It may also be worth remarking that the common ploy of activating platinum electrodes toward adsorption of reactants-e.g., platinization-to try to increase the rate of an electrode reaction may be just exactly the wrong approach for reactants which mimic the behavior of the iodide-iodine couple. LITERATURE CITED
( 1 ) Balashova. N.,' Zh. Fiz. Khim. 32, . 2266 (1958): (2) Balashova, N., 2 . Physik. Chem. (Leipzig) 207, 340 (1957).
(3) Balashova, N., Merkulova, N. S., Proc. 4th Soviet Conf. Electrochem. 1956, p. 48. (4) Christensen, C. R., Anson, F. C., ANAL. CHEM.35, 205 (1963); 36, 495 (1964). (5) Hubbard, A. T., Anson, F. C., Zbid., 36, 723 (1964). (6) Hubbard, A. T., Anson, F. C., J. Electroanal. Chem. 9, 163 (1965). (7) Hubbard, A. T., Anson, F. C., ANAL. CHEM.,38, 58 (1966) (8) Newson, J. N., Riddiford, A. C., J. Electrochem. SOC.108,699 (1961). (9) Osteryoung, R. A., ANAL. CHEM.35, 1100 (1963).
(10) Osteryoung, R. A., Anaon, F. C., Zbid., 36, 975 (1964). (11) Osteryoung, R. A,, Lauer, G., Anson, F. C., J . Electrochem. SOC. 110, 926 (1963). (12) Schuldiner, S., Warner, T. B.,
Anson, F. C., Osteryoung, R. A,, ANAL. CHEM.36, 2.510 (1964). (13) Schuldiner, S., Presby, C. H., J. Electrochem. Soc. 11 1, 457 (1964).
RECEIVED for review December 9, 1965. Accepted March 8, 1966. Worksupported in part by U. S. Army Research Office (Durham). One of the authors (F. C. A.) is an Alfred P. Sloan Research Fellow.
Nuclear Magnetic Resonance Investigation of Ligand Exchange Kinetics in the CaIcium(ll)-EDTA System RICHARD J. KULA and GEORGE H. REED Department o f Chemistry, The University o f Wisconsin, Madison, Wisc.
b
Nuclear magnetic resonance linebroadening techniques have been used to investigate ligand exchange kinetics in the calcium-(ethyleneditetraacetic acid (EDTA) nitrilo) system. The pH dependence of the exchange rate in aqueous solution has been evaluated, and the studies indicate that several reaction paths are available for exchange. In basic solutions second order reactions between calcium-EDTA and free EDTA (both the tetraanion and monoprotonated ligand) predominate. In acidic solutions exchange proceeds through the first order dissociation of protonated calcium-EDTA and through the second order reaction of protonated calcium-EDTA with monoprotonated free EDTA. Evidence is presented suoporting a structure for protonated calcium-EDTA in which only one iminodiacetate segment of EDTA is coordinated to calcium.
-
C
information is available concerning the kinetic exchange processes for various metal ions with metal-ligand complexes, M* ML e M M*L, and for the exchange of metal ions between two metal- ligand complexes, M*L* M L e M*L ML* ( 1 , 2 , 3, 4, 6). Only recently, however, have ligand exchange processes of the type, L* N L e AIL* L , been examined very extensively (IO, 11, 19, 15). These reactions have been studied by conventional methods-e.g., spectrophotometric, polarographic , and radioisotope labeling-which are limited by the rate a t which the system approaches equilibrium. On the other hand nuclear magnetic resonance (NMR) techniques enable the ONSIDERABLE
+
+
+
+
+
+
study of fast ligand exchange processes under equilibrium conditions and require no isotopic labeling. By modifying the Bloch equations to take into account chemical exchange, the chemical shifts and line shapes of resonances from species undergoing exchange can be related to the lifetimes of these species in various chemical environments (14). These lifetimes can then be related to the rate of ligand exchange for the system. This paper describes a kinetic investigation of the calcium(I1)-(ethylenedinitri1o)tetraacetic acid (EDTA) system using proton NMR techniques. I n particular we have examined the pH dependence of exchange reactions of the type
Here Y, represents the free EDTA ligand in its various solution forms, Y-4, HY-3, and HzY+, and Cay, represents the Ca-EDTA chelates in the forms CaY+ and HCaY-. Exchange reactions of the type, *Ca+2 Cay, *Cay, Ca+2, are not observable by proton NMR techniques because ligands containing the magnetically active nuclei, namely carbon-bonded protons, would be exchanging between two chemically equivalent sites, Ca+2 and *Ca+Z. The qualitative exchange behavior for Ca-EDTA as a function of solution pH was noted in an earlier paper where representative NMR spectra may also be found (8). In addition, the CaEDTA and the EDTA systems have been thoroughly investigated using potentiometric techniques, from which the following equilibria and associated constants were evaluated (16) :
+
+
*
Ca+2
Hf
+
Y-4
+
e CaY-2
e HCaYKHC"'- [HCaY-] -
- [H+] ICaY-21
C.Y
+ Ca+2e HCaYH2Y-2
e H+ + HY-3 Ka = [H+] [HY-S]
1
[HzY-'
HY-3 s H+ + Y-4 K4 =
~ + [ Y1- 4 1 [HY-3]
Thevalues of these equilibrium constants are given in Table I, and the relative amounts of EDTA in its various forms for one to one Ca-EDTA solutions a t different pH's are shown in Figure 1. EXPERIMENTAL
General. All p H measurements were made a t 25' C. using a Corning Model 12 p H meter equipped with a glass electrode and a fiber-tip, saturated calomel reference electrode. Before making measurements the Table 1. Equi-
librium expression KfCa' K::;' KPY
K3 K4
Equilibrium Constants
log K ' , p =
0.16MJ
(16)
10.6 3.2 3.5 -6.2 -10.1
log K ,
1.6M 9.4 0.1 2.8 & 0.2 2.4 & 0.2 -6.2 + 0.05 - 9 . 8 f 0.05 p =
VOL. 38, NO. 6, M A Y 1966
*
697
meter was standardized with a saturated potassium bitartrate solution (pH 3.56) and a 0.01M sodium tetraborate solution (pH 9.18). Proton NMR spectra were obtained on a Varian A-60 spectrometer which was operated a t a probe temperature of 32 f 1’ C. Tetramethylammonium chloride (0.01-V) was used as an internal reference, and chemical shifts were measured in c.p.s. from the central resonance of the tetramethylammonium ion (TMA) triplet. In addition to its use as a convenient chemical shift reference, TRlh served as a guide for optimum spectrometer operating conditions. Before obtaining a spectrum the magnetic field homogeneity was adjusted until base line resolution of the three TMX resonances, which are separated by about 0.5 c.P.s., was achieved. Under such conditions the field inhomogeneity contribution to the resonance line widths is minimized and amounts to a few tenths c.p.s. Line widths were measured in c.p.s. a t the half-heights of the resonances, and each line width represents the average from a t least five individual spectra. For line widths less the 5 C.P.S. the uncertainty of the experimentally determined values is estimated to be 0.2 C.P.S. or less, but for line widths greater than 10 c.p.s. the uncertainty may be as great as 0.5 c.p.s. Solutions were prepared from reagent grade calcium nitrate tetrahydrate, tetraprotonated EDTA, and triplydistilled water. Adjustments of solution pH were made with concentrated KOH and HS03 solutions to minimize dilution effects. For studies at varying pH the appropriate amounts of metal salt and EDTA were weighed and diluted, the pH was adjusted, and a 0.5-ml. sample was pipetted into the NMR sample tube. For studies at constant pH an equimolar solution of metal and ligand was prepared, weighed amounts of EDTA were added, and the pH was adjusted. Because relatively high concentrations of EDTA were required for the NMR measurements (0.1 to 0.4M) no inert electrolyte could be added to maintain constant ionic strengths. The ionic strength of the solutions mas normally between 1 and 3, but this varied as the pH was changed or as EDTA was added. No attempt has been made to correct the results reported herein for activity effects. Values for the metal and ligand concentrations employed in the calculations were taken as their analytical concentrations, and the hydrogen ion concentration was taken as the value computed from the measured pH. While it is recognized that these conventions will introduce errors in the measured rate constants, the magnitudes of such errors are probably not much greater than the error from assuming that the solution pH measured a t 25’ C. is unchanged on going to 32’ C. in the NMR probe. Errors in the experimentally determined rate constants because of equilibrium constant variations with ionic strength were minimized by reevaluating the equilibrium constants a t higher 698
0
ANALYTICAL CHEMISTRY
100
80
-
4
n Y
60-
-
40-
-
a IO
IU
0
z
-
20
-
0
2
3
4 PH
Figure 1.
TT2
measured a t half-height in C.P.S. (14). In the case of slow exchange these considerations lead to the result : TCaY
-
5
6
Composition of 1 :1 Ca-EDTA solution as function of pH
ionic strength. The method used was analogous to that of Schwerzenbach (16) in which we employed a total EDTA concentration of 0.010M and a total calcium concentration of 0.15M. The ionic strength was adjusted to 1.6M with KNO?. Rate Measurements. Because EDTA (and also Ca-EDTA) gives two single resonances-one from the ethylenic protons and one from the acetate protons ( L e . , the -CH2groups adjacent to the carboxylates) either of the resonances may be studied to measure the rates (8). Both give identical results as would be expected if intramolecular or additional intermolecular processes do not make significant contributions to the resonance line shapes (13). Whenever overlap was not a problem, the acetate resonance was utilized because its intensity is twice that of the ethylenic resonance. For solutions in which the EDTA concentration exceeded the Ca+2 concentration the exchange kinetics were considered to be slow, intermediate, or fast on the NMR time scale according to the following criteria. For slow exchange separate, nonoverlapping resonances are observed for free and for complexed EDTA species. For intermediate exchange separate resonances are also observed, but they are partially collapsed and somewhat distorted because of overlap between them. For fast exchange the free and complexed EDTA resonances are collapsed into single broadened resonances. In each of these cases the lifetime of a Cacoordinated ligand, T C ~ Y ,can be expressed in terms of the transverse relaxation time, TI, using the Bloch equations modified for transfer of magnetization through chemical exchange. T 2is related to the resonance line shape 1 by w = -, where w is the line width
1 _
-
T(WC.Y
- W’CaY)
where wcsyis the Ca-EDTA line width (either acetate or ethylenic) observed from the spect,riim, and U)‘C&Y is the
corresponding line width in the absence of exchange. In this study W ’ C ~ Y was taken as the line width of the appropriate resonance in a one to one Ca-EDTA solution ( ~ 1 . 1c.P.s.) a t the same pH as that of the measurement. For intermediate exchange in a solution containing equal concentrations of free and complexed EDTA-Le., a one to two Ca-EDTA solution-the expression was determined to be 1 TCaY =
d1/2(AvO2
- Av*)
where AVOis the separation of the free and complexed EDTA resonances (either acetate or ethylenic) in the absence of exchange, and AV is the observed separation of these resonances. For fast exchange the expression employed was (14) TCaY
= WY,CeY
- PYW‘Y - P C S Y W ’ C S Y 4 ~ Y p~ P C , Y A V O ~
w y , is ~the ~ observed ~ line width of the collapsed resonance; w’y is the line width of free EDTA in the absence of exchange (determined for a solution of potassium EDTA a t the same pH); p y and pcsY are the fractional populations of EDTA in the free and complexed forms, respectively. -d[CaY] The rate to be measured is dt which is related to the Ca-EDTA lifetime by ~
Thus for kinetic expressions having the form --d[CaY]/dt = kl[CaY]
+ kz [Cay] [ Y ] + . . .
we obtain 1 TCaY
=
kl .f k2[Y]
+
I
.
.
Plots of ~ ~ us. ~ the ~ appropriate 1 ligand concentration term, give curves whose slopes and intercepts can be related to the various rate constants (7).
By working in carefully controlled pH regions and by utilizing relatively low concentrations of excess EDTA, most of the rate constants could be evaluated using the slow exchange formula. At the extremities of the pH region being invsstigated, greater than 10 or less than 6, it was necessary to employ either the intermediate or fast exchange formulas. Despite the approximations made in deriving the latter two expressions, comparable rate constants were obtained from all three expressions in pH and concentration ranges where the same kinetic processes could be studied. However, results obtained using the slow exchange formula exhibited much less data scatter so that this is considered to be a more reliable working equation.
Cay-2
+
Y-4
[HCaY-] [HY+] k6
+ Ht-3 2 Cay-2
+
kr
ks -
Ca+2
+ HY-3 2 HCaf-
HCaY-
(4)
~ ~ y - 2
+ HY-3 + HY-3
(5)
This expression assumes that the contributions from exchange Reactions 5 , 6, and 7 are the rate-limiting steps in the exchange of ligand at low pH; that is, HCaY- is rapidly formed from C a y -2 through the equilibrium process H + E HCaY-.
(6) Because
+ H2Y+
(7)
Because the data are taken under equilibrium conditions and no labeling of the ligand is necessary, Y* = Y. Also the backward rate constants for several of the exchange processes are equal to the forward rate constants; namely, k2 = kz-, k3 = k3-, k4 = k4-, k6 = ks-, and k, = k7-. The constants kl and ks represent the first order dissociation rate constants of Cay-2 and HCaY-, respectively; they are related to the second order association rate constants,
kl- and k6-, by KYy =
-ki
kl
+
+
+ H2f+ 5 HCaF-
[c~Y-~I
(3)
kr
HCaYHCaY-
+ HY-3
+ H~?-Z
Ca;-2
.os
(8)
and
.20
A plot of us. Yf gives a straight line whose Y , = 0 intercept is kl and [H+l)l whose slope is [k2K4/(K4 [ka [H+I/(Ka [H+])]. If this experiment is carried out at two different pH's, and k3 can be determined from the two slopes. Within experimental error the intercept is zero, and therefore kl is less than 1 second-'. An alternative experiment was performed holding Y constant and varying pH, which give identical results. The rate constants determined in this investigation are listed in Table 11. No direct evidence could be found for contributions from exchange Processes 4 and 7. The limits set on kaand k7 in Table I1 are speculative and will be discussed subsequently. Techniques and considerations similar to those employed for evaluating kl, kp, and ka were applied below pH 8 to determine ks and kg. In Figure 2 7cey-l has been plotted us. the HY-3 concentration a t two different and constant pH values. The slope of the straight line portion of each curve is ke[H+] K c ~ ~ H, and C ~the ~ extrapolation of this
[HCaY-] = [H+]KC;', this [CaY -*I
equation can be further simplified to 1
- = kl TCaY
+ kz[Y-'] + kt[HY-3] +
Table II.
When the solution pH is confined to the region from 8 to 12, only exchange Processes 1, 2, and 3 need to be considered because the concentrations of HCaY- and HzY-2 are negligible. If Y,, the free EDTA concentration, is varied at constant pH, Equation 11 simplifies to
Rate
const. kt
Experimental Rate Constants
Experimental Experimental value, value, M-1 second-' second-' 5 2 . 5 X 100 120 zt 3
kikz ks
+
+
+
(2)
Caf-2
-
(1)
Y-4
2 Ca?-2 +
;-4
2s
Figure 2. Lifetimes of Ca-EDTA as function of excess ligand concentration [Car-*]= 0.25M
From considerations of the solution compositions in this work and the aqueous solution equilibria, several possible ligand exchange processes can be written for the pH region from 12 to 5. ki ky Ca+2 +
-
.O
RESULTS
Cay+
30
51
5 * 4
