5502 (23) R. Deslauriers, I. C. P. Smith, and R. Walter, J. Bid. Chem., 240, 7006 (1974). (24) F. A. Bovey in "Chemistry and Biology of Peptides", J. Meinenhofer, Ed., Ann Arbor Science Publishers, Ann Arbor, Mich., 1972, pp 3-28. (25) 1. C. P.Smith, R. Deslauriers, and R. Waiter in "Chemistry and Biology of Peptides", J. Meienhofer,Ed., Ann Arbor Science Publishers, Ann Arbor, Mich., 1972, pp 29-34. (26) M. Rothe, K. D. Steffen, and I. Rother, Angew. Chem., lnt. Ed. Engl., 4,356 (1965). (27) A. C. T. North, D. C. Phillips, and F. S. Mathews, Acta Crystallogr., Sect. A, 24, 351 (1968). (28) C. L. Coulter, J. Am. Chem. Soc., 05, 570 (1973). (29) C. L. Couiter and N. R. Cozzarelli, J. Mol. Biol., 01, 329 (1975). (30) D. Cremer and J. A. Pople. J. Am. Chem. SOC.,07, 3244 (1975).
(31) "International Tables for X-Ray Crystallography", Vol. IV, Kynoch Press, Birmingham,England, 1974. (32) R. E. Marsh and J. Donohue, Adv. Rot. Chem., 22, 235 (1967). (33) T. Ashida and M. Kakudo, Bull. Chem. SOC.Jpn.. 47, 1129 (1974). (34) J. Donohue in "Structural Chemistry and Molecular Biology", A. Rich and N. Davidson, Ed., W. H. Freeman, San Francisco, Calif., 1968, pp 443465. (35) C. M. Venkatachalam, Biochim. Biophys. Acta, 188, 397 (1968). (36) D. Lavallee, unpqblished, 1973. (37) R. Deslauriers, M. Rothe, and I. C. P. Smith, ref 14, pp 91-96. (38) R. Somorjai and R. Desiauriers, in preparation, 1976. (39) J. E. Kiipatrick, K. S. Pitzer, and R. Spitzer, J. Am. Chem. Soc., 80,2483 (1947). (40) K. S. Pitzer and W. E. Donath, J. Am. Chem. soc., 81, 3213 (1959).
Kinetics and Mechanism of Molybdate and Tungstate Complex Formation with Catechol Derivatives' Katharine Gilbert and Kenneth Kustin" Contribution from the Department of Chemistry, Brandeis University, Waltham, Massachusetts 02154. Received September 22, 1975
Abstract: Rate constants for the complexation of molybdate and tungstate with catechol derivatives have been determined at 25 f 1 O C and ionic strength 0.5 M ("&I) by the approach-to-equilibrium technique on a stopped-flow apparatus. Ligands studied were 1,2,4- and 1,2,3-trihydroxybenzene (pyrogallol), 3,4,5-trihydroxybenzoic acid (gallic acid), 3,4-dihydroxyphenylalanine (L-Dopa), and [3,4-dihydroxyphenyl]-2-methylaminoethanol(D-epinephrine). The formation of the mono (1 : I ) complex is more rapid for protonated than for unprotonated oxyanion. From the hydrogen ion dependence of the relaxation time it was determined that reactions of completely deprotonated ligand with completely deprotonated oxyanion, and completely protonated ligand with protonated oxyanion, do not contribute, within experimental error, to the observed rate of complexation. The relaxation times (standard deviations f5%, except for pyrogallol and 1,2,4-trihydroxybenzene f 10%)consist of acid-independent and -dependent parts which contain kinetically indistinguishable terms for which upper limits could be deduced by setting all but one term equal to zero. Some of the upper limits exceed diffusion control allowing minimum limits to be set for the terms previously set equal to zero. For some pathways the upper and lower limits are approximately the same, leading to the actual value within experimental error and the uncertainties in the associated acid dissociation constants and estimated diffusion controlled rate constants. For molybdate and tungstate complexations with these and other ligands a trend in complex formation rate constant with basicity occurs. Namely, if the oxyanion is protonated the most basic ligand is most reactive. If the oxyanion is unprotonated, the least basic ligand is most reactive. The fastest rate of complex formation occurs when the protonated oxyanion reacts with the most basic ligand fully deprotonated at the binding sites. These trends are explained by assuming that the tetrahedral unprotonated oxyanion reacts by an addition mechanism, and the (postulated) octahedral protonated oxyanion reacts by a substitution mechanism. Ligand basicity then controls complex formation in substitution by assisting elimination of the OH- groups to be replaced through a hydrogen-bond-transfer mechanism, but hinders addition through the same effect. For 1,2,4-trihydroxybenzene the kinetics of formation of mono and bis complexes has been determined at ionic strength 0.1 M. Unlike the formation of the mono complex, the formation rate of the bis complex decreases with decreasing pH. This effect is also explained by the fact that the reactive metal-containing species in the higher order complex formation step is already octahedrally coordinated. There is no conversion to octahedral form upon protonation, and the influence of ligand protonation dominates the process.
yet, addition of a proton to Moo4*- is not diffusion conMetal-containing oxyanions readily form complexes with trolled,I5 implying that a structural change, perhaps tetrahenumerous different types of nucleophilic reagents2 In this regard, they resemble simple, aquated di- and trivalent metal dral to octahedral coordination, accompanies the reaction. ions. For the aquated metal ions, the mechanism of complexCertainly, the known solid-state structures of molybdate and tungstate oxyanion complexes a r e octahedral,16 with cisation is well understood, being based on one essential feature. dioxygen coordination in the absence of full occupation by the Complex formation is a substitution process, controlled by the complexing ligand or ligands. This situation has led some inbreaking of the metal-water bond in the formation of a reduced coordination-number activated ~ o m p l e x Exceptions .~ to this vestigators to regard oxyanion complexation and oxyanion mechanism are few, and do not show wide variations in ligand polymerization (or condensation) as examples of addition rather than s u b s t i t ~ t i o nThis . ~ ~ point, ~ ~ though interesting, is substitution rate constant^.^ W e now have several thorough kinetics studies of oxyanion-ligand systems: c h r ~ m a t e , ~ - ~less fundamental than determining the trends, if any, in the complex formation rate constants with variations in ligand vanadate,* m ~ l y b d a t e , ~and - ' ~ t ~ n g s t a t e for , ~ example. ~ ~ ~ ~ It is thus appropriate to determine the context in which to view properties. the mechanism of these reactions. Ligand discrimination by oxyanions has been discussed for One ambiguity immediately presents itself, however, making Cr042-,7 where it may be present, but is obscured by accompanying catalytic behavior, and for MOO^^- and w0d2- with it difficult to achieve a mechanistic synthesis similar to that for the simple aquated metal ions. The structures in solution substituted 8 - h y d r o ~ y q u i n o l i n e sWith . ~ ~ these ligands, it was of monomeric oxyanions a r e not clear. T h e unprotonated established that the main pathways for complexation involve species ( Mood2-, w o 4 2 - , etc.) a r e probably tetrahedral;14 the protonated oxyanion. No conclusion was drawn with re-
Journal of the American Chemical Society
/
98.18
/ September 1, 1976
5503
spect to the influence of, say, ligand basicity on the rate of complex formation. In order to gain more information on the role played by ligand basicity in this type of reaction, a systematic investigation of the kinetics of complex formation with one ligand and several of its derivatives was undertaken. As complexes between oxyanions and catechol and its derivatives have been well characterized,18-20 and afford a reasonable range in basicity, we are reporting the results of a kinetics study with several of these compounds. A start had already been made in the case of catechol itself." Catecholamines are frequently of potent physiological activity,*' e.g., as hormones, but are not commonly regarded as ligands. These, and the other catechol chelating agents used, are named and shown below. R
I
"OXY
y HmcT:i HO
1,2-dihydroxybenzene: R = R' = H; catechol 1,2,3-trihydroxybenzene:R = OH,R = H; pyrogallol 1,2,4-trihydroxybenzene:R = H, R = OH
40
OH
I
3,4,5-trihydroxybenzoic acid: gallic acid
HoQ CH,
I
H,NCHCOOH 3,4-dihydroxyphenylalanine:L-Dopa
?H
HoQ ~
I H3CNCHZ I H
H
[ 3,4-dihydroxyphenyl] -2-methylaminoethanol:
L-epinephrine (adrenaline)
Experimental Section Materials. The following reagent grade chemicals were used without further purification: 1,2,4-trihydroxybenzene (Aldrich); ammonium hydroxide, pyrogallol, gallic acid, sodium tungstate (Baker); L-epinephrine (Calbiochem.); sodium bisulfite (Na2Sz05),sodium molybdate (Fisher); ammonium chloride (Mallincrodt); and L-Dopa (Nutritional Biochemical Corp.). The ligand solutions were prepared fresh by weight for each experiment; the molybdate and tungstate were taken from 0.50 M stock solutions. Water was doubly distilled. Kinetics Studies. All kinetics studies were run on a stopped-flow apparatus equipped with a Biomation 610B transient recorder and Datacap El03 coupler interfaced to a Teletype 33 ASR for direct digital output on paper tape.22 Least-squares routine^,^) run on a PDP-10 computer, were then carried out to obtain relaxation times (as in the approach-to-equilibrium method), followed by overall forward and reverse rate constant determinations by weighted least squares. The kinetics studies were carried out at 25 f 1 OC and ionic strength 0.5 M ("&I), unless otherwise noted. In the 1:l studies reaction
Gilbert, Kustin
1
4.0
IMO0;l
8
x 10' IMI
I
6.0
I 8.0
I
Figure 1. Plot of l / r o b s d against molybdate concentration for the formation of the 1:l complex between gallic acid and molybdate. Total initial gallic acid concentration = 1.9 X M, T = 25 "C, ionic strength = 0.5 M; 0 = pH 7.3; A = pH 7.7; 0 = pH 8.0; X = pH 8.3. Calculated leastsquares straight lines have been drawn through the data points. At the highest concentrations of oxyanion studied, the data points tend to fall below the calculated values, especially at the lowest pH's studied. This effect is due to the slight amount of molybdate polymerization occurring in these solutions.
YH
H
1
2.0
rates were measured under pseudo-first-order conditions with the concentration of oxyanion (0.25-7.50 X M) in large excess (>25-fold) over that of ligand ( 1 .OO-3.00 X M). To avoid oxyanion condensation, molybdate solutions were all at pH 27.3 and those of tungstate at pH 28.0. Oxidation of the catechol derivatives was minimized by bubbling argon through the ligand solutions and adding sodium bisulfite (0.01 M). Control experiments without bisulfite showed that this reagent did not affect the relaxation times significant I y . After ammonium chloride was added to bring the solutions to 0.5 M ionic strength, the pH was adjusted and buffered with ammonium hydroxide. The hydrogen ion concentration was measured with Corning Model 7 and Radiometer pH meters. The experimental runs were monitored spectrophotometrically at 340 nm. At a given pH and oxyanion concentration, we made at least five experimental determinations of the relaxation times. The standard deviations of the relaxation times were within &5%, except for pyrogallol and 1,2,4-trihydroxybenzene,which were within f 10%. To observe the rate of the second step of chelation to form a 1.2 = metal 0xyanion:ligand complex, 1,2,4-trihydroxybenzene (0.29- 1.52 X M) was present in great excess (at least 200-fold) over the M). Ionic strength was 0.1 M concentration of oxyanion (1.5 X ("&I) and all other conditions and methods were as previously described for the first step. Some studies of the first step of complexation of molybdate with 1,2,4-trihydroxybenzenewere also carried out at ionic strength 0.1 M.
Results and Treatment of Data Oxyanion Dependence. T h e observed pseudo-first-order relaxation times for t h e complexation of molybdate with catechol derivatives are shown in Table I; those for tungstate with catechol derivatives are shown in Table 11. Because t h e concentrations of the metal were always in large excess over t h a t of t h e ligand, close t o equilibrium conditions obtain, and the
/ Molybdate and Tungstate Complexes with Catechol Derivatives
5504 Table I. Observed Relaxation Times for the 1:l Complexation of Molybdate with Catechol Derivatives
Ligand 1,2,4-Trihydrox ybenzene
102[M~042-] (M) 7.3 0.75
1.oo 1S O
1.90 2.00 2.50 2.90 3.OO 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 104[Ligand]o (M) Pyrogallol
104[Ligand]o (M) Gallic acid
0.50 0.75 1.oo 1.50 2.00 2.50 3.00 3.75 4.00 5.00 6.00 7.00 7.50 0.50
1.oo
0.50
1.oo 1S O
2.00 3.00 4.00 5.00 6.00 7.50 104[Ligand]o (M) L-Dopa
0.50
1.oo 1S O
2.00 2.50 3.00 4.00 5.00 7.50 104[Ligand]o (M)
16.8 22.7 31.0
-
30.8 33.8 38.4 42.3
7.7
7.8
8.0
8.2
8.3
8.4
-
-
-
-
-
-
26.2 28.9 32.3 34.2
-
-
-
-
-
-
-
-
-
-
-
27.2
-
-
-
-
46.7
-
23.0 23.2 27.9 37.2
-
45.6 54.3
-
-
36.8
-
29.7 34.3 37.5
-
-
-
-
-
56.1 -
-
-
2.1
-
49.9 51.2 2.1
29.1 42.8 48.8 67.7 71.2 91.2 91.7
-
29.2 35.7 47.5 68.0 80.9 81.6 93.2 115. 112. 155. 195.
-
68.5 74.5
-
84.5 1.0 33.8 63.2 85.3 106. 145. 173. 194. 264. 2.9 9.62
1.0
34.4 53.0 66.0 86.3 115. 155. 191. 262. 1.9 10.05 14.5 16.7 22.0 20.6 28.0 36.0 42.6 42.0
-
-
56.6 1.5
52.4 1.7
-
-
-
-
-
-
-
-
-
11.4 18.9 21.9
-
1.0
32.7
-
90.1
-
-
-
-
-
-
155. 232. 1.9 9.82 13.5 -
-
21.4 27.6 33.5 44.7
-
-
-
-
51.4 1.4 9.59 12.2 -
-
21.8
28.4 35.2 43.3 58.8 2.5
-
36.5 50.7 2.3
observed relaxation times may be represented by 1/Tobsd = klf([Ml + [ L l ) + klr (l) where klf = oveIall forward rate constant, k l r = overall reverse rate constant, [MI = equilibrium concentration of all the metal
/
-
39.2
51.5
132.
Journal of the American Chemical Society
-
--
-
-
-
-
-
22.4 26.3 27.3
47.4
-
-
-
-
-
-
50.2
2.1
1.50 2.00 3.00 4.00 5.00 7.50 104[Ligand]o (M) Epinephrine
l/Tobsd (s-l) PH
98:18
-
-
-
-
-
-
-
-
-
-
-
-
8.5
-
-
-
36.9 -
41.5 42.2 46.2 49.0 48.1 50.9 2.1 -
26.6 --
-
-
_
-
-
46.1 51.7 110.
-
-
-
-
_
92.3 145. 130. 161. 1.0
-
8.7
-
-
-
-
8.6
-
-
-
-
18.2 17.1 24.0 28.4
_
37.4 45.8 47.2 52.9 53.8
-
61.4 1.0
8.8
-
-
-
12.3 14.1
12.8 14.4
-
13.4
14.8 16.2
15.9 17.3
14.4 14.8
17.8
19.6
16.7
-
20.5
-
17.4 19.1
25.1
-
-
-
9.0
_
-
-
-
-
-
-
-
-
-
-
22.6
32.5
31.7
23.6 26.4
-
-
-
-
_
-
-
-
_
-
-
13.0 10.6 12.3 13.9
-
-
15.7 23.4 17.5 20.75 28.6
-
26.0
-
-
1 .o
23.5 41.6 45.1 59.2 84.7 100.8 120. 154. 1.6 9.43 -
19.4
-
37.3
-
49.8 2.0 7.79 11.3 14.5 17.8
7.63 10.5 13.9 18.2 -
-
23.4 26.7 35.1 43.7 2.5
23.6 30.7 37.5 48.1 2.7
14.6 18.4 22.3 29.0 2.3
-
4.81 -
8.18 9.99
oxyanion species, and [L] = equilibrium concentration of all the ligand species present. Since [L] > [ H + ] , and the terms KalKa~Ka3and KalKa2[H+] are negligible with respect to Kal [H+I2and [H+I3.Thus the [ H + ] ) [ H + l 2 ,and, denominator in eq 3 becomes Km(KaI
+
Gallic acid
Epinephrine
L-Dopa
372f 9 368 f 24 369 f 10 357 I 1 2 369 f 21
305 f 14 299 f 12 313 f 17 309 f 13 373 f 21
0.47 f 0.08 0.37 f 0.12 0.88 f 0.12 1.2 f 0.3 0.50 f 0.15
0.54 f 0.16 0.32 f 0.06 1 .O f 0.3 0.95 f 0.22 0.43 f 0.14
k i f (M-I s - ' ) 1030f 1 1500 f 90 1340 f 180 1 1 3 0 f 80 1340 f 110 kl,
(s-1)
1.2 f 0.1 1.3 f 0.5 5.4 f 2.6 4.2 f 1.5 3.4 f 1.0
not contribute significantly to,the overall forward rate constant. The slope of this plot equals k4 k7Kal/Krn= 5.52 X lo2, and the intercept is equal to k3Kal k6Ka1Ka2/K, = 1.67 X lo-* (see Table VIII, footnote a ) . If k4 >> k7K,l/Km, k4 = 5.5 X lo2 (M-I s-l), but if k7Ka1/Krn >> k4, k7 = 6.6 X l o 7 (M-l s-'). If k3Kal >> k&alKa2/Km, k3 = 7.9 X 10' (M-I s-' ), and conversely, if kbKalKa~/Km >> k3Kal, k6 = 5.3 X lo9 (M-] s-l). These values represent upper limits only. T h e treatment of the second step
+ +
ML
+ L*kzr ML2 k2r
+ k7KaiKln[H+l
k s [ H + I 2 (4) Krn A plot of k l f ( K , ~ [H+]) vs. [H+] is linear (Figure 2), which implies that the pathways represented by kl, k2, ks, and kg do
+
Journal of the American Chemical Society
+
is more complicated than that of the first because the rate equations for the first and second step a r e coupled. T h e reciprocal relaxation times are the roots of the associated quadratic characteristic equation and are given by24
/ 98:18 / September 1,1976
5507
+
where a l l = klr([M] [EL+ kir,aiz = klr, a21 = k d [ L l [ E ] ) , and a22 = k2f([ML] [L]) k2r.Under the conditions of these experiments, [ E ] t o t a
