May 20, 1962
POLAR EFFECTS ON RATESAND EQUILIBRIA
[CONTRIBUTION FROM THE SCHOOL OF CHEMISTRY OF
THE
1989
GEORGIA INSTITUTE OF TECHNOLOGY, ATLANTA 13, GA.]
Polar Effects on Rates and Equilibria. V. Relationships between Rates of Corresponding Acid-, Base- and Un-catalyzed Reactions1 BY JACK HINEAND RAYMOND P. BAYER RECEIVED NOVEMBER 27, 1961 Existing qualitative generalizations about the effect of structure on reactivity are applied to certain acid- and/or basecatalyzed reactions. Upper and lower limits for the susceptibility of simple heterolysis reactions to acid catalysis are deduced. From the assumption that if the eguiltbrium constant for the rate-determining step of a given acid-catalyzed reaction i s equal to that of the corresponding base-catelyced reaction the rate constants will also be equal, quantitative relationships between the rates of acid and of basic hydrolysis of ethyl benzoates and between the rates of acid and basic hydrolysis of benzamides are derived. These relationships, whose application requires estimates of the acidity and basicity of such intermediate species as ArC(OH)zOEt’s,are found to agree with the experimental values within a factor of lo2, and therefore within the reliability of the various estimated K’s and p’s.
Bell has put certain qualitative ideas about the accepted that this reaction involves the intereffect of structural changes in the reactants on the mediate formation of RC(OH)2NH27(or a protonshape of the potential energy surface for the re- ated and/or deprotonated form of this species) action into reasonable quantitative forms in dis- and that in acidic solution amides are protonated ~ be shown that the cussing the basis of the Bronsted catalysis equation largely a t o ~ y g e n ,it~ , may and other topics of importance in acid and base reacting species is probably the oxygen-protonated catalysis.2 The methods of Bell and also the gen- rather than the nitrogen-protonated amide. This eralizations of Leffler and of Hammond concerning follows from the fact that the immediate reactant relationships between the nature of the transition I is more stable than the immediate reactant IV and state and that of the reactant and p r o d ~ c t ~ ~ ~certainly the immediate product I11 is more have suggested derivations of equations for lim- stable than the immediate product VI. Therefore itations on the extent of acid and/or base catalysis OH OH OH to be expected in certain cases and also for quanti1 + HzO I +6 I +R-C-NHn tative relations between the catalytic constants for R-C=NHz +R-C-NHz acid-, base- and un-catalyzed reactions in certain I +6dHs I1 +AH2 I11 other cases. I n addition, we shall make liberal 0 0 -6 0use of the Hammett e q ~ a t i o nof, ~Taft’s equations,6 I 1 H2O Ii I and of the discussions these workers have presented R-C-NHa+ --f R-C-NHa+ +R-C-NHs’ concerning the basis and significance of their IV +adHz v +&HI VI equations. In this paper we shall use the term corresponding if all properties (except the total energy contents) reactions in the following restricted sense. Cor- of the transition states may be expressed as linear responding acid- and base-catalyzed reactions are combinations of the properties of the reactants reactions in which the immediate reactants in and and products,3the transition state I1 must be more the immediate products of the rate-determining stable than V and most of the reaction must prostep diiTer only in the nature and extent of their ceed via the oxygen-protonated amide. Analogous protonation ; the transition states differ in this arguments may be applied to the mechanism of acidmanner and may also differ in the extent to which catalyzed ester hydrolysis and many other rethey resemble the immediate reactants and/or actions. products. That is, the reactions must proceed by Acid Catalysis of Simple Heterolysis Reacthe same mechanism, but the transition states may tions.-A somewhat more quantitative approach lie a t different points along the reaction coordinate. may be made to the possible extent of acid catalysis For example, the transformations of ethvlene oxide of simple heterolysis reactions. In the heterolysis to ethylene glycol by S s 2 attack of hydroxide ion of XY it seems clear that XYH+ should react faster on ethylene oxide or its conjugate acid or by Sh-2 than XY and that X + should combine with Y attack of water on ethylene oxide or its conjugate faster than with HY. Whether the reaction is acid are all corresponding reactions. ki Mechanism of the Acidic Hydrolysis of Amides.XY,x++Y(1) The generalizations suggested in this paper may be k- i applied qualitatively in a discussion of the mechakz nism of the acidic hydrolysis of amides. If it is XYII+ X + + HY (3)
(1) For part IV see J. Hine and W. C. Bailey, Jr., J . Org. Chcm.. 2 6 , 2098 (1961). (2) R. P. Bell, “ Acid-Base Catalysis,” Oxford University Press, London, 1941, chap VIII; “The Proton in Chemistry,” Cornel1 University Press, Ithaca, N. Y.,1959, chap. X. (3) J. E. Leffler, Science, 117,340 (1953). (4) G. S. Hammond, J. Am. Chem. SOC., 77, 334 (1955). ( 5 ) L. P. Hammett, “Physical Organic Chemistry,” McCrawHill Book Co., Inc., New York, N. Y.. 1940, chap. VII. (6) R W. Taft, Jr., in M. S. Xewman, “Steric Effects in Organic Chemistry,” John Wiley and Sons, Inc., New York, N. Y., 1956, chap. 13.
k- t kz
> ki; k-1 > k-2
(3)
subject to any significant acid catalysis also depends on the basicity of X-Y. If it is assumed that the (7) J. Hine, “Physical Organic Chemistry,” McGraw-Hill Book Co.9 Inc., New York, N. Y.,1956, sec. 13-4c. (8) A. R. Ratritzky and R. A. Y. Jones, Chcm. & Ind. (London), 722 (1961). (9) I. R. For, P.L. Levins and R. W . Taft, Jr., Tetrahedron Letters, 249 (1961).
1990
JACK
HINE AND RAYMOND P. BAYER
Vol. 84
various proton-transfer reactions involved are much faster than the heterolysis reaction, then the rate constants in the experimentally observed rate equation uf = kn+[H+][XY]-I-k,[XY]
niay be seen to have the significance
0
I1
kn+
k 2 / K x y a + and ku = kl
(4)
Xr-C-X
0-
+Ar-C-X1 kb
f OH-
By combining the equilibrium expressions for reactions 1 and 2 i t follows that kik-zlk-ikz = KHY/KXYE+
OH (P-)
(R)
K X Y H += [ H + ] [ X Y ] / [ X Y H + ]
The rates of formation of H P H + and of P- may be expressed UE+ =
and VOH- =
(5)
where KHY = [H+J [Y-]/ [HY]. Combination of eqs. 3, 4 and 5 gives the following limitations for kH+/k,, a fraction that measures the sensitivity of the reaction to acid catalysis. From eq. 6, in
+final products
1
where
~H+[H+][R]
(8)
koa-[OH-][R]
(9)
In terms of the reaction mechanism given i t may be seen that koH- is identical to k b and that kH+
=
ka [HzO]/KRH+
(10)
where KRH = [Rl [ H + l / [RH +I +
~IKEY > kn+/ku > 1/Kxyn+
(6)
aqueous solution, heterolyses of RI's, RBr's and RCl's should be essentially insensitive to acid catalysis'O; the heterolysis of RF's might be sensitive to acid ~ a t a l y s i s ' ~the ; heterolysis of ROH's would probably be sensitive to acid catalysis, and that of RNHz's should certainly be sensitive to acid catalysis. A Quantitative Relation between the Rates of Corresponding Acid- and Base-catalyzed Reactions.-For the deduction of a quantitative relation between the rate of an acid-catalyzed reaction and that of the corresponding base-catalyzed (or uncatalyzed) reaction an additional hypothesis is required. Hammett and Taft have shown that there are large families of compounds and reactions for which correlations between rate and equilibrium constants may be made.5.e We shall assume that corresponding acid- and base-catalyzed reactions are in this category and therefore that when the equilibrium constants for the ratedetermining steps of such reactions are identical the rate constants will be also.14 As specific examples of the application of this assumption we shall consider the effect of acid and base on the rates of hydrolysis of amides and esters of benzoic acid and its derivatives. \Ye shall assume that these reactions involve the intermediate formation of the species H P H + and Pin acidic and basic solutions, respectively, as (10) Although attempts to find acid catalysis in the solvolysis of certain chlorides in largely aqueous solution were unsuccessfu1,ll such catalysis might be expected and has been observed in more weakly basic solvents such as nitrobenzene.'% (11) S. C. J. Olivier and G. Berger, Rec. Irav. chim., 41, 637 (1922); S . C. J. Olivier and A. P. Weber, ibid., 53, 869 (1934). (12) H. F. Herbrandson, R. T. Dickerson, Jr., and J. Weinstein, J. A m . Chem. SOC.,7 6 , 4046 (1954). (13) For observations of such catalysis see W. T. Miller, J r . , and 7, Bernstein, ibid., 7 0 , 3600 (1948); N. B. Chapman and J. 1,. Levy, J . Chem. .'Yo
