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Kinetic isotopic exchange studies of metal ion substitution in EDTA chelates—II
J. inorg, nuel. Chem., 1967, Vol. 29, pp. 97 to 103. Pergamon Press Ltd. Printed in Northern Ireland
KINETIC ISOTOPIC E X C H A N G E STUDIES OF METAL ION SUBSTITUTION IN EDTA CHELATES--II ZINC (II)-ZINC-EDTA EXCHANGE R. E. JERVIS a n d S. S. KRISHNAN* Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, 5, Canada (First received 11 March 1966; in revised form 12 July 1966)
Abstract--Usingthe method of radioisotopic exchange, the substitution of zinc (II) ion in zinc-EDTA complex was observed to occur at a measurable rate over a concentration range of 1 0 - 5 - 1 0 - s M in both species and within the pH range of 6-7 at room temperature. Because of erratic behaviour of esZn ion at very low tracer concentrations (--~10-x2 M) suggestive of radiocolloid formation, exchange experiments were done using freshly prepared 65Zn-labelledchelate. The substitution rate of zinc 0-I) ion in zinc-EDTA at 20°C in 0.05 M acetate buffer was summarized within experimental error by: R ----kx[Zn'+I[ZnEDTA2-I + k~[ZnEDTA'-I[H+] + k3[ZnEDTA2-][H+12+ k4[ZnEDTA~-] where R is the substitution rate in units of mole/1, per sec and the specific rate constants have the values at 20, 30 and 40°C; kl = 4.13, 26 and 961/mole per see; k2 = 76, 178 and 2561/mole per sec; ks = (1.3, 0.68 and 1.5) × 10812/mole2 per sec; and k4 = (7"7, 15, 17) × 10-5 see-x, respectively. Activation energies corresponding to these values are: 29"2, 12-5, 1"6 and 7.7 keal/mole, respectively. The zinc-EDTA chelate was quite labile and substitution of zinc (II) ion through the spontaneous decomposition of chelate was an appreciable contribution to the overall reaction rate in all experiments. The reaction mechanism postttlated indicated several parallel paths involvingthe unprotonated zinc-EDTA chelate and also the protonated species: ZnHEDTA- and ZnH2EDTA°, suggesting that acid-catalysed decomposition of the chelate facilitated the disruption of metal-chelate bonds in the transition state. Comparison of these results with similar studies of other transition element EDTA chelates indicate that zinc (II) chelate undergoes substitution more rapidly than the d r and d 8 cobalt and nickel chelates. This finding is qualitatively in agreement with crystal field predictions assuming octahedral configuration and a weak field metal-EDTA interaction. INTRODUCTION IN A PREVIOUS paper the exchange of cobalt (II) ion with its E D T A , ethylenediaminetetra-acetate chelate was reported ~1) a n d the kinetics c o m p a r e d with the results o f similar studies with other t r a n s i t i o n elements. T h e purpose of this paper is to outline a detailed investigation o f Z n ( I I ) - z i n c - E D T A exchange by the radiotracer isotopic exchange technique over the permissible range o f low c o n c e n t r a t i o n s a n d very low acidities. K i n e t i c studies of the s u b s t i t u t i o n reactions of other 3d t r a n s i t i o n d e m e n t s with their E D T A chelates have been reported: Fe(III), ~ Co ~1'a'4~ a n d Ni(II). tS~ Previous * Present address: The Centre of Forensic Science, Province of Ontario, Toronto 2, Canada. ~t~ S. S. KmSHNANand R. E. JF.RVlS,J. nucl. inorff. Chem. 29, 87 (1967). ~2j S. S. JONESand F. A. LONG, J. phys. Chem. 56, 25 (1952). ~2~F. A. LONG et aL, Isotopic Exchange Reactions and Chemical Kinetics, p. 106. Brooldaaven Chemical Conference No. 2, (1948). ~4~R. BARBEIRIet aL, Gazz. chim. itaL 87, 1393 (1957). c6~C. H. COOKand F. A. LONG, d. Am. chem. Soc. 80, 33 (1958). 7
97
98
R . E . JERVIS and S. S. KRISHNAN
attempts to study Z n ( I I ) exchange with its E D T A chelate have been few a n d unsucessful: TURCO e t aL ~6~ studied zinc i o n exchange to assess the feasibility o f using the Szilard-Chalmers process i n the chelete to separate the species: the exchange was f o u n d complete within 1 rain i n a p H range o f 3 - 1 1 at the c o n c e n t r a t i o n s used. I n the present study, attempts were m a d e to o b t a i n q u a n t i t a t i v e kinetic data for the reaction a n d it was established i n p r e l i m i n a r y experiments that exchange was m e a s u r a b l y slow at sufficiently low concentrations (10-6--10-s M ) o f metal i o n a n d complex a n d at low acidities. T h e results o b t a i n e d in this work have allowed a c o m p a r i s o n of m e c h a n i s m a n d kinetic factors a m o n g divalent t r a n s i t i o n elements with a different 3d electron configuration i n the structures o f their ions, a n d partial verification of the predictions o f crystal field theory. EXPERIMENTAL Materials. Zinc metal (Baker's Analysed grade), high specific activity (~50 c/g) esZn radiotracer
(Oak Ridge National Laboratory), tetra sodium salt of ethylenediaminetetra-acetie acid (Fisher Certified Reagent grade) and Dowex 50W-X8 (100-200 mesh) cation exchange resin (Baker Analysed) were the major materials used. Other chemicals were guaranteed reagent grade. Zinc (II) solutions were prepared by dissolving a known weight of the metal in ACS reagent grade nitric acid. All solutions were made up in 0.05 M acetate buffer whose pI-I was adjusted to the desired value by addition of sodium hydroxide. In order to eliminate all trace metals at concentrations comparable to the low zinc concentrations used in the exchange experiments, only triply distilled water that had passed through a Dowex 50W ion exchange column was used to prepare solutions. TABLE 1 . - - Z I N C
(II)-zINc-EDTA
EXCHANGE AT 20°C. CONTRIBUTION OF SEVERAL PARALLEL EXCHANGE REACTION PATHS
(Experimental conditions: [Zn~+] = 2 x 10-6 M = [ZnL~-]; pH = 6.35) Bimolecular Protonated Doubly-protonated path chelate chelate (term 1) (term 2) (term 3) (mole/l. per sec) (mole/l. per see) (mole/1. per see) (mole/1.per see) Total rate, R
2"89 × 10-1° (Retie)
0"16 x 10-1° (6 %)
0"67 X 10-l° (23 %)
0"52 X 10-l° (18 %)
Spontaneous chelate* decomposition (term 4) (mole/l. per see) 1"54 X 10-1° (53 %)
* Spontaneous decomposition of e~Zn-EDTA chelate was measured directly at concentration of 2 x 10-6 M and pH: 6.35 at 20°C: ReXla: 1"4 x 10-l° (cf. Roaie = 1'54 X 10-1°.) Procedure. Isotopic exchange experiments were carried out by a procedure similar to that reported previously ~x~except that radiotracer e~Zn was introduced as labelled zinc-EDTA chelate to the equilibrium mixture of metal ion and chelate of appropriate concentrations and pH in a thermostat. As the reaction proceeded, radioactive zinc ion liberated from the labelled chelate was separated rapidly (in less than 1 min) from an aliquot of solution passed onto a Dowex 50W column and the chelate eluted quantitatively with a predetermined volume of buffer solution. A slight zero-time exchange of a few per cent was also observed in zinc exchange experiments. In order to determine the rate of metal ion substitution in the chelate from the exchange data by the MCKAY relation'v~ the fractional exchange at various times was evaluated. For this purpose the tracer activity of the chelate at exchange equilibrium was calculated from the total metal ion and chelate concentrations and the result confirmed in several experiments which were extended over a period of several days. Labelled zinc chelate was used, rather than tracer zinc ion to initiate isotopic exchange as it was found that zinc ion tracer was not chemically stable at 10-l~ M and at pH above 5 but appeared to form radiocoUoid that could be filtered out on a fine-pore glass sinter. Zinc chelate decomposed spontaneously, as indicated by the last term of the rate Equation (I), and Table 1, (footnote) and had to be prepared immediately before each experiment and purified by passing it through a Dowex 50W column. tr~ A. T t m c o et aL, Rieerca scient. 25, 2361 (1955). ~v~H. A. C. McKAY, Nature, Lend. 142, 997 (1938).
Kinetic isotopic exchange studies of metal ion substitution in E D T A chelates---I[ RESULTS
99
AND DISCUSSION
The substitution rate of Zn(II) ion in zinc-EDTA chelate was found to be of fractional kinetic order in zinc ion and hydrogen ion concentration but was precisely first order in chelate concentration as depicted in Figs. 1, 2 and 3 and in Equation (1). The reaction rate increased linearly with metal ion* concentration up to 10-5 M and exhibited a prominent intercept at low concentration (Fig. 1). A parabolic variation of the rate with hydrogen ion concentration is evident in Fig. 2.
EZnL~ ] • 2 x l 0 " S M
32
28 o
~
- 6.035
"o 24 x rr
pH - 6 . 3 5 5
2O
16
12
I
I 2
0
t
J 4
I
I I I 6 8 [ Z n * * ] x I06
I
I I0
I
I 12
I
FIe. l.--Variation of zinc ion-zinc-EDTA exchange rate with zinc concentration, R given in mole/1, per rain at 20°C. (©, • represent experimental results and solid lines, calculation from the best overall rate equation.)
50
[Zn++] = 8 x l 0 " M
40
rznl~]'2
% x
x 'O"M
/ / ~ / / /
30
,-i,.. [ Z n C ] =2 xlO-6 M
20
.~--o
10
0
t 0
I 2
I
I 4
I
L_~_ _! 6 8 [H + ] x l0 T
I
I 10
I
I 12
I
FIG. 2. Variation of zinc ion-zinc-EDTA exchange rate with acidity, R given in mole/l, per min at 20°C. (©, • represent experimental results and solid lines, calculation from the best overall rate equation.) * Metal ion species are considered to include labile aquo and acetato complexes.
100
R . E . JF~VtS and S. S. KRISHNAN
120
['Zn++]=2 x10-eM /
/ ~
6"035
I00
eC
pH=6"355
=o
~6o
40
20
I
0
2
4
6 8 [Znt. = ] x I0 e
I0
i
I
I
12
FIG. 3.--Variation of zinc ion-zinc-EDTA exchange rate with zinc-EDTA chelate concentration, R given in mole/l, per min at 20°C. ( o , • represent experimental results and solid lines, calculation from the best rate equation). TABLE 2.--ZiNc (II)-zrNc-EDTA EXCHANGE AT 20°C [EXPERIMENTAL RESULTS] Exp.
[Zn 2+] × 10e
[ZnL 2-] × 106
pH
*Reap × 1 0 1 °
*Rcale × 101°
1
0.8
2"0
6"355
2.30
2.78
2
2"0
2"0
6"355
2-80
2"88
3
4.0
2.0
6"355
2.72
3.05
4
6"0
2.0
6"355
2.82
3.22
5
8"0
2.0
6"355
3"17
3.38
6
14'0
2-0
6"355
4.02
3.88
7
2-0
0"8
6"355
0"92
1"50
8
2.0
4'0
6"355
6-50
5.80
9
2.0
6'0
6"355
8"9
8"7
I0
2.0
8'0
6"355
11 "9
11 '6
11
2"0
2.0
6"96
1"72
1'90
12
2"0
2.0
6'745
1.90
2.07
13
2"0
2-0
6"12
4.44
4.38
14
2"0
2.0
6"035
5.64
5.37
15
2-0
2'0
5"94
7"5
6.9
16
8.0
2.0
6"03
6.12
5-85
17
2"0
8"0
6"035
21"o
21"~
* R, rate is given in the units: mole/l, per see; concentrations in mole/l. (The mean deviation between Re~,p of column 5 and Rcalc computed from the best fit rate Equation (1), column 6, was 7"8 per cent).
Kinetic isotopic exchange studies of metal ion substitution in EDTA chelates--II
I01
Various empirical rate equations were postulated to account for these observations and were fitted to all of the experimental results by a least squares procedure using an IBM 7090 computer routine. The least consistent deviation over the range of the variables and the least mean difference between experiment and calculation (the two sets of values are compared in Table 2, columns 5 and 6) was obtained using the overall rate equation: R = 4"13 [Zn ~+] [ZnL ~-] q- 76 [ZnL ~ ] [H +] -k-1.3 × l0 s [ZnL z-] [H +] + 7.7 × 10-5[ZnL 2-] (1) where R, the overall reaction rate is given in mole/1, per sec, L denotes the E D T A ligand and square brackets, molar concentrations, at a temperature of 20°C (4- 0.01 o). The mean deviation of Rexp from the Retie values of Table 2 calculated from the best fit rate Equation (1), was 7"8 per cent which was of the same magnitude as the experimental precision of the rate determination. In Figs. 1, 2 and 3, the solid curves have been calculated from the best fit rate Equation (1), and the consistent deviation of the solid line from experiments in Fig. 1 reflects a sensitivity to the choice of the rate constant values in the fitting of all data because of the low order rate dependence on zinc ion concentration. Attempts to confirm the results of these experiments by a separate series in the reverse direction, i.e. exchange initiated by addition of radiotracer zinc in the cationic form were unsuccessful, as indicated above. It was found that, of the total radiozinc added, only a fraction of 5-40 per cent entered into the exchange reaction as estimated from the final equilibrium distribution of radioactivity between the reacting species. It seemed probable, as suggested also by the absorbability of some radiozinc-65 onto glass filters from solutions of less than 10-a° M concentration, that the tracer zinc existed partly in an inert form, such as radiocolloid under these conditions so that only a fraction of it was acutally available for the exchange process. However, this behaviour was not encountered if labelled zinc-EDTA was prepared and used immediately after purification in the exchange experiments. The several terms of the rate Equation, (1), are consistent with the following postulated, parallel reaction paths: Zn2+ -t- *ZnL~----~ *Zn~+ -? ZnL ~*ZnHL----~ *Zn 2+ -t- H L z*ZnHzLo --~ *zne+ + HzL~*ZnL2---+ *Zn~+ -1- L 4The first reaction is the direct substitution of metal ion in the chelate but the others involve dissociation of unprotonated, singly- and doubly-protonated chelates in the rate-determining step.* Similar mechanisms involving the step-wise addition of hydrogen ions to the chelate molecule have been postulated to account for the observed kinetics of other E D T A chelate reactions. ~1-4) There is a progressive increase in the magnitude of the rate constants corresponding to the dissociation of the three species: ZnL 2-, Z n H L - and ZnH2L °, viz. k 4 = 7.7 × 10-5 , k2 = 76 and k s = 1.3 × 10s, respectively at 20°C, although it must be recognized that k2 and k3 include formation constants for the protonated zinc-EDTA chelates.* The activation energies for these * In a previous paper c1~it was shown that a term of the form: k[ML2-I[H+] could be related simply to the rate of formation or dissociation of the species: MHL- and its formation constant.
102
R . E . JERVISand S. S. gatmt--~AN
three reactions, viz. 7"7, 12.5 and 1-6 kcal/mole, are appreciably lower than for the first reaction above, 29 kcal, (Table 3). Presumably the addition o f one or more protons to the chelate weakens the remaining metal-ligand bonds and allows substitution to proceed m o r e readily. Similar observations can be made for C o - C o E D T A and N i - N i E D T A exchange reactions f r o m the relative magnitudes o f the corresponding rate constants and activation energy values. (1,5) TABLE3.--ZINc (II)-zINc-EDTA EXCHANGEAT 20, 30 AND 40°C. ACTIVATION ENERGIES
Temp
kl (l/mole per see)
20°C 4.1 30°C 26 40°C 96 Activation energy: Eiot(kcal/mole) E1 = 29-1
k,
ks
(l/mole per see)
(l'/moles per see)
k4 (see-x)
76 17"8 25.e
1"3 × 10a 0"68 × 108 1"5 × 10a
7"7 × 10-6 15 x 10-' 17 x 10-5
E2 = 12"5
Ea = 1.6
EL ----7.7
2"2
I'S .ll
gt.4
]
I.o 0.6 0.2 32.0
) i 33.0
3 4.0'
( I / T ' K ) xlO 4
FIG. 4.--Variation of reaction rate constants with temperature for zinc ion-zinc~-EDTA exchange at 20°, 30° and 40°C. (All k's are based on minutes scale; © : (log kt) -- 2.0, O: (logk2) -- 3.0; V: (iogks) -- 8-0; and × : (logk+) + 3.6.) The relative contribution o f the several parallel reaction paths to the overall substitution rate is given in Table 1 for a typical set o f experimental conditions. It is evident that the spontaneous decomposition o f z i n c - E D T A chelate is appreciable in all experiments. The activation energy values listed in Table 3 for the several reactions contributing to the overall substitution process were determined by repeating the kinetic experiments at temperatures o f 20, 30 and 40°C (Fig. 4) and assuming that the same f o r m o f rate equation was applicable at all temperatures in this range. F o r a zinc (II) ion d 1°, completely-filled electron orbital configuration, valence b o n d considerations would indicate very rapid substitution reactions with its complexes
Kinetic isotopic exchange studies of metal ion substitution in EDTA chelates--II
103
of the outer orbital type. ~s) These experiments have demonstrated that zinc ionzinc-EDTA exchange is not instantaneous but is measurably slow with exchange half-times of the order of 1 hr at low concentrations. Presumably, the failure to observe slow exchange previously ~n~ was due to the relatively high concentrations of exchanging species used. It is of interest to consider the relative rates of substitution of a series of divalent transition metal ions with different 3d structures in the light of crystal field theory predictions; zinc exchange is more than ten times more rapid than cobalt and 107 more rapid than nickel as is evident by comparison of the magnitude of corresponding rate constants, viz. kl values: 4.1 (Zn), 0.07 (Co) and 8 × 10-7 (Ni, 25 °) 1/mole per see; k 2 values: 76 (Zn), 12 (Co) and 8 × 10-3 (Ni at 25 °) 1/mole per see ca) at 20°C, although the k2 constants include a protonation formation constant which may well vary in a different manner among Zn, Co and Ni. Further, the zinc-EDTA chelate was so labile as to dissociate spontaneously at a rate comparable to the substitution reaction at room temperature (see footnote, Table 1); this was not observed for other 3d divalent metal chelates. Assuming the E D T A ligand to produce weak field metal-ligand interactions, and that Zn, Co and Ni E D T A chelates are octahedral in structure, crystal field calculations tga) would predict the following sequence for the relative rates of substitution of metal ion with E D T A chelate: Zn(II) > Co(II) > Ni(II) Zn(II) > Ni(II) > Co(II)
if dissociative mechanism, and if displacement mechanism
in the reaction transition state. The comparison of rate constants above indicates that the relative substitution rates are in agreement with crystal field predictions for a dissociative mechanism. The involvement of hydrogen ions and the relatively low activation energies also generally support this inference, cgb) On the other hand, the partial order rate dependence on zinc ion concentration would suggest participation of a S~2 displacement mechanism. This discrepancy might be minimized by pointing out that the S~2 mechanism in such reactions does not necessarily involve direct bimolecular collision. The substitution of Zn(II) ion in its E D T A complex may occur through an initial acid-catalysed, step-wise dissociation or uncoiling of the chelate. It is conceivable that Zn~+ZnL ~- ion pair formation could occur even at these extremely low concentration and account for the slight zinc ion effect on the reaction r a t e . Alternately, it might be postulated that, in participating in a displacement reaction, a zinc ion is so far distant from the chelate molecule in the transition state that its influence on the energetics of the reacting system is small. In this respect, the mechanism of zinc-zinc-EDTA exchange appears similar to that involved in cobalt-eobalt-EDTA exchange, while appreciably more rapid. Acknowledgement--The financial support of this research and the award of a research Fellowship to one of the authors (S. S. K.) by the National Research Council of Canada is gratefullyacknowledged. This research was undertaken while one author (S. S. K.) was on a study leave of absence from the Atomic Energy Establishment, Trombay, India.
~s)H. TAum~,Chem. Rev. 5, 69 (1952). ~9~~,~ F. BAsou3 and R. G. PEAaSON,Mechanisms of Inorganic Reactions, p. 108. J. Wiley, London (1958); ~b~ibid. p. 98.
KINETIC ISOTOPIC E X C H A N G E STUDIES OF METAL ION SUBSTITUTION IN EDTA CHELATES--II ZINC (II)-ZINC-EDTA EXCHANGE R. E. JERVIS a n d S. S. KRISHNAN* Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, 5, Canada (First received 11 March 1966; in revised form 12 July 1966)
Abstract--Usingthe method of radioisotopic exchange, the substitution of zinc (II) ion in zinc-EDTA complex was observed to occur at a measurable rate over a concentration range of 1 0 - 5 - 1 0 - s M in both species and within the pH range of 6-7 at room temperature. Because of erratic behaviour of esZn ion at very low tracer concentrations (--~10-x2 M) suggestive of radiocolloid formation, exchange experiments were done using freshly prepared 65Zn-labelledchelate. The substitution rate of zinc 0-I) ion in zinc-EDTA at 20°C in 0.05 M acetate buffer was summarized within experimental error by: R ----kx[Zn'+I[ZnEDTA2-I + k~[ZnEDTA'-I[H+] + k3[ZnEDTA2-][H+12+ k4[ZnEDTA~-] where R is the substitution rate in units of mole/1, per sec and the specific rate constants have the values at 20, 30 and 40°C; kl = 4.13, 26 and 961/mole per see; k2 = 76, 178 and 2561/mole per sec; ks = (1.3, 0.68 and 1.5) × 10812/mole2 per sec; and k4 = (7"7, 15, 17) × 10-5 see-x, respectively. Activation energies corresponding to these values are: 29"2, 12-5, 1"6 and 7.7 keal/mole, respectively. The zinc-EDTA chelate was quite labile and substitution of zinc (II) ion through the spontaneous decomposition of chelate was an appreciable contribution to the overall reaction rate in all experiments. The reaction mechanism postttlated indicated several parallel paths involvingthe unprotonated zinc-EDTA chelate and also the protonated species: ZnHEDTA- and ZnH2EDTA°, suggesting that acid-catalysed decomposition of the chelate facilitated the disruption of metal-chelate bonds in the transition state. Comparison of these results with similar studies of other transition element EDTA chelates indicate that zinc (II) chelate undergoes substitution more rapidly than the d r and d 8 cobalt and nickel chelates. This finding is qualitatively in agreement with crystal field predictions assuming octahedral configuration and a weak field metal-EDTA interaction. INTRODUCTION IN A PREVIOUS paper the exchange of cobalt (II) ion with its E D T A , ethylenediaminetetra-acetate chelate was reported ~1) a n d the kinetics c o m p a r e d with the results o f similar studies with other t r a n s i t i o n elements. T h e purpose of this paper is to outline a detailed investigation o f Z n ( I I ) - z i n c - E D T A exchange by the radiotracer isotopic exchange technique over the permissible range o f low c o n c e n t r a t i o n s a n d very low acidities. K i n e t i c studies of the s u b s t i t u t i o n reactions of other 3d t r a n s i t i o n d e m e n t s with their E D T A chelates have been reported: Fe(III), ~ Co ~1'a'4~ a n d Ni(II). tS~ Previous * Present address: The Centre of Forensic Science, Province of Ontario, Toronto 2, Canada. ~t~ S. S. KmSHNANand R. E. JF.RVlS,J. nucl. inorff. Chem. 29, 87 (1967). ~2j S. S. JONESand F. A. LONG, J. phys. Chem. 56, 25 (1952). ~2~F. A. LONG et aL, Isotopic Exchange Reactions and Chemical Kinetics, p. 106. Brooldaaven Chemical Conference No. 2, (1948). ~4~R. BARBEIRIet aL, Gazz. chim. itaL 87, 1393 (1957). c6~C. H. COOKand F. A. LONG, d. Am. chem. Soc. 80, 33 (1958). 7
97
98
R . E . JERVIS and S. S. KRISHNAN
attempts to study Z n ( I I ) exchange with its E D T A chelate have been few a n d unsucessful: TURCO e t aL ~6~ studied zinc i o n exchange to assess the feasibility o f using the Szilard-Chalmers process i n the chelete to separate the species: the exchange was f o u n d complete within 1 rain i n a p H range o f 3 - 1 1 at the c o n c e n t r a t i o n s used. I n the present study, attempts were m a d e to o b t a i n q u a n t i t a t i v e kinetic data for the reaction a n d it was established i n p r e l i m i n a r y experiments that exchange was m e a s u r a b l y slow at sufficiently low concentrations (10-6--10-s M ) o f metal i o n a n d complex a n d at low acidities. T h e results o b t a i n e d in this work have allowed a c o m p a r i s o n of m e c h a n i s m a n d kinetic factors a m o n g divalent t r a n s i t i o n elements with a different 3d electron configuration i n the structures o f their ions, a n d partial verification of the predictions o f crystal field theory. EXPERIMENTAL Materials. Zinc metal (Baker's Analysed grade), high specific activity (~50 c/g) esZn radiotracer
(Oak Ridge National Laboratory), tetra sodium salt of ethylenediaminetetra-acetie acid (Fisher Certified Reagent grade) and Dowex 50W-X8 (100-200 mesh) cation exchange resin (Baker Analysed) were the major materials used. Other chemicals were guaranteed reagent grade. Zinc (II) solutions were prepared by dissolving a known weight of the metal in ACS reagent grade nitric acid. All solutions were made up in 0.05 M acetate buffer whose pI-I was adjusted to the desired value by addition of sodium hydroxide. In order to eliminate all trace metals at concentrations comparable to the low zinc concentrations used in the exchange experiments, only triply distilled water that had passed through a Dowex 50W ion exchange column was used to prepare solutions. TABLE 1 . - - Z I N C
(II)-zINc-EDTA
EXCHANGE AT 20°C. CONTRIBUTION OF SEVERAL PARALLEL EXCHANGE REACTION PATHS
(Experimental conditions: [Zn~+] = 2 x 10-6 M = [ZnL~-]; pH = 6.35) Bimolecular Protonated Doubly-protonated path chelate chelate (term 1) (term 2) (term 3) (mole/l. per sec) (mole/l. per see) (mole/1. per see) (mole/1.per see) Total rate, R
2"89 × 10-1° (Retie)
0"16 x 10-1° (6 %)
0"67 X 10-l° (23 %)
0"52 X 10-l° (18 %)
Spontaneous chelate* decomposition (term 4) (mole/l. per see) 1"54 X 10-1° (53 %)
* Spontaneous decomposition of e~Zn-EDTA chelate was measured directly at concentration of 2 x 10-6 M and pH: 6.35 at 20°C: ReXla: 1"4 x 10-l° (cf. Roaie = 1'54 X 10-1°.) Procedure. Isotopic exchange experiments were carried out by a procedure similar to that reported previously ~x~except that radiotracer e~Zn was introduced as labelled zinc-EDTA chelate to the equilibrium mixture of metal ion and chelate of appropriate concentrations and pH in a thermostat. As the reaction proceeded, radioactive zinc ion liberated from the labelled chelate was separated rapidly (in less than 1 min) from an aliquot of solution passed onto a Dowex 50W column and the chelate eluted quantitatively with a predetermined volume of buffer solution. A slight zero-time exchange of a few per cent was also observed in zinc exchange experiments. In order to determine the rate of metal ion substitution in the chelate from the exchange data by the MCKAY relation'v~ the fractional exchange at various times was evaluated. For this purpose the tracer activity of the chelate at exchange equilibrium was calculated from the total metal ion and chelate concentrations and the result confirmed in several experiments which were extended over a period of several days. Labelled zinc chelate was used, rather than tracer zinc ion to initiate isotopic exchange as it was found that zinc ion tracer was not chemically stable at 10-l~ M and at pH above 5 but appeared to form radiocoUoid that could be filtered out on a fine-pore glass sinter. Zinc chelate decomposed spontaneously, as indicated by the last term of the rate Equation (I), and Table 1, (footnote) and had to be prepared immediately before each experiment and purified by passing it through a Dowex 50W column. tr~ A. T t m c o et aL, Rieerca scient. 25, 2361 (1955). ~v~H. A. C. McKAY, Nature, Lend. 142, 997 (1938).
Kinetic isotopic exchange studies of metal ion substitution in E D T A chelates---I[ RESULTS
99
AND DISCUSSION
The substitution rate of Zn(II) ion in zinc-EDTA chelate was found to be of fractional kinetic order in zinc ion and hydrogen ion concentration but was precisely first order in chelate concentration as depicted in Figs. 1, 2 and 3 and in Equation (1). The reaction rate increased linearly with metal ion* concentration up to 10-5 M and exhibited a prominent intercept at low concentration (Fig. 1). A parabolic variation of the rate with hydrogen ion concentration is evident in Fig. 2.
EZnL~ ] • 2 x l 0 " S M
32
28 o
~
- 6.035
"o 24 x rr
pH - 6 . 3 5 5
2O
16
12
I
I 2
0
t
J 4
I
I I I 6 8 [ Z n * * ] x I06
I
I I0
I
I 12
I
FIe. l.--Variation of zinc ion-zinc-EDTA exchange rate with zinc concentration, R given in mole/1, per rain at 20°C. (©, • represent experimental results and solid lines, calculation from the best overall rate equation.)
50
[Zn++] = 8 x l 0 " M
40
rznl~]'2
% x
x 'O"M
/ / ~ / / /
30
,-i,.. [ Z n C ] =2 xlO-6 M
20
.~--o
10
0
t 0
I 2
I
I 4
I
L_~_ _! 6 8 [H + ] x l0 T
I
I 10
I
I 12
I
FIG. 2. Variation of zinc ion-zinc-EDTA exchange rate with acidity, R given in mole/l, per min at 20°C. (©, • represent experimental results and solid lines, calculation from the best overall rate equation.) * Metal ion species are considered to include labile aquo and acetato complexes.
100
R . E . JF~VtS and S. S. KRISHNAN
120
['Zn++]=2 x10-eM /
/ ~
6"035
I00
eC
pH=6"355
=o
~6o
40
20
I
0
2
4
6 8 [Znt. = ] x I0 e
I0
i
I
I
12
FIG. 3.--Variation of zinc ion-zinc-EDTA exchange rate with zinc-EDTA chelate concentration, R given in mole/l, per min at 20°C. ( o , • represent experimental results and solid lines, calculation from the best rate equation). TABLE 2.--ZiNc (II)-zrNc-EDTA EXCHANGE AT 20°C [EXPERIMENTAL RESULTS] Exp.
[Zn 2+] × 10e
[ZnL 2-] × 106
pH
*Reap × 1 0 1 °
*Rcale × 101°
1
0.8
2"0
6"355
2.30
2.78
2
2"0
2"0
6"355
2-80
2"88
3
4.0
2.0
6"355
2.72
3.05
4
6"0
2.0
6"355
2.82
3.22
5
8"0
2.0
6"355
3"17
3.38
6
14'0
2-0
6"355
4.02
3.88
7
2-0
0"8
6"355
0"92
1"50
8
2.0
4'0
6"355
6-50
5.80
9
2.0
6'0
6"355
8"9
8"7
I0
2.0
8'0
6"355
11 "9
11 '6
11
2"0
2.0
6"96
1"72
1'90
12
2"0
2.0
6'745
1.90
2.07
13
2"0
2-0
6"12
4.44
4.38
14
2"0
2.0
6"035
5.64
5.37
15
2-0
2'0
5"94
7"5
6.9
16
8.0
2.0
6"03
6.12
5-85
17
2"0
8"0
6"035
21"o
21"~
* R, rate is given in the units: mole/l, per see; concentrations in mole/l. (The mean deviation between Re~,p of column 5 and Rcalc computed from the best fit rate Equation (1), column 6, was 7"8 per cent).
Kinetic isotopic exchange studies of metal ion substitution in EDTA chelates--II
I01
Various empirical rate equations were postulated to account for these observations and were fitted to all of the experimental results by a least squares procedure using an IBM 7090 computer routine. The least consistent deviation over the range of the variables and the least mean difference between experiment and calculation (the two sets of values are compared in Table 2, columns 5 and 6) was obtained using the overall rate equation: R = 4"13 [Zn ~+] [ZnL ~-] q- 76 [ZnL ~ ] [H +] -k-1.3 × l0 s [ZnL z-] [H +] + 7.7 × 10-5[ZnL 2-] (1) where R, the overall reaction rate is given in mole/1, per sec, L denotes the E D T A ligand and square brackets, molar concentrations, at a temperature of 20°C (4- 0.01 o). The mean deviation of Rexp from the Retie values of Table 2 calculated from the best fit rate Equation (1), was 7"8 per cent which was of the same magnitude as the experimental precision of the rate determination. In Figs. 1, 2 and 3, the solid curves have been calculated from the best fit rate Equation (1), and the consistent deviation of the solid line from experiments in Fig. 1 reflects a sensitivity to the choice of the rate constant values in the fitting of all data because of the low order rate dependence on zinc ion concentration. Attempts to confirm the results of these experiments by a separate series in the reverse direction, i.e. exchange initiated by addition of radiotracer zinc in the cationic form were unsuccessful, as indicated above. It was found that, of the total radiozinc added, only a fraction of 5-40 per cent entered into the exchange reaction as estimated from the final equilibrium distribution of radioactivity between the reacting species. It seemed probable, as suggested also by the absorbability of some radiozinc-65 onto glass filters from solutions of less than 10-a° M concentration, that the tracer zinc existed partly in an inert form, such as radiocolloid under these conditions so that only a fraction of it was acutally available for the exchange process. However, this behaviour was not encountered if labelled zinc-EDTA was prepared and used immediately after purification in the exchange experiments. The several terms of the rate Equation, (1), are consistent with the following postulated, parallel reaction paths: Zn2+ -t- *ZnL~----~ *Zn~+ -? ZnL ~*ZnHL----~ *Zn 2+ -t- H L z*ZnHzLo --~ *zne+ + HzL~*ZnL2---+ *Zn~+ -1- L 4The first reaction is the direct substitution of metal ion in the chelate but the others involve dissociation of unprotonated, singly- and doubly-protonated chelates in the rate-determining step.* Similar mechanisms involving the step-wise addition of hydrogen ions to the chelate molecule have been postulated to account for the observed kinetics of other E D T A chelate reactions. ~1-4) There is a progressive increase in the magnitude of the rate constants corresponding to the dissociation of the three species: ZnL 2-, Z n H L - and ZnH2L °, viz. k 4 = 7.7 × 10-5 , k2 = 76 and k s = 1.3 × 10s, respectively at 20°C, although it must be recognized that k2 and k3 include formation constants for the protonated zinc-EDTA chelates.* The activation energies for these * In a previous paper c1~it was shown that a term of the form: k[ML2-I[H+] could be related simply to the rate of formation or dissociation of the species: MHL- and its formation constant.
102
R . E . JERVISand S. S. gatmt--~AN
three reactions, viz. 7"7, 12.5 and 1-6 kcal/mole, are appreciably lower than for the first reaction above, 29 kcal, (Table 3). Presumably the addition o f one or more protons to the chelate weakens the remaining metal-ligand bonds and allows substitution to proceed m o r e readily. Similar observations can be made for C o - C o E D T A and N i - N i E D T A exchange reactions f r o m the relative magnitudes o f the corresponding rate constants and activation energy values. (1,5) TABLE3.--ZINc (II)-zINc-EDTA EXCHANGEAT 20, 30 AND 40°C. ACTIVATION ENERGIES
Temp
kl (l/mole per see)
20°C 4.1 30°C 26 40°C 96 Activation energy: Eiot(kcal/mole) E1 = 29-1
k,
ks
(l/mole per see)
(l'/moles per see)
k4 (see-x)
76 17"8 25.e
1"3 × 10a 0"68 × 108 1"5 × 10a
7"7 × 10-6 15 x 10-' 17 x 10-5
E2 = 12"5
Ea = 1.6
EL ----7.7
2"2
I'S .ll
gt.4
]
I.o 0.6 0.2 32.0
) i 33.0
3 4.0'
( I / T ' K ) xlO 4
FIG. 4.--Variation of reaction rate constants with temperature for zinc ion-zinc~-EDTA exchange at 20°, 30° and 40°C. (All k's are based on minutes scale; © : (log kt) -- 2.0, O: (logk2) -- 3.0; V: (iogks) -- 8-0; and × : (logk+) + 3.6.) The relative contribution o f the several parallel reaction paths to the overall substitution rate is given in Table 1 for a typical set o f experimental conditions. It is evident that the spontaneous decomposition o f z i n c - E D T A chelate is appreciable in all experiments. The activation energy values listed in Table 3 for the several reactions contributing to the overall substitution process were determined by repeating the kinetic experiments at temperatures o f 20, 30 and 40°C (Fig. 4) and assuming that the same f o r m o f rate equation was applicable at all temperatures in this range. F o r a zinc (II) ion d 1°, completely-filled electron orbital configuration, valence b o n d considerations would indicate very rapid substitution reactions with its complexes
Kinetic isotopic exchange studies of metal ion substitution in EDTA chelates--II
103
of the outer orbital type. ~s) These experiments have demonstrated that zinc ionzinc-EDTA exchange is not instantaneous but is measurably slow with exchange half-times of the order of 1 hr at low concentrations. Presumably, the failure to observe slow exchange previously ~n~ was due to the relatively high concentrations of exchanging species used. It is of interest to consider the relative rates of substitution of a series of divalent transition metal ions with different 3d structures in the light of crystal field theory predictions; zinc exchange is more than ten times more rapid than cobalt and 107 more rapid than nickel as is evident by comparison of the magnitude of corresponding rate constants, viz. kl values: 4.1 (Zn), 0.07 (Co) and 8 × 10-7 (Ni, 25 °) 1/mole per see; k 2 values: 76 (Zn), 12 (Co) and 8 × 10-3 (Ni at 25 °) 1/mole per see ca) at 20°C, although the k2 constants include a protonation formation constant which may well vary in a different manner among Zn, Co and Ni. Further, the zinc-EDTA chelate was so labile as to dissociate spontaneously at a rate comparable to the substitution reaction at room temperature (see footnote, Table 1); this was not observed for other 3d divalent metal chelates. Assuming the E D T A ligand to produce weak field metal-ligand interactions, and that Zn, Co and Ni E D T A chelates are octahedral in structure, crystal field calculations tga) would predict the following sequence for the relative rates of substitution of metal ion with E D T A chelate: Zn(II) > Co(II) > Ni(II) Zn(II) > Ni(II) > Co(II)
if dissociative mechanism, and if displacement mechanism
in the reaction transition state. The comparison of rate constants above indicates that the relative substitution rates are in agreement with crystal field predictions for a dissociative mechanism. The involvement of hydrogen ions and the relatively low activation energies also generally support this inference, cgb) On the other hand, the partial order rate dependence on zinc ion concentration would suggest participation of a S~2 displacement mechanism. This discrepancy might be minimized by pointing out that the S~2 mechanism in such reactions does not necessarily involve direct bimolecular collision. The substitution of Zn(II) ion in its E D T A complex may occur through an initial acid-catalysed, step-wise dissociation or uncoiling of the chelate. It is conceivable that Zn~+ZnL ~- ion pair formation could occur even at these extremely low concentration and account for the slight zinc ion effect on the reaction r a t e . Alternately, it might be postulated that, in participating in a displacement reaction, a zinc ion is so far distant from the chelate molecule in the transition state that its influence on the energetics of the reacting system is small. In this respect, the mechanism of zinc-zinc-EDTA exchange appears similar to that involved in cobalt-eobalt-EDTA exchange, while appreciably more rapid. Acknowledgement--The financial support of this research and the award of a research Fellowship to one of the authors (S. S. K.) by the National Research Council of Canada is gratefullyacknowledged. This research was undertaken while one author (S. S. K.) was on a study leave of absence from the Atomic Energy Establishment, Trombay, India.
~s)H. TAum~,Chem. Rev. 5, 69 (1952). ~9~~,~ F. BAsou3 and R. G. PEAaSON,Mechanisms of Inorganic Reactions, p. 108. J. Wiley, London (1958); ~b~ibid. p. 98.