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The kinetics of exchange between lanthanide ions and lanthanum ethylenediaminetetraacetate
i, inorg, nucl.(hem., 197 I, Vol. 33, pp. 127 to 135. PergamonPress. Printed in Great Britain
THE KINETICS OF EXCHANGE BETWEEN LANTHANIDE IONS AND LANTHANUM ETH YLENEDIAM IN ETETRAACETATE W. D ' O L I E S L A G E R * and G. R. C H O P P I N D e p a r t m e n t of Chemistry, Florida State University, Tallahassee, Florida 32306
(Received 23 March 1970) A b s t r a c t - T h e kinetics of the exchange o f C e 3+, Eu 3+ and A m :j+ and L a ( E D T A ) ~- were studied using a radiotracer method. T h e experimental rate equation for the forward exchange reaction was s h o w n to be:
R = k,r[H+][Eu:~+][La(EDTA)I-]/[La:~+]. This equation is found to be consistent with a m e c h a n i s m in which the slow step involves protonation of L a ( E D T A ) ~ followed by dissociation and rapid formation of M ( E D T A ) 1-. T h e high stability of the lanthanide E D T A c o m p l e x e s is determined by the magnitude of the complex formation rate constant whereas the variation in stability of different l a n t h a n i d e - E D T A complexes is governed primarily by the differences in dissociative rate constant. INTRODUCTION
THE KINETICS o f the exchange reactions between transition metal ions and their
polyaminocarboxylate complexes have been the subject of a number of studies, and an excellent discussion of the different possible reaction mechanisms is given by Margerum [ 1]. By contrast, the amount of research on the exchange of lanthanide ions and their polyaminocarboxylate complexes is considerably less [2-5]. In this study we have applied a more complete rate equation to the exchange system La(EDTA)--Eu( I 11). Qualitative results of experiments with C e(I I I) and Am( I I 1) are also reported. EXPERIMENTAL
Materials and reagents Lanthanum perchlorate. Spec. pure LazO:~ (City Chemical Corporation, purity > 99.99 per cent~ was dissolved in a m i n i m u m volume of 60% perchloric acid and the solution evaporated to dryness. To reduce the a m o u n t of perchloric acid, the residue was redissolved in distilled water and evaporated several times, until a solution with pH between 4-5 and 5 was obtained. T h e l a n t h a n u m concentration of this stock solution was determined by a complexometric titration with a standardized N z ~ E D ' I A solution and xylene orange as an indicator. Sodium acetate buffer solutions. T h e stock buffer solutions of 0.2M were prepared by neutralizing *On leave from the Laboratory of Radiochemistry, University of Louvain, l.ouvain, Belgium. I. D . W . M a r g e r u m , Rec. chem. Prog. 2 4 , 2 3 7 (1963). 2. R. H. Betts, O. F. Dahlinger and D. M. Munro, Radioisotopes in Scientific Research Vol. 2. p. 326. P e r g a m o n Press, Oxford (1958). 3. T. A s a m o , S. Okada, K. Sakamoto, S. Taniguchi and Y. Kobayashi, Radioisotopes 14, 363 ( 1965): idem. J. inorg, nucl. Chem. 31, 2127 (1969). 4. T. Shiokawa and T. Omori, Bull. Chem. Soc. Japan 38, 1892 (1965). 5. P. Glentworth, B. Wiseall, C. L. Wright and A. J. M a h m o o d , J . inorg, nucl. Chem. 30,967 (1968). 127
128
W. D ' O L I E S L A G E R and G. R. C H O P P I N
acetic acid solutions of known concentration with standardized sodium hydroxide to the appropriate pH. Chelating agent. A stock solution (0-01M) of Na4EDTA was prepared by dissolving a weighed amount of anhydrous salt obtained from Aldrich Chemical Co., Inc. Radiotracers. Carrier free ls2"4Eu(lll), l~Ce(lll), and 241Am(lll) were obtained from Oak Ridge National Laboratories; samples of these solutions were evaporated and redissolved in sodium acetate buffer solutions to obtain a suitable level of activity. Sodium perchlorate solution. A 5 M stock solution of NaCIO4 was prepared by dissolving a weighed amount of anhydrous sodium perchlorate (G. Frederick Smith Chem. Co.) in distilled water. The concentration was determined by passing samples of these solutions through a Dowex 50W X-4 cation exchanger column in the hydrogen form, and titrating the hydrogen ion concentration in the eluate with standardized sodium hydroxide.
Procedure The reaction mixture was prepared by diluting to 50 ml appropriate amounts of the stock La(CIO4)3 solution, the Na4EDTA solution, the buffer solution of suitable pH, and the necessary amount of the 5 M NaCIO4 solution to obtain an ionic strength of 0.5 M, and a buffer concentration of 0.02 M in all the experiments. To make sure that all the EDTA present is in the La(EDTA)- complex, a small excess of La(CIO4)3 over the EDTA concentration was always added. After temperature equilibration a small amount of the tracer solution (-200/xl) was added to initiate the exchange reaction. At fixed time intervals 2 ml aliquots of this mixture were withdrawn and passed through a column of Dowex 50W X-4 resin in the sodium form, previously preequilibrated with a buffer solution of appropriate pH. The resin was 50-100 mesh and the bed size 1.5 × 1.0 cm. Approximately 5-10 sec were required for passage through this resin bed. The uncomplexed lanthanide ions were retained on the cation exchanger and the complexed lanthanide fraction passed through the column. During each run a 2 ml aliquot is withdrawn and saved without being passed through the column to ascertain the total activity. The reactions were followed for at least two half-life periods and, if necessary, an infinite time sample was also taken. At the end of each run the pH of the reaction mixture was determined with a Beckmann research pH meter and a combination electrode system. The exchange of the radioactive tracer in the EDTA complex was determined by counting the gamma ray activity of the eluate with a NaI(TI) scintillation well-type counter. The total tracer activity was determined by counting the properly diluted unexchanged aliquot.
RESULTS
If the exchange reaction between L a ( E D T A ) 1- and a lanthanide ion, Ln 3+, is written as: kl La(EDTA)
1-+Ln
3+ <
k-i
) Ln(EDTA)
1-+La
3+
(1)
the equilibrium constant is equal to the ratio of the formation stability constants of L n ( E D T A ) 1- and L a ( E D T A ) I - ; i.e. Keq = KLn<~,DTA)/KLa(EDTA).The Keq is large and, hence, the reaction goes nearly to completion when KLn{SDTA) > KLa(EDTA) provided the concentration of La 3÷ is not much greater than that of L a ( E D T A ) ~-. In such cases, the study of the kinetics is simplified. KEu(EDTA)= 10 ~r'99 and KLa(EDTA) = 10 ~'34 [6], SO the system L a ( E D T A ) I - / E u 3+ was chosen for study. Since the concentrations of both the free and the complexed lanthanum were much larger than the concentration of the tracer europium, only the latter changed during the course of the reaction. The linearity of the data in Fig. 1 shows that the reaction is first order for the E u ( l l l ) concentration. The failure of the lines to 6. T. Moeller, D. F. Martin, L. C. Thompson, R. Ferris, G. R. Feistel and W. J. Randell, Chem. Rev. 65, 1 (1965).
Kinetics of exchange
129
15
I0
v /
~ o
pH
0.5 (a) (b) (c) (d)
o r o
6-09 6.344 6.594 6.78
I
I
I
IO
2o
30
i, min
Fig. 1.
extrapolate to the origin at time zero is caused by the non-uniform distribution of europium in the reaction solution when it is initially added. In Fig. 2 the first order rate constants obtained from each of the lines in Fig. 1 are plotted as a function of the hydrogen ion concentration. Again, the linearity of the line indicates that, at least between a pH of 6 and 7, the reaction is first order with respect to hydrogen ion concentration. The line passes through the origin indicating that, within experimental precision, only hydrogen ions but not water or acetic acid catalyze the reaction. Previous workers [2-5] have also found a first order dependency on hydrogen ions. At this stage, the rate equation can be written as: R = k2[H+l[Eu 3+1
(2)
in which L2 = 4.4 × 105M -1 min -1. Earlier investigations [2-5] of the exchange rate dependency on the concentration of the complexed species would predict a first order dependence on La ( E D T A ) 1- concentration. Experiments were performed with constant total concentration of lanthanum but with different amounts of N a 4 E D T A added. The rate constant k2 is a function of the L a ( E D T A ) ~- concentration but as the curvature in line of Fig. 3 shows, it does not seem to be a first order dependency. In fact, even a plot (not shown) for a second order dependency of L a ( E D T A ) 1- concentration does not fit the data on a straight line. U n d e r our conditions of constant total lanthanum concentration, as [ L a ( E D T A ) 1-] was increased, [La ~+] was decreased. If the uncomplexed La 3+ inhibits the reaction, the rate would increase at higher
130
W. D'OLIESLAGER and G. R. CHOPPIN
0.4
0"3
T
0'2
0.1
0 v 0
I 2.5
I 5.0
I 7.5
[H i+] 107 (M)
Fig. 2.
values of [ L a ( E D T A ) ~-] and at lower values of [La 3+] in agreement with the curvature of line a in Fig. 3. T h e plot of k2 as a function of the ratio [ L a ( E D T A ~ - ] / [ L a a+] is shown as line b in Fig. 3. We conclude that, indeed, the reaction is first order with respect to L a ( E D T A ) 1- but it also has a first order inhibition with respect to the concentration of uncomplexed lanthanum. In summary, the experimental equation for the rate of exchange between Eu 3+ and L a ( E D T A ) ~- can be written as: R = kr[H+I[Eua+][La(EDTA)I-]/[La3+].
(3)
Table 1 summarizes the experimental data under different reaction conditions; the kl values are the rate constants taken from plots such as those in Fig. 1 (i.e. R =
Kinetics ofexchange
131
[Lo EF)TAI-]x tO 3 (M) 025
0 50
0 75
i oo
I
I
I
I
25
20 _..... ~c T =E
'_o x
1.5
b
,(
0
1.0
05
0
0
05
1.0[Lo EDT~-] 1.5
I
2.0
25
[Lo~+]
Fig. 3.
kl[Eu3+]). We have not studied the possible influence of complexing by the buffer solution on the rates of exchange. However, Glentworth et al. 15] have shown that in our system such an effect would be small. DISCUSSION
The inhibition effect of the La 3÷ concentration is not consistent with a bimolecular substitution mechanism. Betts e t al. [2] have proposed that the exchange reaction proceeds via a mechanism in which protonation causes dissociation of the E D T A complex and the free E D T A formed reacts very rapidly with the radio-
132
W. D'OLIESLAGER and G. R. CHOPPIN Table 1. Exchange Rates in the System Eu(l l 1) - - La(EDTA)-I; T = 24°C;/z -----0.5M; Acetate buffer = 0.02M [Laa+] [La(EDTA)-] (M X 10a) (M × 103) 1.04 1.04 1.04 1.04 0.84 0.64 0.44
0.40 0.40 0.40 0.40 0.60 0.80 1.00
kl pH 6.780 6.594 6.344 6.090 6.816 6.856 6.970
kr
(min-1) (M-lmin -1 x 10-6) 0.0675 o. 105 0.191 0.348 0.120 0.191 0.270
1.06 1.07 1.10 !. I 1 1.10 1.10 1.10
t r a c e r metal ions. F o r o u r s y s t e m the c o m p l e t e set o f r e a c t i o n steps w o u l d be: La(EDTA)-+ LaH(EDTA)+(x
H + ,--/2-> sJow L a H ( E D T A )
(4)
-- 1)H+ fast :' L a 3+ + H x ( E D T A )
(5)
La3+ + H x ( E D T A ) ~ _ 4 fast ) L a ( E D T A ) - + x H +
(6)
Eu3+ + H ~ ( E D T A ) X _ 4 fast E u ( E D T A ) - + x H ÷ k-Eu
(7)
k-La
Eu(EDTA)- + H + ~
EuH(EDTA)
E u H ( E D T A ) + (x--l)H + fast ~ EU3+ + Hx(EDTA)~_4.
(8) (9)
T h e rate o f f o r m a t i o n (RF) o f E u ( E D T A ) - is given b y the rate o f dissociation o f L a ( E D T A ) - ( E q u a t i o n (4)) multiplied b y the probability that the free Hx ( E D T A ) x-4 reacts with Eu a÷ ( E q u a t i o n (7)) r a t h e r than L a 3÷ ( E q u a t i o n 6). RF = k L a [ H + ] [ L a ( E D T A ) 1-]
k_zu[Eu a+] k_La[La3+] + k_Eu[Eu3+] "
(~o)
T h e rate o f the r e v e r s e reaction, the dissociation o f the E u ( E D T A ) - Can be s h o w n to be e x p r e s s e d similarly as: k_La[Laa+]
Ro = k E u [ H + I [ E u ( E D T A p -] k_La[Laa+] + k_Eu[Eu3+] •
( 1 1)
T h e net rate is the difference b e t w e b n RF and Ro. H o w e v e r , u n d e r o u r conditions w h e r e b y the e x c h a n g e p r o c e e d s nearly to c o m p l e t i o n , the net rate is essentially e x p r e s s e d b y E q u a t i o n (10). M o r e o v e r , since [ L a 3÷] >> [Eu3+], the rate c a n be e x p r e s s e d by: R = kLak-Eu [H+][La(EDTA)I-][Eu3+] k-La [ L a a+]
(12)
Kinetics of exchange
13 3
This expression is exactly the same as the experimental rate equation (Equation (3)) with: kLak-Eu kr = = 1.08 × 10eM-lmin -'. k-La
Since the ratio k_La/kLa is the stability constant for the L a ( E D T A ) - complex, the value ofk-Eu, the rate constant for the fast reaction forming E u ( E D T A ) ' - , may be calculated to have a value 0f2.3 × 1022M-Zmin-'. If the exchange reaction does not go to completion, additional information can be obtained. This can be achieved by use of a tracer lanthanide ion whose E D T A complex is comparable in stability to that of La(EDTA) 1-. The system La ( E D T A ) ' - / C e 3+ is suitable in this respect. Alternately, incomplete reaction can be achieved by increasing the ratio L a 3 + / L a ( E D T A ) ~-. Exchange involving Eu 3+ and Am 3+ was studied by this approach. Assuming that the exchange mechanisms remain the same, Equation (13) expresses the reaction rate. R=
kLak-M [ H+ ] [ L a ( E D T A ) ' - ] [M 3+] k-La [La3+] kM[H+][M(EDTA)I-].
(13)
Since [H+], [La 3+] and [La(EDTA)'-] are constants in each run, the equation may be written simply as: dx R = -d-[ = ka(a -- X) - - k - A ( X ) (14) with ka = kL. • k-M. [H+][La(EDTA) '-] k-L~ [La 3+] and k - A = kM[H+]. 1.5 Am
•
I0
Ce
J
o -J
05
I I0
I 20 t , rain
Fig. 4.
30
23 22 24
Ce Eu Am
5.870 5.450
6.777
pH
1.04 1.40 140 4.0 0.4 0.4
Las+ La(EDTA)(M x 103) (M x 104) 0.091 0.0635 0.105
k (min-1)
8.5 6.1
745
k,, k--Mlk--La (M-l min-* X lo+) 25.7 2.28 1.21
X
1.63 1.9 1.3
k-M 10m4) (M-l min-’ X lo-**)
p = 0.5M, Acetate buffer = 0.02M b (M-l min-’
J. G. Schwarzenbach, R. Gut and G. Anderegg, Helv. chim. Acta 37.93 7 (1954). 8. J. Fuger,J. inorg. nucl. Chem. 5,332 (1958).
WC)
M(II1)
Table 2. Exchange rates in the system M(III) - - La(EDTA)-;
16.80 17.9 18.0
log K
Ref.
18.16[8]
17.34[7]
16~00[7]
log K
Kinetics of exchange
135
This b e c o m e s on integration the familiar equation for a first order reversible reaction. Figure 4 shows that plots of logxe/(xe-x) vs. t are straight lines for Ce :~+, Eu :~+ and A m 3÷. (Xe-----the equilibrium concentration of M ( E D T A ) -~ ). Values of kLa " k-M/k-La and kM can be calculated from the slopes of these lines and are tabulated in Table 2. T h e rate constant for the formation of the M ( E D T A ) 1 complexes, k-M, is calculated by multiplying the values of kLa" k-M/k-La by the t h e r m o d y n a m i c stability constant for L a ( E D T A ) -I and listed in Table 2 next to the dissociation rate constant, kM. While the formation rate constant is much larger, it is relatively invariant for the different metal ions whereas the dissociation rate constants show significant differences. T h e stability constants, K, for the M ( E D T A ) -1 complex formation are also listed in Table 2. C o m p a r i s o n of these values with literature values (/z = 0.1 M) in the last column of Table 2 show satisfactory agreement. It is obvious, then, that the variation in stability of the M ( E D T A ) -1 complexes is determined kinetically by the differences in the dissociation rate constants whereas the magnitude of the stability constant is determined predominantly by the very large association rate constants.
Acknowledgements-Thisresearch was supported by the U.S. Atomic Energy Commission. We wish to thank Mrs. K. R. Williams for her assistance. One of us (W.D'O) wishes to acknowledge financial assistance from the I. I. K.W. (Belgium)for a travel grant.
THE KINETICS OF EXCHANGE BETWEEN LANTHANIDE IONS AND LANTHANUM ETH YLENEDIAM IN ETETRAACETATE W. D ' O L I E S L A G E R * and G. R. C H O P P I N D e p a r t m e n t of Chemistry, Florida State University, Tallahassee, Florida 32306
(Received 23 March 1970) A b s t r a c t - T h e kinetics of the exchange o f C e 3+, Eu 3+ and A m :j+ and L a ( E D T A ) ~- were studied using a radiotracer method. T h e experimental rate equation for the forward exchange reaction was s h o w n to be:
R = k,r[H+][Eu:~+][La(EDTA)I-]/[La:~+]. This equation is found to be consistent with a m e c h a n i s m in which the slow step involves protonation of L a ( E D T A ) ~ followed by dissociation and rapid formation of M ( E D T A ) 1-. T h e high stability of the lanthanide E D T A c o m p l e x e s is determined by the magnitude of the complex formation rate constant whereas the variation in stability of different l a n t h a n i d e - E D T A complexes is governed primarily by the differences in dissociative rate constant. INTRODUCTION
THE KINETICS o f the exchange reactions between transition metal ions and their
polyaminocarboxylate complexes have been the subject of a number of studies, and an excellent discussion of the different possible reaction mechanisms is given by Margerum [ 1]. By contrast, the amount of research on the exchange of lanthanide ions and their polyaminocarboxylate complexes is considerably less [2-5]. In this study we have applied a more complete rate equation to the exchange system La(EDTA)--Eu( I 11). Qualitative results of experiments with C e(I I I) and Am( I I 1) are also reported. EXPERIMENTAL
Materials and reagents Lanthanum perchlorate. Spec. pure LazO:~ (City Chemical Corporation, purity > 99.99 per cent~ was dissolved in a m i n i m u m volume of 60% perchloric acid and the solution evaporated to dryness. To reduce the a m o u n t of perchloric acid, the residue was redissolved in distilled water and evaporated several times, until a solution with pH between 4-5 and 5 was obtained. T h e l a n t h a n u m concentration of this stock solution was determined by a complexometric titration with a standardized N z ~ E D ' I A solution and xylene orange as an indicator. Sodium acetate buffer solutions. T h e stock buffer solutions of 0.2M were prepared by neutralizing *On leave from the Laboratory of Radiochemistry, University of Louvain, l.ouvain, Belgium. I. D . W . M a r g e r u m , Rec. chem. Prog. 2 4 , 2 3 7 (1963). 2. R. H. Betts, O. F. Dahlinger and D. M. Munro, Radioisotopes in Scientific Research Vol. 2. p. 326. P e r g a m o n Press, Oxford (1958). 3. T. A s a m o , S. Okada, K. Sakamoto, S. Taniguchi and Y. Kobayashi, Radioisotopes 14, 363 ( 1965): idem. J. inorg, nucl. Chem. 31, 2127 (1969). 4. T. Shiokawa and T. Omori, Bull. Chem. Soc. Japan 38, 1892 (1965). 5. P. Glentworth, B. Wiseall, C. L. Wright and A. J. M a h m o o d , J . inorg, nucl. Chem. 30,967 (1968). 127
128
W. D ' O L I E S L A G E R and G. R. C H O P P I N
acetic acid solutions of known concentration with standardized sodium hydroxide to the appropriate pH. Chelating agent. A stock solution (0-01M) of Na4EDTA was prepared by dissolving a weighed amount of anhydrous salt obtained from Aldrich Chemical Co., Inc. Radiotracers. Carrier free ls2"4Eu(lll), l~Ce(lll), and 241Am(lll) were obtained from Oak Ridge National Laboratories; samples of these solutions were evaporated and redissolved in sodium acetate buffer solutions to obtain a suitable level of activity. Sodium perchlorate solution. A 5 M stock solution of NaCIO4 was prepared by dissolving a weighed amount of anhydrous sodium perchlorate (G. Frederick Smith Chem. Co.) in distilled water. The concentration was determined by passing samples of these solutions through a Dowex 50W X-4 cation exchanger column in the hydrogen form, and titrating the hydrogen ion concentration in the eluate with standardized sodium hydroxide.
Procedure The reaction mixture was prepared by diluting to 50 ml appropriate amounts of the stock La(CIO4)3 solution, the Na4EDTA solution, the buffer solution of suitable pH, and the necessary amount of the 5 M NaCIO4 solution to obtain an ionic strength of 0.5 M, and a buffer concentration of 0.02 M in all the experiments. To make sure that all the EDTA present is in the La(EDTA)- complex, a small excess of La(CIO4)3 over the EDTA concentration was always added. After temperature equilibration a small amount of the tracer solution (-200/xl) was added to initiate the exchange reaction. At fixed time intervals 2 ml aliquots of this mixture were withdrawn and passed through a column of Dowex 50W X-4 resin in the sodium form, previously preequilibrated with a buffer solution of appropriate pH. The resin was 50-100 mesh and the bed size 1.5 × 1.0 cm. Approximately 5-10 sec were required for passage through this resin bed. The uncomplexed lanthanide ions were retained on the cation exchanger and the complexed lanthanide fraction passed through the column. During each run a 2 ml aliquot is withdrawn and saved without being passed through the column to ascertain the total activity. The reactions were followed for at least two half-life periods and, if necessary, an infinite time sample was also taken. At the end of each run the pH of the reaction mixture was determined with a Beckmann research pH meter and a combination electrode system. The exchange of the radioactive tracer in the EDTA complex was determined by counting the gamma ray activity of the eluate with a NaI(TI) scintillation well-type counter. The total tracer activity was determined by counting the properly diluted unexchanged aliquot.
RESULTS
If the exchange reaction between L a ( E D T A ) 1- and a lanthanide ion, Ln 3+, is written as: kl La(EDTA)
1-+Ln
3+ <
k-i
) Ln(EDTA)
1-+La
3+
(1)
the equilibrium constant is equal to the ratio of the formation stability constants of L n ( E D T A ) 1- and L a ( E D T A ) I - ; i.e. Keq = KLn<~,DTA)/KLa(EDTA).The Keq is large and, hence, the reaction goes nearly to completion when KLn{SDTA) > KLa(EDTA) provided the concentration of La 3÷ is not much greater than that of L a ( E D T A ) ~-. In such cases, the study of the kinetics is simplified. KEu(EDTA)= 10 ~r'99 and KLa(EDTA) = 10 ~'34 [6], SO the system L a ( E D T A ) I - / E u 3+ was chosen for study. Since the concentrations of both the free and the complexed lanthanum were much larger than the concentration of the tracer europium, only the latter changed during the course of the reaction. The linearity of the data in Fig. 1 shows that the reaction is first order for the E u ( l l l ) concentration. The failure of the lines to 6. T. Moeller, D. F. Martin, L. C. Thompson, R. Ferris, G. R. Feistel and W. J. Randell, Chem. Rev. 65, 1 (1965).
Kinetics of exchange
129
15
I0
v /
~ o
pH
0.5 (a) (b) (c) (d)
o r o
6-09 6.344 6.594 6.78
I
I
I
IO
2o
30
i, min
Fig. 1.
extrapolate to the origin at time zero is caused by the non-uniform distribution of europium in the reaction solution when it is initially added. In Fig. 2 the first order rate constants obtained from each of the lines in Fig. 1 are plotted as a function of the hydrogen ion concentration. Again, the linearity of the line indicates that, at least between a pH of 6 and 7, the reaction is first order with respect to hydrogen ion concentration. The line passes through the origin indicating that, within experimental precision, only hydrogen ions but not water or acetic acid catalyze the reaction. Previous workers [2-5] have also found a first order dependency on hydrogen ions. At this stage, the rate equation can be written as: R = k2[H+l[Eu 3+1
(2)
in which L2 = 4.4 × 105M -1 min -1. Earlier investigations [2-5] of the exchange rate dependency on the concentration of the complexed species would predict a first order dependence on La ( E D T A ) 1- concentration. Experiments were performed with constant total concentration of lanthanum but with different amounts of N a 4 E D T A added. The rate constant k2 is a function of the L a ( E D T A ) ~- concentration but as the curvature in line of Fig. 3 shows, it does not seem to be a first order dependency. In fact, even a plot (not shown) for a second order dependency of L a ( E D T A ) 1- concentration does not fit the data on a straight line. U n d e r our conditions of constant total lanthanum concentration, as [ L a ( E D T A ) 1-] was increased, [La ~+] was decreased. If the uncomplexed La 3+ inhibits the reaction, the rate would increase at higher
130
W. D'OLIESLAGER and G. R. CHOPPIN
0.4
0"3
T
0'2
0.1
0 v 0
I 2.5
I 5.0
I 7.5
[H i+] 107 (M)
Fig. 2.
values of [ L a ( E D T A ) ~-] and at lower values of [La 3+] in agreement with the curvature of line a in Fig. 3. T h e plot of k2 as a function of the ratio [ L a ( E D T A ~ - ] / [ L a a+] is shown as line b in Fig. 3. We conclude that, indeed, the reaction is first order with respect to L a ( E D T A ) 1- but it also has a first order inhibition with respect to the concentration of uncomplexed lanthanum. In summary, the experimental equation for the rate of exchange between Eu 3+ and L a ( E D T A ) ~- can be written as: R = kr[H+I[Eua+][La(EDTA)I-]/[La3+].
(3)
Table 1 summarizes the experimental data under different reaction conditions; the kl values are the rate constants taken from plots such as those in Fig. 1 (i.e. R =
Kinetics ofexchange
131
[Lo EF)TAI-]x tO 3 (M) 025
0 50
0 75
i oo
I
I
I
I
25
20 _..... ~c T =E
'_o x
1.5
b
,(
0
1.0
05
0
0
05
1.0[Lo EDT~-] 1.5
I
2.0
25
[Lo~+]
Fig. 3.
kl[Eu3+]). We have not studied the possible influence of complexing by the buffer solution on the rates of exchange. However, Glentworth et al. 15] have shown that in our system such an effect would be small. DISCUSSION
The inhibition effect of the La 3÷ concentration is not consistent with a bimolecular substitution mechanism. Betts e t al. [2] have proposed that the exchange reaction proceeds via a mechanism in which protonation causes dissociation of the E D T A complex and the free E D T A formed reacts very rapidly with the radio-
132
W. D'OLIESLAGER and G. R. CHOPPIN Table 1. Exchange Rates in the System Eu(l l 1) - - La(EDTA)-I; T = 24°C;/z -----0.5M; Acetate buffer = 0.02M [Laa+] [La(EDTA)-] (M X 10a) (M × 103) 1.04 1.04 1.04 1.04 0.84 0.64 0.44
0.40 0.40 0.40 0.40 0.60 0.80 1.00
kl pH 6.780 6.594 6.344 6.090 6.816 6.856 6.970
kr
(min-1) (M-lmin -1 x 10-6) 0.0675 o. 105 0.191 0.348 0.120 0.191 0.270
1.06 1.07 1.10 !. I 1 1.10 1.10 1.10
t r a c e r metal ions. F o r o u r s y s t e m the c o m p l e t e set o f r e a c t i o n steps w o u l d be: La(EDTA)-+ LaH(EDTA)+(x
H + ,--/2-> sJow L a H ( E D T A )
(4)
-- 1)H+ fast :' L a 3+ + H x ( E D T A )
(5)
La3+ + H x ( E D T A ) ~ _ 4 fast ) L a ( E D T A ) - + x H +
(6)
Eu3+ + H ~ ( E D T A ) X _ 4 fast E u ( E D T A ) - + x H ÷ k-Eu
(7)
k-La
Eu(EDTA)- + H + ~
EuH(EDTA)
E u H ( E D T A ) + (x--l)H + fast ~ EU3+ + Hx(EDTA)~_4.
(8) (9)
T h e rate o f f o r m a t i o n (RF) o f E u ( E D T A ) - is given b y the rate o f dissociation o f L a ( E D T A ) - ( E q u a t i o n (4)) multiplied b y the probability that the free Hx ( E D T A ) x-4 reacts with Eu a÷ ( E q u a t i o n (7)) r a t h e r than L a 3÷ ( E q u a t i o n 6). RF = k L a [ H + ] [ L a ( E D T A ) 1-]
k_zu[Eu a+] k_La[La3+] + k_Eu[Eu3+] "
(~o)
T h e rate o f the r e v e r s e reaction, the dissociation o f the E u ( E D T A ) - Can be s h o w n to be e x p r e s s e d similarly as: k_La[Laa+]
Ro = k E u [ H + I [ E u ( E D T A p -] k_La[Laa+] + k_Eu[Eu3+] •
( 1 1)
T h e net rate is the difference b e t w e b n RF and Ro. H o w e v e r , u n d e r o u r conditions w h e r e b y the e x c h a n g e p r o c e e d s nearly to c o m p l e t i o n , the net rate is essentially e x p r e s s e d b y E q u a t i o n (10). M o r e o v e r , since [ L a 3÷] >> [Eu3+], the rate c a n be e x p r e s s e d by: R = kLak-Eu [H+][La(EDTA)I-][Eu3+] k-La [ L a a+]
(12)
Kinetics of exchange
13 3
This expression is exactly the same as the experimental rate equation (Equation (3)) with: kLak-Eu kr = = 1.08 × 10eM-lmin -'. k-La
Since the ratio k_La/kLa is the stability constant for the L a ( E D T A ) - complex, the value ofk-Eu, the rate constant for the fast reaction forming E u ( E D T A ) ' - , may be calculated to have a value 0f2.3 × 1022M-Zmin-'. If the exchange reaction does not go to completion, additional information can be obtained. This can be achieved by use of a tracer lanthanide ion whose E D T A complex is comparable in stability to that of La(EDTA) 1-. The system La ( E D T A ) ' - / C e 3+ is suitable in this respect. Alternately, incomplete reaction can be achieved by increasing the ratio L a 3 + / L a ( E D T A ) ~-. Exchange involving Eu 3+ and Am 3+ was studied by this approach. Assuming that the exchange mechanisms remain the same, Equation (13) expresses the reaction rate. R=
kLak-M [ H+ ] [ L a ( E D T A ) ' - ] [M 3+] k-La [La3+] kM[H+][M(EDTA)I-].
(13)
Since [H+], [La 3+] and [La(EDTA)'-] are constants in each run, the equation may be written simply as: dx R = -d-[ = ka(a -- X) - - k - A ( X ) (14) with ka = kL. • k-M. [H+][La(EDTA) '-] k-L~ [La 3+] and k - A = kM[H+]. 1.5 Am
•
I0
Ce
J
o -J
05
I I0
I 20 t , rain
Fig. 4.
30
23 22 24
Ce Eu Am
5.870 5.450
6.777
pH
1.04 1.40 140 4.0 0.4 0.4
Las+ La(EDTA)(M x 103) (M x 104) 0.091 0.0635 0.105
k (min-1)
8.5 6.1
745
k,, k--Mlk--La (M-l min-* X lo+) 25.7 2.28 1.21
X
1.63 1.9 1.3
k-M 10m4) (M-l min-’ X lo-**)
p = 0.5M, Acetate buffer = 0.02M b (M-l min-’
J. G. Schwarzenbach, R. Gut and G. Anderegg, Helv. chim. Acta 37.93 7 (1954). 8. J. Fuger,J. inorg. nucl. Chem. 5,332 (1958).
WC)
M(II1)
Table 2. Exchange rates in the system M(III) - - La(EDTA)-;
16.80 17.9 18.0
log K
Ref.
18.16[8]
17.34[7]
16~00[7]
log K
Kinetics of exchange
135
This b e c o m e s on integration the familiar equation for a first order reversible reaction. Figure 4 shows that plots of logxe/(xe-x) vs. t are straight lines for Ce :~+, Eu :~+ and A m 3÷. (Xe-----the equilibrium concentration of M ( E D T A ) -~ ). Values of kLa " k-M/k-La and kM can be calculated from the slopes of these lines and are tabulated in Table 2. T h e rate constant for the formation of the M ( E D T A ) 1 complexes, k-M, is calculated by multiplying the values of kLa" k-M/k-La by the t h e r m o d y n a m i c stability constant for L a ( E D T A ) -I and listed in Table 2 next to the dissociation rate constant, kM. While the formation rate constant is much larger, it is relatively invariant for the different metal ions whereas the dissociation rate constants show significant differences. T h e stability constants, K, for the M ( E D T A ) -1 complex formation are also listed in Table 2. C o m p a r i s o n of these values with literature values (/z = 0.1 M) in the last column of Table 2 show satisfactory agreement. It is obvious, then, that the variation in stability of the M ( E D T A ) -1 complexes is determined kinetically by the differences in the dissociation rate constants whereas the magnitude of the stability constant is determined predominantly by the very large association rate constants.
Acknowledgements-Thisresearch was supported by the U.S. Atomic Energy Commission. We wish to thank Mrs. K. R. Williams for her assistance. One of us (W.D'O) wishes to acknowledge financial assistance from the I. I. K.W. (Belgium)for a travel grant.