The complex with Cu(I1) formed at such a low p H that no reliable formation data could be obtained. No region of constant absorbance was found in a plot of pH against absorbance which precluded spectrophotometric determination of the Kt values. Despite the low solubility of QCO itself, the solubility of the complexes with this ligand was greater than those of AMQ or HMQ. The low donor ability of the oxime nitrogen probably prevents the ligand from functioning as a tridentate ligand. Similar behavior was observed for the phenyl-substituted aminoethylsalicylaldimines. Sacconi and coworkers (16-18) have described similar behavior in the chelates of some ”-substituted aminoethylsalicylaldimines. The closing of the second metalocyclic ring in these chelates is strongly influenced by the donor ability and steric requirements of the p group. When the p group contained electron withdrawing substituents, the compound was a bidentate ligand, but when the substituents were small and electron releasing, the compounds were able to perform as tridentate ligands.
(16) L. Sacconi and I. Berlini, Inorg. Chem., 5, 1520 (1966). (17) L. Sacconi, M. Ciampolini, and G. P. Speroni, Ibid., 4, 1116 (1965). (18) L. Sacconi, P. Nannelli, and U. Campigli, Zbid., 4, 818, 943 (1965).
The “-substituted aminoethylsalicylaldimines are somewhat similar to AMQ in that the amino group is isolated from the aromatic system by an alkyl group. The salicylaldimine group is similar to the 8-quinolinol donor system except that six-membered chelate rings formed in contrast to the fivemembered rings obtained with 8-quinolinol. The ligands in this study possess a wide range in the electron donating ability of the substituents. In the case of AMQ, the formation constants and metal to ligand ratio indicate that the compound can function as a tridentate ligand with Mn(II), Co(II), Zn(II), Ni(II), and Cu(II), and probably other metal ions. HMQ, which has a hydroxyl group for the third donor group, is only able to donate its electrons with difficulty, probably not as well as HzO. The solution stability data indicate that the compound is able to function as a tridentate with Ni(II), Zn(II), and Mn(I1). This study has focused attention on several interesting features concerning substituents in the two position of 8quinolinol. Substituents in this position can either hinder chelation through steric interactions or aid it by forming another metalocyclic ring. It seems probable that the main factor responsible for the varying ability of the new compounds to function as tridentate ligands is the large difference in the donor ability of the new substituents. The stability constants indicate that the donor ability of the substituents decreases in the order, aminomethyl > hydroxymethyl > carboxaldehyde oxime. RECEIVED for review March 20,1967. Accepted July 17,1967. Work supported with the financial assistance of the U. S. Public Health Service under Contract No. GM-10853-07.
Kinetics of Ligand Exchange Reactions of Lead and Copper Complexes of Ethylenedinitrilotetraacetate and Propylenedinitrilotetraacetate J. D. Cart-,’ Kenneth Torrance,2 C. J. C ~ I I Z and , ~ C.N. Reilley Department of Chemistry, University of North Carolina, Chapel Hill, N . C. 27514 Nuclear magnetic resonance and optical rotation have been used to measure the kinetics of the ligand substitution reactions of EDTA with the lead complexes of EDTA and PDTA as well as the copper complex of PDTA. The methyl group of PDTA causes its reactions to be 50 times slower than the analogous reaction with EDTA. The acidity dependence of the reactions was analyzed and the rate constants were assigned to differently protonated EDTA species reacting with the metal complexes. Also, the rate of proton-dependent dissociation of lead-PDTA was determined. Much slower reactions at constant pH were observed in the presence of sodium ion than in the presence of potassium. This effect is shown to be due to the associated sodium-EDTA complex being much slower than the non-associated EDTA anion to react with heavy-metal complexes. In addition, the reactions of the lead complexes are somewhat faster in the presence of chloride ion than in the same concentration of nitrate or perchlorate. This effect is thought to be due to chloride ion forming a mixed lead-EDTA-chloride species which reacts faster than the lead-EDTA complex.
1358
ANALYTICAL CHEMISTRY
THE DIFFICULTIES INHERENT in measuring the kinetics of a symmetric or near symmetric exchange reaction have permitted few such systems to be studied in detail (1-5). NMR was used to measure the kinetics of the ligand exchange of 1 Present address, Department of Chemistry, University of Nebraska, Lincoln, Neb. 68508. Present address, Central Electricity Research Laboratory, Leatherhead, Surrey, England. 3 Present address, E. I. du Pont de Nemours, Kinston, N. C.
(1) B. Bosnich, F. P. Dwyer, and A. M. Sargeson, Nature, 186, 966 (1950). (2) . , B. Bosnich. Ph.D. Thesis, Australian National University, Canberra, A.C.T., 1962. (3) W. J. Huber, M.S. Thesis, Purdue University, Lafayette, Ind., 1963. (4) R. J. Kula and G. H. Reed, ANAL.CHEM., 38,697 (1966). ( 5 ) J. L. Sudmeier and C. N. Reilley, Inorg. Chem., 5,1047 (1966).
EDTA with lead-EDTA (Equation 1, with protons omitted) in a manner similar to previous studies on calcium-EDTA ( 4 ) and cadmium-EDTA (5). Abbreviations used are: PDTA or L, EDTA or Y , ethylenedinitrilotetraacetate; propylenedinitrilotetraacetate; CyDTA, 1,2-cyclohexylenedinitrilotetraacetate; M , metal ion.
+ P b Y 2 * PbY-2 + Y-4
(1)
In this work, optical rotation was used to follow the ligand exchange kinetics of EDTA with the lead and copper complexes of optically-active PDTA (Equations 2 and 3) in an effort to elucidate the A?
Y-4
+ PbL-z F? P b P 2 +
L-4
(2)
+ L-4
(3)
k-2
Y-4
+ CuL-2
k3
e CuY-2 li-3
effect of subtle changes in ligand structure on the reaction kinetics. The reaction kinetics were measured over a wide range in pH (6-12) and the acidity dependencies analyzed. A chain reaction involving double ligand exchange between lead-EDTA and copper-PDTA (Equation 4) was studied, and the kinetics K4
PbY-2
+ CuLMze PbLM2+ C u F 2
(4)
observed were those predicted from a general equation describing coordination chain reactions (6). EXPERIMENTAL
A standard solution of EDTA was prepared by dissolving a weighed amount of the recrystallized material in a minimum amount of KOH and titrating with a standard copper solution. The disodium salts of I-PDTA and d-PDTA were prepared by the method of Dwyer and Garvan (7). When necessary, the sodium was removed from Na2PDTA by passing a solution through a cation exchange resin (Dowex 50W-X8) in the hydrogen form. There was no difficulty from precipitation of the completely protonated PDTA as this form of the optically pure ligand is extremely slow to come out of solution. Copper-PDTA prepared from sodium-free d-PDTA was prepared by addition of a small excess of copper nitrate to a Ligand solution and removal of the excess metal by precipitation as the hydroxide at pH 10-11. The lead complexes of EDTA and I-PDTA were prepared by the addition of standard ligand solution to a stoichiometric amount of lead perchlorate or lead nitrate. Vigorous stirring is necessary to prevent the formation of the insoluble Pb(PbY) or Pb(PbL) (8). The solution ionic strength was maintained at 0.50 in the polarimetry experiments with KCI, KN03, NaCl, NaN03, or NaClO.,. The reason for the use of several different inert salts will be discussed later. In the polarimetry experiments, the pH was measured at the completion of each reaction on a Leeds & Northrup Expanded (6) J. D. Carr and D. W. Margerum, J. Am. Cliem. SOC.,88, 1645
(1966). (7) F. P. Dwyer and F. L. Garvan, Zbid.,81, 2955 (1959). (8) N. Tanaka, K. Kato, and R. Tamamushi, Bull. Chem. SOC. Jupurz, 31, 283 (1958). (9) R. J. Kula, D. T. Sawyer, S . J. Chan, and C. M. Finley, J . Am. Chem. SOC.,85, 2930 (1963). (10) R. J. Day and C. N. Reilley, ANAL.CHEM., 36, 1073 (1964). (11) J. A. Pople, W. A. Schneider, and H. J. Bernstein, “High
Resolution Nuclear Magnetic Resonance,” McGraw-Hill, New York, 1959. (12) R. A. Charles, J . Am. Clzern. SOC.,78, 3946 (1956).
Scale pH meter equipped with a Corning semimicro combination electrode. Acid-base titrations of EDTA and PDTA were carried out at 0.5M ionic strength using this same equipment and a Gilmont microburet. Titrations indicated that the pK4 of EDTA and PDTA are 10.0 and 10.6, respectively, in 0.50M K N 0 3 , and these values were used throughout the resolution of the polarimetry data. Values of the third and fourth dissociation constants of EDTA, measured at the high concentrations and ionic strengths used in NMR (0.1 to 0.3M reactant or ionic strength approaching 3.0, 25’ C . ) ,were pK3 = 6.2 and pK, = 9.9 (5). NMR. Proton magnetic resonance spectra were recorded on a Varian A-60 spectrometer at a probe temperature of 32” =t 1 ” C. Sodium 3-(trimethylsilyl)-l-propane-sulfonate, abbreviated TMS*, was used as an internal reference for chemical-shift measurements and also provided a convenient means of monitoring changes in the magnetic field inhomogeneity. Under optimum instrumental conditions, it had a halfwidth of 0.35 cps using an RF of 0.03 mgauss. Linewidths were measured from spectra recorded on the 50 cps scale and a sweep rate of 0.1 cps/sec and the W I / Staken as the mean of at least 5 resonance peaks. The precision of these measurements was 1 0 . 0 5 cps up to a W112 of 2 cps. The uncertainty was greater for broader peaks, but no measurements were made over 3 cps. NMR spectra of solutions containing lead-EDTA and free EDTA exhibit two separate sets of resonances which can be assigned to the acetate and ethylenic protons of the complex and ligand (9, 10). In the pH range 8-10.5, the resonances of the lead complex are sufficiently downfield and free of overlap from those of the free acid that they can be used to measure the rates of intermolecular exchange. In all experiments W1lZwas taken from the acetate resonance of the complex. The kinetic process of ligand exchange was related to the broadening of recorded spectra by the slow exchange approximation, valid under conditions when 6 w r >> 1, where 6w (rad sec-I) is the chemical-shift difference between exchanging species, and r (sec) is the average lifetime in a particular environment. In this case, the average lifetime of a particular ligand on a particular metal ion, T P ~ Y is , related to the linewidths by 1 1 - = Tz’ T2
+
1
or W1,z’ cps = WIi2cps
~
TPbY
1 + ___
(7)
TTPbY
where Tz’ and TZ are the transverse relaxation times in the presence and absence of exchange, respectively (11). In these experiments, a series of linewidths were measured over a range in pH for a given metal-to-ligand ratio yielding a region, pH 6-8, in which W1lzwas minimized and constant. No exchange processes were observable by line broadening in this region, and the constant linewidth provided a vhlue for T2. This choice of TZhas the advantage that it was chosen in conditions of viscosity and solution environment similar to those of the broadening measurements. It has the disadvantage of precluding measurement of exchange reactions involving the acid species which would be predominant a t these pH’s (H Y-3 and HZY-3. This did not curtail interpretation of experimental results because all measurements of W1lzof the complex tend to this value regardless of the amount of free EDTA. Thus, within the accuracy of the linewidth experiments, exchange involving H Y and HzY are negligible at pH 6-8. All solution preparation and pH measurements were carried out at room temperature (25” C) rather than at the temperature of the NMR probe. No additional electrolyte was added to control the ionic strength, and calculations did not include activity corrections. Concentrated acid or base ( H N 0 3 or KOH) was added from a microburet to degassed solutions containing known amounts of metal and ligand. Aliquots (0.5 ml) were taken at appropriate pH’s and transferred to sample tubes. The dilution involved was neglected VOL. 39, NO. 12, OCTOBER 1967
1359
Table I. Molar Rotations of L, PbL, and CuL p = 0.50 T = 25' C X = 365 mp Species [a] (I-deglcm-mole) PbL +55.S0 CUL $3.69 L-4 (pH 12.10) -4.66 HL-3 (pH 8.35) -2.78 HzL-' (PH 4.41) -4.47 These values are those obtained for I-PDTA and its complexes. Table 11. Observed Stability Constants of CuL and PbL T = 25" C p 0.50 (KNOB) [yo = [PbLIo = 1.17 X lO-3M PH K2 K p by/KpbL 7.20 11.11 11.37 11.62
0.378 0.427 0.465 0.467
T = 30" C
0.419 0.215 0.118 0.118
0.102 0.100 0.104 0.114
Figure 1. Lifetime of lead-EDTA as a function of [ Y-41 [PbYJ = 0.180M
32" C
p = 0.50 (KNOI)
[ y l r = 0.090M
[no= [CULI~= 1.55 x 1 0 - 3 ~
a
PH
ffob9365
KS
8.89 9.69 11.42
0.0180 0.0197 0.312
0.419 0.323 0,099
KcuYIKcuL
0.111 0.107 0.089~
This value is felt to be low since at pH 11.42 Cu(0H)L and
Cu(0H) Y would have formed.
since the pH range investigated was only 1-2 units. This method avoided large changes in viscosity which could affect line width (5,12). Polarimetry Experiments. The exchange reactions (Equations 2 and 3) were followed polarimetrically a t 365 mp in a 10-cm cell thermostated to 25" k 0.5" C in a PerkinElmer Model 141 polarimeter with a Sargent Model SR recorder attached. This afforded a direct read-out of optical rotation ( a ) as a function of time. Complete optical rotation spectra (600-300 mp) were obtained on a Cary Model 60 recording spectropolarimeter. Values of tile molar rotation of I-PDTA, lead-I-PDTA, and copper-l-PDTA are expressed in units of liter-degreeslcm-mole, and the appropriate values are shown in Table I. Different initial reactant concentrations were used and indicated that, in the pH region from 7-12, the reactions were first-order in EDTA and first-order in metal-PDTA. In most cases, a sufficient excess of EDTA was present t o cause the reaction to proceed to completion and to allow the use of Equation 5 as the rate expression when the subscript T denotes the total EDTA concentration and k y T h f L denotes the rate constant for the reaction of EDTA with the M L complex. rate = kyT-IfL[ yl,[ML] = k,b,[ML]
(5)
Values of kobrare obtained from plots of - h ( a - a,,) DS. time which were linear for a t least 2-3 half lives. For cases in which insufficient EDTA was present to cause the reaction to proceed to completion, the data were calculated on a basis of a first-order forward, second-order reverse equation. Conditional equilibrium constants for reaction 2 (K2')were measured by mixing equal concentrations of lead-l-PDTA and EDTA and allowing them to attain an equilibrium rotation. An equilibrium constant was calculated from this rotation and the molar rotations which are shown in Table I. It was shown that the conditional equilibrium constant (Table 11) can be explained by the different acidities of the two ligands, EDTA and PDTA. 1360
ANALYTICAL CHEMISTRY
Equation 6 holds where K P b l Y f = {[P~Y]T/[P~]T[Y]T] ~ ] , and these and a L = [ L ] T / [ L - ~a p]b, y = [ P ~ Y J T / [ P ~ Y -etc., terms are calculated as shown by Ringbom (13). No stability constant for a mixed hydroxy-EDTA-lead complex could be detected spectrophotometrically, and no change in the chemical shift of the complex protons was observed in NMR experiments, even up to pH 13. Consequently, essentially all of the lead-PDTA and lead-EDTA were present as the dinegative species and aPbY = a P b L = 1.0. The ratios of Kcuy/KcuLand K p b Y I K p b L were calculated to be 0.110 and 0.102, respectively (Table IT), from the conditional equilibrium constants and the calculated values of u y and uL. This leads to a value of log KC"L = 19.76, but the uncertainty in the stability constant of lead-EDTA (14) prevents a value of K P b L being calculated from this ratio. The chain-reaction studies were carried out polarimetrically a t 365 mp and 25.0" C . The molar rotation oflead-PDTA, being much greater than that of copper-PDTA (Table I), affords a large change in rotation as the chain reaction proceeds to completion. All chain reactions studied had an initial concentration of lead-EDTA in excess over copyerPDTA. The concentration of free EDTA was always less than 2 0 % of the latter. RESULTS
The exchange reaction which was considered is Y-4
+ PbY+
s Y-4 + PbY-2
(8)
and this is related to TPbY by Equation 9:
The slope of a plot of 1/7pbY cs. [ Y-'] (Figure 1) yields a value of the second-order rate constant k y P b Y . The plot linearity and zero intercept confirm the negligible contribution to the (13) A. Ringbom, "Complexation in Analytical Chemistry," Interscience, New York, 1963. (14) L. G. Sillen and A. E. Martell, "Stability Constants of MetalIon Complexes," Special Publication No. 17, The Chemical Society, London, 1964.
Table 111. Second-Order Rate Constants, kyPbY T = 32" C
p =
[Pi, Yl
YI
0.180 0.180 0.208 0.138 0.138
Table IV. Observed Second-Order Rate Constants for Equation 2
1.5-2.0(KN03) kyPbY,
0.090 0.090 0.052 0.138 0.138
T = 25" C
M-l sec-I
PH 8.98 9.53 9.68 9.76 9.91 10.12 10.12 10.13 10.28 10.35 10.57 11.52
67.0 64.0 58.4 65.0 71.0
Av. value: 65 f 3M-l sec-l
overall rate by exchange of (or PbHY). Table I11 presents the results of these experiments and shows that the reaction is first-order in each component. The value of the second-order rate constant kyPbY is 65 f 3M-l sec-'. Interpretation of spectra below pH 6 was limited by the overlap of the resonances of free acid and lead-complex together with the precipitation of the former between pH 3-4. Preliminary experiments of this nature with the exchange of I-PDTA with the lead complex of I-PDTA indicate that the exchange is too slow between pH 8-12 to be observed by NMR line-broadening techniques at normal probe temperature. However, a value for the exchange constant of dPDTA on the lead complex of I-PDTA has been obtained polarimetrically from preliminary experiments using the racemic form of the free ligand. The rates of the ligand exchange reactions of EDTA with lead-l-PDTA and copper-l-PDTA were measured polarimetrically. The pseudo-first-order rate constants observed at L, pH > 7.5 were converted to ky,PbL and k y T C U respectively, by dividing the total EDTA concentration (Tables IV and V) and then were resolved into the individual contributing rate constants by graphical application of Equation 10a or 10b where KnY and KH?yare the fourth and third acidity constants of EDTA. k y T-"'L[ Y]T[ML]=
8.07 8.57 8.83 9.07 9.50 9.73 9.91 10.09 10.10 10.62 11.12 11.28 11.98
8.80 8.86 9.13 9.13 9.39 9.78 10.00 10.45 10.60 11.07
+ kay"L[HY-3][kfL] (10)
kyl'f"L[y-4][ML]
+
(")KHY
kYAxrL kHy-TrL
0.50 (KNOB) k2(M-lsec-l) 0.107 0.265 0.409 0.478 0.594 0.667 0.750 0.769 0.917 0.803 1.01 1.24 0.029 0.066 0.116 0.122 0.153 0.170 0.174 0.167 0.200 0.184 0.214 0.237 0.253 0.077 0.002 0.146 0.143 0.306 0.558 0.750 1.20 1.24 1.51
Table V. Observed Second-Order Rate Constants for Equation 3 p = 0.50 (KiYOa) T = 25" C [ylaX 103 [CuLIa x 104 ka (M-1 sec-1) 0,033 48.4 7.90 7.90 0,020 48.4 0.018 98.6 7.90 7.90 0.021 48.4 7.90 0.039 48.4 7.90 0.053 48.4 0.095 48.4 7.90 0.113 48.4 7.90 7.90 0.121 32.2 0.120 48.4 7.90 0.129 48.4 7.90 0.145 48.4 7.90 7.90 0.166 48.4 7.90 0.172 48.4 0.176 48.4 7.90 0.190 96.6 15.8 10. l o a 7.90 0.204 10.12a 96.6 0.23 79.1 7.90 10.79a u = 0.75 (KN03).
PH 6.63 8.47 8.51 8.60 9.30 9.50 9.81 10.02 10.10 10.11 10.46 10.76 10.93 11.09 11.38
(lob)
Figure 2 is a graph of Equation 10a for the lead reaction. The intercept of near zero indicates a value of kHyPbL less than 0.01M-1 sec-1, and the slope affords a value of k y P b L . The data for the copper exchange (Equation 3) were plotted according to both Equations 10a and lob. Values of kyCuL and k H y C Uobtained L, at an intercept on one graph and a gradient on the other, are in mutual agreement and are shown in Table VI. This same resolution procedure was carried out for the lead reaction in ionic strength 0.50 adjusted with KCI, instead of KN03. The resolved rate constants from these KCI runs are included in Table VI. The rate constants k~~~~~and kHSyPbL could also be expressed as k y P b H L and k H y P b Hrespectively. L, Since PbHL represents less than 0.1 (log KpbLPbHL = 2.8) of the total lead-EDTA concentration at the lowest pH studied, the rate constant resolutions were based on PbL instead of PbHL. This will be fully discussed later in this paper.
p =
[PbLIo x 104 2.34 25.8 2.34 25.8 2.34 21 .o 2.34 25.8 2.34 12.9 2.34 21 .o 2.34 25.8 2.34 12.9 2.34 12.9 2.34 25.8 2.34 12.9 2.34 12.9 p = 0.50(NaN03) 2.04 9.04 2.04 9.04 2.04 9.04 2.04 9.04 2.34 11.3 2.04 9.04 2.04 9.04 2.34 11.3 2.04 9.04 9.04 2.04 2.34 11.3 2.04 9.04 2.34 11.3 p = 0.50 (KC1) 10.05 42.0 2.34 12.9 10.05 42.0 10.05 42.0 2.34 25.8 5.00 21 .o 12.9 2.34 12.9 2.34 12.9 2.34 12.9 2.34
[yloX lo3
a
There is shown to be a large difference in the observed rate constant when NaNOB is used to control the ionic strength of the reaction. Such behavior has been observed previously by Sudmeier and Reilley ( 5 ) as well as by Kula and Reed VOL. 39, NO. 12, OCTOBER 1967
1361
I
t
!
0.1
0
0.2
0.3
[Na'l
Figure 2. Resolution of k$bL and kHyPbL 25" C.
=
kobs[Y], =
k y P b L [P
4]
+
+
kAyPbL[HY-3] kh-,yPbL[NaY-3](1 1)
The application of Equation l l a to data at variable sodiumion concentrations, but with the ionic strength held constant with K N 0 3 , results in Figure 3, assuming that the kaYPbL[H+]/ K L Iterm ~ is negligible. The definitely positive slope of this graph shows that sodium-EDTA is a reactive species and attacks the lead complex much more rapidly than does monoprotonated EDTA. For NaY not to be reactive (Le., the slope of Figure 3 to be zero), the log of the sodium-EDTA stability constant would have to be 1.1, considerably below the measured value of 1.4 i 0.1. Acid-Dissociation of Lead-PDTA. Two general mechanisms are possible for the exchange of lead-PDTA by EDTA: one involving the direct reaction of EDTA with the metal complex (Equation 2) and the other involving protonassisted dissociation of the lead complex followed by a rapid scavenging of the free lead ion by the high concentration of EDTA (Equations 12 and 13). In conditions more (15) G. Schwarzenbach and H. Ackermann, Helc. Chirn. Acta, 30, 1798 (1947). (16) V. Paiaty, Can. J . Chem., 41, 18 (1963).
1362
ANALYTICAL CHEMISTRY
I
1
I
0.5
0.6
,M
Figure 3. Influence of sodium ion on the rate of exchange of Y with PbL 25' C. p = 0.50 (KNO3 and NaN03). pH 10.4 [PbLla
0.50 (KNOa)
(4). This is, undoubtedly, due to the formation of the reported sodium-EDTA complex. Stability constants of this complex have been reported for different ionic strength conditions (log K = 1.66 at 20" C in O.lOMKCl(15) and log K = 2.61 in p < 0.10 (16). Acid-base titrations of EDTA in the presence of 0.50M NaN03 led to a value of log KxaY= 1.4 f 0.1 for this stability constant in these high-ionic-strength conditions, and this value was used in all subsequent calculations. Under these same experimental conditions, the stability constant for the corresponding sodium-PDTA complex was shown to be log KNaL= 2.2 =t0.1. In order to determine whether the rate decrease is due solely to a decrease in the concentration of the EDTA tetraanion or whether sodium-EDTA is also a reactive species, the rate data were resolved in the following manner.
I
0.4
2.34 X 10-4M [Ylo = 9.04 X 10-*M
=
alkaline than pH 7.5, the proton-dependent term is unimportant, as H+
+ PbL-2 Pb+2+ HL-3 + Pb+' e PbY-2
(12) (1 3)
Y T
shown by the first-order dependence of EDTA, but in the pH region 6.0-7.3, a plot at constant pH of the observed rate ~
~~
Table VI. Values of Resolved Rate Constants ( A 4 - I sec-I) Alternative proton assignment 65.0 i 3 . 0 8.4 = 1.0 1.23 k y p b L (KCI) 1.60 kHyFbL < I x 10-3 k yPbHL < i x 104b kn?y P b J , 2 x 10-2 k=LPbHL 4 x lo'* kHPbL 2 x 10% kx,yPbL 8 . 6 x lo-% kLPbL 0.4" kyCUL 0.172 kHyCuL 0.015 kyCuHL 3.9 x 1026 a Preliminary result from reaction of d,l-PDTA with leadI-PDTA. b Value of KPbyPbIIy and KcuyC~HY used as estimates for KpbLPbHL and K ~ , , L C U ~ I , . k yPbY kx,yPbY kyPbL(KNO,)
Table VII. Results of Low pH Studies of EDTA Lead-PDTA
+
[PbLIn pH 5.93 5.97 6.00 6.51 6.58 6.64 6.60 6.72 6.83 6.81 7.14 7.30 7.20 7.31
=
2.34 X
[EbTAlo x 102 1.29 2.58 6.44 1.29 2.58 2.58 6.44 1.29 2.58 6.44 1.29 2.58 6.44 6.44
kobs
p =
X
lo5 32.7 42.1 80.7 13.9 19.8 20.0 33.7 6.60 9.52 19.6 4.58 9.81 18.6 20.4
OSO(KNO3)
kHPbL
(M-I sec-l) 1 . 8 X lo2
k y TPbL (M-1 sec-1) 10.7 X
3.1 X lo2
4.21 X 10-3
1 . 9 X 10'
2.59 X
3.4 X lo2
2.76 X
.0
Figure 5. Proposed reaction intermediates in the exchange of EDTA with PbY and PbL
0
1
2
4
3
[EDTAITX 10
*
5
6
.M
7
Figure 4. Resolution of EDTA-dependent and EDTAindependent terms in exchange of Y with PbL. The approximate pH values of these rates are indicated on the figure. See Table VI1 for exact values. 25' C.
=
0.50 (KNOa)
constant us. EDTA concentration shows a positive intercept, proportional to the concentration of hydrogen ion, interpreted as the rate of the exchange which is independent of incoming ligand (Figure 4). The rate constant kyTPbL is obtained from the slope of such a plot. The following equation describes the rate behavior in this pH region, and the results of this study are presented in Table VII. kobs = k ~ " ' ~ [ H + l k y r p b L [ f l ~ (14)
+
An attempt to further resolve the term of kyTPbL into its component terms using Equation 15 by a method similar to that used in Equation 10 met with only limited success. kyTPbL[ flr
=
k~?y~"[H Y-*] ,
+
+
k~y'~'[HY-~l kyPbL[Y-'1
(15)
The previously determined value of kyPbLwas substituted directly into Equation 15. This approach gave an approxi~and an , upper ~ mate value of 2 X 10-2M-1 sec-' for k limit of 1 x 10-3~4-1 sec-1 for kEyPbL. DISCUSSION
The rate of EDTA attack on lead-EDTA is about 50 times faster than that of EDTA attack on lead-PDTA. This large difference between reactions of very similar molecules can be attributed to steric requirements of the methyl group and its effect on the course of the reaction mechanism. A further threefold decrease in reaction rate was observed when dPDTA was used as the exchanging species with lead-l-PDTA. Several metal complexes formed from a particular optical isomer of PDTA have been shown to exist in only a single geometric isomer in which the methyl group is in a position equatorial to the five-membered chelate ring (17) (Structure A).
'/
0
(A) The other conformer, in which the methyl group is axial, is sterically unfavored. In accordance with the above findings and accepted nomenclature, the complex formed upon addition of the I-PDTA is in the L configuration and that of d-PDTA is in the D configuration. The observed exchange rate of these two mirror-image isomers with EDTA should be the same. This was confirmed in experiments with both isomers in the copper system. Ligand substitution reactions of multidentate ligands have been shown to proceed via a series of intermediates in equilibrium with one another in which a successively greater number of coordination sites are occupied by the incoming ligand and fewer by the departing ligand (18). It is necessary that there be a symmetrical intermediate in the reaction of EDTA with lead-EDTA because the reverse reaction is identical to the forward reaction. Figure 5 shows the proposed series of intermediates in the EDTA reaction with lead-EDTA. When the reaction reaches Structure V, the EDTA segments are identical, and the two ligands are equally likely to leave. Structure IV represents the most stable of the proposed intermediates based on known stability constants of lead(I1) complexes (19) and using arguments wherein the stability ~constant ~ of a~ mixed intermediate of this type is equal to the product of the stability constants of its composite parts (18). The estimated stability constants of species I1 through V and the values used for their evaluation are shown in Table VIII. The reaction of EDTA with lead-PDTA (Equation 3) is expected to proceed through a series of intermediates analogous to those in Figure 5. The methyl group of a fully coordinated PDTA tends to keep the dentate groups in a position favorable for bonding by hindering the rotation of the iminodiacetate groups away (17) F. P. Dwyer and F. L. Garvan, J . A m . Chem. SOC.,83, 2610 (1961). (18) D. B. Rorabacher and D. W. Margerum. I m r g . Clrmi., 3, 382 (1964). (19) G. Schwarzenbach, G. Anderegg, W. Schneider, and H. Senn, Helc. Chim. Acra, 38, 1147 (1955). VOL. 3 9 , NO. 12, OCTOBER 1 9 6 7
1363
Table VIII. Estimation of Stability of Reaction Intermediates (19)a
Table IX. Predicted Ratios of kyAMY/kHyMY (or ky"lL/kHyML) (kyMY/kHpuY)
Predicted from Eq. 18
M
from the central metal ion. This results in an additional energy barrier which must be overcome in proceeding to the proposed intermediate analogous to Structure IV (Figure 5 ) and gives rise to a decreased reaction rate. In addition to this, the electron-donating properties of the methyl group increase the basicity of the PDTA nitrogen atoms as compared to those of EDTA, and increase the strength of the metalnitrogen bonds. Effect of Protonation. It is impossible from the proton dependence of a rate constant to assign unequivocally the proton(s) to a specific reactant. For example, kntyafLcan be alternatively expressed as k E y M Hor L k y M H z LThese . rate constants are interrelated as shown in Equation 16 by protonation constants of the ligand and the metal complex.
Alternative rate constants of this nature can be eliminated from consideration if: 1) the rate constant exceeds the rate constant calculated from diffusion-controlled processes, 2) the rate exceeds that of a microscopic step (e.g., rate of solvent loss from the metal ion or rate of metal-ligand bond breakage) known to be a part of the reaction, or 3) it requires a protonated species known not to exist in the reaction conditions. Alternative choices of protonated reactants do not necessarily lead to differently protonated reaction intermediates. Proton-transfer reactions are extremely rapid (ZO), and the protons of the reaction intermediates will tend to be in the position of greatest basicity regardless of the specific assignment of protons to the reactants. This feature is represented in the following manner: H2Y
+ MY k\
(H2Y2M)-+ HY-M-YH
2
HY
-
(20) M. Eigen and L. DeMaeyer, "Techniques of Organic Chemistry." A. Weissburger, Ed., Vol. VIII, Interscience, New York, 1963, p. 895. ANALYTICAL CHEMISTRY
>1200
W4)
63
24
11 >>43
The position of the proton in the transition-state complex influences the change of rate constant with pH. Usually the rate constant will increase with decreasing pH if the protons are more attracted to the leaving group and vice versa. For example, in the reaction of EDTA with nickel-polyamines (18), the leaving group has a greater number of strongly basic sites and the rate constant increases with decreasing pH. However, in the reaction of polyamines with copper-EDTA (.?I), the entering group has the greater number of strongly basic sites and the rate constant decreases with decreasing pH. In the present case, apparently the first proton added remains with the entering EDTA group on the uncoordinated nitrogen site of the incoming ligand (Structure IV, Figure 5 ) and slows the reaction as this entering group is rapidly dissociated again in preference to completion of the substitution reaction. Structure V can not occur prior to the ratedetermining step in the reaction of the monoprotonated species since the two uncoordinated nitrogens are of equivalent basicity and it would be expected that the proton would be equally likely to be associated with the leaving group as with the incoming group. There would then not be so marked a change in the rate constant as is observed. The presence of two protons on the reaction intermediate species increases the reaction rate over that of the monoprotonated case. This same general behavior has been reported for the cadmium (5) and calcium ( 4 ) exchanges with EDTA. In the structure analogous to IV, the second proton must be associated with the negatively charged, uncoordinated carboxylate groups; the most negative of these being on the departing ligand as the presence of the first proton on the uncoordinated nitrogen of the entering ligand reduces the negative charge concentration on the unbonded iminodiacetate segment of the entering ligand. This second proton then serves to loosen the remaining bonds between the leaving EDTA molecule and the lead ion, speeding its release rather than hindering the approach of the entering ligand as was the result of the first protonation. The rates of reaction of protonated EDTA on lead-EDTA, lead-PDTA, and copper-PDTA are much slower than those of the unprotonated ligand. Using Structure IV (Figure 5 ) as a model for the intermediate prior to the rate-determining step, the ratio of the rate constants of the unprotonated and protonated reactions can be approximated by Equation 18. kynrY
+ MHY
1364
580 5800 320
kHyJWY
products (17)
Observed
Pb cu Cd(5)
-
kms kRDs
(
[YMY]
) --
[HYMY]
- KHYMY
KYMY
(1 8)
Values for the stability constants K y M yand K H ~ Mare Y estimated using Structures B and C as models for the unprotonated and protonated (21) J. D. Carr, R. A. Libby, and D. W. Margerum, Inorg. Ckem., 6 , 1083 (1967).
CH3
CHz--COO-
/
H~C-C-(CH~)Z-N
I
\
CH2-COO-
CH3
(B) CH3
CH24OO-
/
H3C- +N-(CH&-N
1
\
CH3
CH24OO-
(C) CHz--COOHzN-( CH 2)2-N
/
\
CHpCOO-
(D) segments, respectively, of the incoming EDTA and Structure D for the leaving EDTA or PDTA segment of the intermediate prior to the rate-determining step (19). Ratios of kHyavY/ky”lY or kHy’uL/ky.ML for Pb, Cu, Cd, and Ca are presented in Table IX. The values for kHyCdYand kHyCaY are both reported with large experimental errors. Consequently, the ratios reported in Table IX are highly uncertain; the trends, however, are approximately correct except for copper. Apparently, the copper reaction proceeds via some modified reaction pathway. Proton-Dependent Dissociation of Lead-PDTA. Margerum er a[. (22) measured a value of 23M-I sec-’ for the rate constant of hydrogen ion-assisted dissociation of lead-CyDTA in 0.10M NaC104 and were unable to assign a specific mechanism to this reaction. Bril et al. (23) and Tanaka and Ogino (24) used polarography to measure, respectively, values of 20M-i sec-’ in 1M K N 0 3and 8OM-i sec-’ in 0.2MKN03for the analogous reaction with lead-EDTA. The value of kHPbLcalculated from the present work is 2OOM-1 sec-’. NaY Exchange. The observed decrease in reaction rate when sodium is used as counter ion can be accounted for by the presence of the associated species sodium-EDTA. This effect is similar to the observed reduction in reaction rate with the monoprotonated species and has been reported for the cadmium-EDTA and calcium-EDTA systems. However, previous work (4) found no sodium dependence on the observed exchange rate when [Na+]/[YIr > 1. This is in contrast to our findings (Figure 3) and may be explained by the lack of sensitivity of line-broadening techniques for small changes in rate constant. The structure of sodium-EDTA in solution is unknown. Titrations of iminodiacetate ion (IMDA) in the presence of a large excess ( 0 . 5 M ) of N a N 0 3 gave identical acidity constants to those obtained with an equal concentration of KNO,. This shows that Na+ does not complex with IMDA to the same extent as it does with EDTA. Previous NMR studies (9) have suggested the involvement of the nitrogen atoms of EDTA in alkali metal complexes. In the case of PDTA with its more basic nitrogen atoms, titrations show an (22) D. W. Margerum, P. J. Menardi, and D. L. Janes, Inorg. Clrern., 6,283 (1967). (23) K. Bril, S. Bril, and P. Krumholz, J . P l i y ~ .Clrem., 59, 596 (1955). (24) N. Tanaka and H. Ogino, B d . Ckenr. SOC.Japan, 36, 175 ( 1963).
even greater stability (log K xaL-=2.2 =t0.1) for the sodium complex. Using the experimentally determined value of log KNay= 1.4 & 0.1 at ionic strength of OSM values of kyBPbLY and kXsyPbLwere obtained (Table VI). The decrease in rate in the presence of sodium ion is due to the lowering of the stability of intermediate IV (Figure 5) as previously discussed for the proton case. The decrease in nitrogen basicity could be greater in the case of the protonated than in the sodium complex; hence, the rate decrease caused by protonation of EDTA is greater than that caused by reaction of the sodium complex. Anion Effect. Table VI shows that the value of kyPbLis dependent on the nature of the anion of the background electrolyte (KCl, KNO,). This effect is in addition to the previously discussed sodium effect as the same anionic-rate dependence was noted for kwaliPb in solutions containing NaCI, NaN03, and NaC104. Both of these rate constants were greater in the presence of chloride than in nitrate or perchlorate. This is presumably due to the formation of a mixed ligand complex of the type Pb(C1)L which facilitates the exchange of the lead species. A similar but larger effect has been reported by Janes and Margerum in their study of the rate of dissociation of Hg(X)Cy in which the polarizability of a halide ion weakened the mercury-ligand bonds and caused the complex to dissociate more rapidly (25). Since the rate of lead-nitrogen bond breakage is important in our study, similar complexes could explain the rate increase in the presence of chloride ion. Attempts to observe this mixed ligand complex directly were unsuccessful. Ultraviolet spectra were identical for lead-EDTA in the presence and absence of 0.5M KCl, and no difference in the chemical shift in the NMR spectrum could be detected in the different environments. Inconsistent results have been obtained for the stability constant of lead-EDTA when measured in different ionic media (26, 27). These results indicate the possible formation of mixed species Pb(X) Y. In both the NMR and optical-rotation studies of the lead exchanges, the first-order rate constant was observed to increase very rapidly at the pH of the first acidity constant of EDTA, the rate of increase being independent of EDTA concentration. This effect was seen only in reactions in which sodium was used as a counter ion because the sodium slowed the attack of EDTA sufficiently to allow the hydroxide reaction to contribute significantly to the reaction kinetics. The kinetic order in hydroxide could not be determined because of experimental scatter. Chain Reaction Studies. An understanding of the kinetics of the individual copper and lead exchange reactions allows the prediction of a double-ligand exchange reaction involving these complexes. Agreement between the observed and predicted kinetics of such a double-ligand exchange reaction would confirm interpretations of the separate reactions. The exchange reaction, shown as Equation 4, is predicted to be a coordination chain reaction with kinetics governed by a previously derived equation (6,28,29). This chain reaction is
(25) D. L. Janes and D. W. Margerum, Ztiorg. Clzenz., 5, 1135 (1966). (26) V. L. Hughes and A. E. Martell, J . Pliys. Chem., 57, 694 (1963). (27) G. Schwarzenbach and E. Freitag, Helc. Chim. Acta, 34, 1503 (1951). (28) D.W. Margerum and D. C. Olson, J . Am. Chem. Soc... 85., 297(1963). (29) D. W. Margerum and J. D. Carr, Ibid.,88, 1639 (1966). VOL. 39, NO. 12, OCTOBER 1967
1365
i
5.0
103
200
300
I
400
TIME (min)
1.o
0
I
2.0
Figure 7. Deviation from first-order kinetics caused by low initial ratio of reactant complexes 25" C.
M
E D T A , x~ lo4, ~ ~
Figure 6. Influence of EDTA on the rate of the chain reaction 25' C. [PbYIo
I.L= 0.75 (KN03). pH 10.69 = 6.25 X 10-2M[CuL]oX 1.04 =
[Y
lO+M
of special interest since it would have an equilibrium constant (K4% 1) much lower than any previously studied coordination chain reaction and would be a test of the equation under these different conditions. The chain-propagating steps of the overall exchange are Reactions 19 and 20. k3
Y-4
+ CuL-2 k-F! CuY-2 + L-4
(1 9)
a
L-4
+ PbY+
k-2
PbL-2 kl
+ Y-4
Table X. Relative Values of Terms of Equation 18 [PbYlo = 6.25 X lo-* [CUL]~= 1.04 x 10-3 [PbYJa = 6.25 X [CuLIo = 1.04 X
ksk-n[C~L][PbY] k-akn[C~Y][PbL] k-s[Pb Y ] ka[CuLl k-a[Cu Y ] kdPbL1
1366
First half life A B 181 16.8 1.5 1.5 98 1 90.7 0.18 0.18 1.8 0.80
ANALYTICAL CHEMISTRY
1.8 0.80
4-LIT
0.75 (KN03). pH 10.69
ksk-Z[CuL][Pb yl - k--3kz[C~yJ[PbL] K' 4- k-a[Cu r ] f kz[PbL] ~ ~ [ C UfL k-dPb ]
--
1) all of the product of Reaction 4 is formed via the chainpropagation steps and 2) the total uncomplexed ligand concentration, [ Y LIT,is constant throughout the reaction. Reactant concentrations were chosen such that many of the terms in Equation 21 remain small for the first two half lives of the reaction so that Equation 21 simplifies to Equation 22. The relative values of the six terms in Equation 21 are shown
+
(20)
The concentration of uncomplexed ligand controls the rate of Equation 4 but has no effect on the equilibrium concentrations of reactants and products. The EDTA dependence of the observed rate constant is shown in Figure 6. The negative intercept on the EDTA axis indicates imperfect stoichiometry (Le., about 0.1 excess EDTA) of the stock solution of lead-EDTA. The generalized expression for the rate of a coordination chain reaction in which the chain-propagation steps are reversible has been shown (6) to be Equation 21. Assumptions necessary for Equation 21 to hold are
A B
- -rate
p =
Second half life A B 90.4 8.0 3.3 3.3 978 86.7 0.24 0.24 0.925 0.925 1.2 1.2
in Table X at both one and two half lives for two sets of initial reactant concentrations. In case A , Equation 22 is valid for at least two half lives, but in case B, the k-ak2[Cufl[PbL] term becomes significantly large and should cause negative deviations from first-order kinetics described in Equation 22. This is exactly what is observed and is shown in Figure 7. The only denominator term which contributes to the rate expression in both cases is k-n[PbY]. Early in the chain reaction, Equation 22 should be followed for case B as well as for case A , and the initial slopes of both A and B should be equal to k3[Y]. The difference observed arises from the relative amounts of EDTA present in the two reactions as impurity from the lead-EDTA solution. Although the concentration of added EDTA is the same, in case A the impurity represents about 20% of the added EDTA while in case B the corresponding fraction is one tenth of this or 2%. Accounting for the concentration of EDTA impurity, the two rate constants, 0.25 and 0.24M-' sec-I, are in excellent agreement. This also is in excellent agreement with the value of k3 at 0.75M ionic strength and pH 10.7, shown in Table V to be 0.23M-I sec-l. RECEIVED for review October 6, 1966. Resubmitted July 19,1967. Accepted August 7,1967. Work supported by the National Institutes of Health Grant GM-12598-02.
