The influence of acids on the hydrolysis of glycopyranosides

45

CARBOHYORATE RESEARCH

THE INFLUENCE OF ACIDS ON THE HYDROLYSIS OF GLYCOPYRANOSIDES C. K.

DE BRUYNE AND

J.

WOUTERS-LEYSEN

H.I.K. W., Lab. Anorgan. Scheikunde A, State University, Ghent (Belgium) (Received July 2nd, 1970; accepted for publication, August 6th, 1970)

ABSTRACT

In order to determine if someglycopyranosides hydrolyse via a bimolecular pathway, with participation of water in the rate-limiting step, the influence of the concentration of aqueous acids on the rate parameters was investigated. In each case, the entropy criterion is in accordance with a unimolecular (A-I) mechanism, without participation of water. The Zucker-Hammett criterion indicates an A-I mechanism in hydrochloric acid, but is useless in sulphuric acid, since the slopes are significantly different from - 1. The Bunnett criteria suggest a bimolecular pathway. The mechanistic interpretation of the parameters, w, w*, and ([> is discussed, and the conclusion reached that, for the glycosides under investigation, the values of these parameters do not prove the bimolecular mechanism, but are only another illustration of the failure of acidity functions as general mechanistic criteria. INTROOUCTION

The accepted mechanism for the hydrolysis of glycopyranosides involves a rapid, equilibrium-controlled protonation of either the glycosidic oxygen atom or the ring oxygen atom, to give the corresponding conjugate acid 1-10. Although the protonation of the ring oxygen atom cannot be entirely excluded, the available evidence 3 • 11 favours the protonation of the glycosidic oxygen atom. The conjugate acid, in a slow, rate-limiting, unimolecular heterolysis, decomposes to a glycosyl carbonium-oxonium ion, which then adds water. Thus, the rate-controlling step is unimolecular, without participation of water. This conclusion has been reached, using mainly the following criteria: the Zucker-Hammett criterion 12, the magnitude of the entropies of activation 2.5.13.14, and the Bunnett 15 criteria. However, on the basis of the latter criteria, Bunnett suggested, although with some reservation, that, for some glycopyranosides, the rate-controlling step should involve the participation of water as a nucleophile, and hence that the hydrolysis should proceed by a bimolecular mechanism. This would be the case for methyl and phenyloc- and fJ-o-glucopyranosides. Bunton et al.4, on the other hand, concluded that all these glycosides hydrolyse via the unimolecular mechanis~. Carbohyd. Res., 17 (1971) 45-56

c.

46

K. DE BRUYNE, J. WOUTERS-LEYSEN

The present investigation was initiated to obtain further evidence for the unimolecular, or for the bimolecular mechanism. Thus, methyl oc-D-glucopyranoside and phenyl P-D-glucopyranoside were hydrolysed in aqueous hydrochloric and sulphuric acid. Sufficient data were collected to test the Hammett and Bunnett criteria, and to calculate the activation parameters, in particular the entropy of activation. RESULTS

Hydrolysis of methyllX-D-glucopyranoside in hydrochloric acid at 70°

Rate constants and other calculated values at various concentration of hydrochloric acid are reported in Table I. A plot of log 106k 1 versus H ° indicates a linear function. Regression analysis leads to the equation: log 10 6 k 1 = 0.688-1.005 H o , with slope b = -1.005 ±0.013, number of points n = 12, the correlation coefficient r = - 0.9992, and the standard error of the estimate Sy/x = 0.03. Carefull inspection of the points, however, indicates that the function line is slightly curved, with a decreasing slope at higher concentrations of the acid. The departure from linearity is also evident from the better fit of a quadratic equation: log 10 6 k 1 = 0.662-1.119 Ho-0.057[HoF, with Sy/x and n = 12.

= 0.007,

R

=

-0.99995,

Values of log 10 6 k 1 , calculated from this function, are included in Table I. TABLE I DATA FOR THE HYDROLYSIS OF METHYL CX-D-GLUCOPYRANOSIDE

HCI -Ho (M)

log J0 6 k 1 log I06k 1 (sec- 1) (observed)

log J0 6 k 1 (calc.)

0.5 -0.20 1.0 0.20 1.5 0.47 2.0 0.69 2.5 0.87 3.0 1.05 3.5 1.23 4.0 1.40 4.5 1.58 5.0 1.76 5.54 1.95 6.05 2.13

2.73 7.59 14.5 25.2 38.9 58.7 90.2 134 189 278 420 610

0.4363 0.8839 1.1758 1.4074 1.5929 1.7746 1.9527 2.1175 2.2884 2.4556 2.6281 2.7877

0.4357 0.8805 1.1608 1.4007 1.5904 1.7688 1.9552 2.1284 2.2769 2.4444 2.6228 2.7850

(50mM)

Ho + log J0 6 k 1

0.6357 0.6805 0.6908 0.7107 0.7204 0.7188 0.7252 0.7284 0.6969 0.6844 0.6728 0.6550

IN

He!

AT

70°

log J0 6 k 1 Ho + log [HCl] -log [HC/] 0.7367 0.8805 0.9848 1.0997 1.1924 1.2918 1.4112 1.5264 1.6239 1.7454 1.8788 2.0030

-0.101 -0.200 -0.294 -0.389 -0.472 -0.573 -0.686 -0.798 -0.927 -1.061 -1.206 -1.348

Of course, this small deviation does not invalidate the Zucker-Hammett criterion, and, according to this criterion, the hydrolysis proceeds by the unimolecular Carbohyd. Res., 17 (1971) 45-56

47

HYDROLYSIS OF GL YCOPYRANOSIDES

A-I mechanism. However, it will be shown that the decrease of the slope has a definite influence on the determination of the Bunnett parameters. If the data are divided in two groups, regression analysis yields the equations: from M to 4M, log 10 6 k 1 Sy/x = 0.007, and n = 7;

= 0.676-1.041Ho,

with b

=

from 4M to 6M, log 10 6 k 1 = 0.853-0.907Ho, with b Sy/x = 0.007, and n = 5.

-1.041 ±0.OO6, -0.907 ±0.012,

The deviations of the slopes are significant, at better than the 0.99 level of singificance (t- and F-test). From these equations, it follows that the slope has an absolute value > I at low concentrations of acid, takes the value 1 at 3M hydrochloric acid (H ° =

- 1.05), and then further decreases. If, according to Bunnett 15 , log 10 6 k 1 +Ho is plotted versus log A (A = activity water), the line is curved and passes through a maximum at '" 3M hydrochloric acid. At this maximum, the parameter w (the slope of the line) changes from a negative (graphical estimate -0.5) to a positive value (+0.7) at higher concentrations of the acid. The strict application of the criterion should mean that the reaction is proceeding via a mixture of unimolecular and bimolecular pathways, and that, as the concentration of the acid increases, a larger number of molecules hydrolyse via the bimolecular pathway. If this were true, the change in mechanism should be reflected in the value of ASt, as one can expect that ASt will be larger for unimolecular cleavage reactions than for bimolecular reactions, involving the addition of water in the rate-limiting step. Accordingly, we determined the activation parameters for the hydrolysis of methyllX-D-glucopyranoside in M and 5M hydrochloric acid. In each case, In kl is a linear function of liT, and, as can be seen from Table V, the activation parameters remain constant. Thus, there is no indication of a change of mechanism, and the entropy of activation is consistent with the unimolecular heterolysis throughout the whole range of acid concentration. We also tried to calculate the Bunnett w* parameter, by plotting log kl -log[HCl] versus log A, but, again, the plot is distinctively curved and calculations are impossible. A rough graphical estimate shows that w* changes from -13 to -4 at higher concentrations of the acid, which indicates that a bimolecular mechanism operates at all of the concentrations. A plot of Ho + log k 1 versus H 0+ log [HCI], which defines the third Bunnett 17 parameter
0

Rate constants and calculated values are presented in Table II. Graphical analysis of log 10 6 k 1 versus Ho indicates a slightly curved line. Regression analysis Carbohyd. ReI., 17 (1971) 45-56

48

C. K. DE BRUYNE, J. WOUTERS-LEYSEN

yields the equations: log 10 6 k 1 = 1.796-0.935Ho, with b = -0.935 ±0.0l2, Sy/x = 0.02, r = -0.9994, and n = 10; and log 10 6 k 1 = 1.783 -1.0l6Ho -0.05[Ho]2, with Sy/x = O.oII, R = 0.9998, and n = 10. Although the calculations clearly show that the slope significantly differs from - I (t-test), and slightly decreases (in absolute value) with increasing acid strength, these

deviations are not sufficient to invalidate the Zucker-Hammett criterion, which indicates an Al mechanism. TABLE II DATA FOR THE HYDROLYSIS OF PHENYL P-D-GLUCOPYRANOSIDE

HCl -Ho (M)

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

-0.20 0.20 0.47 0.69 0.87 1.05 1.23 1.40 1.58 1.76

10 6k 1 (sec- I)

log lO6k l

38.9 93.4 172.8 286 427 639 918 1287 1872 2512

1.5898 1.9703 2.2373 2.4568 2.6305 2.8058 2.9628 3.1096 3.2723 3.4000

(50mM)

IN

Hel

AT

70°

Ho + log l06k l log l06k 1 -log [HCIl

1.790 1.770 1.767 1.767 1.761 1.756 1.733 1.710 1.692 1.640

Ho + log [HC/I

1.891 1.970 2.061 2.156 2.233 2.329 2.419 2.508 2.619 2.701

-0.\01 -0.200 -0.294 -0.389 -0.472 -0.573 -0.686 -0.798 -0.927 -1.061

Again, it was impossible to calculate the Bunnett wand w* parameters, since neither the Ho+log kl' nor the [log k 1 -(HCl)] plot is linear. In this case, however, w does not change its sign. Graphical estimation yields: w, from + 0.3 to + 1.3; w*, from -9.5 to -4, suggesting a bimolecular mechanism. On the other hand, a plot of Ho+log 10 6k 1 versus Ho+log [HCl] results in a nearly straight line, and the Bunnett cI> parameter can be calculated:

Ho + log 106k 1 = 1.813 + 0.136(Ho + 10g[HCI]), with cI> = 0.016, r = 0.94, and n = 10.

=

0.136±0.017,

Sy/x

On the basis of the Bunnett calibration reactions, this cP value is intermediate between a value (cI><0) for a reaction in which water is not involved in the rate-limiting step, and a reaction (0.22 < cI> < 0.56) in which water is involved as a nucleophile. Thus, except for the Zucker-Hammett criterion, none of the other criteria has a clear-cut mechanistic significance. Experimental values of kl (5M HCl) at different temperatures are presented in Table III. Aplot ofln kl versus liT is linear and LISt shows a positive value. Although this low positive value cannot be regarded as proof of the Al mechanism, because of the positive value of the standard entropy change in the proton-transfer reaction, it makes an A2 mechanism very improbable. Carbohyd. Res., 17 (1971) 45-56

49

HYDROL YSIS OF GL YCOPYRANOSIDES

TABLE III ACTIVATION PARAMETERS FOR PHENYL P-D-GLUCOPYRANOSIDE

HCI(5M)

44.40 50.05 54.80 60.00 65.75

55.40 61.05 65.80 70.30 76.00 79.70

96.7 208 403 821 1653

49.4 105 196 343 690 1085

EA = 29.0 ±0.2 kcal/mole LIst (70°) = +4.1 e.u.

EA = 28.5 ±O.I kcal/mole LIst (70°) = +2.6 e.u.

TABLE IV DATA FOR THE HYDROLYSIS OF METHYL IX-D-GLUCOPYRANOSIDE (50mM) IN H 2 S0 4 AT 70°

H 2 SO 4 (M)

-Ho

lO6k 1 (sec- 1)

log lO6k 1

Ho + log lO6k 1

log J0 6k 1 -log [H2 SO 4 ]

Ho + log [H2 SO 4 ]

0.492 0.983 1.475 1.966 2.458 2.949 3.441 3.932 4.424 4.915

-0.140 0.243 0.545 0.823 1.097 1.350 1.590 1.820 2.020 2.240

3.17 6.17 11.62 19.60 30.55 44.83 67.5 95.6 138.8 196.2

0.5012 0.7905 1.0652 1.2923 1.4860 1.6516 1.8292 1.9803 2.1424 2.2929

0.6412 0.5475 0.5205 0.4693 0.3880 0.3016 0.2396 0.1603 0.1324 0.0529

0.8092 0.7979 0.8964 0.9987 1.0947 1.1919 1.2925 1.3857 1.4966 1.6014

-0.168 -0.250 -0.377 -0.529 -0.766 -0.880 -1.050 -1.225 -1.369 -1.548

Hydrolysis of methyl rx.-D-glucopyranoside in sulphuric acid at 70°

Experimental and calculated values are collected in Table IV. Graphical analysis indicates a nearly linear dependence of log k 1 on H o. Regression analysis yields the equations: log lO 6 k 1 = 0.635-0.750Ho, withb = -0.750±0.01l,sy/x = 0.026, r = -0.9991, and n = lO; or log lO 6 k 1 = 0.614-0.827Ho-0.036[Ho]2, with Sy/x = O.oI5, R = 0.9997, and n = lO. In contrast to the hydrolysis in hydrochloric acid, the requirement of unit slope is no longer fulfilled, although there remains a linear dependence op H o. Small deviations from the unit slope are usually tolerated, but the observation of a slope of -0.75 makes a useful mechanistic application of the Zucker-Hammett hypothesis of doubtful value. On the other hand, plotting oflog kl against log [H+] gives severe curvature, and thus the reaction does not fit either of the Zucker-Hammett categories. Carbohyd. Res., 17 (1971) 45-56

c.

50

K. DE BRUYNE, I. WOUTERS-LEYSEN

Again, the Bunnett wand w* parameters depend upon the concentration of the acid; the w value changes from ca. + 3.7 to + 1.8, and the w* value changes from - 9 to -3. The plot of Ho+log kl versus Ho+log [H 2 S04 ] is linear: Ho+log 10 6 k 1 = 0.678+0.41(Ho +log [H 2 S04 ]), with Sy/x = 0.02, r = 0.996, and n = 10.

=

([>

0.41 ±0.01,

These three parameters indicate a bimolecular mechanism, whereas the high positive value of ASt (Table V) is inconsistent with this mechanism. TABLE V ACTIVATION PARAMETERS FOR METHYL OC-D-GLUCOPYRANOSIDE

HCI(M)

70.00 75.05 79.80 85.05 89.00

HCI (5M)

8.54 16.26 33.08 66.70 99.9

59.65 64.95 70.70 74.20 78.30

EA = 32.9 ±0.5 kcal/mole ASt (70°) = + 11.1 e.u.

66.3 141.5 302 504 876

4.32 9.99 21.1 40.2 79.2 152

60.20 65.50 70.15 75.25 79.80 84.70

EA = 32.1 ±0.2 kcal/mole ASt (70°) = + 11.4 e.u.

EA = 34.4 ±0.3 kcal/mole ASt (70°) = + 14.1 e.u.

TABLE VI DATA FOR THE HYDROLYSIS OF PHENYL P-D-GLUCOPYRANOSIDE

H 2 SO4 (M)

-Ho

0.492 0.983 1.475 1.966 2.458 2.949 3.441 3.932 4.423 4.915

-0.140 0.243 0.545 0.823 1.097 1.350 1.590 1.820 2.010 2.240

J0 6 k I

IN

H 2 S0 4

AT

70°

log lO6k I

Ho + log lO6k I

log lO6k I -log [H2 SO4 ]

Ho + log [H2 SO 4 ]

1.8345 2.0166 2.2808 2.5148 2.7292 2.9088 3.0993 3.2526 3.4322 3.6038

1.9745 1.7736 1.7358 1.6918 1.6322 1.5588 1.5093 1.4326 1.4222 1.3638

2.143 2.024 2.112 2.221 2.339 2.439 2.563 2.658 2.786 2.912

-0.168 -0.250 -0.377 -0.529 -0.706 -0.880 -1.050 -1.225 -1.364 -1.548

(sec-I)

68.3 103.8 191 327 536 811 1257 1789 2705 4016

(50mM)

Hydrolysis of phenyl P-D-glucopyranoside in sulphuric acid at 70 0 The experimental and calculated values are listed in Table VI. A plot of log kl versus H ° is linear. Regression analysis yields the equation:

log 10 6 k 1 = 1.884-0.762Ho, with b = -0.762±0.013, Sy/x = 0.03, r = -0.999, and n = 10. Carbohyd. Res., 17 (1971) 45-56

HYDROLYISS OF GLYCOPYRANOSIDES

51

Again, the slope differs significantly from -1 in the Zucker-Hammett plot, the wand w* parameters depend on the concentration of the acid (w changes from +0.7 to +0.2; w* from -9.5 to -3.5), but Ho+log k1 versus Ho+log [H 2 S04 ] gives a straight line: Ho + log 10 6 k 1 = 1.856 + 0.33(Ho+log [H 2 S04 ]), with if> = +0.32 ±0.01, Sy/x

=0.013, r = 0.997, and n = 10.

Whereas these parameters indicate a bimolecular mechanism, the positive value of LlSt (Table III) does not support this mechanism. DISCUSSION

Hammett-Zucker criterion and w parameter

In hydrochloric acid, there exists a linear correlation with H 0, and the requirement of unit slope is fulfilled. Together with the positive ASt values, this clearly indicates a unimolecular mechanism. In sulphuric acid, however, the slope differs significantly from -1, although there remains a linear correlation. Furthermore, the plot of log k1 against log [H+] gives severe curvature, and thus the reaction does not fit either of the Zucker-Hammett categories. We believe that, even in acids other than hydrochloric acid, the mechanism remains unimolecular, and that other factors, especially the electrolyte effects 1 8,1 9, on both the initial and transition state, cause a deviation from the unit slope. The behaviour of these and other glycosides 8 then only underlines the general, well-known problem in comparing the catalytic effectiveness of the acids, and the failure of the Zucker-Hammett hypothesis as a general, reliable test of mechanism. In all the cases under discussion, the w parameter, although not constant, indicates a bimolecular mechanism, in one case, even a change in mechansim. From our results, it follows as an experimental fact that the plots of log k 1 against H ° give nearly straight lines, even if the slopes are different from unity. Thus, the Hammett equation reads: log k1 = aH+bHo , and aH equals log k1 at the concentration of acid where H ° becomes zero. If we suppose that the Bunnett w-equation is valid, it reads Ho+ log kl = a B+ wlogA. At the acid concentration where Ho = 0, log A takes the, a priori, known value log A o, and the equation reduces to aH = aB+w log A o, or aH - aB = wlog Ao. Substitution of log k 1 in the Bunnett equation by its value from the Hammett equation yields: aH+bHo+Ho = aB+wlog A, Ho(b+ 1) = aB-aH+wlogA = w log [A/A o], and w = Ho(b+l) = P(b+l). log [A/Ao]

In this formula, b is always negative, whereas Ho and log [A/Ao] can be either Carbohyd. ReI., 17 (1971) 45-:-56

52

C. K. DE BRUYNE, J. WOUTERS-LEYSEN

negative or positive. The signs, however, are correlated, since, if H 0 is positive (negative), log [A/Ao] will also be positive (negative). Thus, P is always positive, and the sign of w is determined by the value of the slope b in the Hammett plot. For b = -1, w becomes zero; if b< -I (e.g. -1.1), w becomes negative; if b>-l (e.g. -0.9), then w takes a positive value. The mere fact that the slope b varies from -1.04 to -0.91, and therefore passes through b = -I, explains why w changes its sign. The curvature of the Zucker-Hammett plot may be due to experimental errors, but, even if this curvature is real, the only possible conclusion is that, since b approaches unity, w must approach zero, suggesting a unimolecular mechanism. For the other glycosides, the Hammett function is nearly linear and the absolute value of the slopes never exceeds unity, and thus, the w parameters are, and remain, positive. When the Hammett plot is linear, even the absolute value of w cannot be constant because, under these conditions, Pin w = P (b+ I) has to be independent of the concentration of the acid, which is not the case. A plot of P against the molarity of the acid shows severe curvature, especially at low concentrations. In these regions, P decreases with increasing strength of acid, and, if b is constant, the absolute value of w necessarily parallels P. The w parameter can be constant only if the ZuckerHammett plot itself shows severe curvature. The assumption that both the Hammett and Bunnett equations can be written as linear functions, with band w constant is incorrect. In our case, the fundamental question is the deviation of the slope b from unity, rather than the sign and/or value of w. Moreover, the Bunnett approach uses the Hammett acidity functions, although with hydration changes in the protonation of the indicator base, so that incorrect assumptions (e.g. the small medium-dependence of activity coefficient ratios) of the Hammett theory still play a role in the Bunnett approach. But even if this were not the case, and w therefore measures the difference in hydration between initial substrate and transition state, the question remains whether this difference is due to a nucleophilic attack of a water molecule in the rate-limiting step, or to a simple change of hydration caused by the more polar character of the transition state 20 • The w* parameter The w* parameter, calculated from our data, indicates a participation of water, but, although there can be no doubt that this parameter reflects some hydration changes, it seems less clear that it indicates a participation of water in the rate-limiting step. According to Bunnett, w* = t-s-n, where t, s, and n represent the number of water molecules bound to the transition state (st), the unprotonated substrate (S), and the proton. If the substrate adds no water (t = s), then w* equals n, the number of water molecules liberated on protonation of S.

For the reaction scheme: S+H+(H 2 0)n ¢ SH+ +n H 2 0 SH+ ¢ SHt

--+

products,

Carbohyd. Res., 17 (1971) 45-56

53

HYDROL YSIS OF GL YCOPYRANOSIDES

which comprises a rapid equilibrium to the conjugate acid, followed by the ratelimiting transformation to the transition complex, one can derive the equation 15:

If we assume, in a manner similar to that of Bunnett 15, Bascombe and Bell 21 , Perrin 2 2, and others, that the f-term is independent of medium, the equation reduces to:

Experimentally, however, we found that the function is not linear and that n (= w*) changes with varying concentrations of acid. One reason is probably that the f-term is, in fact, medium-dependent, but the observed deviation from linearity seems much too large to be accounted for completely in this way. The derivation of the above equation is based on the assumption that only one type of proton-hydrate exists, although, according to Perrin 22, this approach must be modified to allow for a variable hydration change of the proton, so that [H+(H 2 0)n] no longer equals [HX], the stochiometric concentration of the acid. For each of the possible proton-hydrates, the equation is:

and the assumption that the f-term is medium-independent is maintained. Then, the standard state 22 for every proton-hydrate is chosen, so that in dilute ideal solution, the activity of the proton-hydrate approaches [HX]. In dilute solution, Is, 1s t , and A approach unity, but f H+ (H2 0 )" takes the value [HX]/[H+(H 2 0)JD' where D stands for "in dilute solution", and the logfterm changes to [HX]/[H+(H 2 0)n]D' Since we assume that the log f term is medium-independent, equation (1) becomes: log kl -log [H+ (H 2 0)n] = constant - nlog A -log [H+(H 2 0)n]D. [HX]

(2)

When we plotted log kl -log[HX] versus log A, to determine w*, this was equivalent to plotting log kl -log [H+ (H 2 0)n] -log

[HX] , whereas it should [H+(H 2 0)n]

have been log kl -log[H+ (H 2 0)n]. Consequently, in equation (2), the term log [H+ (H 2 0)n] is added on each side, [HX] Carbohyd. Res., 17 (1971) 45-56

54

C. K. DE BRUYNE, J. WOUTERS-LEYSEN

yielding: log k -log [H+(H 0) ]+log [H+(HzO)n] = 1 Z /I [HX] constant-nlog A+log [H\HZO)n] [H+(HzO)n]o' or (3): log kl -log [HX] = constant - nlog A + log

[~\HzO)n]

.

[H (HzO)/I]o This means that, even if we assume the f-term to be constant, the last term on the right will cause departure from linearity. This term is the proportion of the concentrations of protons, present as n-hydrate in a given solution, to the concentration in dilute solution, and thus, a function of the concentration of the acid (or of the water). If there is only one hydrate species, the last term drops out and the equation reduces to the original Bunnett formulation. In his theory of variable hydration changes, Perrin 22 arrived at the equation for a Hammett base: - Ho = - n log A + log [HX] + log [H:CHzO)n] . [H (H 2 0),,]o Substitution in equation (3) yields: log kl = constant - H 0, i.e., the original Hammett equation (with slope -1). For the hydrolysis in hydrochloric acid, the requirement of unit slope is fulfilled. In this case, the Hammett equation can be rearranged to: log kl -log [HX] = constant -(Ho+log [HX]), where Ho+log [HX] represents the "excess acidity". This quantity can be expanded in a power series in log A, and, according to Perrin 2 z, the slope of the tangent to the curve is a measure of the hydration change accompanying protonation of the substrate. If we plot log kl -log [HX], this is equivalent to plotting the excess acidity versus log A. Thus, the line necessarily will be curved, and w* will not be constant, since it is now a measure of the variable hydration change on protonation. Perrin calculated that the relative concentration of the proton-tetrahydrate reaches a maximum near 6.5M perchloric acid. Therefore, in the neighbourhood of this concentration, the protonation should liberate four water molecules. Experimentally, we found that the w* parameter, for all of the glycosides tested Z3 ,z4, approaches the value 4 to 5 near 5M hydrochloric acid. It remains to be seen if this is more than a coincidence. In sulphuric acid, the Hammett slope is not - 1, and the correlation with the excess acidity is not so simple. Nevertheless, we believe that, in this case too, w· reflects the variable hydration change on protonation of the glycoside. In addition to this variable hydration, however, specific electrolyte effects 18 of the acids, the fact that the logfterm can be medium-dependent, and the simple change in hydration occurring during the transformation to a polar transition state ZO , all must have a profound effect on the parameter w*. This parameter should then reflect more than the participation of a water molecule in the formation of the transition complex. Carbohyd. Res., 17 (1971) 45-56

HYDROLYSIS OF GLYCOPYRANOSIDES

The

55

~

parameter The ~ values, calculated from our data, indicate a bimolecular mechanism (~: 0.22 to 0.56). In one case, methyloc-D-glucopyranoside in hydrochloric acid, this parameter changes its sign, and thus should indicate a change from a unimolecular to a bimolecular mechanism. However, this change of sign is caused by the fact that the Hammett slope b passes through -1. From the Hammett equation log kl = aH+bHo, and the Bunnett equation Ho+log kl = aB +4i(Ho+log[H+]), one easily deduces, in the same way as was used for the w parameter:

where [H+]o is the concentration of the acid at which H ° becomes zero. Because the absolute value of Ho always exceeds log [H+]/[H+]o, the sign of Q will always be positive, whereas the sign of ~ will be determined by the value of b. If b> -1, 4i is positive, whereas, if b < -1, ~ is negative. This is the reason why the sign of 4i changes in the case of methyl oc-D-glucopyranoside in hydrochloric acid. Furthermore, for a constant value of b (linear Hammett plot), rp cannot be constant unless Q is independent of the concentration of the acid, which is not the case. However, in contrast to P, the change of Q with increasing strength of acid is much less pronounced, so that ~ can be approximately constant, even if the Hammett plot is only slightly curved. As for the mechanistic interpretation of our rp values, we feel that they do not warrant the conclusion that the mechanism is bimolecular, mainly because Bunnett 17 himself warns about this mechanistic interpretation of 4i (and w) values for reactions of weakly basic substrates. CONCLUSION

The evidence presently available does not indicate that certain glycosides hydrolyse via a bimolecular mechanism, with participation of water in the rate-limiting step. The mechanistic criteria, on the contrary, point out that, in hydrochloric acid, the reaction proceeds via carbonium ions, generated unimoleculary from the conjugate acid. In other acids, some of the criteria are not in accordance with the unimolecular mechanism. We argue, however, that this is due to the uncertainty as to the real meaning of these criteria, and not to a change of mechanism. The case of the glycosides tested is thus only another illustration of the failure 25 • 26 of acidity functions as general mechanistic criteria. EXPERIMENTAL

The glucopyranosides were commercial products, further purified by several crystallisations from methanol. Hydrochloric acid solutions were prepared from Merck Titrisol. The concentrations of the sulphuric acid solutions were determined Carbohyd. Res., 17 (1971) 45-56

56

C. K. DE BRUYNE, J. WOUTERS-LEYSEN

by titration with standard (Merck Titrisol) sodium hydroxide, using Methyl Orange as the indicator. The polarimetric measurements were carried out at 436 nm, with a Perkin-Elmer model 141 photoelectric polarimeter, in jacketed tubes, connected to an ultrathermostat bath. Solutions of the glucopyranosides (50 mM) in the appropriate add were placed in the tube, and readings were started after the temperature equilibration was completed. The first-order rate coefficients (In e; sec- 1) were calculated from least-squares straight-line plots of log(oct±oc",) versus time, or by the Guggenheim 27 method. Both methods gave the same value within the estimated error. The oc'" values were determined experimentally for corresponding solutions of D-glucose. The energy of activation, log A, and the estimated standard deviations were calculated from the least-squares, straight-line fits of Arrhenius plots. Calculations of the other thermodynamic activation-functions were based on the absolute-reaction rate theory 28. Ho and log A values were taken from Ref. 29. REFERENCES

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