as the intersection of the two branches. Nickel(II), copper(II), and zinc(I1) can be titrated at either pH = 5 or pH = 10. A direct titration of chromium(II1) with D(-)PDTA was attempted using a thermostated flow-through cell. The titration was performed at 60 "C, but the results were unsatisfactory due to the very slow kinetics of the reactions. Advantages. The main advantages of this technique are its versatility, simplicity, and the elimination of the subjectivity associated with visual end points. Only three buffers are required for spectropolarimetric titrimetry with D(-)PDTA. Because a stereospecific titrant, D(-)PDTA, is used, the maximum rotations of the metal D(-)PDTA complexes are obtained, allowing high sensitivity. Thus the titrant and the complexes formed serve as selfindicators permitting the maximum quantitative pH range of the metal complexes to be utilized. Because the determination of the end point is obtained through the relative measurements of optical activity, the spectropolarimetric titrations
are usually capable of achieving greater precision than visual methods. I n the construction of the titration plots, the best straight line is drawn through a number of experimental points in order to minimize the spectropolarimetric error associated with each point. The extrapolated end point is not adversely influenced by high electrolyte concentrations; therefore, this technique is suitable for use with many separation schemes. Present investigations in this laboratory are being carried out to determine the feasibility of using a polarimeter with a wider wavelength range to determine metals in the microgram range. RECEIVED for review July 30, 1969. Accepted November 3, 1969. Presented in part at the 157th National Meeting of the American Chemical Society, Division of Analytical Chemistry, Minneapolis, Minnesota, April 1969. This work was supported by The Robert A. Welch Foundation Fellowship Grant A-262.
Kinetics of Ligand Exchange Reaction of Ethylenediaminetetraacetate Ion with Ethylenediaminetetraacetatonickel(11) James D. Carr Department of Chemistry, Unioersity of Nebraska, Lincoln, Neb. 68508
C . N. Reilley Department of Chemistry, University of North Carolina, Chapel Hill, N . C . 27514
The rate for the ligand exchange reaction of ethylenediaminetetraacetate ion (EDTA) with the nickel(l1) complex of EDTA is measured by NMR techniques with deuterated EDTA. The pH dependency of the reaction rate is analyzed and the rate constant for the EDTA tetraanion attack on nickel-EDTA determined to be 1.95 X 10-3 M-lsec-l at 33 OC. The activation energy of this reaction is 14.0 kcal/mole and the log of the frequency factor is 7.1 (M-lsec-1). A rate determining step is assigned which is also consistent with the analogous EDTA ligand exchange reactions with Ca2+, Cd2+, and SrZf and with the metal exchange reaction *Ni2+ Ni-EDTA + *Ni-EDTA Nie.
+
+
SEVERAL PAPERS have appeared recently discussing the symmetric ligand exchange reactions of EDTA (ethylenediaminetetraacetate ion or Y 4-) with a metal complex of EDTA (Equation l with charges omitted for clarity) where M has been calcium ( I ) , cadmium (2),lead (3),and strontium (4), all labile, diamagnetic ions. Each of these reactions was studied by nuclear magnetic resonance (NMR) line-broadening techniques. ky""
Y*
+ MY 1_ MY* + Y
(1)
(1) R. J. Kula and G. H. Reed, ANAL.CHEM.,38, 697 (1966). (2) J. L. Sudmeier and C. N. Reilley, Znorg. Chem., 5 , 1047 (1966). (3) J. D. Carr, Kenneth Torrance, C. J. Kruz, and C. N. Reilley, ANAL.CHEM.,39, 1358 (1967). (4) R. J. Kula and D. L. Rabenstein, J . Amer. Chem. Soc., 89, 552 (1967).
In order to measure the rate of Equation 1 for nickel(II), a paramagnetic, sluggish, transition metal ion, it became necessary to devise a different measurement technique. Cook and Long have previously measured the rate of the symmetric electrophylic substitution, or metal exchange of nickel-EDTA (Equation 2) by use of radioactive 63Ni(5). They found several reaction pathways depending on hydrogen ion concentration. Ni*
+ NiY
__
kNih'iY
Ni*Y
+ Ni
(2)
The rate constant for exchange without hydrogen ion involvement was later shown to fit into a series of rate constants of various metal ions substituting nickel in nickel-EDTA (6). This latter study showed that the rate determining step in the reaction is the breaking of the nickel to nitrogen bond when the leaving nickel is bonded to EDTA through a glycine segment and the entering nickel bonded through a iminodiacetate segment.
EXPERIMENTAL Method of Following Kinetics. EDTA was prepared 98% deuterated in the acetate positions as described by Terrell and Reilley (7). They showed that the exchange of acetate methylene hydrogens with solvent water is quite slow even at near boiling temperatures both for uncomplexed ligand ( 5 ) C. M. Cook and F. A. Long, J . Amer. Chem. SOC.,80,33 (1958). (6) D. W. Margerum, Rec. Chem. Progr., 24, 237 (1963).
(7) J. B. Terrell and C. N. Reilley, ANAL.CHEM., 38,1876 (1966).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
51
r\
Table I. Observed Rate Constants for Equation 2 Temperature 32 "C [NiY], = [YD]~ kobs x 1O4(kf-'SeC-') PH 6.43 0.368 1.17 0.368 0.659 6.98 8.85 0.337 2.35 9.18 0.308 3.90 9.31 0.306 4.46 9.40 0.302 5.80 9.50 0.306 6.43 0.302 9.62 5.80 9.78 0.303 12.1 9.92 0.326 9.74 0.296 16.0 10.44 10.60 0.288 18.9 10.78 0.294 17.4 0.291 22. I 10.94 9.10 9.32 9.60 9.81
Temperature 51 "C 0.307 0.305 0.300 0.296
10.51 11.69 13.00
Temperature 10.5 "C 0.296 0.287 0.283
i /
28.3 35.5 45.3 59.4 3.0 3.18 3.16 Figure 1. NMR traces of EDTA in reaction mixture as function of time
and for EDTA complexed to a variety of metal ions including nickel. A standard solution of nickel-EDTA was prepared from nondeuterated EDTA and reagent grade nickel nitrate. This material was reacted with deuterated EDTA in an NMR tube and the reaction monitored by repetitive measurement of the area of the NMR resonance peak assigned to the acetate protons of EDTA ions which are not coordinated to a nickel ion. Potassium ion is used as the counter ion when preparing all EDTA solutions. The reaction followed is shown in Equation 3 with charges omitted for clarity and typical NMR traces are shown in Figure 1.
(3) Peak areas were measured with a K&E compensating planimeter and the times assigned as the time that the peak maximum was recorded. Reaction half-times varied from approximately 15 minutes to 300 minutes. Protons which are part of an EDTA ion which is coordinated to a nickel ion cannot be observed on the Varian A-60 NMR spectrometer used in the kinetic experiments because of the very large paramagnetic contact shift. The peaks for the noncoordinated EDTA were broadened somewhat but were easily observable. This broadening is primarily due to outer sphere solvent relaxation as discussed by Pearson and Lanier (8). The chemical shift of the peaks were measured DS. internal TMS* (sodium 3-(trimethylsilyl)-l-propanesulfonate) and found to be the same as reported for uncomplexed EDTA in the absence of any metal ion (9) although both EDTA and TMS* resonances were shifted with respect to external TMS*. The peak due to the ethylenic protons remained of constant area during the reaction and was used to check the stability of the instrument during a run and between the end of the kinetic experiment and the equi-
(8) R. G . Pearson and R. D. Lanier, J . Amer. C/zem. SOC.,86,
765 (1964). (9) J. L. Sudmeier and C. N. Reilley, ANAL.CHEM.,36, 1968 ( 1964). 52
Left-hand trace (downfield) is that of the acetate proton and upfield trace is ethylenic protons. pH 10.78; (NiY), = (YD), = 0.294; Time to peak of trace 1) 1.6 min; 2) 3.4; 3) 5.25; 4) 10.2; 5) 14.9; 6) 20.2; 7) 16.9 min; and 8) 24 hours. 32 "C
librium measurement usually made on the day following the kinetic run. The solutions were adjusted to probe temperature before mixing. Probe temperature was measured using a copperconstantan thermocouple. Reagents were usually added directly to the NMR tube by means of a Gilmont micrometer buret. Measurements of pH were made at the temperature of the experiment after the kinetic run on a Corning model 12 pH meter equipped with a Corning semimicro combination electrode. Potassium hydroxide or nitric acid were used to adjust the solution pH but no other buffer or ionic strength control was added. Treatment of Data. Most kinetic runs were carried out with equal concentrations of the two reactants. The usual kinetic expression for a second-order, reversible, equal concentration experiment (10) was simplified by assuming an equilibrium constant of unity to yield the expression shown in Equation 4. An additional tacit assumption required for Equation 4 to be valid is that there is no product-i.e., nondeuterated EDTA-present at zero time. This and the requirement for equal concentrations of reactants demand a very high degree of deuteration of the reactant EDTA. A plot then of -ln(Area, - Areat) us. time gives a linear plot with a slope of 2[Y,]k,b,.
(4) Relative concentrations of differently protonated species of EDTA and nickel-EDTA were calculated from values of
(10) A. A. Frost and R. C. Pearson, "Kinetics and Mechanism," 3rd Ed., John Wiley & Sons, Inc., New York, N. Y . , 1961, p
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
188.
appropriate protonation constants. The pK4 values used are 9.9 (32 "C) and 9.4 (51 "C). These values result from the AH of ionization of EDTA (ZZ) and the measured pK, at high ionic strength ( I , 2). RESULTS
1
I
I
I
- ai-
I
f
/
The observed rate constants obtained for the ligand exchange reaction are compiled in Table I. The hydrogen ion dependence of the reaction is expressed in Equations 5 and 6. Equation 5 is the same general expression found before in the symmetric ligand exchange reactions of calcium, strontium, cadmium, and lead complexes of EDTA.
+ 3-)(NiY) + k2::(HzY2;)(NiY)
kOb,(YD)(NiY)= k;"(Y4;)(NiY) k?:(HY
(5) Figure 2. Resolution plot of Equation 4 of32 "C data
Equation 6 comes directly from Equation 5 and is valid in the pH range above 7 where the reaction rate due to kgf; is negligibly small. K3 and K4 are the third and fourth acid dissociation constant of EDTA, respectively. Figure 2 shows a plot of Equation 6 for data taken at 33 "C which shows an intercept value of kF$ indistinguishable from zero (less than 2 x 10-5 M-1 sec-1) and a slope from which k y y = 1.95 X 10-3 M-1 sec-I) are obtained. A similar plot of data taken at Direct measure51 "C gives a value of k y y = 8.0 X ment of k F y at 10.5 "C gives a value of 0.32 X M-l sec-1. These values yield an activation energy of 14.0 kcal mole and a frequency factor of lo7. h4-I sec-'. Attempts to measure this rate constant with one reagent in tenfold or greater excess on a Varian A-60D were largely unsuccessful because of the small change in signal, the short times involved, and the extreme ionic strengths encountered ( I 2 5). Results of experiments in which EDTA concentrations were varied from 10X to 20 X that of nickel-EDTA are sufficiently constant, however, to demonstrate the first-order behavior of the reaction in EDTA concentration. The observed second-order rate constant begins to increase again at the most acid conditions. This effect is noted but not experimentally pursued in detail since the chemical shift of the acetate hydrogens is quite close to the water peak in this pH range. This effect is interpreted as in prior systems (Z-3), as a second proton helping the loss of the leaving ligand whereas the first proton hinders the bond formation of the incoming ligand. Equation 3 is rearranged so that the dependent [YIT variable is :k; ___ - k y y which is plotted against [HY -1 [H+I hydrogen ion for the two observed rate constants below pH 7. A4-I sec-l and Such a plot yields a value of k":; of 4 X M-l sec-l. An alternate interpretation k?: of 5 3 X is to express k;: as k 2 q y as described previously (3). The consistent value of k z F Yis 3 X 10-l M-lsec- l. Another possible mechanism contributing to the total ligand exchanges involves hydrogen ion assisted dissociation of nickel-EDTA followed by rapid reaction of the freed nickel ion with deuterated EDTA (Equations 7, 8).
5
NiY
+ xH+ + Ni2+ + H,Y
(7)
The rate of dissociation of nickel-EDTA and its hydrogen ion dependence have been measured and been found to be much too slow to contribute to product formation even in the most acidic of our experiments (5,Z2). DISCUSSION
It is inferred from the reaction order that intermediates in this system involve two EDTA molecules, one breaking one bond at a time with its place being taken by a solvent water molecule; the other forming one bond at a time as the solvent water molecules are lost in turn until the ligand substitution is complete. Such a sequence is suggested in numerous other ligand exchange reactions. Examination of possible sequences of intermediates then shows structures with alternating n and n 1 water molecules in the primary coordination shell. One can propose reaction sequences with 12 = 0 and n = 1 as shown in Figure 3 if the following criteria are observed: an acetate group will be the first dentate to form a bond from an EDTA ion to nickel because of steric problems of a nitrogen approaching the metal ion without prior acetate bond formation; subsequent bond formation will be only to dentates which will complete a five-membered chelate ring; and each bond rupture will destroy only a single chelate ring. Intermediates with three or more water molecules in the first coordination sphere are regarded as being of too low stability to be of importance in the reaction pathway. Intermediates with both EDTA molecules bonded through one N atom each such that the N's are cis are demonstrated by Fisher-Taylor-Hirschfelder models to be sterically impossible. The observed rate constant of such a reaction is related to the rate constant of the rate determining step and the stability constant of the intermediate prior to the rate determining step in the following manner.
+
(7)
If values of K$hly can be estimated and krds assigned for a variety of possible choices of rate determining step, a predicted value of k;ly can be obtained. Discovery of a mechanism
(8)
for which the predicted value of kFY agrees well with the observed value will be evidence for selecting such a mechanism as correct.
(11) L. G. Sillen and A. E. Martell, "Stability Constants of Metal Ion Complexes," Special Publication No. 17, The Chemical Society, London, 1964.
(12) D. W. Margerum, D. L. Janes, and H. M. Rosen, J. Amer. Chem. SOC.,87,4463 (1965).
Ni2+
+ YD
-+
NiYD
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
53
IPb
Ilb
mb
Figure 3. Possible intermediates and microscopic reactions leading to exchange of EDTA The approach taken to the problem of estimating the stability constants of the proposed intermediates is to estimate the stability constant of species IVa, for example, as being the and K ~ i ( ~ 1 These ~ ) ~ . values are tabproduct of KNI(EDDA) ulated as K?&, and are shown in Table 11. These values ought to be reduced in magnitude because of electrostatic repulsions of the -4 EDTA and the -2 nickel-EDTA complex being greater than those of the model compounds nickel-EDDA (zero charge) and glycine (- 1 charge). Calculations of this diminution using the ion-ion attraction equations of Rorabacher (13) give hopelessly weak complexes, probably because the equations assume point charges instead of the actual, very complicated charge distributions. Margerum and Rosen have recently shown that the rate of a bond rupture of water or ammonia from nickel depends strongly on the nature of other ligands coordinated to the nickel ion (14, so one must be very careful in making a choice of such a rate constant for the intermediates of unknown structure encountered in this study. The rate of breakage of a nickel-nitrogen bond when the nitrogen forms part of a five-membered chelate ring wherein both ends of the chelate are amine nitrogens has been shown to be much slower than the simple breaking of a nonchelated nitrogen (15) and also slower than loss of a chelated nitrogen when the other end of the chelate is a carboxylate as is the case with nickel-glycine (16). Ahmed and Wilkins have measured the rate constant for the breakage of the first nitrogen to nickel bond in monoethylenediaminetetraaquonickel(I1) to be sec-'at 0.6 "C (15) or 1.45 X 10-I sec-l at 25 "C 1.3 X and activation parameters to be E, = 20.5 kcal mole and log
(13) D. B. Rorabacher, Znorg. Chem., 5 , 1891 (1966). (14) D. W. Margerum and H. M. Rosen, J . Amer. Chem. SOC.,89, 1088 (1967). (15) A. K. S. Ahmed and R. G. Wilkins, J . Chem. Soc., 3700 ( 1959). (16) G. G. Hammes and J. I. Steinfeld, J. Amer. Chem. Soc., 84, 4639 (1962).
54
PZ = 16.0 min-I (17). These results lead to a value of the rate constant for bond breakage of the first nitrogen of nickelethylenediamine of 0.3 sec-' at 33 "C. This number is taken as the best approximation of the rate constant for breakage of the first EDTA nitrogen to nickel bond although electrostatic and steric effects are also operable. A value of ktEf$ equal to Yk\$' = 1.5 X 104 sec-1 is chosen since in all cases in which this term is used, the intermediate has two nitrogens and either two or three acetates bonded to the nickel so that the electronic environment of the nickel ion in such an intermediate is quite similar to that in a nickel-EDTA molecule. Also, the charge of the complex has been shown to be not directly related to lability of coordinated water molecules (14). In Figure 3, a choice must be made first for the correct branch of the predominant reaction pathway at structures 111, V, and VI as well as the choice of rate limiting step for the entire reaction. Path kaa involves the rapid loss of a coordinated water molecule whereas path kabinvolves the loss of a chelated nitrogen, a much slower process. Fisher-Hirschfelder-Taylor molecular models show that structure IV can be formed with difficulty because of steric blocking by the acetate (methylene) hydrogens of the 1eavin.g EDTA ion. Structure I11 will probably progress to V by way of the rapid loss of water leading to IVa however, rather than uia the relatively slow path through unhindered IVb. The choice of pathway afforded intermediate V is less clear, but the rate of water loss from V to give VIa (ca. 1.5 X l o 4sec-I) is undoubtedly greater than the loss of a chelated acetate to give VIb (ca. 2 X los sec-1). The pathway uia Va and \'IC will not lead to exchange since molecular models indicate that formation of VIc is impossible. Intermediate Va can be formed but only with some difficulty similar to that observed in forming ~
(17) A. K. S. Ahmed and R. G. Wilkins, J. Chem. Soc., 2901 ( 1960).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
5
Table 11. Values of Predicted Rate Constants (M-l sec -I) Structure K;LiY/K.q:Y to form 111 6.3 x IVa IVb IVC IVa 5.0 x V Va IVb 2.5 X V V 2.0 x 10-7 VIa VI b VIa 1.0 x 10-4 V VIb 2.5 x ¶O-8 V Less than k - H * O (1.5 X 104) but greater than 400 k-" (2.3 X lo3)(18).
for Possible Rate Determining Steps krds
(SeC-')
kyNiY(predicted) 1.0x loo 2 x 10-6 6 X 10-1 1.5 x 10-2 5 x 102 4 x 10-6 3 x 10-3 2 x 10-3 1.0x 10" 4 x 10-4
k - ~ z o= 1.5 x 104 k-" = 0.3 k - O A c gg 1 X 1040 k-S = 0.3 k - O A c E 1 X 104 k-H20 = 1.5 X 104 k-HzO= 1.5 X lo4 k-OAa S 1 X 104 k-OAC G 1 x 104 k - ~ z o= 1.5 x 104
Table 111. Calculation of Predicted Ligand Exchange Rate Constants for Other Metals
Metal
log
~M'l'hTe1DA)b
M log K;'''') 8.26 3.61 1.5 x 104 Ca 2.5 X lo8 3.75 1.35 Cd 4 x 108 6.77 3.18 2.85 0.91 Sr N 2 x 108 Values taken from Ref. (20). MeIDA is abbrev. for N-methyl-iminodiacetic acid. Values from Ref. (19).
k-HiOo
Ni
0
*
IVa. The rate at which a chelated acetate arm of EDTA is dissociated from nickel ion is unknown but it is surely slower than the rate of water loss or acetate would not form a stable complex and it is greater than the rate of nickel-nitrogen bond breakage by at least a factor of 400 (18). This means that intermediate I11 is more apt to form species IVa than to form IVC. The reaction path by which most of the product is formed is likely to be I-Ila or IIb-111-IVa-V-VIa, Structure VIa is a symmetric intermediate. When it has been formed, exchange is assured since either ligand can leave with equal ease by the reverse of the steps used in its formation. Attempts to envisage a reaction pathway which does not involve a symmetric intermediate result in postulations of intermediates with extremely low predicted stabilities so any such pathway would be of much higher energy than that described above. Application of Equation 7 to the microscopic reactions shown in this sequence shows that the loss of water from V is the slowest step and that the predicted rate constant agrees surprisingly well with the observed value. The assignment of step V + VIa as rate determining also gives good agreement with data for calcium, cadmium, and strontium EDTA ligand exchange reactions (Table 111). The rate of water loss from lead ion is not known so kPybY cannot be compared with prediction. The remarkable agreement between predicted and observed rate constants implies a common mechanism for these complexes although the rate constants vary over a range of lo6. A comparison of the rate constants of nickel attack and EDTA attack on nickel-EDTA (8 X lo-' and 1. 1 X M-1 sec-I, respectively, at 25 "C and ionic strength greater than 1.O) can help in assigning a mechanism to the ligand displacement reaction. The intermediate in the nickel attack case (Equation 2) has been shown to be structure A in which Ni* designates the entering nickel ion. The observed rate constant is the product of the rate constant of the rate limiting microscopic reaction step and the stability constant of A, the (18) T. J. Bydalek and D. W . Margerum, Znorg. Chem., 2, 678 (1963).
log KZY 18.62 10.70 16.5 8.53
Predicted 3 x 10-3 160 120 3500
Observed 1.95 x 10-3 120 (1) 130 (2) 1100 (4)
intermediate prior to the rate determining step (designated NiYNi) divided by the stability constant of the reactant nickelEDTA.
Since the observed k;ly is 1.5 X lo3 greater than k;iY, either the intermediate stability or the microscopic rate constant is larger for kZlY. It must be noted that a simple electrostatic argument would predict less than k z f Y . The k z z N i has been identified as the rate of breakage of the nitrogen to leaving nickel bond and the KS,YK~ estimated as the product of the stability constants of nickel iminodiacetate and nickel glycine. Except for electrostatic attractions (important in these high ionic strengths), the stability of intermediate V (Figure 3) would be the same as that of A; but the rate constant by which V reacts, loss of water from the primary coordination sphere is much more rapid than breakage of a nickel-nitrogen bond in A. Qualitatively, this predicts the faster reaction of EDTA attack on nickel-EDTA. The rate of nickel-nitrogen bond breakage in the case of metal displacement can be calculated to be 10 sec-I (6). The ratio of rate determining steps then for ligand and metal exchange reactions is kGG$/k;sN, = 1.5 x 103, in excellent agreement with the ratio of the observed exchange rate constants. RECEIVEDfor review July 28, 1969. Financial Assistance from the University of Nebraska Research Council and National Institutes of Health Grant GM-12598-02 is gratefully acknowledged. Presented in part, Midwest Regional ACS Meeting, November 1967, Columbia, Mo. (19) G. Schwarzenbach, G. Anderegg, W. Schneider, and H . Senn, Helu. Chim. Acta., 38, 1147 (1955). (20) M. Eigen, Pure Appl. Chem., 6,97 (1963).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
55
