THE THEORY O F PROTOLYTIC REACTIONS AND PROTOTROPIC ISOMERIZATION KAI JULIUS PEDERSEN Chemical Laboratory of the Royal Veterinary and Agricultural College, Copenhagen, Denmark Received October 23, 1933
According to Bronsted's (3) definition of acids and bases any neutraI molecule or ion which can give off a proton is called an acid, and any neutJral molecule or ion which can take up a proton is called a base. When
;P an acid and B the corresponding base. Lowry (27) has independently suggested the same definition. The proton being incapable of independent existence, an acid can only give off a proton to a base. Thus the characteristic acid and base function is the transference of protons from the acid t o the base as expressed in the scheme
A
AI
+ Bz S BI + Az
(1)
where the base B1 corresponds to the acid A1, and the acid A2 to the base Bz. Bronsted (6) calls this a protolytic reaction. The relative strength of two acids or bases is defined by means of the degree of displacement of equilibrium 1. If KA is the strength of an acid A and KBthat of a base B, we use the definition
In this way we can compare the strengths of two acids or bases in any solvent. The relative strength is usually dependent on the solvent. Ii the solvent, S is a base we get the equilibrium -41
+S
Bi
+ SEIT
In this case we define the strength of the acid AI and the base B, in the solvent by
581
582
'
KAI JULIUS PEDERSEN
Where there can be no misunderstanding we often call the ion SH+ the hydrogen ion and denote it by H+. In the solvent water SH+ is the hydroxonium ion H30+. Protolytic reactions are generally very rapid. It has not yet been possible to show with certainty that the interaction of ordinary acids and bases takes a finite time. Only the so-called pseudo acids, which will be dealt with later, react in some cases with measurable velocity. By means of the flowing stream method of Hartridge and Roughton (20) it has been shown by Saal (38) that the reaction between hydroxyl ions and different weak acids and between hydrogen ions and different weak bases is complete in less than 0.004 second. La Mer and Read (24) found by the same method that the reaction between 0.05 N solutions of acetic acid and ammonia a t 25°C. was only 95 per cent complete 0.002 second after mixing. These authors intend to repeat the experiment with an improved apparatus. It will be of interest to see whether the result will be confirmed. I t is reasonable to assume that the velocity of the protolytic reaction is to some extent determined by the strength of the reacting acid and base. The weaker the acid and base the slower the reaction. However, by purely static considerations we cannot find a relation between the velocity and , and T A ~B*, , the strengths of the acid and base. If we denote by V A ~B~ respectively, the velocity and the bimolecular velocity constant for the transference of a proton from A, to B, (scheme l),we have ZJA>,B~ =~
At equilibrium
A ~ , B ~0%) (AJ
vA1, B2 = vAz, Bl,
and
UA*,B~ =
~ A ~ , B(Bd ~ ( A ~
and consequently
By means of equation 2 we get the relation
Only the ratio between the velocity constants of the balanced reaction 1, not the separate constants, is given by expression 4, which is all we oan get in this way. Only kinetic experiments can decide whether the velocity is determined by the strengths of the acid and base. It has been found, first by Bronsted and his coworkers (7-10, 12-15), afterwards by many other investigators (16,17,23,26,31,33,34,35,36,42), that a great number of reactions are catalyzed by acids or bases in general, that is, all sufficiently strong acids or bases catalyze, and the effect increases with increasing acid or basic strength of the catalyst. Bronsted has developed a theory of this general acid and basic catalysis (4, 5).
PROTOLYTIC REACTIONS AND PROTOTROPIC ISOMERIZATION
583
According to this theory the velocity is determined by a protolytic reaction between the substrate and the catalyst. We have general acid or basic catalysis if the substrate molecule by receiving or by giving off a proton gets into an unstable state which immediately (or very quickly compared with the velocity of the protolytic reaction) leads to the reaction which we examine. If in acid and basic catalysis we call the substrates R and R H respectively, the velocities are determined by the reactions R+A
---f
RH++B
(5)
R-+A
(6)
and RH+B
-+
The substrate is an extremely weak base or acid, and since the corresponding acid (RH+) or base (R-) disappears practically immediately after its formation, it is possible to follow the protolytic reaction. If the velocity of the protolytic reaction is determined mainly by the strengths of the reacting acid and base while other factors have a minor influence, by plotting the catalytic constants (kA for the acid catalyst A, and k~ for the basic catalyst B) for a series of catalysts of the same reaction against the acid or basic strength, we should get points which fall not far from a continuous curve. Actually it has been found for a great number of reactions that the points fall very close to a straight line when log k~ is plotted against log KA and log kg against log KB. Thus it follows from the experiments that we may express the dependence of the catalytic constant upon the strength of the catalyzing acid or base by the equations l z = ~ TA,R = ~ K A "
(7)
and kB = TRH,B = g K B a
(8)
The influence of the strength of the catalyzing acid or base is expressed by CY and p are constants characteristic of the reaction examined. The factor g usually does not vary much within a series of acid or basic catalysts of the same reaction. For the transference of a proton from RH+ to B we get by means of equation 4
K;i or K$ respectively, where
If we assume that an increase of KA tends to increase T A , while an increase of KB tends to increase QHt, B, both CY and 1- 01 must be positive, that is 0 < CY < 1. In the same way we find that 0 < p < 1. ' These results are in agreement with the experiments.
584
KAI JULIUS PEDERSEN STATISTICAL FACTORS (CF. BRONSTED
(4, 5,
AND
12))
The number of protons which an acid molecule can give off and the number of vacant places on a base molecule where a proton can be taken up has an influence on the velocity of transference of a proton from the acid to the base, and therefore on g in the expressions 7 and 8. We assume that g = G when A can give off only one proton and B can take up only one proton. We shall compare this simple case with a more general one where A has p protons, each bound with the same strength as in the simple case, and B has p vacant places, each with the same tendency to take up a proton as in the simple case. It is a necessary, though not sufficient, condition for a transference of a proton from A to R that the active part of the molecule R hits A within a certain area round a proton which can be given off. If we assume that the active areas of A do not overlap, 7rA, R will be p times as great as in the simple case. We find in the same way, when we assume that the active areas of B do not overlap, that TRH+, B will be q times as great as in the simple case. By means of equation 4 we find that ICA will be p / q times as great. Consequently we get
or g
= pl-a qa
G. By similar considerations we find for basic catalysis
or g = q l - 8 p S G. It seems reasonable to assume that more protons bound to the same atom in an acid count as one when determining the statistical factor. Thus p = 1for H30*and PITH4*,while p = 2 for H2S04. Similarly, when a base can take up more protons a t the same atom, this place is only counted as one. Thus p = 2 for CH3C02- and q = 1 for OH-. T H E INFLUENCE O F THE ELECTRIC CHARGE O F T H E CATALYST
The value of g in equations 7 and 8 depends on the electric charge of the catalyst. Let us consider basic catalysis and only reactions where the substrate RH is uncharged. We assume that equation 8 holds for a series of bases with no electric charge when g has the value go, and for a series of bases with one negative charge when g = g-. We now consider two hypot,hetical bases B- and B differing only in their electric charge. We compare the reactions RH+B-
~2
R-+BH
(11)
RH+B
~3
R-+BH+
(12)
and
PROTOLYTIC REACTIONS AND PROTOTROPIC
ISOMERIZATION
585
We assume that p in equation 8 is independent of the charge. We have
Hence
We have kB _ --TRH,B , K B = -TRH,B , kB-
TRH,B-
and KB- = -
TBH+,R-
TRH,B-
TBH,R-
which we introduce into equation 13. Hence
9” = 4-
TRH,B
(rRH.B->’”
TBH+,R-
’
(G)
In going from reaction 11 to 12 the velocities change in the following way. It will be more difficult for B to take up a proton than for B-, but it will be easier for BH+ to give off one than for BH, and, in addition to this effect, the electric attraction between BH+ and R- will increase the velocity of the reaction from right to left. From this we conclude that the following relation will probably hold TBH+,RTBH,R
TRH B-
>->l
TRH,B
By introducing this into equation 14 we find, that go < g- when p is very small, and go > g- if p is sufficiently great and always if p > l/2. The influence of more negative charges can be examined in the same way. For a base with two negative charges (g = g--), we find that g-- > g when p is very small, and g-- < g- when p is sufficiently great and always if ,!3 > 1/2. If we compare bases of the same strength we may express the effect of the electric charges as follows. The base with the greatest number of positive charges (smallest number of negative charges) is the strongest catalyst, when p is sufficiently great, and always if p > 1/2. The greater 0, the greater the effect. When is very small the effect goes in the opposite direction. The attraction between R- and a positive ion is greater and increases more rapidly with increasing electric charge of the ion than the repulsion between R- and a negative ion, the former being on the average nearer together than the latter. Consequently, the effect will increase more rapidly in the series B-, B, B+, B++ . . . than it will decrease in the series B-, B-- . . . . For acid catalysis we find analogous rules. Among acids of the same strength the strongest catalyst is the one with the greatest number of
586
K A I JULIUS PEDERSEN
negative charges (smallest number of positive charges), when a! is sufficiently great, and always if a! > 1/2. When a! is very small the effect is opposite. The effect will increase more rapidly in the series A+, A, A-, A-- . . . than it will decrease in the series A+, A++ , , ,
.
THE SALT EFFECT
Addition of salt will generally alter both the velocity constant (ICA or and the strength (KAor K B )of the catalyzing acid or base. When the substrate is uncharged the primary (5, 12) kinetic salt effect is generally small, but there is a considerable salt effect on KA (except when A has one positive charge) and on K B (except when B is uncharged). Therefore we may expect to get a better agreement with experiment when in formulas 9 and 10 we use, instead of K.4 and Kg, their values a t infinite dilution, KAO and Kg': Icg)
and
If the substrate molecule is charged it is very important not to neglect the different effect of salts on the velocity and on the acid and basic strength. As an example of the application of the theory we shall give a summary of experiments on the decomposition of nitramide in aqueous solution at 15°C. HzN202 --$ NzO
+ HzO
It was through the study of this reaction that general basic catalysis was first found (Bronsted and Pedersen (12)). The work has been continued by Bronsted and Duus (8) and by Bronsted and Volqvarts (14). Recently Bronsted and Vance (13) have examined the reaction in amyl alcohol. Acids have no catalytic effect on the decomposition of nitramide in aqueous solution. In dilute solutions of strong acids a slow reaction with the unimolecular constant ko" = 0.00038 min.-l was found. (By an asterisk we denote that the constant has been calculated by means of decadic logarithms. Thus k" = 0.4343k.) This so-called spontaneous reaction is simply explained as basic catalysis by the water. In solution containing bases B the velocity constant can be written IC = k o Zlkg(B) or, if we ~ consider the water as a base of the concentration 55.5 and write k H , = k0/55.5, in the simpler way k = ZkB(B). Since the publication of the first paper our views on the effect of statistical factors have altered somewhat. Here the results have therefore been
+
587
PROTOLYTIC REACTIONS AND PROTOTROPIC ISOMERIZATION
recalculated in accordance with formula 16. We have also in some cases deviated from the original papers in the determination of the statistical TABLE 1 The decomposition of nitramide at 16°C. CATALYST
Bases with on( negativl charge j3 = 0.80 G* = 7.2 x 10-5
Bases with twl negativ charges j3 = 0.87 GI = 2.07 x 10-5 Bases with no charge @ = 0.75 G* = 17.0 x 10-5
Propionate ion Acetate ion Acid succinate ion Phenylacetate ion Benzoate ion Formate ion Acid malate ion Acid tartrate ion Acid phthalate ion Salicylate ion Primary phosphate ion Dichloroacetate ion Secondary phosphate ion Normal succinate ion Normal malate ion Normal tartrate ion Normal oxalate ion
0
9
L02X
. o c ~ K B o G* X 106
0.036 0.029 0.020 0.007 0.000
0.51-1 0.40-1 0.20-1 0.06-1 0.97-2 0.61-2 0.58-2 0.26-2 0.16-2 0.01-2 0.60-3 0.54-4
-~ 4.57 7.1 4.44 7.1 4.19 7.1 3.98 7.6 3.89 7.2 3.38 8.1 3.40 7.2 3.01 7.1 2.92 6.6 2.70 7.1 2.30 (5.8) 1.00 (5.5)
86 1.8 0.72 0.165 0.104
1.46 0.66-1 0.26-1 0.62-2 0.42-2
kB*
--___ 1 2 0.649 1 2 0.504 2 2 0.320 1 2 0.232 1 2 0.189 1 2 0.082 2 2 0.076
2 2 2 2 1 2 3 2 1 2
-____ 2 1 1 1 1
3 4 4 4 4
x
10-5
7.06 5.02 4.51 3.79 3.57
2.09 1.95 2.19 2.09 2.04
-1
--___ 1 1 1.16 1 1 0.64 1 1 0.54 1 1 0.38 1 1 0.21 1 1 0.081 1 1 0.018 1 1 8%10
0.06 0.81-1 0.73-1 0.60-1 0.32-1 0.91-2 0.26-2 0.85-6
1 1 3,96 1 1 449 2 1 328 2 1 135 6 1 121 6 1 32.7 6 1 2.28
2.598 2.652 2.516 2.130 2,083 1.515 0.358
-____ Bases with t w positive charges j3 = 0.82 G* = 780
-~
5.15 4.82 4.70 4.54 4.04 3.52 2.68 -1.74
15.8 15.5 16.2 15.8 19.5 18.6 17.8 (14)
-5.86 5.69 5.52 5.20 5.73 4.68 2.98
620 980 1000 740 (240) 480 830
factors by using the rules given above, The strengths of the bases are usually those given in the three papers (8, 12, 14). For the primary and secondary phosphate ion they are taken from the investigation by Bjer-
588
KAI JULIUS PEDERSEN
rum and Unmack (2), and for the succinate, malate, tartrate, and oxalate ion from Larsson’s measurements (25). A study of table 1 and figure 1 will show that there is a good agreement between the theory and the experiments. Formula 16 holds well within a group of bases with the same electric charge. The change of cataljrtic effect on going from one type of bases to another goes in the direction we
1
FIG.1. THEDECOMPOSI~ON OF NITRAMIDE Dependence of catalytic constant upon basic strength
would expect. In agreement with the theory, the effect of bases with two positive charges is especially great, about one hundred times as great as of bases with the same strength and one negative charge. The catalysis by water has the order of magnitude we would expect when me use for the basic strength of water the value KB = (H30+)/(HzO)(H30+) = 55.5-l. Nitramide is a weak acid. Bronsted and King (11) have found by measurements of electrical conductivity that its apparent strength is KO = 2.55 X lo-’ a t 15°C. It is seen from their measurements that the
PROTOLYTIC REACTIONS AXD PROTOTROPIC ISOMERIZATIOX
589
protolytic reaction by which the dissociation equilibrium is attained is very much quicker than the decomposition. Therefore the protolytic reaction which leads to decomposition must be another. We assume that the following equilibria are attained practically instantaneously HZNN02 F? HN:NOz-
+ H + e ":NOOH
Thus a constant, but very small, fraction of the undissociated nitramide is in the form HN:NOOH. We may explain the decomposition as taking place when the last proton bound to the nitrogen atom is given off to the base. This explanation is supported by the fact that nitramines of the type RHNN02,e.g. methylnitramine, are stable. Thus Thiele and Lachmann (40) have found that methylnitramine undergoes boiling with potassium hydroxide without decomposition. From this fact we may conclude that body hydrogen atoms in nitramide play a part in the decomposition. It has been found by Bronsted (11,14) that the nitramide ion is unstable and decomposes about twenty times more quickly than undissociated nitramide in pure water. This is also in conformity with the explanation. Owing to the negative charge of the ion HN:NOz- the proton is bound much more strongly than the corresponding proton in HN:NOOH, and the protolytic reaction which leads to decomposition will therefore be much slower, but, on the other hand, all the nitramide ion is in the unstable form, while this is only the case with a small fraction of the undissociated nitramide. For other examples of general basic or acid catalysis we refer to the literature (4, 5 , 7-10, 12, 13, 14-17, 23, 26, 31, 33-36, 42). One of the best known forms of reversible isomerization is that characterized by the change of position in the molecule of a proton, which may be accompanied by a rearrangement of bonds (valency electrons). Lowry (28) has called this form of isomerism prototropy. Although Lowry only considers isomerizations with both proton- and bond-shifting it seems reasonable to include under the name prototropy also those where only proton-shifting takes place, e.g., H2NCHzCOOH +H3NCH2C02-. However, we shall deal here mainly with the former class of prototropy. The greatest number of reactions in which general acid or basic catalysis has been found are prototropic isomerizations. Thus the mutarotation of glucose (9, 31) and the enolization of acetone (17) are catalyzed by both acids and bases, while the enolization of acetoacetic ester and acid (35, 36) and the isomerization of nitromethane (34), CH3N02--$ CH2: NOOH, are catalyzed only by bases. The best examined prototropic systems belong to the triad- or the ringchain systems, respectively, H.X.Y:Z
+
X:Y.Z.H
and
(A),//x Y*Z.H
e
(A) /X.H \Y: Z
590
KAI JULIUS PEDERSEK
where X,, Y , and 2 may be chosen among the three atoms 0, N, and C (41). Of the prototropic reactions mentioned above, mutarotation belongs to the latter class, while the others belong to the former. A great deal of work on prototropic systems has been carried out by Thorpe, Ingold, and their coworkers, although not from the point of view of general acid and basic catalysis. We shall here mention some of their most important results. The hydrogen atom is much more mobile when it goes from one nitrogen atom to another than when it goes from one carbon atom to another, and there is no doubt that it is even more mobile when it goes from oxygen to oxygen. Compared with this the nature of the third atom in the triad Y is of minor importance (21). Thus the mobility increases in the same order as the tendency to give off a proton (methane is a weaker acid than ammonia and this weaker than water). The mobility is dependent on substituents in the prototropic molecule. Electronegative groups, which increase the tendency to give off a proton, increase the mobility (22, 39). The mobility is catalyzed by bases, and in some cases also by acids, although usually to a less extent. The strong bases are the strongest catalysts, in water OH-, in ethyl alcohol C2H60-,etc. From work in this field it seems justifiable to conclude that the hydrogen cannot move spontaneously from one place to another in the molecule. If the prototropic equilibrium is apparently attained without catalyst, it has often been possible to show that the reaction is catalyzed by small amounts of acid and basic impurities. Thus, while the keto-enol equilibrium is attained quickly in acetoacetic ester of ordinary purity, Meyer (32) and Rice and Sullivan (37) have shown that the stability of the enol form can be increased apparently without limit by careful purification. Rice and Sullivan found that addition of traces of bases to the purified enol form increased the velocity of isomerization immensely. Thus the addition of 4 X 10-5 M ammonia increased it 4000 times, while M oxalic acid increased it only 3.2 times. The necessity for a catalyst has been shown most clearly by Lowry and Richards (30) for the mutarotation of tetramethylglucose. They even find that both an acid and a base must be present. If the solvent is both an acid and a base, like water, this alone can catalyze the reaction. If it is only an acid or only a base, no reaction can take place, unless we add respectively a base or an acid. Thus the mutarotation takes place with measurable velocity in water and is catalyzed by acids and bases, e.g., cresol and pyridine. I n pure and dry pyridine or cresol the reaction is completely arrested, but in a mixture of pyridine and cresol it takes place with great velocity. Supported by these experiments Lowry has given an explanation of the mechanism of prototropic isomerization in his electrolytic theory of cataly-
PROTOLYTIC REACTIONS AND PROTOTROPIC ISOMERIZATIOK
591
ais (as),according to which it is a trimolecular reaction between the substrate, an acid, and a base. The following three things take place simultaneously: (a) the substrate molecule gives up a proton to the base, (b) it receives one in another place from the acid, and (c) a rearrangement of valency electrons takes place. Another mechanism has been suggested by Ingold, Shoppee, and Thorpe (22). They assume that (a) and (b) are consecutive bimolecular reactions. This idea is supported by experimental work of Baker (1). In order to examine Lowry’s explanation we consider the prototropic reaction RH -+ SH in a medium containing the acids A,, A2 . . . and their corresponding bases B1, B2 . . . According to Lowry the isomerization is the result of the reaction
.
Am
+ RH + Bn+
Bn
+ SH +
(17)
An
and the analogous reactions with the other acids and bases. If the trimolecular velocity constant of reaction 17 is called IC*,, Bn, we get the following expression for the total velocity where the sum should be taken for all combinations of m and n. Actually both Lowry’s and other investigators’ experiments in aqueous solution agree with the formula where the sum is taken for all acids and bases present. Expressions 18 and 19 agree only if one of the partners in reaction 17 is always (or nearly always) a solvent molecule, because the solvent is the only catalyzing substance whose concentration has not been varied in the experiments. Thus it follows for aqueous solutions that water is always a partner in the reaction, acting as a base in acid catalysis and as an acid in basic catalysis. It seems unlikely that this consequence of Lowry’s theory is in agreement with experimental facts. Let us consider Dawson’s (17) experiments on the enolization of acetone. From his results we calculate the relative velocities of the water, acetate ion, and acetic acid catalysis in an aqueous solution of 0.3 M acetic acid and 0.1 M sodium acetate. They are given below together with the trimolecular reaction by which that part of the total reaction takes place according to Lowrry’s theory. Water catalysis Acetate ion catalysis Acetic acid catalysis
HzO Hz0 HAC
+ RH + Hz0 + RH + Ac+ RH + HZO
Relative vsloritu
1 61 18
From a comparison of the first two reactions it is clear that, when RH receives a proton from a water molecule, the amount of acetate ion present THE JOURNAL OF PHYSICAL CHEMISTRY, VOL. XXXVIII, NO.
8
592
KAI JULIUS PEDERSEN
takes up a proton from RH much more quickly than the water does. This will probably also be the case when R H receives a proton from an acetic acid molecule. We would therefore expect the reaction HAC RH Ac- -+ to be quicker than the third reaction in the list. But actually it has not been possible to detect this reaction (cf. formula 19). We may add that if one of the partners is always water, the acid catalysis of water would always have the same strength as its basic catalysis because HzO 4. However, both correspond to the same reaction HzO RH some reactions are only catalyzed by bases. Thus the enolization of acetoacetic ester (35, 36) is catalyzed by water and bases, while even the strong acid, the hydroxonium ion, does not catalyze. It, therefore, seems unlikely that the very weak acid water has a considerable power as an acid catalyst. From this examination we conclude that it is very unlikely that the prototropic isomerization is a trimolecular reaction between the substrate, an acid, and a base. We must therefore assume that the reaction is initiated by a bimolecular reaction in which a proton is either given off to the base or taken up from the acid. Lowry (29) rejects this mechanism for the following reason, using the mutarotation of glucose as an example. “The initial stage in this action is, however, an endothermic process, in which the molecules of the sugar are converted into ions of such an unstable character that the dissociation constant is said to be of the order of 10-13 and 10-19. The exact amount of energy required to produce these ions is unknown, but it is obvious that, if we can regard the entrance and the exit of the proton as simultaneous, no energy a t all is needed beyond the small amount that is required to cover the difference in energy content of the two isomerides, and perhaps to overcome the frictional resistance t o the migration of an electron through the sugar.” Lowry seems to forget the part played by the activation energy. This energy is not negligible. Thus Kilpatrick and Kilpatrick (23) found 19.3 kg-cal. for the mutarotation of glucose catalyzed by hydrogen ions. I n the following we shall discuss a mechanism of prototropic reaction based upon the results to which we have now come. It is, especially for basic catalysis, very similar to the mechanism suggested by Ingold, Shoppee, and Thorpe (22). We assume that an intramolecular rearrangement in which only valency electrons are moved takes place spontaneously and very rapidly. If we as an example consider the triad system HXsY: Z X : Y . Z H , the bondshifting may take place by the following balanced reaction
+
+
f
-
HX.Y:Z e H X : Y * Z (RH) + X.Y:ZH @ X:Y.ZH (SH) X.Y:Z F? X : Y . Z (I-)
+
+
HX*Y:ZH iS HX:Y*ZH (IH,*)
+
+
PROTOLYTIC REACTIONS AND PROTOTROPIC ISOMERIZATION
593
The equilibria being attained immediately we may consider each pair of tautomers as a single substance, which we may denote as given in brackets above. At first we leave open the question by which of the reactions (20 to 23) the bond-shifting takes place. We shall see that the prototropic rearrangement R H @ SH appears as a general basic catalysis when the mechanism is as expressed by the scheme RH + B + I- + A e SH B (24)
+
while it appears as a general acid catalysis when the mechanism is the following (25) RH + A IH2+ B SH A
+
+
We first consider scheme 24. For simplicity we examine an irreversible prototropic isomerization RH -+ SH. We may obtain the one-way reaction by removing the form SH as soon as it is formed. We assume that the medium contains the acids AI, A2 . . and their corresponding bases B1, Bz . . . . The concentrations of the acids and bases are constant during the reaction. We may therefore formally consider all the bimolecular reactions of scheme 24 as unimolecular, which simplifies the scheme to
.
kl
kz
RH @ I- -+ SH IC-1
where lel, pressions
le-1,
and kz are unimolecular velocit'y constants given by the ex-
h = ZTRH,B(B),
k-I = ZTA,I-(A)
and
k z = ZT;J-(A)
Here dA, I- denotes the bimolecular velocity constant for that particular transference of protons from A to I- which leads to RH, while T'A, I- is the constant for the protolytic reaction between A and I- leading to SH. If the subscript E denotes equilibrium concentrations, and if K is the constant (H+)E (I-)E/(RH)B we have, according to scheme 26,
We nom make the assumption that the hydrogen-ion concentration is so great that (I-) < < (RH) even if the equilibrium RH @ SH were attained. This is nearly always the case under ordinary experimental conditions. Consequently we have IC-, > > ICl. If c is the initial concentration of R H and c - 5 its concentration at the time t we find, remembering that (I-) is negligible compared with (RH), the following differential equations for reaction 26,
594
KAI JULIUS PEDERSEN
from which we get by eliminating (I-)
Thus the reaction follows the ordinary unimolecular law with the constant
We now distinguish between three cases: k-, < < kz. By introducing this into equation 28 we find k = iiL = 2 T R H , B (B). In this case we have general basic catalysis. We measure the velocity of transference of protons from R H to B. Case 2: k-l > > ICz. By equations 28 and 27 we get Case 1:
As seen from the last expression the reaction appears to be a basic catalysis of RH, but in reality we measure a general acid catalysis of the ion I-, whose concentration is inversely proportional to the hydrogen-ion concentration. Case 3: k-l kz. Here we get from equation 28
-
The ratio k-& is independent of the hydrogen-ion concentration, since k-l and kz are independent of the concentrations of the bases, and if we increase the concentrations of all the acids in a certain ratio both I’C-~ and kz are increased in the same ratio. Thus, in this case also, the reaction appears as a general basic catalysis. In reality it is composed of a basic catalysis of R H and an acid catalysis of I-. We have found that the mechanism expressed in scheme 26 leads to a reaction which will always appear as a unimolecular reaction catalyzed by bases in general, when the hydrogen-ion concentration is so great that (RH) > > (I-). If I- takes up protons t o form mainly SH, we measure the velocity of the protolytic reaction between R H and B, that is, the velocity of dissociation of the very weak acid R’H. If I- takes up protons to form mainly RH, the apparent basic catalysis is a disguised acid catalysis of the ion I-. If neither of the two possibilities is specially favored, we get an apparent basic catalysis which is the result of both a protolytic reaction between R’H and the bases and between the acids and I-. It is impossible to decide from the kinetic experiments under these circum-
PROTOLYTIC REACTIOXS AND PROTOTROPIC ISOMERIZATION
595
stances which of the three possible cases we have in a given reaction. However, we may do this, if we take a solution which is so alkaline that the prototropic substance is completely ionized, suddenly add an excess of strong acid, and examine how much is formed of each of the two isomerides. If the mechanism in scheme 25 is analyzed mathematically in the same way as scheme 24 an analogous result is obtained. If the hydrogen-ion concentration is so small that the concentration of the ion IHz+ is negligible compared with that of RH, the reaction R H -+ SH appears as a unimolecular reaction catalyzed by acids in general. If IHz+ by giving up a proton to the base B is predominatingly transformed into SH, we have a genuine acid catalysis of RH. In this case we measure the velocity with which RH receives protons from the acids present. If, on the other hand, the transformation of IH2+into R H is highly favored we have a disguised basic catalysis of IH2+,whose concentration is proportional to the hydrogen-ion concentration. We here measure that particular protolytic reaction between IHz+and B by which SH is formed. If neither of the two possibilities is specially favored, we get an apparent acid catalysis which is the result of both protolytic reactions. The results found here for protolytic reactions with bond-shifting should also hold for those with only proton-shifting mentioned on page 589, but it has not yet been possible t o measure the velocity in any such system. In order to study the mechanism of prototropic isomerization in more detail we must consider the question b y which of the reactions 20 to 23 the bond-shifting takes place. We denote by one dash the bond configuration of HX.Y:Z, and by two dashes that of X:Y.ZH. Hence we may write the tautomeric equilibria 20 to 23 in the following way RH’ e RH’’,
SH‘ e SHN,
I-‘
c +
I-”
and IH2+’
IH2+”
T h e total isomerization RH’ -+ SH” may take place in the ways contained in the following scheme, where we have left out the acids and bases which t,ake part in the protolytic reactions.
One of the tautomeric forms of the equilibria 20 to 23 may often be present only in very small quantity compared with the other. Thus the equilibria 20 and 21 will for electrostatic reasons always be highly displaced in favor of the uncharged forms RH’ and SH”. It is often possible to predict from the constitution which of the tautomers of equilibria 22 and 23
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KAI JULIUS PEDERSEN
is predominating. Thus in the case of acetone the concentration of I-’ (CH2.CO-CHS) will probably be very small compared with that of I-”
.
(CH~ :CO CH,) Strictly, we cannot speak in the ordinary sense of concentration of the single tautomerides. However, in a given reaction a certain fract,ion will behave as if it had one constitution, the rest as if it had the other. If we ascribe to the single members of the above tautomeric equilibria a definite concentration, this therefore implies the assumption that the same fraction of a given tautomeric substance behaves as if it had one of the constitutions in all protolytic reactions concerned. One or more of the reactions in scheme 29 may be excluded for structural reasons. If the atom X in the original molecule H X - Y:Z has a complete octet of shared electrons, a bond-shifting can take place only after X has given off a proton. This is the case when X i s a carbon atom. Thus, when RH’ is the keto form of acetone, the reactions 20 and 23 are excluded. It has been found by Dawson (17) that the enolization of acetone is catalyzed by both acids and bases. The only possible mechanism for the acid catalysis is that expressed by the scheme CHa.C0.CH3 (RHO
CHI.(C:6H).CH3 $ CH2.(C:6H).CHs (IHz+’)
(SH’)
CH2:COH.CH3
(SH”)
i-
There can be no doubt that the ion CH,. (C: OH).CHdwill give off a proton bound to the oxygen atom much more easily than one bound to a carbon atom. Consequently, the reaction denoted by a heavy arrow in the scheme determines the velocity of the prototropic isomerization. Here the apparent acid catalysis is a basic catalysis of the ion
+
CH,. (C: OH) ‘CH,. If it were possible to follow the opposite reaction, the ketonization of the enol form of acetone, we would also find general acid catalysis. In this case we would have a genuine acid catalysis of the form
+
CH2- (C :OH) CHd, which is, however, present only in extremely small concentration. If both X and Z in the original molecule have complete octets of shared electrons, the only way of bond-shifting is by reaction 22 in scheme 29. Thus the prototropic isomerization of a pure three-carbon system (that is a system where the only possible prototropy is of the type C . C : C $ C :C C) proceeds in the following way RH’ + I-’
e I-’’ e SH”
(31)
According to this mechanism the reaction is catalyzed by bases, but not by acids. As far as known, acid catalysis has never been found in such sys-
PROTOLYTIC REACTIONS AND PROTOTROPIC ISOMERIZATIOK
597
tems. However, it has been found in some three-carbon systems of the type 0 : C . C : C . C Ft O:C.C.C:C, e.g., glutaconic acid (18). Here it + may be explained as a basic catalysis of the ion HO :C C :C C. The mechanism expressed in scheme 31 seems to be very common in prototropic reactions. It is the only one which we can never exclude. It is of interest to examine it a little further in order to find which of the single reactions determines the velocity of isomerization. The ordinary (apparent) acid strength of the prototropic system
-
is no measure of the real strengths of the acids R H and SH. These may formally be defined by the equations
where it is assumed that equilibrium 31 is attained. The apparent strength is between the real strengths of the two acids. If the fraction eof the prototropic system is of the form SH when equilibrium is attained, we have
+
+
If the medium contains an acid A the reactions I-’ A -+ RH’ B and I-’’ A -+ SH” B will take place with velocities which we denote by v‘ and v” respectively. v’ and v” depend upon the concentrations and basic strengths of I-’ and I-”. By means of formulas 8 and 32 we get
+
+
the following approximate expression for the ratio of the velocities
From this equation we get the following rules. When SH is a very much stronger acid than RH and E is not extremely small, we have v” > > v‘, that is, the velocity of the prototropic reaction is determined by the protolytic reaction between RH and the bases. If, on the other hand R H is very much stronger than SH and 1- E not extremely small, we have v‘ > > v”, that is, the velocity of the prototropic reaction is determined by the protolytic reaction between I-‘’ and the acids. As an example we shall discuss the basic catalysis of the enolization of acetoacetic ester CH3COCH2COOC2H5(35, 36). For simplicity we only
598
KAI JULIUS PEDERSEN
write O:C-CH2. Frcm scheme 29 we find the following two possible mechanisms
O:C.CH,
@ O:C*CH
a
(I-f)
(RH’)
and
O:C*CHz (RH’)
O:C.CH
O.C:CH (1-ff)
+
a
HO*C:CH (SH”)
-
Ft- HO:C-CH @ HO*C:CH
(I-’)
(SW
(33)
(34)
(SH”)
The acid strength of the enol form SH” is undoubtedly so much greater than that of the keto form RH’ that, although E is only 0.004, the ion Iwill mainly form SH’’ when it reacts with acids. Consequently the reaction denoted by a heavy’arrow determines the velocity of the total process 33. However, when we consider scheme 34, the ion I-’ will undoubtedly take up protons much more quickly a t the carbon atom than a t SH’ will be much the oxygen atom. In other words, the reaction I-’ slower than RH’ --+ I-’. From this we conclude that the mechanism in scheme 34 is of no importance for the isomerization. This proceeds by reaction 33. We measure the velocity of dissociation of the extremely weak acid, the keto form of acetoacetic ester. If we measured the opposite reaction, the ketonization of the enol form, we would also find general basic catalysis, but this would in reality be a reaction between the ion I-’ and the acids: I-’ A -+ RH’ B. The basic catalysis of the enolization of acetone follows probably the same mechanism, but here the conclusions are less safe, because E is so small that it has been impossible to measure it. Protolytic reactions between ordinary acids or bases are generally too rapid to be measured. When the acid or base is so weak that we might expect to find a slow reaction, it is generally impossible to measure the rate because equilibrium is attained when too little of the corresponding system is formed. The reason why it is sometimes possible to measure the velocity of protolytic reactions in prototropic systems is to be sought in the tautomerisms 20 to 23. The rate of the protolytic reaction of one of the acids (or bases) in scheme 29 is measurable if the acid (or base) is sufficiently weak and its corresponding base (or acid) is transformed sufficiently completely into its tautomer. It may be measurable even when the acid (or base) is not especially weak, if the concentration of the acid (or base) is kept sufficiently small by a tautomerism. Examples of these two types of protolytic reactions may be found in the discussion of acid catalysis of the isomerization of acetone (scheme 30). We may add a few words on the pseudo acids. The usual idea of the mechanism of dissociation (Hantzsch (19)) is expressed by the scheme ---f
+
+
RH
e SH
S-
+ H+
(35)
PROTOLYTIC REACTIONS AND PROTOTROPIC ISOMERIZATION
599
RH is called a pseudo acid, and SH the aci-form. This opinion is not supported by the points of view maintained in this paper. The system RH SH is an ordinary prototropic system. The mechanism of neutralization follows not scheme 35 but 31. There is no difference in principle between the acid character of the pseudo and aci-form. They are both genuine acids, but the pseudo form is a much weaker acid than the aciform (cf. the discussion of scheme 31). The so-called pseudo acids are not false acids, but acids with false strength. SUMNARY
Bronsted’s theory of acid and basic catalysis and our knowledge of protolytic reactions have been discussed. Experiments on the decomposition of nitramide have been compared with the theory. Some of the main results in the study of prototropic reactions have been pointed out. Lowry’s electrolytic theory of prototropic reactions has been criticized. Another mechanism of prototropic reactions has been discussed. My thanks are due to Professor Niels Bjerrum for kind interest in my work. REFERENCES
(1) BAKER:J. Chem. SOC.1928, 1583, 1979; 1929, 1205. (2) BJERRUM AND UNMACK: Kgl. Danske Videnskab. Selskab Math. fys. Medd. 9, No. l(1929). (3) BRONSTED: Rec. trav. chim. 42,718 (1923); J. Phys. Chem. 30, 777 (1926). (4) BRONSTED: Chem. Rev. 6, 231 (1928). (5) BRONSTED: Trans. Faraday SOC.24, 630 (1928). (6) BRONYTED: Z. angew. Chem. 43, 229 (1930). AND BELL: J. Am. Chem. SOC.63,2478 (1931). (7) BRONSTED (8) BRONSTED AND D u m : Z. physik. Chem. 117,299 (19251). (9) BRONSTED AND GUGGENHEIM: J. Am. Chem. SOC.49, 2554 (1927). (IO) BRONSTED AND KANE,Ross: J. Am. Chem. SOC.63,3624 (1931). (11) BRONSTED AND KING: J. Am. Chem. SOC.49, 193 (1927). AND PEDERSEN: Z. physik. Chem. 108, 185 (1924). (12) BRONSTED (13) BRONSTED AND VANCE: Z. physik. Chem. 163A, 240 (1933). AND VOLQVARTS: Z. physik. Chem. 166A, 211 (1931). (14) BRONSTED (15) BRONSTED AND WYNNE-JONES: Trans. Faraday SOC.26, 59 (1929). (16) CONANT AND COWORKERS: J. Am. Chem. SOC.64, 2881, 4048 (1932). (17) DAWSON AND COWORKERS: J. Chem. SOC. 1926, 2282, 2872, 3166; 1927, 213, 458, 756; 1928,543, 1239, 1248,2844; 1929, 1217, 1884, 2530; 1930, 79, 2180; 1931, 2658; 1932,2612; 1933,49, 291. (18) FITZGERALD A N D PACKER: J. Chem. SOC.1933, 595. (19) HANTZSCH: Ber. 32, 575 (1899). A N D ROUGHTON: Proc. Roy. SOC. London 104A, 376 (1923); Proc. (20) HARTRIDGE Cambridge Phil. SOC.22, 426 (1925); 23, 450 (1926).
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(21) IXGOLD AXD COWORKERS: J. Chem. SOC.121, 2381 (1922); 1929, 447, 1199. (22) INGOLD, SHOPPEE, AND THORPE: J. Chem. SOC.1927,1477. (23) KILPATRICK A N D COWORKERS: J. Am. Chem. Soc. 63, 8217, 3698 (1931); J . Phys. Chem. 34, 2180 (1930). (24) LA MER AND READ:J. Am. Chem. SOC.62, 3098 (1930). (25) LARSSOK: Z. anorg. Chem. 166,247 (1926). J. Am. Chem. SOC.64, 2393 (1932). (26) LIVINGSTOX: (27) LOWRY:Chemistry & Industry 42, 43 (1923). (28) LOWRY:Chem. Rev. 4,231 (1927). (29) LOWRY:J. Chem. SOC.1927, 2554. (30) L O ~ T R A NYD RICHARDS: J. Chem. Soc. 127, 1385 (1925). (31) LOWRY AND SMITH:J. Chem. SOC.1927,2539. (32) MEYERAND COWORKERS: Ber. 63, 1410 (1920); 64, 579 (1921). (33) N Y L I ~ NStudien : uber organische Phosphorverbindungen. Dissertation, Uppsala, 1930. (34) PEDERSEX: Kgl. Danske Videnskab. Selskab Math. fys. Medd. 12, No. 1 (1932). (35) PEDERSEN: Den almindelige Syre- og Basekatalyse. Dissertation, Copenhagen, 1932. (36) PEDERSEN: J. Phys. Chem. 37, 751 (1933). (37) RICEAND SULLIVAX: J. Am. Chem. SOC.60,3048 (1928). (38) SAAL:Rec. trav. chim. 47,90 (1928). (39) SHOPPEE:J. Chem. SOC.1930,968; 1931, 1225. (40) THIELE. ~ X DLACHMANN: Ann. 288,269, 270 (1895). AND INGOLD: Union internationale de la chimie pure et appliquee (41) THORPE (1923). (42) WATSON AND YATES:J. Chem. SOC.1932, 1207.
