MOLECULAR STRUCTURE AND DEVIATIONS FROM T H E BRPNSTED RELATION' R. P. BELL
Physical Chemistry Laboratory, BallioE College, Ozford Universily, England Received August 10, 1960
The relation which is commonly known by the name of Br0nsted is now recognized as a particular case of a family of linear free-energy relationships for rates and equilibria, but it still remains the best established example of such a relationship. I t was first put forward by Bronsted and Pedersen (11) in 1923 in connection with the decomposition of nitramide, and has since been found to apply to a number of reactions eshibiting general catalysis by acids or bases.? The Brflnsted relation connects the catalytic powers of a series of acids or bases for a given reaction with their acidic or basic dissociation constants, and may be written in the form k, = G,K," k b = G& (1) where k. and kb represent catalytic constants of acids and bases, K , and Kb are acidic and basic dissociation constants, and G,, G b , a, and @ are constants characteristic of the reaction, the solvent, and the temperature, a and p being positive and less than unity. Various attempts have been made to give a theoretical explanation of equation l (2, 13, 14, 16). lheee are all suggestive rather than convincing, but all indicate that equations such as equation 1 are likely to hold only for a series of catalysts of very similar structure- for example, a series of carboxylic acids or substituted anilines. Most of the experimental work in this field does in fact deal with related series of this kind, and only isolated observations are available on the effect of varying chemical structure. Rransted and his coworkers (10, 11, 12) did irivestigate three very different classes of base (carboxylate anions, substituted anilines, amine cations) as catalysts for the decomposition of nitramide, but here the position is complicated by simultaneous variations of the charge on the catalyst. I t therefore seems worthwhile to consider under what conditions changes of chemical structure will cause large deviations from the Bwnsted relation, and to seek for experimental evidence on this point. Some information may be obtained by considering the effect of varying the substrate rather than the catalyst. I t is now generally accepted that the ratedetermining step in reactions eshibiting general acid-base catalysis is a protolytic reaction, which in the simplest cases takes place directly between the catalyst and the substrate, the latter acting as a weak acid or base. It is therefore Presented hefore the Symposium on Anomalies in Reaction Kinetics which wad held under the auspices of the Division of Physical and Inorganic Chemistry and the Minneapolis Section of the American Chemical Society at the University of Minnesota, June 19-21, 1950.
For u. general account cf. Bell (3).
885
886
R . P. BELL
reasonable to suppose that equations such as equation 1 will also represent the relation between the reaction velocity and the acid-base strength of the substrate. So far there is little direct evidence on this point, since substrates are commonly such weak acids or bases that the usual methods of measuring acidbase strength are not applicable; however, in the base-catalyzed prototropy of ketones there are signs of a rough parallelism between rate and acidic strength, and the effect of substituents is in the expected order (4). On the other hand, this parallelism breaks down if we compare the prototropy of ketones with that of nitroparaffins. For example, acetoacetic ester and nitromethane have similar acid dissociation constants (2 X IO-" and 6 X 10-l' at 25OC.) and their rate of halogenation in the presence of a basic catalyst is believed to depend on the loss of a proton to the catalyst; nevertheless, the rate of bromination in the presence of acetate ions is about 6OOO times as great for the ester as it is for the nitroparaffin (17, 19). There is also a marked anomaly within the series of nitroparaffins, whose rate of reaction with hydroxyl ions varies in the opposite sense to their acid diasociation constants (15, 21, 22). I t is possible that similar discrepancies would be found for other types of substrate, but data on their acidbase strengths are scanty, and in many instances the rate-determining proton transfer is preceded by an equilibrium between the catalyst and the substrate. The classes of substrate mentioned above (ketones and nitroparaffins) are both pseudo-acids, in the sense that their ionization involves an electronic rearrangement, with the appearance of the negative charge on an atom other than that from which the proton has been detached, Le.,
(This shift of charge is responsible for the occurrence of reactions of measurable speed with basic catalysts, since normal acids of pK 10-11 react very rapidly with bases.) This circumstance suggests that large deviations from the Br0nsted relation are likely to be found with catalysts whose ionization involves a considerable shift of charge, and that these catalysts will have an abnormally small effect. There are a number of isolated observations which confirm this idea. For example, in their original work on the decomposition of nitramide, BrZnsted and Pedersen (11) found that the nitrourethan ion had an unexpectedly small catalytic effect, which they attributed to the pseudo-acid nature of nitrourethan. Similarly, the abnormally low catalytic effect of the picric acid molecule in a number of reactions (1, 9) may be related to the spread of negative charge to the nitro groups in the picrate ion. The effect of structure on catalytic power has been shown clearly in recent
MOLECULAR STRUCTURE AND DEVIATIONS FROM BRdNSTED RELATION
887
work on the catalyzed dehydration of acetaldehyde hydrate according to the equation :
CHaCH(0H)t + CHiCHO
+ H20
The experimental study and mechanism of this reaction are discussed in a paper by Bell and Higginson (6). The reaction is catalyzed both by acids and by bases, the acid catalysis having been studied in detail. Forty-five carboxylic acids and phenols, with acid strengths ranging over ten powers of 10, obey 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 considerable deviations from the relation which is valid for carboxylic acids and for phenols. These deviations are given in table 1. The TABLE 1 Dahydration of acetaldshyds h y d r a : deviations from the Br#natod r e l a t h
Benzoylacetone enol. ........
Benzophenone oxime.. .... Acetophenone oxime. Diethyl ketoxime., Chloral hydrate. .......... Water. ...................
-1.4
(dimedone). ............... Nitromethane. .............. 1-Nitropropane. ............. Nitroethane. ................ 2-Nitropropane. ............. Nitrourethan. ...............
+1.2 +1.4 +2.1 +0.7 +1.6
..... .......
1,3-Diket0-5,5-dimethylcyclohexane enol
-1.1 -1.4 -1.5 -1.7 -1.9 -0.4
left-hand side of the table shows that, as suggested above, catalysts which are pseudo-acids are much less active (by one to two powers of 10) than carboxylic acids or phenols of the mme dissociation constant. The structural change occurring in the ionization of nitroparaffins has already been considered, while for the &diketone monoenols the process is
-C-CH=C-
II
0
1
OH
+ -C-CH=C-
I/
0
+
c--h---\
I
0-
-C=CH-C-
1
0-
II
0
H+
the anion being a resonance hybrid in which the charge is shared equally between the two oxygen atoms. The right-hand side of table 1 shows that certain catalysts exhibit large positive deviations from the Bransted relation. This can be interpreted if we remember that both the carboxylic acids and the phenols undergo some structural rearrangement on ionization: the carboxylate anion contains two equivalent carbon-oxygen bonds in place of one single and one double bond, while the high
888
R. P. BELL
acid strength of phenols relative to alcohols is commonly interpreted by supposing that their ions involve structures such as
0and
0
0
whereby the negative charge is partly distributed over the benzene ring. On the other hand, for the five acids on the right-hand side of table 1 there is no formal poasibility of structural change on ionization, and they might therefore be described as having “less pseudo-character” than the carboxylic acids and phenols; this falls into line with their enhanced catalytic activity. It is tempting to use the same kind of correlation with charge distribution and structural change to account for some of the smaller divergences from the Brfinsted relation. For example, in the dehydration of acetaldehyde hydrate, if the data for carboxylic acid catalysis are examined in detail it is found that benzoic acid and its meta and para derivatives are somewhat more effective catalysts than are ortho-substituted aromatic or aliphatic acids of the same dissociation constant. In order to explain this we must consider the factors which determine the strengths of aromatic acids. In the series CaHsCOOH.. ...................................................... C~HSCHICOOH.................................................... CIH&H&HEOOH. ..............................................
K. 6.6 X lo-’ 4.9 X 10-’ 2.2 X 10-*
there appears to be some factor reducing the strength of benzoic acid, which on a normal inductive basis should have K , rtt least 2 X (cf. formic acid, K , = 1.8 x lo-‘)). This factor is probably the contribution of structures such as I (and similar structures with a positive charge in the ortho position) to the mesomeric state of the molecule.
0/O-
+ o c , 0-
OH
I
I1
The corresponding structure (11) for the anion is relatively improbable, since it involves the loss of the normal resonance energy of a carboxylate ion and the proximity of two negative charges; hence the effect of such structures is to reduce the strength of the acid by stabilizing the molecule relative to the ion. This effect is the reverse of the one already considered in pseudo-acids (the stabilization of the anion by electronic rearrangements which cannot occur in the acid molecule), and we should expect it to have the opposite kinetic effect, Le., to increase the reaction velocity. This agrees with the fact that aromatic acids are better catalysts than aliphatic acids of the same strength, and it also ex-
MOLECULAR STRUCTURE AND DEVIATIONS FROM B R ~ ~ N S T E D RELATION
889
plains the inclusion of cinnamic acid among the aromatic acids, since structures such as
0-
‘OH are possible. The same picture accounts for the high dissociation constants of the ortho-substituted benzoic acids, and the fact that they behave kinetically like aliphatic rather than like aromatic acids. A structure such as I above demands that the carboxyl group shall lie in the plane of the ring, and this is impossible if there is an ortho-substituent; hence the special factor which stabilizes the molecules of aromatic acids cannot operate. This kind of interpretation must remain rather speculative until a larger amount of experimental material is available, but further kinetic data should a t least provide a new approach for investigating the nature of the charge distribution in acid-base pairs. I t seems likely, in view of modern valency theories, that the acids commonly classed as pseudo-acids do not differ in principle from most other acids, but only in the magnitude of the electronic shifts involved in their ionization. The kinetic approach offers a possibility of obtaining a quantitative measure of the extent to which different acids behave as pseudo-acids. The slow protolytic reactions of pseudo-acids (most easily observed by using them as catalysts) can be accounted for in terms of potential energy curves. For example, if we compare a nitroparaffin with a phenol of the same dissociation constant, the energy curves for removal of a proton will be something like those drawn in figure 1. For small displacements of the proton the nitroparaffin curve (curve a) will be essentially that of a C H bond, and hence much steeper than curve b for the 0-H bond of the phenol, but for greater separations the anion of the nitroparaffin is stabilized by the shift of charge to the oxygen atoms, and the final energy of dissociation is the same for the two curves. If the proton is transferred to a base (e.g., a substrate in a catalytic reaction), the activation energies in the two cases will be represented by the intersections with a curve such as curve C, and it is clear that the pseudo-acid will react more slowly than the ordinary acid of the same strength. The magnitude of the difference will depend upon the position of the proton in the transition state and may vary widely from one reaction to another. Similar considerations apply to proton transfer in the opposite direction, and to the converse case where the undissociated state is stabilized by an electronic rearrangement. The above explanation of deviations from the Brensted relation depends on the partial occurrence in the transition state of some effect which operatss to a still greater degree in the initial or final state of the system. In principle, positive deviations will also occur if some stabilizing effect is present in the transition state but cannot occur in either the initial or the final state. This behavior has been recently encountered in the bromination of various ketones and esters,
890
R. P. BELL
catalyzed by carboxylate anions (5). It was found that positive deviations (up to 300 per cent) occur whenever both the substrate and the catalyst contain large groups (halogens or hydrocarbon radicals) near the seat of reaction, a result which was attributed to the proximity of these two large groups in the transition state. The resultant stabilization may be partly due to van der Waals forces between the groups, but a more important factor is probably the necessity of making a cavity in the solvent, thereby doing away with some of the interactions between the water molecules. When the two large groups are close together they will cause the separation of fewer water molecules than when they are apart, and this factor will tend to make the transition state more stable. It can easily be shown that this effect is ample to account for the observed positive deviations, and it is hoped that measurements of the energies and entropies of activation will throw further light on the problem.
L
DISTANCE OF PROTON
FIG.1. Energy curves for removal of a proton
Finally, a brief account will be given of some apparent anomalies in catalysis by amines. I n the decomposition of nitramide in aqueous solution the catalytic effect of e v e n nuclear-substituted anilines conforms accurately to a Brensted relation (lo), but isolated data for tertiary amines show considerable deviations from this relation (18). A recent study of the same reaction (7) shows that primary and tertiary bases each obey a relation like equation 1, with the same value of 0,but that the value of Gg for tertiary bases is about four times as great as that for primary bases. This can be interpreted in general terms by saying that substitution on the nitrogen atom is too drastic a structural change to be included in a single relation between reaction velocity and basic strength, but a more specific explanation can also be advanced. It has been pointed out (7, 20) that the cations of amines will be strongly solvated in aqueous solution (probably by hydrogen bonding) and that this solvation will decrease in the order primary amine, secondary amine, tertiary amine, owing to the replacement of the hydrogen atoms by bulky alkyl groups. This solvation will stabilize the cation and therefore tend to increase the strengths of the three classes of amines to different degrees. If this varying solvation is allowed for, a reasonable account can he
MOLECULAR STRUCTURE AND DEVIATIONS
FROM B R ~ N G T E DRELATION
891
given of the apparently anomalous effect of alkyl substitution on dissociation constants, and the observed entropies of dissociation are also qualitatively explicable. In the amine-catalyzed decomposition of nitramide the transition state will involve only a partial separation of charge, so that stabilization by solvation will be less marked than in the cation, and primary amines will be less active catalysts than tertiary ones of the same dissociation constant. This type of explanation suggests that the “anomalies” are present in the aqueous dissociation constants rather than in the kinetic data or in the structure of the amines themselves, and this idea receives confirmation from measurements in nonaqueous solution. Measurements have been made of the amine-catalyzed decomposition of nitramide in anisole solution (8) and if log (catalytic constant in anisole) is plotted against log (dissociation constant in mater) it is again found that the points for primary and tertiary amines lie on two parallel straight lines. Here, however, the difference between the two classes is much greater, Gb for tertiary amines being about ten times as great as Gb for primary amines, corresponding to a much reduced solvation in anisole solution. Moreover, if the catalytic constants are compared with basic strengths measured in anisole or chlorobenzene solutiona instead of with dissociation constants in water, then a single relation serves to represent the data for primary, secondary, and tertiary amines. It therefore seems most likely that the apparent kinetic anomalies observed with amines have their origin in the variable contribution of hydration to the dissociation constants in aqueous solution. REFERENCES BELL:Proc. Roy. SOC.(London) Al43, 377 (1934). BELL:Proc. Roy. SOC.(London) AlM, 414 (19%). BELL:Acid-Base Catalysis. Oxford University Press, London (1941). BELL:Trans Faraday SOC.99, 253 (1943). BELL, GELLES,A N D MOLLER: Proc. Roy. SOC. (London) AlW, 308 (1949). BELLAND HIOGINSON: Proc. Roy. SOC.(London) A M , 141 (1949). BELLAND WILSON:Trans. Faraday Soc. 46, 407 (1950). BELLAND TROTMAN-DICKENSON: J. Chem. SOC.1949,1288. BR@NBTED AND BELL:J. Am. Chem. SOC.63, 2478 (1931). BR@NSTED A N D Duus: Z. physik. Chem. 117,299 (1925). BR@NBTED AND PEDERSEN: Z. physik. Chem. 108, 185 (1923). BR@NSTED AND VOLOUARTZ: Z. physik. Chem. 166A, 211 (1931). EVANSAND POLANYI: Trans. Faraday SOC.I,1340 (1936). HORIUCAIAND POLANYI: Acta Physicochim. U.R.S.S. 2, 505 (1935). MARONAND LA MER: J. Am. Chem. SOC.80, 2588 (1938). PEDERSEN: J . Phys. Chem. 88, 581 (1934). PEDERSEN: J. Phya. Chem. 88,99,601 (1934); Kgl. Danske Videnskab. Selskab Math.fys. Medd. 12, 1 (1932). (18) PFLUQER: J . Am. Chem. SOC.80, 1513 (1938). (19) REITZ: Z. physik. Chem. 176A. 363 (1936). (20) TROTMAN-DICKENSON: J . Chem. SOC.1949, 1293. (21) TURNBULL AND MARON: J. Am. Chem. SOC.66, 212 (1943). (72)WAELAND A N D FARR: J. Am. Chem. SOC.66, 1433 (1943). (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)
* Indicator measurements by Mr. J. W.Bayles in this laboratory.
892
DISCUSSIOS
DISCUSSION H. C. BROWN(Purdue University) communicated the following comments: Dr. Bell has s'uggested several possible causes for deviations from the Brgnsted linear free-energy relationship. For some time we have been investigating the chemical effects of steric strains and we wish to suggest that steric effects are probably the most important cause for such deviations. Consider the two similar reactions: CsHsN: CSHIN:
+ +
H+ CsHsN:H+ B(CHs)s F? CsHsN:B(CHs)a
Substituents in the 3- or 4-position of the pyridine nucleus have similar effects upon the two reactions. However, in the 2-position such substituents frequently have markedly different effects. Thus the ionization constant increases regularly from 10-9 for pyridine (I) to lo-* for 2-picoline (11) to lo-' for 2,6-lutidine (111) :
I K g
= lo+
K g
I1 lo-*
=
K g
111 = 10-I
Yet trimethylboron forms a very stable addition compound with pyridine (AH = 17.0 kcal.), an unstable derivative with 2-picoline ( A H = 10 kcal.), and no compound with 2,6-lutidine. Obviously this series does not conform to the Brgnsted relationship. Suppose that one were studying a reaction in which the rate-determining step involved the removal of a proton from a sterically hindered position.
0
R-C< 0
+
@+
PRODUCTS
It is apparent that changes in R relatively far removed from the carboxyl group will not affect the steric relationships and the rate will be affected by the structural changes in a regular manner in accordance with the change in basicity of the carboxylate anion. On the other hand, the three pyridine bases will show markedly different behavior. In such a reaction the pyridine molecule (I) with its low steric requirements would probably be far more effective than the stronger bases, 2-picoline (11) and 2,6-lutidine (111), with their much larger steric requirements. In such a reaction these three bases would not conform to the B d n sted relationship, although in another reaction involving the removal of a relatively unhindered proton, the same three bases might conform rigorously. In this way the positive deviations observed by Dr. Bell for water and ketoximes could well be due to the relatively small steric requirements of these molecules.
893
DISCUSSION
Finally, I should like to comment upon Dr. Bell’s suggestion that the unusual weakness of tertiary amines is to be attributed to weak solvation, presumably resulting from the steric hindrance of the three alkyl groups. Some six years ago we considered this problem and concluded that there were strong arguments against this explanation. At that time we proposed instead that steric strain, resulting from the crowding of the three alkyl groups attached to the small nitrogen atom, is the primary cause of the observed weakness of such amines.
R
\ R-N /
R
+
R
Strained
H+
\ /
R-N-H+ R
More strained
The introduction of an alkyl group into the ammonium ion decreases its acidity. The observed effect on the acidity constant must be the result of the inductive effect of the alkyl group minus the hydration energy of the nitrogenhydrogen bond. Since a decrease in acidity is observed, the inductive effect must be the more important. A second such substitution is also effective in the same way; the third alkyl group has the reverse effect. To bring in solvation as an explanation for the abnormally high acidity of trimethylammonium ions requires the postulate that the steric interference of the three alkyl groups prevents or minimizes solvation of the nitrogen-hydrogen bond.
In the case of 2,6-lutidine the nitrogen atom is much more hindered than in the case of trimethylamine. Trimethylboron forms a stable compound with trimethylamine, but none with 2,6-lutidine. Yet we observe no abnormality in the base strength of 2,6-lutidine in aqueous solution. The effect of the second methyl group in increasing the strength of the pyridine base is practically identical with the effect of the first methyl group. It therefore appears undesirable to call upon steric hindrance of the hydration of trimethylammonium ion as a major factor in the high acidity of the ion. We have recently studied the base strengths of the methylphosphines. Here, the increased size of the phosphorus atom should reduce the crowding which is a t the basis of our explanation. I t is not apparent that there should be any marked change expected in the relative importance of solvation. Yet by every procedure we have used to compare the base strengths, in aqueous systems, in nonpolar solvents, in the gas phase, etc., trimethylamine turns out to be a weaker base than dimethylamine, whereas trimethylphosphine turns out to be a stronger base than dimethylphosphine. This invest(gation, carried out with the assistance of Dr. Sei Sujishi, strongly points to the value of the B-strain concept in accounting for the weakness of aliphatic tertiary amines.
,.
