Kinetics of dissociation of magnesium aminocarboxylate complexes

r&m”, Vol. 21, pp. 1017 10 1020 0 Pergamon Press Ltd 1980. Printed in Great Britain

KINETICS OF DISSOCIATION MAGNESIUM AMINOCARBOXYLATE

OF COMPLEXES

JAMESD. CmRt and MARK G. O-ERWIN Department of Chemistry, University of Nebraska, Lincoln, Nebraska 68588, U.S.A. (Received 24 March 1980. Accepted 29 May 1980)

Summary-The kinetics of dissociation of magnesium aminocarboxylate complexes of the EDTA type have been examined and the results used to determine the rate constants for formation of the complexes and to find the rate-determining steps in the mechanism. The results indicate that loss of the first water molecule from the hydration sheath of the magnesium ion and formation of the first metal-ligand bond is the rate-determining step. When the formation rates of metal complexes are compared for EDTA, DPTA, DBTA and DATA*, two types of behaviour are noted.’ Nickel, cobalt(H), copper(H), zinc and cadmium react with all the ligands at nearly the same rate to form complexes, but calcium, strontium and lead react with the ligands at rates in the order EDTA>> DPTA > DBTA > DCTA. The metal ions in the first of these groups all have fairly slow characteristic water-loss rates ( 104-10’ see- ‘) and are formed from main group elements which form strong metal to amino-nitrogen coordinate covalent bonds; those in the second group all have very rapid water-loss rate constants (107-1010 set- ‘) and come from main group elements which form only weak metal-amino-nitrogen bonds. Magnesium is a main group element having ions which form only weak bonds to amino nitrogen-donors but also have a small water-loss rate constant. Examination of the dissociation kinetics should indicate whether the behaviour is governed by the water-loss rate or by equilibrium or periodic table relationships. The dissociation rate constants of many metal complexes of EDTA and related polyaminocarboxylates have been measured and mechanisms have been proposed. From such observed dissociation rate constants and formation equilibrium constants, formation rate constants can be computed and compared with predictions based upon Eigen’s model for complex ion formation.’ This model originally dealt with unidentate ligands and assumed that aqueous metal ions first form outer-sphere complexes with aqueous ligand molecules or ions. The metal ion of such an outer-sphere complex then loses a solvated water molecule and the ligand moves from the outer sphere to the inner sphere to form the complex ion. Three types of metal ion behaviour were identified. Type 1 metal ions are those from which water loss is very rapid-so rapid that formation of the outer-

sphere complex is rate-determining. Type 2 metal ions have a slower water-loss rate so that formation of the outer-sphere complex may be regarded as at equilibrium before the rate-determining water loss. Type 3 metal ions are those which have extremely slow water-loss rate, so slow that hydrolysis of co-ordinated water (base-catalysed) becomes a preferred pathway foi vacating a co-ordination site. Complexation by multidentate ligands must involve formation of the first metal-ligand bond in the same way as for unidentate ligands and also appropriate rotation of the non-bonded portions of the ligand molecule to achieve the correct position for subsequent bonding. The difficulty of performing such rotations will presumably depend on the degree of steric hindrance and should be in the order DCTA > DBTA > DPTA > EDTA, but be largely independent of the identity of the metal ion bonded. If the rotation is fasi compared to the loss rate for the first water molecule, formation of the first bond will be rate-determining, but slower rotation can shift the rate-determining step to formation of the second bond. The reactions were monitored by polarimetry in this work since the ultraviolet absorption spectra of these complexes do not provi’de enough information about the extent of reaction. Each of the following reactions was studied at a variety of pH and concentration values. d,l-DCTA

d,l-DCTA

d-DCTA d-DCTA

* Abbreviations used: EDTA = ethylenediaminetetraacetic acid; DPTA = 1,2-diaminopropanetetra-acetic acid; DBTA = 2,3-diaminobutanetetra-acetic acid; DCTA = trons-1,2-diaminocyclohexanetetra-acetic acid. t Reprint requests.

+ Mg-/-DPTA-+ Mg-d,l-DCTA

+ I-DPTA

(1)

+ Mg-d-DBTA --* Mg-d,l-DCTA

+ d-DBTA

(2)

+ Mg-meso-DBTA -* Mg-d-DCTA + meso-DBTA

(3)

+ Mg-EDTA-+ Mg-d-DCTA

+ EDTA

(4)

Jensen3 and Margerum4 have measured the dissociation kinetics of Mg-DCTA by related methods. 1017

JAMESD. CARRand MARK G. CHERWIN

1018 EXPERIMENTAL

where Km is the stability constant of the outer-sphere

Optically active DCTA, DBTA and DPTA as well as meso-DBTA were prepared as described previously.‘*s All other reagents were reagent grade and were used as received. Nitric acid or tetramethylammonium hydroxide (TMAOH) was used to adjust pH, and the DCTA served as buffer. The solution pH was constant to kO.03 over the first 2-3 half-lives of a reaction. All ligand solutions were prepared by dissolving the appropriate tetra-acid in distilled demineralized water with the addition of about twice as many moles of TMAOH. Magnesium complexes were formed by mixing stoichiometric amounts of standard magnesium nitrate and ligand solution. TMAOH was used to avoid the presence of alkali metal ions which complex these ligands and possibly affect the reaction kinetics6 The temperature was maintained at 25.0” by a water-bath with water circulating from a thermostatic tank. Solution ionic strength was controlled only by the DCTA and in most cases was > 0.1M. The reactions were monitored on a Perkin-Elmer Model I41 polarimeter equipped with a transmitting potentiometer allowing strip-chart recording of optical rotation (a) vs. time. The exchange reactions of racemic DCTA with magnesium complexes of optically active DPTA and DBTA were monitored at 365 nm and the reactions of optically active DCTA with magnesium complexes of EDTA and meso-DBTA were monitored at 345 nm. This latter wavelength required that the instrument be modified with a xenon discharge source and monochromator as described previously.’ The reagents were mixed externally and transferred to constant-temperature cells as rapidly as possible. Half-times of reactions ranged from 1 to 90 min. The molar rotations of the magnesium complexes at 365 nm are as follows: Mg-I-DPTA([a] = -3.82 at pH 9.86 and - 1.78” at pH 11.26); deg.I.mole-‘.cm-’ Mg-d-DBTA([a] = + 1.69 deg.l.mole-‘.cm-’ at pH 8.19 and +0.70 at pH 12.98). Pseudo first-order rate constants (koba)were calculated from the slopes of plots of -In(a, - a,) where a, and a, are the rotations observed at time t and at equilibrium respectively. Plots of !f& us. concentration of incoming ligand, at constant pH, give a slope of k2 and intercept of k, [see equation (8)]. These values are tabulated for all systems in Table I. Values of kpL, kfsL and k&‘,!f are obtained from the pH-dependence of kl either by plots of kl VS. [H’] or [OH-] or by non-linear least-squares fit of k, and [H’], where kpL is the dissociation rate constant. Resolved. values of these terms are compiled in Table 2. Values of the formation rate constants of both the. unprotonated and monoprotonated ligands are calculated from equations (5) and (6) and are included in Table 3. L4- + Mg2+ $. MgL’-

CMgL2 -1

K w- = [Mg2+l[L4-l

kFg = p

kyg = KMgLkygL

(5)

complex. Values of 50 and 13 for Km for Mg2+ + L“- and Mg2+ + HLs- respectively4 and a characteristic waterloss rate constant’ of 1 x lo5 for Mg” are used in these calculations. RESULTS

conditions and rate constants Experimental obtained are presented in Table 1. All the reactions are shown to proceed according to the rate law rate = k, [MgL] + k,[MgL] [DCTA]

where k, is the observed dissociation rate constant, k, Table la. Reaction conditions and kobs values for Mg-lDPTA + DCTA in the presence of TMAOH

PH 8.18 8.90 9.18 9.42 9.46 9.62 9.86 10.12 10.18 10.19 10.30 10.50 10.53 10.65 10.64 10.65 10.79 11.26 11.82 11.88 Il.94 12.06 12.22 12.44 12.58 12.62 12.62 12.86 12.98

PH

CL4-ICH’I

CMisLZ-l = [L4-][Mg’+] =

’

[HL3-]

Kup~K4

k$f = KYpLK4QL

(6)

Also included in Table 3 are values of the rate constants calculated according to Eigen through equation (7). k, = K,k,,Hzo

(7)

[Mg-I-DPTA], 10-3M 6.50 5.39 5.39 5.39 6.49 5.39 5.39 5.39 5.39 5.07 5.39 5.07 5.39 5.39 5.27 3.54 5.39 5.05 4.00 4.00 4.00 4.00 4.00 4.00 4.00 2.90

1.50 4.00 4.00

CDCTAIT 3

k,,,

10-3M

x 10’

62.5 53.8 53.8 53.8 62.3 53.8 53.8 53.8 53.8 55. I 53.9 55.0 53.8 53.9 120.7 145.8 53.8 54.8 38.2 38.2 38.2 38.2 38.2 38.2 38.2 54.6 73.5 28.1 38.2

15.6 5.11 3.06 2.22 2.19 2.53 2.05 1.51 I .23 1.31

1.48 0.928 I .06 1.17 1.19 1.40 0.995 0.821 0.793 0.93 0.874 1.08 1.40 2.05 2.52 2.46 2.15 3.68 3.66

Table lb. Reaction conditions and kob, values for Mg-lDPTA + DATA in the presence of KOH

HL3- + Mg’+ $ MgL*- + H+

[MgL2-lCH+l k!,! Ke, = [HLJ-][Mg2+] = w

(8)

= kabaCMgLl

9.19 9.30 9.45 9.77 10.06 10.35 10.15 10.56 10.62 10.79

[Mg-I-DPTA], 10-3M 5.27 5.27 5.01 5.26 5.27 5.24 5.26 5.28 5.11 5.28

CDCTAI, .

k,,

lo-‘M

x lo4

51.7 51.7 49.2 51.6 51.7 51.4 51.6 51.8 50. I 51.8

3.28 5.32 3.67 2.61 2.48 I .48 2.35 2.42 3.60 1.37

Dissociation of magnesium aminocarboxylate Table lc. Reaction conditions and kobs values for Mg-dDBTA + DCTA in the presence of TMAOH [Mg-d-DBTA], PH 7.65 7.92 1.93 1.93 1.92 8.05 8.19 8.18 8.18 8.18 8.65 8.63 8.64 8.63 8.90 9.31 9.31 9.31 9.32 9.13 10.75 12.98

10-3M

4.96 4.96 4.66 4.66 4.66 6.90 4.97 6.90 6.90 6.90 4.96 5.01 5.01 5.01 4.96 4.97 4.97 4.97 4.91 4.96 4.91 4.42

CD(JTAIT.

x 10’

51.9 51.9 83.3 116 149 345 52.0 138 172 207 51.9 90.2 125 160 51.9 52.0 124 174 224 52.0 52.0 46.3

4.39 2.46 2.83 3.10 3.61 3.99 1.52 2.05 2.24 2.56 0.688 0.799 0.843 0.914 0.407 0.184 0.360 0.412 0.467 0.142 0.0507 0.0318

Table Id. Reaction conditions and kobs values for MgEDTA + d-DCTA in the presence of TMAOH

PH 9.22 9.50 9.46 9.46 9.48 9.84 9.79 9.86 9.80 9.15 9.15 9.71 10.05 10.20 10.22 10.24 10.36 10.77 10.97 11.16

[Mg-EDTA], lo-.‘M 7.61 7.60 7.64 7.61 7.59 7.61 5.70 3.80 3.04 1.64 7.67 1.19 7.61 7.64 1.62 7.59 1.61 7.61 7.61 7.62

Cd-DCTAh,

ko,,.

10-3M

x lo2

1.57 1.49 11.3 16.9 22.5 7.58 7.50 7.50 7.50 11.3 15.1 26.1 7.50 11.3 17.0 22.5 7.58 7.58 7.50 7.51

1.75 1.22 1.77 2.76 4.24 1.09 1.10 1.03 1.50 1.16 1.65 2.68 1.01 1.30 1.53 1.75 0.925 1.05 1.23 1.39

Table le. Reaction conditions and kobs values for Mgmeso-DBTA + d-DCTA in the presence of TMAOH

PH 9.15 9.30 9.56 9.93 10.27 10.39 10.55 10.88 10.91 11.66

[Mg-meso-DBTA], 10-4M 7.60 7.60 7.60 7.61 7.6 1 7.61 7.61 7.61 7.6 1 1.62

[d-DCTA]r, lo-‘M 7.57 7.57 7.51 7.51 7.58 7.58 7.58 7.58 7.58 1.59

kobs x 10’ 1.93 8.79 7.23 7.15 6.65 5.52 5.00 4.50 4.33 3.93

1019

Table 2. Values of the total dissociative and total liganddependent rate constants for Mg-d-DBTA + DCTA and Mg-EDTA + d-DCTA at the various pH values employed

L.

IO-‘M

complexes

PH 1.92 8.18

Mg-d-DBTA + DCTA k, x 10“ k2 x 10’ 18.5

8.64 9.31

PH 9.47 9175 10.22

10.1 5.96 1.22

11.5

1.39 2.01 1.63

Mg-EDTA + d-DCTA k, x IO3 kz (0.00) 1.24 8.46

1.61 0.964 0.402

UCH+lIfL) X 10-Z 17.0

6.01 0.566 0.0983 k,fCH +I/&) X 10-3 6.71 2.11 0.298

is an observed ligand-dependent rate constant, and the incoming ligand is always in > IO-fold excess over MgL. The emphasis in this work was on the value of k, , which can be further resolved into three terms: k, = k,MgL[H+]+ kygL + /@,” [OH-]

(9)

involving an intrinsic, non-catalysed dissociation rate constant (GgL), a proton-catalysis constant (kfi(oL)and a hydroxide-catalysis constant (/$jfiL). Not all the terms were observed for each system. The value of k2 is also expected to be pH-dependent because the unprotonated incoming ligand is expected to react at a different, and much greater, rate than the protonated species.* In order to calculate @ and I$$, values of K4 and KhlpL for each ligand are necessary. These values should be obtained under the conditions used for the kinetic’ experiments (i.e., 25” and OS4 TMA’). Literature values must be corrected to correspond to these conditions. Most importantly, the presence of O.lM K+ in the measurements of KMsLmust be corrected for because of the complexation of potassium by these ligands. 5,10.‘1 The value used for KMgLis the appropriate literature value’ * multiplied by (1 + KKLCK+I). The rate constants for formation of the magnesium complexes from the unprotonated ligands show values which are all very similar to each other, with a value of about 3 x 10’ I. mole- ’ . set- ‘. The consistency of these values implies that the loss of the first water molecule is the rate-determining step. The value 3 x 10’ is about six times larger than is expected from keHD = 1 x lo5 and Km = 50. Our interpretation is that the small magnesium ion allows a closer approach of the fully dissociated anion and accordingly the Kos value is actually larger than that for other doubly charged but larger cations. The rate constants for the formation of a magnesium complex from the protonated ligand (Table 4) agree well for DPTA with the value expected from the characteristic water-loss rate constant and an outersphere stability constant of 50. The values for DBTA and DCTA are considerably lower than the DPTA

JAMES D. CARRand MARK G. CHERWIN

1020

Table 3. Dissociation and formation rate constants for magnesium complexation

DPTA QDBTA DCTA Eigen mechanism prediction

1.12 x 10-s 3.0 x 10-s 7.7 x 10-57

3.51 x 1O’O 9.84 x 10” 2.00 x 10”

3.93 x 2.95 x 1.54 x 5.0 x

10’ 10’ 10’ lo6

* Values are chosen from reference and corrected for potassium ion concentration. t Value reported by Larsen and Jensen3 Table 4. Proton-catalysed

dissociation rate constants and formation rate constants with protonated ligands kzpL

DPTA d,l-DBTA DCTA Eigen mechanism prediction

3.19 x 106 1.42 x lo5 7.70 x 106

&w

3.51 x 1O’O 9.84 x 10” 2.00 x 10”

K4*

k%

9.77 x lo-l2 4.90 x lo-‘3 8.13 x lo-l4

1.09 x lo6 6.85 x 104 1.25 x 105

kgf x a non-chelated

7.3 x 3.1 x 1.2 x 1.3 x

lo6 lo6 10’ lob

* From references 5,10,11. value. If, however, the fraction of the protonated ligand in an open, or non-chelated, form is considered (Table XI in reference 2), the formation rate constants

are all very similar and agree quite closely with the value predicted from the Eigen mechanism, 1.3 x lo6 1.mole- 1. set- I. This assumes that the closed, or chelated-proton, form of the ligand is much slower to react than is the open form. Again, the DF’TA value is about six times greater than the Eigen mechanism predicts. The minor differences in values from DATA to DCTA are probably not significant when the uncertainties in the calculations are considered. The general conclusion is similar in each case, the relatively slow water-loss rate for magnesium allowing the formation of the first metal-ligand bond to be be rate-determining. Rate data from magnesium-EDTA could not be satisfactorily resolved into the various terms described. This is principally due to the rapidity of these reactions and the very small changes in optical rotation (ca. 0.040”) characteristic of these reactions. In addition, apparently all the terms in equations (8) and (9) apply to the Mg-EDTA substitution reaction. Approximate resolved values for attack of H2DCTA on Mg-EDTA and Mgd-DBTA are

2.7 x lo3 and 0.58 l.mole- ’ . set- ’ respectively and for attack of HDCTA on these same complexes are 0.15 and 1.0 x lo-’ l.mole-l.sec-‘. Attack by the unprotonated ligand, DCTA4-, was not observed. REFERENCES 1. M. Eigen, Pure Appl. Chem., 1963, 6, 105. 2. J. D. Carr and D. G. Swartzfager, J. Am. Chem. Sot., 1975,97, 315. 3. N. R. Larsen and A. Jensen, Acta Chem. Stand., 1974, A 28, 638; A. Jensen and N. R. Larsen, ibid., 1973, 27, 1838. 4. J. B. Pausch and D. W. Margerum, Anal. Chem. 1969, 41, 226. 5. J. D. Carr and D. G. Swartzfager, J. Am. Chem. Sot., 1973, 95, 3569. 6. J. D. Carr and D. R. Baker, Inorg. Chem., 1971, 10,

2249. 7. P. E. Reinbold and K. H. Pearson, Anal. Chem., 1971, 43, 293. 8. A. E. Martell and L. G. Sill&, Stability Constants of Metal Complexes, Special Publications 17 and 25, The Chemical Society, London, 19. 9. D. W. Margerum, P. J. Menardi and D. L. Janes, Inorg. Chem., 1967, 6, 283. 10. J. D. Carr and D. G. Swartzfager, Anal. Chem., 1971, 43, 583. 11. Idem, ibid., 1971, 43, 1520.