences would be expected in the rate of racemization of optically active nitro compounds, but here the position has been complicated by reports (Kuhn and Albrecht, 45; Shriner and Young, 46) that these compounds do not lose their activity completely on conversion to the ion. However, it has recently been shown (Kornblum et al., 47, 48) that the residual activity in these observations was due to the presence of alkyl nitrate as an impurity. The mutarotation of a-nitro camphor represents a similar type of reaction: it is catalyzed both by acids and bases (Lowry, 49), and a quantitative study of acid catalysis in chlorobenzene solution has been made (Bell and Sherred, 50). Lowry and most subsequent writers have supposed that the observed change of rotation is due t o conversion to the aci-nitro form (11),i.e.,

..;/'

170

R. P. BELL

co

'

-+

CaH~I/I

HbN02

0-

\ C: N +/

O 'H

(1)

(11)

but it is much more likely that what is observed is a change of configuration about the carbon atom marked with a n asterisk. Since the molecule contains a second asymmetric center this will lead to miitarotation rather than racemization. I n catalysis by bases this will ta,ke place through the ion

c:o

\

0-

with a charge distribution somewhere intermediate between the two structures shown. I n acid catalysis th e intermediate may be the aci form (11) above, or it may be the enol (111). C.0H

(111)

There is some evidence th at the mi form is involved, but the question is not settled. The nitroparaffins differ from the ketones in that t:hey are sufficiently strong acids (pK = 8-10) to be completely neutralized hy aqueous solutions of sodium hydroxide. It is well known that this neutralization takes place a t a measurable rate (Hantzsch and Veit, 51). and Hantzsch and others have supposed that the nitro compound is f'rst converted slowly into the aci form, which then reacts rapidly with hydroxyl ions. However, according to modern views, the aci form cannot be produced without the intermediate formation of the anion, and the slow process must therefore be 0

\CH.&/

/

\

+OH--+

0-

\

/

+/ C:N

\

0-

+HzO 0-

a particular case of the reaction with bases (13a). In this case, therefore, the slow protolytic reaction can be observed directly, without having

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

171

recourse to indirect processes such as halogenation, racemixation, or isotope exchange. The decomposition of nitramide has been studied extensively as an example of general basic catalysis, but its mechanism has been little discussed. Nitramide is a weak acid (pK 7), but the loss of a proton cannot be the step concerned with the decomposition, since neutralization and deuterium exchange take place rapidly and without decomposition. There is still some doubt about the structure of the nitramide molecule. It is usually written NHZN02, as suggested by its discoverers (Thiele and Lachmann, 52). Hantasch (53) maintained for many years tjhat it was a stereoisomer of hyponitrous acid, HON:NOH, but eventually abandoned this structure in favor of NH: NO.OH (Hantzsch, 54) in view of optical evidence on the structure of the anion of phenylnitroamine (Cambi and Szego, 55). Other optical evidence (Kortiim and Finck, 56) suggested that in aqueous solution the equilibrium NH2NOz N H :NO.OH is set up, with the form NH :NO.OH predominating, but some kinetic evidence (Bell and Trotman-Dickenson, 57) favors the view that NHzNOz is the predominant form. Measurements of dipole moment were inconclusive (Hunter and Partington, 58) but led to the

-

- +

suggestion of N:N(OH)z, a structure not supported by any other evidence. The most likely mechanism of decomposition seems to be that suggested by Pedersen (59) B

+ NH:NO.OH -+

A

+ N10 + OH-

(13a)

which will be applicable independent of how much of the form N H : NO.OH is present in solution. c. Reversible Addition of Hydroxy Compounds to the Carbonyl Group. Many reactions involving addition to a multiple bond (or the reverse process) are catalyzed by acids and bases, and we shall take here as an example the addition of hydroxy compounds to a carbonyl group. The egneral equation is

\

/

C=O

+ R.OH

’

OH

G! 3 (‘’

‘OR

and the simplest case (R = H) is the hydration of carbonyl compounds. The earliest direct investigation deals with the reversible hydration of carbon dioxide, COz HzO H&03 which exhibits general acid-base catalysis (Booth and Roughton, 60). The same is true for the hydration of acetaldehyde in aqueous solution (Bell and Darwent, 61) and for the dissociation of the same hydrate in aqueous acetone (Bell and Higginson,

+

172

R. P. BELL

62). The carbonyl group of ketones is hydrated only to a very small extent, but the kinetics of the process can be studied by observing the rate of exchange of the isotope 0l8between acetone and water (Cohn and Urey, 63). This exchange is also catalyzed both by acids and by bases. When R is an ethyl group, Eq. (14) represents the reversible formation of a semi-acetal. This reaction is known to be catalyzed (e.g., Dieckmann, 64, 65), but most of the quantitative information available relates to slightly more complicated reactions. I n particular, the ring structures now attributed to the simple sugars involve a semi-aoetal link between the carbonyl and hydroxy groups, and the interconversion of different configurations of the ring involves the breaking of this link. This interconversion is just what is observed in the mutarotaizon of glucose and similar substances, already quoted as one of the best established examples of general acid-base catalysis. An exactly analogoils ring formation occurs in the reversible dimerization of a-hydroxy aldehydes and ketones, according to the scheme

and it is in fact found that the depolymerization of climeric dihydroxyacetone (Bell and Baughan, 66) and glycolaldehyde (Bell and Hirst, 67) exhibit general acid-base catalysis with kinetics very similar to those of the mutarotation of glucose. In this reaction the observed kinetics provide strong support for the structure of the dimer given in Eq. (15). It had been suggested on chemical evidence (Bergmann, 68) that only a loose association took place between the two monomer molecules, though later work (Bergmann and Miekeley, 69) provided an alternative interpretation of this evidence, and confirmed the structure (15) for the dimer. The catalyzed exchange reactions which take place between esters and alcohols (Schaefgen, Verhoek, and Newman, 70) are also explained by a reversible addition to the carbonyl group, i.e.,

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

173

and the mutarotation of certain a-keto esters (McKenaie and Mitchell, 71; McKensie and Ritchie, 72) in presence of alcohol is probably due t o the asymmetric addition of alcohol to the keto group. All these reactions thus fall under the general scheme (14), and in view of the acid character of the hydroxyl group and the basic properties of oxygen reasonable mechanisms for acid and basic catalysis are : Acid catalysis OH

\c/

OH

+A$\C/

/

/ \OR

\o/

0

\/ /

+ROH+A

+‘H

Basic catalysis OH

\c’

R+B+

’

0-

+ B A /

/ ‘OR

(16)

+A=

\OR

\c/

0

/

+ROH+B

We shall discuss later the relative rates of these successive steps, and also the question of whether they can be split up into simpler consecutive reactions. d. Esteri3cation and Hydrolysis of Carboxylic Esters. The general reaction is:

//

0

R‘,C

+ HzO

R’.COOH

+ ROH

\OR

being catalyzed in both directions by acids. The hydrolysis of esters can of course be also effected by alkali, but this reaction is not reversible. Moreover, alkaline hydrolysis is a bimolecular replacement of OR- by OH-, rather than an acid-base reaction and will not be considered here. The usual acid catalyst employed is the hydrogen ion, and it is doubtful whether catalysis by other acid species is established with certainty for hydrolysis in aqueous solution (Dawson and Lowson, 73). On the other hand, undissociated acid molecules certainly act as catalysts for esterification in alcoholic solution (Rolfe and Hinshelwood, 74; Hinshelwood and Legard, 75), and any mechanism must therefore be consonant with general acid catalysis. A great variety of mechanisms have been proposed, but many of them are in fact equivalent, differing only in the extent to which the reaction is dissected into steps, and in the assumptions made about the relative rates of the consecutive steps. The following version is that given by Day and Ingold (76):

174

R . P. BELL

R’.C

//

0

0 +A=

\OR

+

R e R ’ .C=O

R’.C

+ R.OH

\O’

+ H ‘

0

Under different conditions different steps may become rate determining, and the further discussion of this mechanism will not b,e attempted here. 3. Kinetic Steps in Acid-Base Catalysis

In all the mechanisms described above the initial step involves the transfer of a proton between the catalyst and the substrate, but it is only rarely that the observed reaction consists solely of this transfer. It is commonly followed either by a second proton transfer from another part of the substrate molecule (thus regenerating the catallyst), or by some other reaction of the species initially formed. We shall now inquire under which conditions it is possible, from kinetic or other data, to obtain information about the relative velocities of the consecutive steps involved in such a mechanism. The following sections follow largely the treatment given by Pedersen (77). a. Reactions Involving a Single Proton Transfer. In any truly catalytic reaction the initial proton transfer must be followed by a transfer in the reverse direction, so that the catalyst may be regenerated, but in many reactions this second transfer does not atiect the kinetics of the reaction. For example, the mechanism (13a) suggested above for the decomposition of nitramide will be followed by the simple acid-base OH---+ B HzO, regenerating the basic catalyst B, but reaction A this will take place rapidly and does not affect the decomposition of the nitramide. We shall take as an example the reaction of a substrate S to

+

+

ACID-BASE CATALYSIS A N D MOLECULAR STRUCTURE

175

give products X, catalyzed by an acid A in aqueous solution. The reaction scheme is (a)

(b)

S+A=

ki

k -1

SH+

SH++ X

+B

(18)

ki

where we suppose for the sake of simplicity that the reaction is irreversible. If the concentrations of A and B are kept effectively constant, the kinetics of the system are described completely by the three first order constants k l , Ll, and kz. The values of k , and k-1 depend upon the nature of A and B and are proportional to their respective concentrations. Information can be obtained about their ratio by considering what happens if the equilibrium (18a) were set up without interference from the reaction (18b). If asterisks denote equilibrium concentrations we then have

where KBH+ measures the acid strength of SH+ (being inversely proportional to the basic strength of S). It should be noted that Eq. (19) does not imply that equilibrium is actually set up in the first stage of the reaction, but only that kl and k-1 have the same values which they would have at equilibrium. [Hf] in Eq. (19) is strictly speaking the hydrogen ion concentration which would obtain if reaction (18a) were a t equilibrium, but this differs inappreciably from the actual value of [H+]in the system for all the cases considered below with the exception of (iib). The state of affairs now depends on the relative values of kl, k-1, and kZ,and the different possibilities can be classified as follows. (i) First assume k l << L1: this will be so in most reactions, since S is normally a much weaker base than B. The amount of SH+ will then remain very small throughout the reaction, and we can equate its rates of formation and destruction. This shows that the formation of the products X will take place with a first order velocity constant k given by

There are now three possibilities, according to the relative values of kz and k-1. (ia) k z >> Ll. Equation (20) becomes k = k l = T A . ~ [A], where T ~is ,a constant ~ characteristic of the proton-transfer reaction between the catalyst A and the substrate S. If the solution contains a number

176

R. P. BELL

of different acid catalysts, this can be generalized to k =

ri[Ai) i

Under these conditions the observed reaction velocity is determined by the rate of the initial proton transfers, and general acid catalysis will be observed. (ib) kz << k-1. (20) becomes k = Iclkz/k-l, and hence from (19)

+

+

In this case the system S A SH+ B is in equilibrium throughout the reaction, and the rate-determining step is the further reaction of SH+. Moreover, the velocity is proportional to the hydrogen ion concentration, although the initial proton transfer takes place from tQe acid A, and it would be classed experimentally as an instance of specific hydrogen ion catalysis. It is easily seen that Eq. (22) is still valid if the solution contains a number of different acid catalysts, and the same conclusion holds. (ic) k z k-1. This gives

-

The velocity now depends partly upon actual proton transfers, and partly on an equilibrium controlled by the hydrogen ion concentration. The reaction would appear to be catalyzed by acid species other than the hydrogen ion, but the quantitative behavior would be complex, and it is doubtful whether this case has been observed in practice. (ii) As an alternative assumption let k-I k l . This will be so if the substrate is a base of moderate strength or if the ratio [A] :[B] (and hence the hydrogen ion concentration) is high. There are, as before, three sub-cases. (iia) k2 >> k-1. The concentration of SH+ will remain small, as in case (i), and the rate is determined by the proton tra-nsfers (lsa), giving a first order velocity constant k = si[Ai], i.e., general acid catalysis.

-

+ i

+

(iib) k z << Ll. The system S A S SH+ B will be in equilibrium throughout, the rate being determined by k z . The fraction of the total amount of substrate present in the form SH+ is k l / ( k , k-l), which is appreciable, since k-1- k l . Unless the substrate concentration is

+

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

177

much smaller than [A] and [B], the two latter concentrations (and hence also [H+]) will not be the same as they would be in the absence of substrate and may tend to vary during the course of the reactions. We shall take [A], [B], and [H+] to represent the actual concentrations in the reaction mixture, and assume that they are maintained a t constant values throughout the reaction. Under these conditions the first order constant for the disappearance of the substrate is given by = (S]

+ [SH+]dt (IS1 + [SH+ll -1

d

from (19). The reaction velocity is thus a function of hydrogen ion concentration only (specific catalysis) and will be directly proportional to [Hf] for low values of the latter. However, as soon as [H+] becomes comparable with K N Hthe + velocity will increase less rapidly than the hydrogen ion concentration, and for very high values of [H+]it will reach a limiting value corresponding to the complete conversion of S into SH+. (iic) k2 k-I. In this case the variation of substrate concentration with time is given by an expression w’ith two exponential terms (Rakowski, 78) and the reaction will not follow first order kinetics. This behavior is encountered only in isolated cases (Bartlett, 79; Zucker and Hammett, 80). An exactly similar treatment can be applied t o basic catalysis. The important general result of these considerations is that if general acidbase catalysis is observed in a reaction involving only one proton transfer, then this proton transfer is rate determining. However, it is not safe to assume that the converse is true, i.e., that the substrate and catalyst are effectively in equilibrium in reactions found experimentally t o be specifically catalyzed by hydrogen or hydroxyl ions. This is because (as shown in Sec. 11.4) catalysis by species other than H+ or OH- may frequently escape observation, giving a false impression of specific catalysis. The existence of a preequilibrium between catalyst and substrate (leading to a genuine specific catalysis) can, however, be shown unequivocally if Ll kl in the above scheme, i.e., if the substrate has sufficiently marked basic (or acidic) properties, and the concentrations of hydrogen ions (or hydroxyl ions) are sufficiently high. Under these conditions the reaction velocity in solutions of strong acids or bases will increase less rapidly than [H+] or [OH-], corresponding to the conversion of an appreciable proportion of the substrate into its cation or anion [cf. case iib and Eq. (24) above]. The test cannot often be applied, since the

-

-

178

R. P. BELL

necessary values of [H+] or [OH-] are usually so high that measurement becomes impossible. However, a few cases are known in which the data provide good evidence for the existence of a preequilibrium. Thus in the hydrolysis of acetamide by aqueous solutions of strong acids (Euler and Olander, 81) the apparent catalytic constant of the hydrogen ion decreases by 28% between 0.1 N and 1 N , and by 58:!& between 0.1 N and 3 N . Although the magnitude of this change is little greater than might be expected for a primary salt effect, it is significant that such effects appear always to be positive for hydrogen ion catalysis (cf. Sec. II.l), and a positive salt effect has in fact been observed in the hydrolysis of acetamide (Taylor, 82). There is thus little doubt that the initial step in the hydrolysis is the setting up of the equilibrium CH3CONHt

+ H80++ CH3C06H3+ H 2 0

followed by a slower step such as

+

CH3CO&H3 H10 --* CH3COOH

+ &H
b. Reactions Involving T w o Proton Transfers. This is the case most frequently met with in practice, and in particular it includes the so-called prototropic isomerizations represented by the scheme HX.Y:Z

X:Y.ZH

or the ring-chain equivalent

&)’I

Z

/ *(A) ‘YXH \

(25)

ZH (26)

Y:X

where the atoms X and Z may be carbon, nitrogen, 0-r oxygen, and Y is carbon or nitrogen. (Other atoms or groups are of course attached to X, Y, and Z to satisfy their normal valencies.) The best known case of prototropic isomerization is keto-enol tautomerism, already discussed in Sec. III.2a1 and other examples are lactam-laction, nitroso-isonitroso, nitro-acinitro, and three-carbon tautomerism. By analogy with the discussion in Sec. 111.2 the mechanism of basecatalyzed prototropic isomerization will be

where the anion will in general be a hybrid of the two structures shown, the actual charge distribution depending on the nature of the atoms

179

ACID-BASE CATALYSIS A N D MOLECULAR STRUCTURE

X, Y, and Z. We are assuming here that the two proton transfers take place successively rather than simultaneously. The possibility of two simultaneous transfers (the so-called ternary mechanism) will be discussed in the next section. For brevity the scheme (27) will be written ki

ke

k-i

k-z

HR ;=:R- eRH

(28)

Provided that the concentrations of catalyst acids and bases remain constant during the reactlion (ie., the concentration of R- is small throughout) the kinetics of the process can be described by first order velocity constants k l , k-l, k z , k-2, whose values depend upon the catalysts present. We shall also assume that the reaction goes completely from left to right (i.e., kL2 = 0) : this can be ensured if necessary by moving R H as quickly as it is formed. Under these conditions the kinetic analysis follows the lines of the last section. There are three cases: (iiia) k 2 >> k-l. The ion R- is transformed into R H as soon as it is formed, and the observed first order velocity constant is k l * k l represents the rate a t which the various basic species present can remove a proton from HR, and will therefore be of the form zai[Bi]; i.e., general basic catalysis is in principle observable. (iiib) k z << Ll. The equilibrium HR

c i

+

R-

Bi

+ 2 Ai is praci

i

tically undisturbed, and the velocity is determined by the rate at which R- adds on protons to give RH. The expression for the velocity can therefore be written in the form v = k z [ R - ] = [R-] ?ril [A& However,

i

since H R and R- are in equilibrium with each acid-base pair Ai - Bi, we have [Bi][HR]/[Ai][R-] = Ki’, and hence v = [R-]

c

c i

ri’[Ai] = [HR]

c i

ni’[Bi]/Ki’

(29)

The first order constant for the transformation of HR is therefore ?ri‘[Bi]/Ki’ which is experimentally indistinguishable from ~i[Bi]

1 i

i

found in case iiia. The reaction thus appears experimentally as a general basic catalysis of HR, though the rate is in fact determined by proton transfers from acid catalysts to the ion R-. of the ions R- formed (iiic) k z k-1. Only a fraction kz/(lcz iLl) from HR is transformed into RH, and the first order velocity constant is

-

+

180

R. P. BELL

If only a single acid-base pair has any catalytic effect klkz/(kz+ L1). we can write

ki

=

r[B], k2 = r’[A],

k-i = r ” [ A ]

and hence for the observed velocity constant

which is indistinguishable from the results of iiia or iiiib. However, the matter is more complicated if several acid-base pairs axe effective simultaneously. We shall then have

giving k =

2

’

ri‘[Ail

i

+ 2 ait’[Ail *

i

This expression can only be simplified if it is possible to write

where /3 is the same for all catalyzing acids. Equation (31) then becomes

which again corresponds to the usual Iaw for general basic catalysis. However, there is no reason why (32) should be generally valid, especially for catalysts of widely differing strength or structure. When (32) fails, the reaction will show the qualitative characteristics of basic catalysis of HR, but will not follow the usual quantitative laws. In particular, the effect of several basic catalysts present simultaneously will not be additive. There is no clear evidence that this behavior haa been encountered in practice, though it may account for the kinetic anomalies observed in some reactions (King, 83; King and Bolinger, 84). Similar considerations apply to acid-catalyzed prototropy, the analogous scheme for the transformation being HX.Y:Z

+A

{HT*y:in) + HX :v.ZH

lj

1

(34)

181

ACID-BASE CATALYSIS A N D MOLECULAR STRUCTURE

In this case, however, the representation of the intermediate ion by a hybrid structure is not always correct. For example, in keto-enol

l l + I

tautomerism [cf. Eq. (lo)] the cation can only be written as HC.C:OH, since the alternative form would give carbon a covalency of five. In the

I l l I I

I l l I I

so-called three-carbon tautomerism, H C C : C S C: GCH, and the Schiff

I

l

l

1

base isomerism, HC*N:C G? C:N.CH, neither form shown in (34) is , I I I I I

I l l

allowable, and the actual structures of the cations must be H C . C C H

I

/ + I

1

and H C - N C H respectively, with a sextet of electrons on the central

l + l

atoms. The formulation given in (34) is correct only when the atoms X and Z each have an unshared pair of electrons in their normal valency

I 1

I I

state, e.g., in the tautomerism of the amides, H N C :0 s N :G O B , the

I 1

I 1 +

cation can be written as HN :C.OH or H N C :OH. In either event (34) can be abbreviated as HR

ki k-1

(HRH)+

kz k-2

+

RH

(35)

by analogy with (28)) and the further treatment is exactly analogous. If we again assume that the concentration of (HRH)+ is always small, and that the formation of R H is irreversible, our conclusions can be stated briefly as follows. If k , >> k-1 the rate is determined by proton transfers from acid catalyst species to the molecule HR. If k z << k-l the ion (HRH)+ is throughout in equilibrium with HR, and the rate is determined by proton transfers from this ion to basic catalyst species. In either case general acid catalysis of HR will be observed. If k z k M 1 the rate is determined by both of the consecutive reactions, and the effect of several catalysts acting simultaneously may not be additive. The results of the above analysis of reactions involving two proton transfers may be compared with those for reactions in which only a single transfer is kinetically relevant (Sec. III.3.a). For a single transfer the existence of an equilibrium between catalyst and substrate always produces the appearance of specific catalysis by hydrogen or hydroxyl ions, and the detection of general acid-base catalysis therefore excludes

-

182

R. P. BELL

the existence of such an equilibrium. This is not the case when two proton transfers are involved, since here the existence of .B preequilibrium does not affect the observation of general catalysis by acids or bases. It is easy to show that the observation of a quantitative :relation between catalytic effect and acid-base strength is similarly unaffected. For example, consider case iiib above, where there is preequilibrium between the substrate R H and the basic catalyst Bi, the rate being determined by proton transfers between R- and the acid A;. From (29), the catalytic constant observed for the base Bi will be rjl/K,', where IG' is the equilibrium constant [Bi][HR]/[Ai][R-].Ki' is equal to Ki/KH Rl where K, and K H Rare the acid dissociation constants of Ai and HR, and ri' will be related to Ki by an expression of the form ril = GKp, where G is the same for a series of similar acids and a is less than unity. The observed catalytic constant for the base Bi is therefore equal t o GKHR(l/Ki)l-a, and since KHR is the same for a series of catalysts this is exactly the same as the relation normally found between catalytic power and acid-base strength [cf. Eq. (9)]. c. Kinetic Mechanism in Nonaqueous Solvents. The analysis given in the two preceding sections will apply in principle not only to aqueous solutions but also to those in similar solvents such as the alcohols, though its application in practice would be more difficult because of our incomplete knowledge of acid-base equilibria in solvents other than water. The position is different] however, in the so-called aprotic solvents (cf. Sec. 11.3) which are devoid of both acidic and basic properties. In the first place the solutions contain no analogues of the hydrogen or hydroxyl ion, so that there is no meaning in speaking of' specific catalysis by these ions, and in the second place the strengths of acids and bases can no longer be defined by the usual dissociation constants] which involve reference to a reaction with the solvent. Consider acid catalysis of a reaction involving only a single proton transfer, which we can write as S

+ Ai k-1ki

SH+-+ X ka

SH+

+ Bi-

I

We shall assume that the amount of SH+ present is throughout much smaller than [S] or [Ail. If the first step is rate determining] then the reaction will be first order with respect to both catalyst and substrate, with a catalytic constant depending on the nature of Ai. It is reasonable to suppose that, for a series of similar catalysts the catalytic constants will run parallel with their acid strengths, but since acids do not dissociate in the aprotic solvents being considered, some other reaction must be

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

183

used. This may be either reaction with a standard base (e.g., an indicator) in the solvent being considered, or dissociation in some other solvent (usually water) possessing basic properties. Experience shows that the relative strengths found for a Aeries of acids are approximately independent of the solvent, and either method may therefore be used for comparison with the catalytic effect. If the second step (b) is rate determining, the rate is proportional t o the concentration of SHf, which is governed by the equilibrium [SH+][Bi-]/[S][Ai] = Ki. In contrast with aqueous solutions, [Bi-] is not now determined by the reaction of A; with the solvent. If none of the base Bi- has been added, and if the reaction product X has no basic properties, then Bi- can be formed only by the reaction of Ai with s, and we have [ B i ] = [SH+]. Under these conditions the reaction velocity will be proportional to [S]’*[Ai]’, i.e., the reaction will no longer be first order. This result will be modified if the product X has some basic properties, but we shall not pursue the various possibilities, as it is doubtful whether they have been encountered in practice. The position is simpler if two proton transfers are involved. For example, consider an acid-catalyzed prototropic change, proceeding according to the scheme HR

+ Ai

ki k-1

(HRH)+

+ Bid+

ki

RH

+ Ai

(37)

assuming as usual that the concentration of (HRH)+ is always small, and that the formation of R H is irreversible. If the first step (a) is rate determining, we shall have general acid catalysis following the usual laws. If (a) is in equilibrium and (b) rate determining, then the velocity will be proportional to [HRH+][Bi-], and hence by the law of mass action t o [HR][Ai]. The reaction thus again shows general acid catalysis with normal kinetics, and (as in aqueous solution) the question of whether (a) or (b) is the rate-determining step cannot be directly decided from kinetics. In the above treatment it has been assumed that the ions (HRH)+ and B; exist in the free state, as they undoubtedly do in aqueous solution. However, solvents which are aprotic, e.g., hydrocarbons, normally have such low dielectric constants that the majority of ions present will exist at least as i9n pairs, and partly as larger aggregates. This circumstance may well affect the kinetics. For a reaction involving only a single proton transfer the concentration of ion pair will be directly proportional to the concentrations of catalyst and substrate, so that the kinetics will be simpler than when free ions are present. On the other hand, in reactions involving two proton transfers, if the first product of

184

R. P. BELL

reaction between HR and Ai is the ion pair (HRH)+(B,)-, there are several possibilities for the subsequent reaction. If the second proton transfer to give R H and A, can take place within this ion pair, then we shall still observe normal kinetics, as described in the last paragraph. However, it may well be that the orientation of the components in the ion pair is unsuitable for the formation of RH, and reaction will then be completed only by collision of the ion pair with anothier species, e.g., a second ion pair or a second molecule of HR. This will obviously lead t o more complex kinetics. To sum up, acid-base catalysis may often follow normal kinetics in nonaqueous solvents, which may then be used for investigating reaction mechanisms in the ordinary way. On the other hand, more complicated kinetics may sometimes occur, especially in aprotic solvents, and caution must be exercised in drawing conclusions without investigating the kinetic behavior experimentally. d. The Use of Deuterium in Determining Kinetic .Mechanisms. We have already seen (Sec. III.2.a) that observations on the rate of hydrogendeuterium exchange can be used to elucidate the mechanism of other chemical processes. It is also possible t o obtain useful information by studying the velocity of a catalyzed reaction when the hydrogen in the catalyst or the substrate (or both) is replaced by deuterium. From a theoretical point of view it is certain that the transfer of a deuteron will always take place more slowly than the transfer of a proton, because of the higher zero point energy in the link containing the lighter isotope. On the other hand, if there is a pre-equilibrium such as S H30+$ SH+ HzO, the effect of isotopic mass will involve the relative values of the two constants KH = [H3O+][S]/[SH+]and KD =- [D3O+J[S]/[SD+], i.e., the dissociation constants of the acids SH+ and SD+. It is not possible to predict the relative magnitudes of KH and KD on theoretical grounds, but experiment has shown that in aqueous solution KH > KD. This means that under comparable conditions the con centration of SD+ will be greater than that of SH+, and the pre-equilibrium will therefore tend to make the deuterium compound react faster than the hydrogen one. Examples are in fact known of both kD/kE> 1 and kD/kH < 1, where kE and kD are the velocity constants for the hydrogen and deuterium compounds respectively. If b e find experimentally kD > kH in a catalyzed reaction, then an acid-base equilibrium must always be involved in the kinetic scheme, If the reaction involves only one proton transfer, then the converse is also true for catalysis by hydrogen ions, i.e., if k H > h D , then there is no pre-equilibrium. On the other hand, in a reaction involving two successive proton transfers the pre-equilibrium and the subsequent proton

+

+

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

185

transfer may be affected in opposite directions by isotopic substitution, SO that the observation that kH > kD does not indicate whether or not there is a pre-equilibrium. The isotope effect is therefore not so helpful as was at one time supposed in elucidating kinetic mechanisms, but examples will be given in the next section of how it can be used in conjunction with other data. It is also possible in principle to obtain information by studying rates in a series of solvents varying in isotopic composition from 100% HzO to 100% DzO, but the method is not a sensitive one and there has been some difference of opinion about the interpretation of the results (Gross, Steiner, and Suess, 85; Orr and Butler, 86; Nelson and Butler, 87; Brescia and La Mer, 88; Brescia, 89; WynneJones, 90; Gross, 91; Reitz, 92; Hamill and La Mer, 93). e. Examples of Kinetic Analysis. The preceding paragraphs have given in some detail the possibilities which exist for determining the nature of the rate-determining step when the mechanism is qualitatively established. There are not many cases where such an analysis has been carried through in practice, and in this section we shall give only a few examples in which the conclusions are fairly well established. In the halogenation of ketones and allied reactions (e.g., isotope exchange, racemization) we have seen in Sec. III.2.a that a distinction must be made between acid and base catalysis. In catalysis by bases the reactive species is the anion formed in the first step of the reaction, and the reaction thus involves only a single proton transfer. The independence of halogen concentration and the identity of rates of halogenation, racemization and isotope exchange prove that this proton transfer is rate determining. This conclusion is borne out by the fact that all these reactions exhibit general basic catalysis and is consonant with the fact that kH > k D for catalysis by acetate ions (Wilson, 94). I n acid catalysis, on the other hand, the above reactions depend upon the actual formation of the enol, involving two successive proton transfers. There is good reason to believe that the first step,

\ / \ /* CH.C:O + A + CH.C:OH / /

+B

is in equilibrium, the subsequent removal of a proton from the action being rate determining. This is most convincingly shown by the isotope effect, where kD > k , for hydrogen ion catalysis (Reitz, 94a), showing the existence of a preequilibrium. Further it is found that the addition of acids t o optically active ketones in nonaqueous solvents causes an instantaneous change of rotation, followed by a slow racemization. The instantaneous change is presumably due to reaction (38), and this view

186

R. P. BELL

receives confirmation from cryoscopic studies (Bell and Caldin, 95; Bell, Lidwell, and Wright, 96). Indirect evidence on the same point comes from a comparison of the rates of acid-catalyzed halogenation for a series of ketones. If (38) were rate determining, there should be a parallelism between the reaction velocity and the basic strength of the ketone. If, on the other hand, (38) is in equilibrium, this parallelism may be absent, since the second step of the reaction involves the removal of a proton from a different part of the molecule. Hammett and his co-workers have measured the relative basic strengths of a number of substituted acetophenones by observing their ultraviolet absorption spectra in sulfuric acid-water mixtures (Flexser, Dingwall, and Hammett, 97 ; Flexser and Hammett, 98) and have also measured the rates of halogenation of the same ketones under acid conditions (Zucker and Harnmett, 99). No parallelism was found between the two sets of measurements again confirming the view that reaction (38) is in equilibrium. If it is possible to measure the actual rate of formation of an enol from its keto isomer (or vice versa), then of course two successive proton transfers are involved in catalysis by both acids and bases. It is rarely feasible to study this interconversion directly, but it is sometimes possible to obtain indirect evidence about its kinetics. The typical scheme for the base-catalyzed conversion of keto to enol is

\ / / \ / C:C.OH + B C H C : O + l3z \C:C.O- + A + / k-i / kl / where we assume that the enol is removed as soon as it is formed. If the ketonic substance is a sufficiently strong acid, it will be possible to prepare a solution in which it is chiefly present as the anion. If this solution is acidified, the anion will be converted into keto and enol in the proportion k-l:kz. This experiment has been carried out with acetoacetic ester (Pedersen, 100) where the product of acidification is 100% enol, i.e., in this case kz>> k-I. This means that practically every anion formed is converted into enol, and the rate of enolization by bases will be identical with the rate of ionization (or halogenation). This result contrasts with that obtained for a Substance of similar constitution, the menthyl ester of a-phenylacetoacetic: acid. By comparing the rates of mutarotation and enolization of this substance, catalyzed by a solution of piperidine in hexane, Kimball (101) concluded that for every anion which goes on to form enol, approximately two revert to the keto form. There is no obvious explanation of this difference between two apparently similar compounds, but it may be that the interpretation of the data in hexane solution is invalidated by some of the kinetic complications described in the preceding section.

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

187

It is also possible to draw some conclusions about the detailed kinetics of the aldol condensation, which also goes by way of the anion of an aldehyde or ketone. We shall assume that the sequence of reactions is that given in Eq. (12). The condensation of two molecules of acetaldehyde to acetaldol in presence of hydroxyl ions is, surprisingly, of the first order with respect t o aldehyde (Bell, 102), demonstrating that the first step (a) must be rate determining, followed by two faster steps, (b) and (c). This means that the reaction should in principle exhibit general basic catalysis, but this has not been detected experimentally. There are no direct kinetic observations on the condensation of acetone to diacetone alcohol, but the reverse depolymerization reaction is well known to be of the first order, so that the condensation reaction must be of the second order in acetone. This suggests that for this substance reaction (a) is in equilibrium, with reaction (b) as the probable rate-determining step. Under these conditions the reaction should exhibit specific catalysis by hydroxyl ions, as is in fact observed, the catalysis exerted by amine molecules depending on a different mechanism (Westheimer and Cohen, 103; Westheimer, 104; Westheimer and Jones, 105). Further evidence comes from a study of the rate of deuterium interchange with acetone (Walters and Bonhoeffer, 40). The rate of Condensation of two acetone molecules can be calculated from the known rate of depolymerization of diacetone alcohol, and the measured equilibrium constant. I t is found to be very much slower than the observed rate of isotope interchange. Since interchange will take place every time the anion is formed, this result supports the view that in the condensation reaction (a) is in equilibrium, the rate being determined by the slower reaction (b). There is less evidence available for the reuersible addition of hydroxy compounds to the carbonyl group (cf. Sec. III.2.c). If we accept the mechanism in Eq. (16), it is likely that the reactions on the left are in equilibrium both for acid and base catalysis, since they represent simple protolytic reactions with no change of bond structure (cf. the discussion in Sec. V.2). The only reaction of this class for which the isotope effect has been investigated is the mutarotation of glucose (Pacsu, 106; Moelwyn-Hughes, Klar, and Bonhoeffer, 107 ; Moelwyn-Hughes, 108; Hamill and La Mer, 109). It is found that deuterium substitution causes a decrease in velocity for catalysis by water, acetate ion and hydrogen ion, but we have just seen that in a reaction involving two proton transfers this does not exclude the possibility of a preequilibrium. There are two instances in which the value of kD/kHdepends upon the conditions under which a reaction is carried out. In the acid-catalyzed hydrolysis of ethyl orthocarbonate Wynne-Jones (110) finds kD/k, > 1 for catalysis by hydrogen ions, but k,/k, < 1 for catalysis by acetic acid.

188

R. P. BELL

Wynne-Jones takes this to mean that preequilibrium is set up in hydrogen ion catalysis, but not in catalysis by acetic acid; however, another explanation seems preferable. In hydrogen ion catalysis the value of ko/ka depends upon the ratio of the two equilibrium constants, [SU+]/ [S][D,O+]and [SH+]/[H30+][S],which is normally greater than unity. For catalysis by acetic acid the corresponding equilibrium constant is [SH+][CH3COO-]/[S][CH3COOH],which may be written as the ratio of two constants [SH+]/[H30+][S]and [CH3COOH]/[H30+][CH3COO-]. Each of these last two constants will be increased by replacing hydrogen by deuterium, and their ratio may well decrease, leading to k D / k H< 1. The other example is the hydrolysis of acetarnick in slolutions of strong acids, where it has been found that k D / k H= 1.50 in 0.1 N acid, 1.00 in 2.3 N acid, and 0.86 in 4.0 N acid (Reitz, 111,112). This accords excellently with the conclusions reached in Sec. III.:3.a, according to

+

which a large proportion of the acetamide is present as the ion CH3CONH3 in the strongly acid solutions. In the more dilute solutions the value kD/kH > 1 depends upon the greater proportion of acetamide converted t o cation in the deuterium system. In concentrated mid, on the other hand, most of the acetamide will be present as cation in both systems, and kD/k,

+

< 1 because the ion CHICOND3 reacts +

further more slowly

than CH3CONH3. f. The Question of Ternary Mechanisms. In all the above treatment it has been assumed that when two proton transfers occur they do so successively in two distinct steps. It is equally possible to imagine that both transfers take place simultaneously by the approach of an acid and a base to different parts of the reacting molecule; for example, in a prototropic change HX*Y:Z -+ X :Y.ZH the reaction would be

Such a mechanism has been advanced many times (Lowry and Faulkner, 113; Lowry, 114) but has not generally been accepted. However, recent work has shown that some of the arguments advanced against it are of questionable validity, and we shall therefore discuss t'he question here. The kinetic consequence of a ternary mechanism is t8hatin any mixture of acids and bases the reaction velocity should be given by an expression of the form

ACID-BASE CATALYSIS A N D MOLECULAR STRUCTURE

189

instead of the usual expression

which we have shown to follow from the assumption of two consecutive proton transfers. In the ternary mechanism there is no distinction between acid and base catalysis, and any acid can cooperate with any base in the “push-pull” mechanism represented by Eq. (39). However in water or a similar solvent it is not easy to distinguish experimentally between (40) and (41), since a large proportion of the observed velocity will be due to terms in which the solvent (present in high and constant concentration) is acting either as the acidic or as the basic partner. There is in fact only one set of data in aqueous solution which appears to show the existence of a ternary term. Dawson and Spivey (115) found that the rate of iodination of acetone in acetic acid-acetate buffers could be represented by the expression 10% = 0.006

+ 560[H30f] + 7 X 1OB[OH-]+ 1.3[CHaCOOH] + 3.3[CH3C00-] + 3.5[CH3COOH][CH3COO-]

(42)

The quantitative interpretation of the data may be open to some doubt, since the experiments were carried out at high and variable ionic strengths, but the existence of a measurable contribution from the last term in (42) is probably established. Nevertheless, it has been usually held that the reaction cannot go exclusively or even chiefly by a ternary mechanism, using the following argument due to Pedersen (116). Omitting the terms in [HaO+] and [OH-], the remaining terms of (42) will be represented as follows on the ternary scheme: (a) (b) (c)

(4

Acid HzO HAc

Base

+ acetone + HzO + acetone + HzO H 2 0 + acetone + AcHAc + acetone + Ac-

Relative Velocity 0.006 1.3 3.3 3.5

By comparing (a) and (b) it will be seen that on changing the acid from HzO to HAc (the base being in each case H20) the rate is increased by a factor of 220. We should therefore expect a similar increase in going from (c) to (d), where the acid again changes from HzO to HAc and the base is in both cases Ac-. The observed value for reaction (d) thus appears to be 200 times smaller than might be expected on the termolecular hypothesis. However, it has been recently shown by Swain (117) that the above criticism of the termolecular picture is not valid. He points out that there is an ambiguity in interpreting the fourth and fifth terms of Eq. (42)

190

R. P. BELL

on the termolecular hypothesis. Because of the dissociation equilibria of acetic acid and water it is impossible to distinguish kinetically between HzO and H30+ acetone Ac-, or the systems HAc acetone between Acacetone H20 and OHacetone -4- HAc. Swain makes the reasonable assumption that the relative reactivities of different acids are independent of the base with which they cooperate (and similarly for different bases); i.e., that Eq. (40) can be rewritten as

+

+

+

+

+

+

+

thus reducing the number of constants. On this basis it can be shown that on the ternary hypothesis the term 3.3[Ac-] in (42) arises mainly acetone HAc, and not from Acacetone from the reaction OHHzO. Under these conditions the above criticism of the ternary mechanism is no longer valid, and it can in fact be shown that the term in [Ac-][HAc] corresponds within a factor of two to the predictions of (43). Swain has also shown that the corresponding term would not be detectable experimentally in the mutarotation of glucose. Less direct support for a ternary mechanism come:3 from measurements by Ingold and his collaborators (118,119) on the base-catalyzed interconversion of azomethines in alcoholic solution. It was possible to measure both the rate of racemization of one isomer and its rate of conversion to the other isomer. These two rates were found to be equal. If the mechanism involved the formation of a free anion, the rate of racemization should be greater than that of conversion, since the known position of equilibrium shows that an appreciable fraction of the anions would revert to the original compound instead of going on to form the isomer. The experimental findings thus suggest that rto kinetically free anion is formed, and support a ternary mechanism for this reaction. It should in principle be easier to test the ternary hypothesis when there is not present a constant excess of acidic or basic solvent molecules, i.e., by using solutions of acids and bases in inert solvents. There are very few experiments of this kind, but an observation which is often quoted in favor of a ternary mechanism is that of Lovvry and Richards (120), who found that the mutarotation of tetramethylglucose took place very slowly in dry pyridine (possessing no acid properties) or in dry cresol (possessing hardly any basic properties), but was rapid in a mixture of the two solvents, or in either solvent when moist. This observation shows that the reaction is facilitated by the simultaneous presence of an acidic and a basic substance, and can readily be interpreted in terms of the ternary picture.

+

+

+

+

ACID-BASE

CATALYSIS AND MOLECULAR STRUCTURE

191

However, in spite of these various pieces of evidence in favor of a ternary mechanism, it is doubtful whether it can be accepted as valid for acid-base catalysis in general, as there are a number of arguments in the reverse direction. Although further work on the acetone-iodine reaction (Bell and Jones, 120a) has confirmed the magnitude of the term in [HAc][Ac-] found by Dawson and Spivey (115), the same authors show that no product term is detectable in glycollate buffers, although calculation by Swain’s method predicts a much larger contribution than in acetate buffers. Further evidence adverse t o the ternary mechanism comes from a study of the hydration of acetaldehyde, a reaction which is chemically very similarly to the mutarotation of glucose (cf. Sec. III.2.c). Bell and Clunie (121a) failed to detect any product term in a kinetic study of this reaction, even under conditions where Swain’s treatment predicts that 75% of the total velocity should derive from such a term. In nonaqueous media, it is difficult to interpret with certainty the observation of Lowry and Richards (120), since such drastic changes of medium are involved in going from pure pyridine to pure cresol. Other observations on acid-base catalysis in nonaqueous solvents speak against the ternary hypothesis. The interconversion of the two forms of mesityl oxide oxalic ester (an example of ring-chain tautomerism) in the aprotic solvent chlorobenzene is catalyzed by dilute solutions of acids or bases, but the velocity in a solution containing both acid and base is no greater than the sum of the velocities due to the acid and the base separately (Bell and Rybicka, 121). This result is in direct contrast to that obtained by Lowry and Richards for the mutarotation of tetramethylglucose, and the system studied by Bell and Rybicka has the advantage that dilute solutions in the same solvent were used throughout, showing definitely that the ternary hypothesis cannot apply to their reaction. The same conclusion may be drawn from the fact that solutions of acids or bases alone in aprotic solvents frequently show a reproducible catalytic effect with simple kinetics. In conclusion it should be pointed out that the ternary picture cannot be dismissed merely on the grounds that a triple collision is an improbable event. Exactly the same result is achieved kinetically if two of the molecules concerned associate together loosely (e.g., by hydrogen bonding) before the approach of the third. Although the modern tendency is to split up complex reactions into consecutive bimolecular steps (Hinshelwood, 122) there appear to be cases in which this cannot be done (Bell and Darwent, S l ) , and the ternary hypothesis must certainly be considered as one of the possible mechanisms for reactions catalyzed by acids and bases.

192

R. P. BELL

IV. THEVELOCITY OF ACID-BASEREACTIONS 1. Pseudo-Acids and Pseudo-Bases

I n the preceding sections we have frequently postulated reactions which take place a t a measurable speed, which are formally acid-base reactions involving the transfer of a proton from one molecule t o another. Since such reactions are commonly thought of as being very fast, we must examine how far the idea of acid-base reactions of measurable speed is consistent with information outside th e field of acid-base catalysis. It is common experience that many acid-base reactions (e.g., dissociation, hydrolysis, neutralization) take place too rapidly to be followed by ordinary methods, even when very weak acids and bases are involved. However, a few instances are known in which a slow reaction can be observed, the best known of which is th e reaction of nitroparaffins with hydroxyl ions. For example, nitromethane, CHaN02, is neutralized at a measurable speed by hydroxyl ions t o given an anion whose structure 0-

+/

is presumably CH2:N

\

.

This phenomenon was discovered by

0Hantzsch (123), who introduced the term pseudo-acid to describe th e nitroparaffins and similar substances. Hantzsch supposed that the slow change was t he transformation of the nitroparaffin into the aci form, e.g., OH

+/

CH2:N

\

,

which then reacted rapidly with hydroxyl ions.

How-

0ever, we have already seen (cf. Sec. III.2.b) that the interconversion of two tautomers of this kind is now believed to involve the anion as a n intermediate, and we should now regard the actual loss of a proton from the methyl group to the hydroxyl ion as a slow process. A similar reaction has been investigated recently by Lewis and Seaborg (124). The substance tri-(p-nitropheny1)-methane reacts with sodium ethoxide t o give a colored anion with the structure

-

0

-/ \ d = ~ =c(p.C,H,No*). 0

in which the negative charge will be equally distributed between th e three nitro groups. If this alcoholic solution is acidified at -80" with

ACID-BASE

CATALYSIS AND MOLECULAR STRUCTURE

193

various weak acids, the color changes at a measurable rate owing to the slow regeneration of the original compound. This case is of particular interest, since there is an approximate correlation between the rate of reaction (which was not measured accurately) and the strength of the acid used for neutralization, showing an obvious analogy with Bronsted’s relation between catalytic power and acid-base strength (cf. Sec. 11.4).* In the examples quoted above there is a considerable difference in electronic structure between the pseudo-acid and its anion, and it may be surmised that the relative slowness of the reactions observed is connected with this electronic reorganization. The change in electronic structure is also associated with a change in absorption spectrum, and Hantzsch has proposed that this latter change should be used as a criterion for pseudo-acids. On the basis of slight optical changes on ionization he has concluded (126,127,128) that almost all acids (e.g., halogen hydrides, nitric acid, sulfuric acid, carboxylic acids) are pseudo-acids, but his interpretation has been challenged by a number of authors (Fajans, 129; von Halban, 130; Ley and Hunecke, 131). I n any case, such a wide extension of the term would destroy its usefulness, and it is best to reserve it for the more extreme types of behavior, though we shall see later that it is impossible to draw any sharp line of demarcation between pseudo-acids and “true ” acids. In many instances it is not practicable to investigate directly acidbase reactions of the ordinary type, since if very weak acids or bases are involved the extent of reaction is very small. Under these conditions measurements of rates of racemization or of deuterium exchange may serve as an indirect method of measuring rates of ionization. For example, hydrogen attached to the a-carbon atom of ketones, carboxylic acids, esters, nitriles, and similar substances exchanges very slowly (if a t all) in neutral aqueous solution, but a t a measurable speed in presence of hydroxyl ions (Bonhoeffer, 132). Although the amount of anion present is very small, even in strongly alkaline solution, the rate of H-D exchange can be used to measure the rate of its formation. Similarly, the rate of C6Hs racemization of the ion

\ CDCOO/

in alkaline solut,ion is

CH3CsH4 equal to its rate of isotope exchange (Ives and Wilks, 133), both rates being determined by ionization at the asymmetric carbon atom.

* Lewis and Seaborg (124) give a different and more complicated explanation of the observed facts, but there are good arguments for rejecting their interpretation (cf. Kilpatrick, 125).

194

R. P. BELL

All the instances of slow acid-base reactions mentioned so far involve a considerable structural change in one of the acid-base pairs taking part in the reaction. This statement rests partly on theoretical considerations (notably the improbability of structures with a charge on a carbon atom), and partly on direct observations of the change in absorption spectrum accompanying the reaction. These reactions are of exactly the same type as those occurring in the schemes proposed.in Sec. 111.2 for various acid-base catalyzed reactions, and the behavior of pseudo-acids thus supports the conclusions already reached about these mechanisms. In catalyzed reactions involving two steps it is frequently the case that one of these involves a structural change and the other does not. For example, in the acid-catalyzed prototropy of ketones

\ / CH*C:O + HA /

\

A

CH*C:OH

+ A-

/ \ / -+ C:C.OH + H A /

(b)

step (a) involves no rearrangement of valencies, while in step (b) there is a shift of the double bond. As we have already seen, there is evidence that the equilibrium (a) is set up rapidly, while (b) is a slow reaction. This again accords with the picture of pseudo-acids given above. In extreme cases the valency rearrangement may involve the break-up of a molecule into two separate pieces, or the reverse process. For example, in the reversible reaction between an aldehyde and a hydroxy compound (cf. Sec. III.2.c) the rate-determining step is believed t o be R-CHO

+ HA + R’*OH

/OH RCH R

+ A--

\O/

and

+H ‘

/ R.CHO + B + R’.OH S R.CH \

OR

+ 13H’

0-

for catalysis by acids and by bases respectively. Although on paper each of these processes can be dissected into two conseciitive bimolecular reactions in a number of ways, closer examination shows that none of these dissections is consonant with the facts (Bell and Darwent, 61).

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

195

The rate-determining steps thus involve simultaneously a proton transfer and a change in the number of molecules, thus showing analogy with the usual picture of a pseudo-acid. The term pseudo-base has been used less widely and less consistently than pseudo-acid. Logically it should be applied t o a species which undergoes a change of structure when it adds on a proton. This would include the anions of the pseudo-acids discussed above, and a few uncharged species such as coloring matters (e.g., anthocyanins and flavones) derived from y-pyrone, where the addition of a proton involves the reaction /CH:CH \ C:O 0

\

/

+ H + e +O/

\

CH: CH

CH.CH

%.OH CH: CH

/

However, the term pseudo-base has been more widely used to describe compounds which can lose a hydroxyl ion with change of structure, and hence undergo slow reactions with acids, which are reversed by the addition of base. Examples are the “carbin01 bases” of various triphenylmethane dyes, such as crystal violet, and derivatives of pyrazine and acridine (Hantzsch and Kalb, 134; Aston, 135, 136). However, this kind of change is not strictly analogous to an ordinary acid-base reaction, and it is probably better not to use the term pseudo-base in this connection. I n any case, processes involving transfer of hydroxyl ions are not believed to play any important part in catalyzed reactions. We have seen that acid-base reactions proceeding a t a measurable rate frequently involve structural changes, but this is not always the case. If an acid-base reaction involves an acid or base which is extremely weak, it will be considerably endothermic in one direction, and the activation energy for reaction in this direction must be at least as great as the endothermicity, independent of any structural factors. For example, acetylene and water do not exchange deuterium under neutral conditions, but do so in presence of a considerable concentration of hydroxyl ions (Reyerson, 137). This process must depend upon the HzO, which does not involve slow reaction CzHz OH- -+ CtHstructural change, but which is presumably markedly endothermic. The same applies to the slow ionization of aliphatic amines in alcohol observed by Ogston (138), where the slow stage may be the ionization of the alcohol itself; similarly, in the zero order halogenation reactions studied by Hughes (139) the rate-determining step is probably the endothermic protolysis HOCl H 3 0 + - +[H20Cl]+ HzO (cf. Bell and Gelles, 140) rather than the production of C1+.

+

+

+

+

196

R . P. BELL

2. The Molecular Interpretation of the Bronsted Relation

If it is accepted that reactions catalyzed by acids or bases involve at some stage a slow acid-base reaction, then the Bronsted relation (cf. Sec. 11.4) assumes a reasonable aspect. The constants used to express the strengths of the catalyzing species are usually defined with reference to an equilibrium with some standard acid-base system such as the solvent, but they could in principle be defined in terms of the (hypothetical) protolytic equilibrium between the catalyst and the substrate. The Bronsted relation then amounts to a parallelism between the rates and equilibrium constants of a series of similar reactions. The general form of the relation can in fact be inferred without rtny reference to a molecular interpretation. Suppose that we have any acid-base equilibrium Ai+Bz=Az+Bi governed by the equilibrium constant [AZI[BII/[AII[BZ]= K

and let the velocities of proton transfer in the two direc.tions be

If K1 and K z are the strength constants of A1 and A2 on any scale, then clearly

=

m,&?,i

K = Ki/Kz

Now let A2, B2 be a fixed acid-base pair (corresponding to the substrate) while A1, B1 varies through a series of substances (catalysts) of increasing acid strength in A, and hence decreasing acid strength in B1. As we pass , increase ~ steadily along the series it is reasonable to suppose that ~ 1 will while 7r2,1 will decrease. Since, however, the ratio ~ 1 , 2 / 7 r 2 , 1 must be proportional to K1, we must suppose that rl,:, increases less rapidly than K1, while r 2 , decreases 1 less rapidly than l/Kl. This inay be expressed by writing d log ~ - d log ~

1

(45)

= g.4z(l/K1)'-a

(46)

= ad log K1 = (1 - m ) d log K I

1 . 2

2 , i

where 1 > a > 0. If a is effectively constant over some range of acid strengths these equations can be integrated to give ~ 1 . 2=

gBZKP,

TZ,I

where gA2and gB2 are characteristic of a given substrate, solvent, and temperature. If the measured reaction velocities are i:n fact determined

ACID-BASE CATALYSIS A N D MOLECULAR STRUCTURE

197

by q 2 or 7r2,1, then these equations are identical with the Bronsted relation as usually expressed. The molecular picture behind this reasoning can be demonstrated by the use of potential energy curves. Subject t o certain reservations (cf. Bell, 3, Chapter VIII) the transfer of a proton can be represented by the passage of a point along the full curves in a diagram like Fig. 1. If the reaction is X H Y X HY, then curve I represents the energy of XH for varying separation of the proton, and I1 is the corresponding curve for HY. E represents the energy of activation for the reaction

+

+

~

\

I

I

DISTANCE OF PROTON

FIG.1.

from left to right, and e is the total energy change for the same reaction. If now the nature of Y is changed a little by chemical substitution, curve I1 will be replaced by a slightly different curve 11', and the new energies of activation and reaction are respectively E' and e'. If the change in Y involves only a vertical displacement of curve I1 and not any change in its shape or horizontal position, then it is clear from the geometry of the figure that 6E

= ci6t

(47)

where a is a quantity less than unity such that a / ( l - a) is the ratio of the slopes of the two curves a t their point of intersection. Equation (47) is clearly equivalent t o (45) if we can write 6 log P =

RTsE,

6 log K = RT6t

(48)

198

R. P. BELL

Equation (48) is of the expected form for relations between reaction velocities and activation energies on the one hand, and between equilibrium constants and heats of reaction on the other. However, there are difficulties in the way of using (48) as a quantitative basis-for the Bronsted relation. In the first place, the quantities E and B in the diagram refer strictly to the behavior of the system at absolute zero r3ince no account is taken of the internal thermal energy of the molecules. In the second place experiment shows that even in a series of similar reactions the observed velocities and equilibrium constants often involve variations in entropies of activation and of reaction, and not only energy changes. These difficulties are not yet fully resolved, but there seems little doubt that diagrams such as Fig. 1 represent the essential molecular basis of the Bronsted relation. This presentation makes clear several additional points arising from such relations. Figure 1 [also Eqs. (44)and (45)] makes no distinction between substrate and catalyst, and we should theref'ore expect t o find (for a given catalyst) relations between the reaction velocity and acidbase strengths of a series of substrates. There is little direct experimental evidence for this, mainly because substrates are iisually such weak acids or bases that the ordinary methods for measuring acid-base strength are not applicable. However, there is limited evidence for the validity of such relations, and it is probably safe to use them for estimating the acid-base strength of very weak substrates. For example, data on the rates of ionization of a series of ketones and similar substances have been used to estimate that acetophenone has an acid dissociation constant in water of about lO-'9, in agreement with estimates based on independent evidence (Bell, 141; McEwen, 142). On the other hand, this parallelism is only present for substrates of closely similar structure, and when comparing substances of different chemical types there may be wide divergencies. For example, acetoacetic ester, and nitromethane have similar acid dissociation constants (2 x 10-l' and 6 >< l O - l l ) , and their rate of halogenation in presence of a basic catalyst is 'believed to depend on the loss of a proton to the catalyst. Nevertheless, the rate of bromination in presence of acetate ions is about 6000 times as great for the ester as it is for the nitroparaffin (Pedersen, 29,42; Reita, 43). The general question of the effect of structure will be treated in Sec. V. 3. Statistical Efects The velocities of proton transfer in a series of similar acid-base systems may be affected by purely statistical features, and when this is the case some modification is necessary in the simple Bronsted relations expressed by Eq. (46). The point can be best explained by means of

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

199

an example. Suppose that we have as catalyst a carboxylic acid CH, (CHz),COOH whose catalytic effect is given by the equation k~ = GAKA"

(49)

and that we wish to compare with it a dibasic acid COOH (CH2),COOH, where n is so great that the mutual effect of the carboxyl groups is negligible. The tendency of the carboxyl groups t o lose a proton will be essentially the same in the two acids, but the first dissociation constant of the dibasic acid (KA')will be twice as great the monobasic acid ( K A ) , since the ion COOH-(CHz);COO- can be formed by losing a proton from either end of the chain. Similarly, the catalytic effect of the dibasic acid (kA') will be twice as great as that of the monobasic acid, since in the former case the substrate molecule can approach either end of the acid molecule. This is not, however, what is predicted by Eq. (49) as it stands, which gives ka'lka = (KA'/KA)"= P The error can be removed if we reckon both the acid strength and the catalytic power per carboxyl group, giving the observed result ik~'= GA(+KA')== GAKA" = k A

A simila'r problem arises if we compare the two acids and where again n is great. In this case the tendency to lose a proton from the carboxyl group (and hence the catalytic power) will be the same for two acids. On the other hand, the dissociation constant of (I) will be only half that of (11),since the conjugate base COO-.(CHz);COO- has two equivalent points at which a proton can be added, while COO-. (CH2),*COOCH3 has only one such point. Here again the straightforward use of Eq. (49) will not predict correctly the observed catalytic behavior, and for the acid I it is necessary to multiply the observed dissociation constant by two before inserting it in Eq. (49). These arguments can easily be generalized. Thus if we have a conjugate acid-base pair A-B in which A has p dissociable protons bound equally firmly, while B has q equivalent points at which a proton can be attached, then the catalytic power of A is related to its acid strength by the equation

200

R. P. BELL

A similar treatment for basic catalysis by B gives

Analogous equations can be developed (Westheimer, 143) for the case in which the various protons or points of attachment are not all equivalent, though it is then necessary t o know the relative tendencies of losing or gaining a proton at the different points. The idea of a statistical correction was originally put forward in an incomplete form by Bronsted and Pedersen (15) and later stated correctly by Bronsted (144). Although it is undoubtedly correct in principle, there is very little experimental evidence which can be quoted in support of it, almost the only clear-cut example being the catalysis of the nitramide decomposition by the anions of polycarboxylic acids (Bronsted and Pedersen, 15). I n the majority of cases various ambiguities arise in determining the correct values of p and q t o use in Eqs. (50) and (51). It is often doubtful whether several protons attached t o the same atom should be reckoned independently or not, e.g., is it correct t o take p = 4 for the acid NH4+? The hydrogen atoms are so close together t h a t the chance of proton transfer on collision is probably less than four times the chance for an analogous ion containing only one hydrogen atom. I n any case, the concept of a n analogous ion is a somewhat nebulous one, since in a system of this kind it is impossible t o substitute some of the hydrogen atoms by other groups without affecting the nature of the remaining hydrogens. Difficulties also arise in deciding upon the correct values of q, and are often related t o the particular views as t o the electronic structure of the species concerned. For example, if the structure 0 of the carboxylate ion is written as -C

// , we should have q \

=

1, but

0-

the mesomeric formulation with the charge shared equally between the two oxygens would suggest q = 2. Similar problems arise in the ions of oxy acids such as HsPOd and H2S04. The mesomeric structures for these ions are presumabIy the correct ones, but it is again doubtful how far oxygen atoms attached t o the same central atom can be regarded as kinetically independent. It is difficult t o subject any of these points t o experimental test, since (as we shall see in Sec. V) the presence of mesomerism is likely t o cause deviations from the Bronsted relation much greater than those depending upon statistical corrections. The above considerations have been applied t o iche comparison of different catalysts, but are also relevant in the comparison of differ-

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

20 1

ent substrates. For example, in comparing reactions of the ketones CHBCOCH3 and C6HBCOCH3,we must take into account the different numbers of methyl groups. The same difficulties arise in considering several protons bound to the same atom, e.g., in comparing the groups

-CH3,

\ \ CH2, and -CH, / /

though these ambiguities are frequently of

minor importance compared with the large effects which can be produced by chemical substitution.

V. THE IMPORTANCE OF MOLECULAR STRUCTURE 1.

The Structure of the Substrate

The variation of velocity in a series of similar substrates will be related t o their acid-base properties, and there are some instances in which kinetic measurements represent the only experimental approach t o these properties, e.g., when dealing with acids or bases which are so weak that no equilibrium measurements are feasible. For very weak bases equilibrium measurements often become possible if a solvent of sufficiently high acidity is employed, but for very weak acids no analogous strongly basic solvents are available, and rate measurements (e.g., of base-catalyzed deuterium exchange or halogenation) represent the only method of comparing acidities. Data of this kind can thus be used for testing theoretical predictions about the effect of chemical structure on acidity. As an illustration, Table I shows data for the base-catalyzed halogenation of a number of ketones and similar substances. I n this table, R is the catalytic constant (in liters/mole/minute) of the anion of a hypothetical acid of dissociation constant obtained by interpolating data for carboxylate anions. In computing R a statistical correction has been made for the number of equivalent hydrogen atoms in the substrate, counting as independent atoms attached t o the same carbon. 0 is the exponent in Eq. (51). The last column of Table I contains values for the pK of the substrate in water, estimated from the kinetic data. The range of velocities covered is very wide (about lo9), and the value of p shows a steady decrease as the rate increases. In integrating the relation d log R = pd log K , it is therefore not allowable to take ,f3 as a constant, and the usual Bronsted equation [cf. Eq. (51)] must be replaced by log K , =

1f

d log R

+A

where A is an inteqation constant and p is now a function of R.

(52)

The

202

R. P. BELL

values of pK, in Table I are derived from this equation, the value of A being obtained by using the directly measured value pK, = 10.5 for acetoacetic ester. Values of pK, have also been measured directly for acetylacetone (pK, = 8.9) and for benzoylacetone (pK, = 9.4), in fair agreement with the table. It is difficult to check the values for the very weak acids a t the top of the table, but fortunately McEwen (142) has TABLE I Substrate

logio R

P

PK*

CHsCOCHs CHsCOCeHs CHsCOCHzCHzCOCHo CHsCOCHzCl CH3COCH2Br CHsCOCHClz CHZCOCHCOOCzHr ‘(CH213CH3COCHzCOOCzH6 CHzCOCHCOOCiHs 4CH2&CHsCOCH2COCeHa CH3COCHBrCOCaHh CH&OCHBrCOOCzHs CH3COCHzCOCHs CH~COCHB~COCHI

-6.78 -6.07 -5.46 -3.51 -3.25 +2.00 -0.98

0.88 0.89 0.82 0.82 0.82 0.64

20.0 19.2 18.7 16.5 16.1 14.9 13.1

+0.72 +1.18

0.59 0.58

10.5 10.0

+1.33 +1.33 +1.35 +1.54 +2.04

0.52 0.52 0.48 0.42

9.7 9.7 9.7 9.3 8.3

I

I

~~~~~

~

Source

a

d

~~

Bell and Lidwell, 30. * Bell. 141. c Bell and Goldsmith, 145.

Bell, Smith, and Woodward. 146. Bell, Gelles, and Molbsr, 147.

4

estimated the acid strength of acetophenone by a series of displacement reactions and finds pK = 19, in excellent agreement with our value of 19.2. Neither value would be expected t o be more certain than a power of ten, but the agreement strengthens our confidence in the general method employed in estimating K,. The values of K , thus derived can in many cases be interpreted in terms of molecular structure. The increase in acidity (- 4 pK units) produced by introducing a halogen atom into acetone can be classified as an inductive effect, depending upon the stabilization of the anion by interaction between its charge and the carbon-halogen dipole, e.g., a+

8-

CH8.C: CHCl

A-

This effect is of course paralleled in the effect of halogen substitution on the strength of aliphatic carboxylic acids, though here it is of smaller

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

203

magnitude (- 2 pK units for a-substitution) because of the greater distance between the dipole and the negative charge. The still larger increase in K , which occurs when we pass from simple ketones to P-diketones or keto esters demands a different type of explanation, and this is found in the occurrence of mesomerism in the ion, resulting in the distribution of negative charge between two oxygen atoms. For example, the anion of acetylacetone can be given the equivalent structures CH3.COCH:CO-.CH3 and CHa.CO-: CH*CO.CHs,and it is well known that in this situation the species concerned is more stable than would be expected for a single structure. The substitution of a halogen atom in the 0-diketones and keto esters produces a small increase in velocity, but much less than in the simple ketones. It is not clear why the effect of halogen substitution should be so much reduced, since the inductive effect would be expected to operate in roughly the same way in all these compounds. Another feature of the table which is difficult to explain is the large difference (a factor of over 100) between the rates for 2-carbet hoxy cy clopentanone and 2-carbet hoxycyclohexanone , though there are other similar anomalies in the reactivities of such ring systems, Interest also attaches to the variation of the exponent p among this series of compounds. The range of velocities covered is very much greater than is normally investigated when studying a series of catalysts for a given substrate, and constancy of p is therefore less likely. Since p is related to the slopes of two intersecting energy curves (cf. Fig. l ) , its change could be interpreted as due to a change of slope when traversing a considerable part of the energy curve. This view was put forward by Lidwell and Bell (148), but it was found difficult t o account for the relatively large changes observed. It seems more likely that the variations of B are associated with changes in the shape of the potential energy curves, and not merely in their position. Such changes of shape are likely when considerable changes of structure are involved (especially those involving mesomerism), and will be considered further in the next section in connection with the effect of structure of catalysts. An extreme instance of changes in the shape of energy curves is met with when the chemical nature of the substrate is drastically altered. As already mentioned, although acetoacetic ester and nitromethane have similar acid dissociation constants, their rates of ionization are in the ratio 6000 :1 (Pedersen, 29,42; Reitz, 43). Although the proton is lost from a carbon in both compounds, the structures of the resulting ions are very different, and the energy curves would be expected to differ considerably in shape. Another point of interest arises when considering the series CH3N02,C2HsN02, CH3CH2CH2N02,(CH3)2CHN02. The acid strengths of these increase in the order given (Turnbull and Maron,

204

R. P. BELL

149; Wheland and Farr, 150), but their rates of reaction with hydroxyl ion are in the reverse order, so that the dependence of velocity upon acid strength is the exact opposite of t h a t usually found. Moreover, the effect of alkyl substitution in increasing the acidity is 1,he opposite of the usual inductive effect (e.g., in the carboxylic acids). It seems likely t h a t the sequence of acid strengths results from the stabilization of the undissociated molecule by a hyperconjugative effect which depends on the number of hydrogen atoms on the carbon adjacent to the nitro group, e.g., in nitromethane we can write three structures of the type H+

H-C=N

H

/

0-

+ / ~

\

0-

This type of structure is not possible for the anion (or for carboxylic acids). The sequence of velocities is then explained on the basis of the ordinary inductive effect (Cardwell, 151).

2. T h e Structure of the Catalyst This problem is in principle the same as that of the structure of the substrate, but there are some differences in practice. I n the first place, the acid-base strength of the catalyst is usually me:asurable by direct means, and a large part of the variations in reaction velocity merely parallel these variations in acid-base strength. I n the second place, it is rarely practicable t o vary the strength of the catalyst over a very wide range (because of the catalytic effect of the molecules or ions of the solvent). Moreover, most measurements on catalyzed reactions have been confined t o a series of very similar catalysts, and little evidence is available as t o how far catalysts of widely differing structure conform t o a single Bronsted relation. From what has already been said, it might be expected that a pseudoacid would have a smaller catalytic effect than a “normal” acid of the same dissociation constant. This may be made cleairer by reference t o Fig. 2. Curve (a) is the potential energy curve for the removal of a proton from a pseudo-acid, and (b) is the corresponding curve for a “normal” acid of the same strength. For the sake of definiteness we can suppose t h a t (a) refers t o a nitroparaffin, and (b) t o a phenol. For small displacements of the proton the nitroparaffin curve will be essentially that for a C-H ionization, and hence much steeper than (b) for the 0-H ionization of the phenol, but for greater separations the anion of the nitroparaffin is stabilized by the shift of charge t o the oxygen atoms, and the final energy is t h e s a m e for the two curves. If the proton is

ACID-BASE CATALYSIS A N D MOLECULAR STRUCTURE

205

transferred t o a base (e.g., the substrate in a catalyzed reaction) the activation energies in the two cases will correspond t o the intersections of (a) and (b) with a curve such as (c), and it is clear that the pseudoacid will react more slowly than the ordinary acid of the same strength. The magnitude of this difference will depend upon the position of the proton in the transition state (corresponding to the intersection of the curves in Fig. 2), and may vary widely from one reaction to another. Similar considerations apply to proton transfers in the opposite direction,

1

POSITION OF PROTON

FIG.2.

.

and to the converse case where the undissociated state is stabilized by an electronic rearrangement. The same kind of explanation will obviously account for the variation of the exponent in the series of ketones referred to in the last section, and also the large disparity in rates between substrates of similar acid strength but widely differing chemical nature. I n its application t o catalysts, the preceding paragraph suggests that pseudo-acids or bases will be ineffective catalysts compared with other acids or bases of the same strength; i.e., they should exhibit negative deviations from the Bronsted relation. There are a number of isolated observations which confirm this idea. Thus Bronsted and Pedersen (15) found that the nitrourethane ion had an unexpectedly small catalytic

206

R. P. BELL

effect in the decomposition of nitramide, which they attributed to the pseudo-acid nature of nitrourethane. Similarly, the abnormally low catalytic effect of the picric acid molecule in a number of reactions (Bronsted and Bell, 151 ; Bell, 152) may be related t o the spread of negative charge to the nitro groups in the picrate anion. More systematic evidence is provided by the results of Bell and Higginson (62) for the reaction CHaCH(OH)2+ CHaCHO H 20, the mechanism of which has already been discussed (Sec. 111.2.12). A detailed study of acid catalysis was made, and it was found that 45 carboxylic acids and phenols, with acid strengths ranging over 10 powers of ten, obeyed a Bronsted relation with a maximum deviation of 0.3 logarithmic unit, and a mean deviation of 0.1 logarithmic unit. On the other hand, catalysts of other chemical types exhibit large deviations from the relation which is valid for carboxylic acids and phenols. Some of the deviations are shown in Table 11. The left-hand side of the table shows that nitro-

+

TABLE I1 Dehydration o j .4cetaldehyde Hpdtate-Deviations from the Briinsled Relation Negative Deviations

Positive Deviations

Logarithmic deviation

Catalyst Benzoylacatone enol 1,3 diketo-5-dimethylcyclohexane cnol (dimedone) Nitromethane 1-Nitropropane Nitroethane 2-nitro propane

-1.4 -1.1 -1 . 4

-1.5 -1.7

Logarithmic deviation

Catalyst Benzophenone oxime Acetophenone oxime Diethyl ketoxime Chloral hydrate Water

+1.2 +1.4 +2.1

+0.7 +1.6

-1.9

paraffins and the enols of @-diketonesare 10 to 100 times less efficient as catalysts than carboxylic acids or phenols of the same dissociation constant. The nitroparaffins have already been discussed as examples of pseudo-acids, while the ionillation of 8-diketone enols involves the distribution of a negative charge between two separated oxygen atoms, i.e., -C-CH=C-

I\

-C-CH=C AH4

8

b-

-C=CH--C

b-

!I

+ 11

+

The right-hand side of Table I1 shows that certrtin catalysts exhibit. large positive deviations from the Bronsted relation. This can be interpreted if me remember that both the carboxylic acids and the phenols undergo some structural rearrangement on ionization. The carboxylate

ACID-BASE CATALYSIS AND MOLECULAR STRUCTURE

207

anion contains two equivalent carbon-oxygen bonds in place of one double and one single bond, while the high acid strength of phenols relative t o alcohols is commonly attributed to the occurrence of structures such as

in the anion, whereby the negative charge is partly distributed over the ring. On the other hand, in the five acids on the right-hand side of Table I1 there is no formal possibility of structural change on ionization, and they might therefore be described as having “less pseudo-character than the carboxylic acids and the phenols. This falls into line with their enhanced catalytic effect. In the paper by Bell and Higginson (62) a number of other suggestions are made for correlating individual deviations from the Bronsted relation with the structures of the catalysts concerned. Although several of these suggestions are speculative, it seems possible that further kinetic data will at least provide a new approach for investigating structural problems concerning acid-base pairs. It may be suggested that there is no sharp distinction between pseudo-acids and other acids, but rather a whole range of types of acid, varying in the magnitude of the electronic shift which accompanies ionization. The kinetic approach offers a possibility of obtaining a quantitative measure of the extent t o which different acids behave as pseudo-acids, and hence of testing views as to their electronic structure.

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