J. A. Leisten Sheffield Universitv England
II
Homogeneous Catalysis A reexamination o f definitions
T o what extent is the action of a catalyst understood? Does it always lower the activation energy? Does it never affect the position of equilibrium? How is it best defined? What is special about acid-base catalysis? This article is concerned with these and similar questions which are considered briefly, or not a t all, in most textbooks. The answers are sought by examining various examples of catalysis1 beginning with some which most chemists would accept as typical.
which through rearrangement of electrons (as shown by the arrows) could form the products; but it is unlikely that IV would be formed to any great extent because 0 . . .H-C hydrogen bonds are weak and fourmembered rings are strained. In fact no easy direct path for this reaction can be visualized. The next reaction, the racemization of ketone V, is an example of catalysis in solution (3). The hydrogen atom on the asymmetric carbon atom of this ketone 0
CHX
Typical Cases of Catalysis
The dehydration of t-butanol vapor occurs a t 315°C in the presence, and a t a rate proportional to the concentration, of hydrobromic acid: CHx
-
CH.
\
\CcH, CH.
/I
OH
c = cH, + n,o
/
CH,
A reason for this catalysis is easily found. Strong hydrogen bonding between the two components can be expected to produce the six-membered ring complex, I ; and a redistribution of electrons in the ring, as in 11, would lead to the products, 111. .(The electronic shifts are thought to occur somewhat out of phase ( I ) . ) CHI
H
\
CH,
\
cH,c-C/--H
/"
cH,-CCH
'
H
H-dr
H-Br I1
I
CHa
H
\
cH,-c=& HO
\
/"
H Br 111
The idea can be embodied in a reaction mechanism which explains the rate observations:
-
Ghutanol complex I
SIOV
has a tendency to ionize as a proton, and since the proton can reattach itself to form either a Zevo or a dextro molecule, the ketone is able to racemize. The most obvious catalyst for tbis process is of course a base, such as the acetate ion: n
+ HBr = comulen I isobutene + H1O + HBr
(1)
The rate is governed by the slow breakdown of I, the concentration of which, [I], is proportional t o [HBr] in the equilibrium stage; thus the rate is proportional to [HBr]. To complete the picture we need to understand why the reaction follows the catalyzed path rather than a direct one. It is easy to represent an internally hydrogen-bonded complex, IV,
According to tbis mechanism the first step determines the rate, which should therefore be proportional to the concentration of the catalyst. The observed kinetics are in fact the same as in the previous example. I n each case the substrate, S, disap~earsaccording to a first-order rate equation:
The first-order constants (!cab) in mixtures containing different concentrations of the catalyst C are found to fit the equation: k&
=
(4)
Combination of equations (3) and (4) shows that the complete rate equation is second order:
CHI
Since this article is not concerned with catalysis at surfaces, but only with homogeneous catalysis, the qualifying word will usually beomitted.
Volume 41, Number 1 , Jonuory 1964 j 23
The variation of the observed rate constant with the catalyst concentration is often given by equation (4), often by other equations such as (6) and (7). kdr =
k,
+ EJCI
(6)
kos.
=
ke[Clz
(7)
Equation (6) applies to the mutarotation of glucose, catalyzed by amino acids. A different value of lc, (the catalytic constant) is found for each amino acid, but k, is common to them all (0.73 hrr' a t 18°C). There is only one reasonable interpretation: the amino acid catalyzed reaction is supplemented by an uncatalyzed reaction which proceeds a t the same rate in the amino acid solutions as it does in water. Typical results for the amino acid betaine are shown in the table (3). Concentration of Betoine (molesAiterl
knh. (h7-l)
Equation (7) applies to the reduction of ceric salts by dissolved hydrogen, catalyzed by silver ion (4). This is consistent with the mechanism
+ HS
doa
+ 2Hi fast Ag + Ce4++Agt + Ce3+ 2Ag+
----t
2Ag
(8)
One more example will complete a representative group. The recombination of iodine atoms in the presence of benzene vapor has been studied by flash photolysis. It follows second-order kinetics, but separate experiments show the second-order constant to be proportional to the benzene concentration, and so the complete rate equation is
There is no difficulty in explaining why the catalyzed process occurs in preference to recombination by a simple collision of two iodine atoms, for the latter cannot occur a t all: the colliding atoms must fly apart unless a third body is present to remove some of their energy. I n fact the mechanism of the benzenecatalyzed recombination was once thought to be just such a three-body collision: 21
+ CsHs
-+ I
CaHe
(10)
This and the alte~native mechanism (11) account equally well for the observed rate equation, but (11) is now favored on other grounds (5). I
+ CeH6= I
/
" .
Some Less Typical Examples
Although benzene does not react perceptibly with acetic anhydride by itself, it is readily acetylated in the presence of anhydrous aluminum chloride. It is not therefore surprising that aluminum chloride is described as a catalyst in this Friedel-Crafts reaction. However, since aluminum chloride is a Lewis acid it readily forms oxonium complexes, and the stoichiometry of the reaction is more accurately represented by equation (13) than by equation (12).
CeHs
The formation of a charge-transfer complex in a fast equilibrium is followed by a rate-determining attack by iodine atom. In all of these examples the rate of reaction is simply related to the catalyst concentration, and this concentration is effectively constant throughout the reaction. Many thousands of reactions have the same 24
experimentally observable characteristics, so it is worth looking for other generalizations. Our examples show several basically different reasons for catalysis; but as seen in the mechanisms of equations (I), ('4, (8), (lo), and ( l l ) , the catalyst in all cases is treated as a reactant which exerts a normal mass-action (or mass-law) effect on the rate and is then regenerated. It is only in the regeneration that it differs from an ordinary reactant. There is now a feeling of certainty in this kmd of explanation. Each individual mechanism is in doubt and open to revision, but in modern work a disproved mechanism is always replaced by another, as shown in the recombination of iodine atoms. Another interpretation which is common to all the examples is that the addition of catalyst does not alter the rate of a reaction which is already taking place, albeit slowly; it enables an alternative reaction to occur which gives the same products. This has important consequences. Since, for example, the catalyzed reaction cannot proceed in the opposite direction to the uncatalyzed one, i.e., away from equilibrium, this kind of catalysis must always be positive, though it can of course be very weakly positive as in the betainecatalyzed mutarotation of glucose. (The hydrolysis of ketals is so sensitive to hydrogen ion catalysis that the rate is proportional to [H+] even in alkaline solutions. It follows from k, = [OH-] [H+] that under these conditions the rate will be inversely proportional to [OH-]. This indirect kmd of negative catalysis is not uncommon.) Finally, since the catalyzed and uncatalyzed reactions have no special relation to one another except that they give the same products, there is no basis for generalizing about the relative temperature coefficients of the rates; and the catalyzed reaction dor.s ~ m nrcrasnrily t have thr lower tww#y of activation. 'l'hr ucid-cat~~l\~zerl hvdrnlvsis of u-mrtl~ouvdiol~t~~it~l " " " benzoate has a considerably higher activation energy than the uncatalyzed hydrolysis; yet in moderately acid solutions hydrolysis occurs entirely by the catalyzed route because this has much the higher Afactor (6).
Journal of Chemicol Education
It follows that AICla is required in equivalent quantities, and that its concentration will affect the equilibrium. I n fact it is a normal reactant. I n practical terms it is a catalyst because it facilitates acetylation: in this sense the difference between equations (12) and (13) is unimportant. (The mechanism of Friedel-Crafts catalysis is discussed in many textbooks.) The hydrolyses of ethyl acetate and acetamide are said to be
catalyzed by acids, for in dilute mineral acids the rates of the two reactions are proportional to [HaO+]. Careful studies have shown that the mechanisms are similar. Yet in one case the hydrogen ion is really a normal reactant: CH,CONH,
+ HsO+
-
CHsCOnH
+ NHr+
There are many cases of this k i d , in which the catalyst is consumed in the reaction. A particular type of catalysis is associated with chain reactions. The thermal decomposition of acetaldehyde vapor can be understood in a general way from the following simplified mechanism: CHaCHO
-
CHI
+ CHO
reaction (15) on the other hand, the inert salt should decrease the rate by stabilizing the reactants more than the transition complex, which this timc has only a single charge.
+
Ca(H20)6Br++ OH--
Co(HzO)sOHf+
+B
r
(15)
For dilute solutions of ions in polar solvents such as water the quantitative treatment of these ideas leads to the Br@nsted-Bjerrum equation, a test of which is shown in the figure, for the reactions (14) and (15). Ionic strength is a simple function of the total salt concentration, k is the second-order rate constant, and k. the same constant at zero ionic strength. The lines are derived from the theory and the points are experimental (7).
The second and third steps are very fast, and as well as giving the final products they propagate a chain by regenerating free radicals. The overall reaction will therefore occur readily providing sufficient radicals are produced in the first, chain-initiating, step. This happens normally a t about 500°C; but if a little azomethane is added, the decomposition of acetaldehyde occurs a t temperatures as low as 300°C. The explanation of this catalysis is that azomethane is relatively unstable and decomposes to give chain-carrying methyl radicals: CHsN=NCHs
-
ZCHJ
+ N1
Other substances, e.g., nitric oxide, can retard the reaction, even when present in low concentrations. The retardation is due, a t least partly, to the fact that nitric oxide is an odd-electron molecule which can combine with free radicals by electron pairing, and so remove the chain carriers. The chain length in this reaction may be several hundred, and a single molecule of azomethane may therefore cause many molecules of acetaldehyde to decompose. Nevertheless azomethane is necessarily destroyed in the process. Similar considerations apply to nitric oxide. Catalysts of this k i d are sometimes called chain initiators or sensitizers and the negative catalysts are called inhibitors. All the previous examples of catalysis have depended on reactions between definite numbers of molecules or ions, and the dependence of the rate upon the catalyst concentration has been calculable from a reaction mechanism and the mass law. The next examples illustrate a different kind of catalysis. Although the tendency of an ion in solution to attract oppositely-charged ions is opposed by thermal jostling, it is nevertheless likely to have an excess of oppositely charged ions in its neighborhood, and for this reason it is stabilized by electrostatic interactions, as it would be (though to a greater extent) in a crystal. I n the reaction between thiosulfate and bromoacetate ions, which is thought to occur in the single step (14), SzO,-
+ BrCH,CO,
+ S20,CH,C0,-
+ Brr
(14)
the addition of an inert salt to the system should stabilize the transition complex which has a triple charge more than the less highly charged reacting ions. The free energy of activation should therefore decrease and the rate should increase as the inert salt is added. In
0
0.02
0.04
0.06
0.08
Ionic Strength% Bronsted-Bierrum =aheffects.
Many reactions in solution are subject in some degree to effects of this k i d ; and although the quantitative treatment is generally less successful than in the cases above, where all the reactants are ions and the solutions are very dilute, the relation between the rate and the salt concentration is generally complex, as in the figure. This helps to distinguish these effects from mass-law catalysis. For example, in the reduction of ceric ion by hydrogen, Ag+ is clearly a mass-law catalyst because it has a precise second-order influence on the rate (see equation (8)). The distinction is not always made so easily (8). This k i d of catalysis is caused by the interaction of indefinite numbers of ions (and sometimes molecules), and the catalyst is best considered as altering the rate by the normal route rather than providing an alternative route. Since acceleration and retardation are explained by essentially the same theory, positive and negative catalysis are simple opposites. I n all of these ways this catalysis differs from mass-law catalysis, from which it is usually distinguished by the name kinetic salt effect. Definitions of Catalysis
The cases discussed above introduce many ideas, and no short definition would encompass them all. For example, a catalyst i s a substance which accelerates a reaction without being easumed excludes most of the cases under the previous heading. The definition of catalysis is a matter of preference; but if a choice is to be made between restrictive definitions, it seems reasonVolume 41, Number 1, Jonuory 1964
/
25
able that the one adopted should be in harmony with the current interest in reaction mechanisms. Let us see where this criterion leads. In several of the above examples a rate equation has been derived from a reaction mechanism by application of the mass law. (In practice of course it is the other way around: the rate equation is determined experimentally and then used to make deductions about the mechanism.) Kot surprisingly it is a convention that the rate equations should express only mass-law effects, so that they can be more easily interpreted. When necessary kinetic salt effects are eliminated by determining the rate equation in solutions of high ionic strength so that the reaction proceeds in a constant electrostatic environment (9). All of this shows that there is a need for terminology which separates masslaw and salt effects, and that the separation can be achieved by reference to the rate equation. A catal!lst is a substance which appears in the rate equation but not in the stoichiometrical equation is the simplest definition to exclude salt effects. It has been elaborated by Bell so as to include autocatalysis, as in the reaction
+
-
CClaC02CH3 HYO
CClrC09H
Acid-Base Catalysis
Of the special features associated with catalysis by acids and bases perhaps the most obvious is that acidcatalyzed reactions are often catalyzed by bases as well, and vice versa. The reason can be understood from examples. The crucial step in the hydrolysis of ethyl acetate is almost certainly the formation of an addition complex, with the transfer of electrons shown by arrows in equation (16).
If we think of acids (A) as electron acceptors, and bases (B) as electron donors, it seems reasonable that both species should be able to facilitate this step by acting a t the positions shown in VI.
The same idea can be expressed in terms of Brgmsted's definitions of an adid as a proton donor and a base as a proton acceptor. By virtue of the charges created, proton addition as in VII will pull electrons, and proton removal as in VIII will push electrons in the direction which facilitates hydrolysis. The rate of racemization of ketone V is, according to equation ( Z ) , the rate of ionization of the or-hydrogen atom. The movement of electrons which accompanies this ionization is shown in IX. As might be expected this reaction is also catalyzed by acids and by bases.
/
Journal of Chemical Education
/\
CH1 C2Hj IX
To generalize, if a reaction is facilitated by the presence of an acid a t a point near the reaction site, then a basic species situated on the opposite side of the reaction site will also accelerate the reaction. It remains to show why there are some exceptions. An example already given is the acid-catalyzed hydrolysis of ketals, which is actually slower in alkaline solutions than in pure water. The steps which are helieved to determine the rate are given below:
+ CHOH
in which the rate is proportional to the concentration of trichloracetic acid: a substance i s said to be a catalyst for a reaction in a homogeneous system when its concentration appears in the velocity expression to a higher power than it does i n the equilibrium elpression (10).
26
.;c,;r
CeHsC-C
H
Obviously the proton should accelerate this reaction, but a base cannot do so because unlike the last two cases there is no suitably placed hydrogen atom for it to remove. If it donated electrons instead of removing a proton, the octet of the oxygen atom would he exceeded. There are similarly reactions which can be catalyzed only by bases. Another important feature is that of general and spec-fic catalysis. I n equation (2) the rate-determining step is the transfer of a proton to a basic catalyst. If there were a number of different bases (B,, B2,. . .) in the solution, this number of simultaneous processes would occur, each contributing to the observed rate constant, and it would he reasonable to expect the rate expression: koaa = ktIB;l kzlR11 +. . . This can actually be observed (by successively varying [B1], [B2],.. .) and is known as general base catalysis. Many cases both of general base and general acid catalysis are known. It is clear from this example that the observation of general catalysis throws light on the reaction mechanism, but, as always, more than one mechanism is capahle of explaining the same kinetic results. The demonstration of general catalysis narrows the range of possibilities but does not lead to a unique conclusion. The same is true of specific catalysis, which again is exemplified by the hydrolysis of ketals. I t follows from equation (17) that the rate of this hydrolysis is proportional to the concentration of the ketal's conjugate acid, which in turn is governed by the pre-equilibrium. The observed first-order rate constant therefore varies in differentacid solutions according to the equation
+
koh = k'[HaO+l /lH90)
(1x1
or, since [HD] is virtually constant in dilute solutions, k,sa = k[H30t!
(19)
These equations are valid even in the presence of other acids besides the hydrogen ion, because the equilibrium in equation (17) will still hold. This is usually called
specific hydrogen ion catalysis. However, if A is one of the other acids and B is its conjugate base, there will also be the equilibrium and the variation in kD0,will be described just as well by the equation k& = k"[A]/[B]
as by equations (18) and (19). The essential feature of specific catalysis is not a unique relationship between kOh and [H80+],but the fact that in mixed acid solutions ICg" is described by a single-tern equation, whereas in general catalysis there is a term for each acid. For this reason specific acid catalysis is perhaps a better name than specific hydrogen ion catalysis. Similar arguments apply to specific base catalysis. In dilute solutions of strong acids, up to about 0.5 M equilibria such as that in equation (17) are effectively ideal; but it is known from indicator studies that as the concentration of acid is further increased the concentration of the substrate's conjugate acid increases sharply. The power of the solution to protonate the substrate under these conditions is quantitatively described by an acidity scale (Hammett's acidity function, h.) which is in fact determined experimentally by using indicator-substrates. As might be expected from this, the hydrolysis of ketals, and related compounds such as acetals and methylal, obeys equation (18) in solutions up to about 0.5 M acid, but in more concentrated acids the values for hob,are much higher than those given by the equation. Under these conditions good correlation is found with Hammett's acidity function: kd'
=
kh,
The marked acid catalysis in concentrated solutions appears to be quite consistent with equation (17). The application of acidity and basicity functions to studies of reaction mechanism is the main activity in acid-base catalysis a t the present time (11). Teaching Catalysis
The emphasis in this article is on explanations of catalysis, rather than on phenomenological description.
The writer feels that little is gained, for example, by learning the equations associated with general and specific catalysis if their mechanistic significance is not appreciated. I t might he helpful to conclude by offering some suggestions for teachmg this topic. ( 1 ) Explain how mass-law catalysis occurs, by showing in one or two examples that a catalytic mechanism can account for the experimental facts, including the exact dependence of rate upon catalyst concentration. (2) Explain why mass-law catalysis occurs, by taking examples such as the acetate-catalyzed racemization of ketones, in which one can show convincingly why the catalyzed route is a favorable one. Emphasize that the catalyzed and uncatalyzed reactions are independent of one another, and that both may contribute significantly to the observed rate. (3) Distmguish kinetic salt effects, of the kmd associated with Bransted and Bjerrum, from mass-law catalysis. (4) A student who sees a difficulty in defining catalysis is probably in a better position than one who has learned a standard definition. Literature Cited (1)
MACCOLL, A,,
AND
STIMSON, V. R., J . Chem. Soe., 1960
2836.
C. K., "Stru~tureand Mechanism in Organic (2) INGOLD, Chemistry," Bell and Cu., London, 1953, p. 570. (31 F. H.. J . 0 7 0 . Chem..,2.431 (1938). , ~ WEGTHEIMER. , . . . (4) WEBSTER,A. H., ANI) HA~.PERN, J., J . Phys. Chen~., 60,280 (1956). G., D i s m ~ ~ i o Faraday ns Soe., 33,198 (1962). ( 5 ) PORTER, V. R., J. Chem. Soe., 1960 (6) JonNs, S. It., AND STIMSON, 467. (7) For discussion and refs. see DAVIES,C. W., "Progress in Reaction Kinetics," Pergxmon Press, 1961, p. 165. (8) WYATT,P. A. H., and DAVIES,C. W., Y'TansactiomFarady Soc.., 45.77411949). . , , (9) See, e g., SWAIN.C. G., AND KAISER,L. E., J. A m . Chem. Soe., 80,4089 (1958). (10) BELL,R. P., "Acid-Base Catalysis," Oxford University Press, 1941, p. 3. (11) See, e.g., LONG,F. A., and PAUL,M. A,, Chem. Rev., 57, 935 (1957): BUN NET^, J. F., J . A m . Chem. Soe., 83,
The present day heterogeneity of the Amrriean university i s both appalling and appealing. If some students attend uniuemities merely to increase earning power, others ale willing to wark for advanced degrees and enter fields where the remuneration will ntuw be i n the upper brackets. New PhD's i n science often go into industry at salaries equal to those of projessan who have devoted lifetimes t l training students. And yet goad universities have no great difieulty i n recruiting the best PhD's to their faculties provided they are able to promise facilities and time fo? scholarly work. The life o f seholamhip and of teaching, the nm-materialistic side of human endeavor, has a great appeal to properly inspired students. W. ALBERTNOYES, JR., Raccalau~eateAddress Univwsity of Rochester, June 1863
Volume 41, Number 1, January 1964
/
27
