- Email: [email protected]
The kinetics of exchange between americium(III) and europium ethylenediaminetetraacetate
J. inorg,nucl. Chem., 1973,Vol. 35, pp. 4255-4269. PergamonPress. Printed in Great Britain.
THE KINETICS OF EXCHANGE BETWEEN AMERICIUM(III) A N D EUROPIUM ETHYLENEDIAMINETETRAACETATE G. R. CHOPPIN and K. R. WILLIAMS Department of Chemistry, Florida State University, Tallahassee, Florida 32306 (Received 15 February 1973) Abstract--The kinetics of exchange has been studied for Am a+ and EuEDTA- in an aqueous solution of 0"1 M total ionic strength with acetate buffer. It was found that the kinetic equation involved both acid dependent and acid independent terms, Possible mechanisms consistent with the complete rate equations of the two (acid dependent and acid independent) paths are proposed. The two paths have approximately equal probability at pH 6-4. An increase in the acetate buffer concentration increases the rate of the acid dependent pathway but decreases that of the acid independent one. The effects of buffer concentration can be explained in terms of complexation by acetate of either the free metal ions or the metal-EDTA complex. INTRODUCTION
THE KINETICS of the exchange reactions between lanthanide cations and lanthanide ethylenediaminetetraacetate complexes have been studied by a number of groups [ 1-9]. The kinetic expressions are consistent with a mechanism which involves the decomposition of the complex by protonation. This is followed by a rapid complexation of the ligand by the incoming metal ion. In contrast to this acid dependent mechanism, Asano et al.[2] found that the kinetics for the exchange of LuEDTA- and XVTLu3+ above pH 6 were consistent with an acid independent mechanism involving direct attack of the complex by a cation to form a binuclear intermediate. Glentworth et a/.[5] were not able to find support for such an acid independent mechanism for the reaction between CeEDTA- and 144Cea+, although the system CeDCTA- + 144CeS + did provide evidence for this mechanism. An investigation of the exchange of LaEDTA- with 152-4EuS+, 144Ce3+ and 24XAm3+ in this laboratory[9] gave data consistent with the acid dependent mechanism. Margerum[10] has discussed the evidence for both an acid dependent and an acid independent mechanism in the 1. R. H. Betts, O. F. Dahlinger and D. M. Munro, In Radioisotopes in Scientific Research (Edited by R. C. Extermann) Vol. II, p. 326. Pergamon Press, New York (1958). 2. T. Asano, S. Okada, K. Sakamoto, S. Taniguchi and Y. Kobayashi, Radioisotopes 14, 363 (1965); J. inorg, nucl. Chem. 31, 2127 (1969). 3. P. Szarvas and E. Briicher, Mh. Chem. 101, 1321 (1970). 4. E. Briicher and P. Szarvas, lnorg. Chim. Acta 4, 632 (1970). 5. P. Glentworth, B. Wiseall, C. L. Wright and A. J. Mahmood, J. inorg, nucl. Chem. 30, 967 (1968). 6. P. Glentworth and D. A. Newton, J. inorg, nucl. Chem. 33, 1701 (1971). 7. T. Shiokawa and T. Omori, Bull. chem. Soc. Japan 38, 1892 (1965). 8. W. D'Olieschlager, G. R. Choppin and K. R. Williams, J. inorg, nucl. Chem. 32, 3605 (1970). 9. W. D'Olieschlager and G. R. Choppin, J. inorg, nucl. Chem. 33, 127 (1971). 10. D.W. Margerum, Rec. Chem. Prog. 24, 237 (1963). 4255
4256
G. R. CHOPPIN and K. R. WILLIAMS
exchange reaction of transition metal ions and their aminopolycarboxylate complexes. In this paper we report the results of a study of the kinetics of exchange between EuEDTA- and 241Am3+. EXPERIMENTAL
Materials Europium chloride. A slight excess of Eu20 a (>99.9 ~ purity) from American Potash and Chemical Corporation was boiled in hydrochloric acid until the pH was neutral. The solution was filtered and the pH adjusted to about 2.5 with HCI. The europium concentration was determined by complexometric titration with standard disodium ethylenediaminetetraacetate, Na2EDTA, using a pH 5 acetate buffer and xylenol orange as indicator. Chelating agent. Na2EDTA. 2H20, from J. T. Baker Chemical Company, was dried at 85°C, checked for purity by potentiometric titration with standard NaOH, and used without further purification. A weighed amount of the disodium salt was dissolved in two equivalents of standard NaOH and diluted to a known volume. Acetate buffers. Acetic acid (1.00 N) was prepared from an Acculute from Anachemia Chemicals, Inc. according to the accompanying instructions. A 50 ml aliquot of this solution was brought to the required pH with 10 M NaOH, and the resulting solution was diluted to 250 ml. The concentration of total acetate in these stock solutions was 0-20 M. Sodi,m dlloridt'. Reagent grade NaCI from Matheson, Coleman and Bell was dried at 110°C, weighed, and diluted without further standardization. Radiotracer. Americium-241 was obtained from Oak Ridge National Laboratory. Chemical impurities were removed by ion exchange techniques. The purified solutions were evaporated to dryness and the residue redissolved in 0.01 M HC1. The Am-241 was checked by alpha spectroscopy for purity from other actinide elements. Reaction mixture. Appropriate aliquots of the Eu 3 ÷ and EuEDTA- solutions, 5.0 ml acetate buffer, and enough standard NaC1 to obtain a total ionic strength of 0.1 M (assuming complete dissociation of acetic acid) were placed in a small beaker. The pH was adjusted to the approximate desired value with dilute NaOH, and the solution was transferred and diluted to 50-0 ml. Ion exchange resin columns. Rapid, quantitative separation with a small eluant volume was provided by use of a column of cation exchange resin. A set of nine glass columns of 1.2 cm i.d. were filled to a depth of 1.7 cm with CGC-240 cation exchange resin, 100-200 R (J. T. Baker Chemical Co.) in the sodium form. Each column had a capillary of 5.7 cm length below the wide section. A 1 ml sample was passed through the resin bed in 10 sec and three 1 ml additions were required (also 10 sec passage time each) for complete rinsing of the bed (4 ml total collected volume). Before a run each column was equilibrated with 0-02 M acetate buffer of the same pH (+ 0.1 pH unit) as the reaction solution. Procedure Kinetics run. A stopwatch was started when the tracer (~ 250,000 counts/min) was added to the reaction solution. At fixed time intervals a 1 ml aliquot was withdrawn and passed through a column which was then rinsed with three 1 ml portions of acetate buffer. The eluant fractions were caught in a liquid scintillation vial containing scintillator solution. The aliquots were withdrawn from the reaction mixture for a time corresponding to two reaction half-life periods. (The half-lives ranged from about 15 min to about 40 min.) After a period equal to at least eight half-lives two equilibrium samples were taken. One was passed through a column, the other (the "total activity sample") was transferred directly to a scintillation vial which contained scintillator plus three ml of acetate buffer. Radioactivity measurements. All samples were counted on a Packard No. 3320 Liquid Scintillation Counter. The dioxane-cellosolve scintillator "cocktail" solution was prepared according to Bruno and Christian[l 1], except for the omission of the POPOP (1,4-bis[2-(5-phenyloxazolyl)]-benzene), which tended to precipitate in the present work. A slight shift ( < 0.2 per cent) in the spectral peak was noted for the total-activity sample because of the greater total ionic concentration, but this could usually be ignored. 11. G. A. Bruno and J. E. Christian, Analyt. Chem. 33, 1216 (1961).
Kinetics of exchange for A m 3 ÷ and E u E D T A -
4257
Determination oJ pH. In order to avoid problems caused by precipitation of KCIO4 in the frit of the reference electrode, a 0.1 M ionic m e d i u m was used with NaCI rather t h a n N a C 1 0 4 as the inert electrolyte. Measurements were made with an A. H. T h o m a s No. 4858-Q 15 combination electrode a n d a Beckmann Research p H Meter. Before each p H reading the electrode was standardized with an NBS phthalate buffer prepared according to Bates[12]. Since concentrations were used for all species, it was necessary to know the concentration of hydrogen ion (pcH) rather than its activity (pH). The combination electrode was calibrated as follows : a solution of 0-00100 N HC1 (# = 0.1 NaCI) was titrated potentiometrically with 0.00100 N N a O H (# = 0.1 M NaC1); the calculated pcH was plotted vs the measured p H and the straight line between pH ~ 3 and 4 was extrapolated to the region of interest (pH ~ 5.5-6.5). Results from two such runs were averaged to give an equation relating pcH to pH. This resulted in an estimated error in pcH of + 3 per cent. RESULTS
The overall equation for the exchange reaction is : EuEDTA-
+ A m 3÷ ~--~---Eu 3÷ + A m E D T A - .
(1)
D u r i n g each experiment the concentrations of E u E D T A - and Eu 3 + were constant and only the concentrations of A m 3 ÷ and A m E D T A - vary. Figure 1 s h o w s that the exchange obeys a reversible first-order rate law : Rate = k r [ A m 3÷] - k R [ A m E D T A - ].
(2)
The slope of this plot gives the first-order rate constant, k 1, which equals the sum of the forward and reverse rate constants (i.e. kl = kF + kR). 2.00
1-50
1-00
0"5
,
0
I
Time,
Fig. l. Plot
xe of In xe-x,
I
,
2000
I000
,
d
3000
sec
vs time for the exchange of A m 3 + and E u E D T A - at 25°C, 0.1 M
ionic strength, 0 . 0 2 M acetate, 2.51 x 1 0 - 6 M H +, 1.04 × 1 0 - a M E u E D T A - and 1.20 x 10- 3 M Eu 3 +. X e = specific activity of A m E D T A - at equilibrium and X~ = specific activity of A m E D T A - at time t. 12. R. G. Bates, J. Res. natn. Bur. Stand. A66, 179 (1962).
4258
G. R. CHOPPIN and K. R. WILLIAMS
I0"00f
O-04M/j
/// /// 0
8'00 r
/
~0 x 6.0C
//
/,//
/" "~"
4.00
2.00
0
I
I
1.00
I
I
2"00
,
I
3.00
,
!
4 O0
[H*], MxlO6 Fig. 2. Plot of kF vs [H÷] for Am3+/EuEDTA- systemstudied at three differentacetate concentrations(1.20 x 10-3 M Eu3+, 1.04 x 1 0 - 3 M EuEDTA-). Figure 2 shows the variation of k~ with hydrogen ion concentration for three different concentrations of acetate buffer. (Plots of kR give analogous results.) For each buffer concentration the data fit a straight line, indicating that the reaction is first-order with respect to hydrogen ion. Results of previous studies on the Am(III)/ EuEDTA- system[8, 9] have been shown to obey a rate law containing only aciddependent terms. However, Fig. 2 shows that the kl versus [H +] lines have measurable non-zero intercepts. The equations for kr and kR must contain, therefore, both aciddependent and acid-independent terms: kF = kA[H ÷] + kB
(3)
k R = k c[H + ] + k o.
(4)
In order to determine the dependency with respect to free and to complexed europium of both the acid-dependent and acid-independent terms, seven sets of concentrations of Eu 3+ and EuEDTA- were studied as a function of [H ÷] ([acetate] = 0.02 M; /~ = 0-1 M). Least squares slopes and intercepts were determined for each of the kr and kR vs [H +] lines. Table 1 lists the reaction conditions and the slopes. The data indicate that kc, the slope of the k R vs [H ÷] line, is independent of [Eu a÷] and [EuEDTA-]. Most of the values overlap within one standard error, and all overlap within + 2a. The average value of k c has an uncertainty of about 10 per cent. Likewise, when the slopes of the kF vs [H +] lines (i.e. ka) are divided by [EuEDTA-]/ [Eu 3+], constant values are obtained. Again, all the values overlap within + 2a, and the uncertainty in the average is 10 per cent.
[EuEDTA-]
(M x 10 3)
1.04 0.714 0-714 1.43 2.14 1.79 0-893
[Eu 3 +]
(M x 10 ~)
1-20 1.27 1.67 4-60 1.50 1.91 2.19 1.15 1-78 2.34 3.22 0.701 1.07 2.45
[EuEDTA-]
jell 3 +]
_ ± ± ± ± ± ±
0.04 0-01 0.026 0.031 0.10 0.09 0.025
I × 10-z)
Average values
1-60 1.03 0.716 0.691 2.42 1.69 0-816
(M-lsec
k A = slope kF
+ 0.03 ± 0.03 _+ 0.04 ± 0.12 +_ 0-04 ± 0.06 ± 0.06
1 x 10 -2)
1.39 ± 0.13
1.34 1.38 1.23 1.55 1-25 1.43 1.53
(M-lsec
k c = slope k R
Table 1. Variation of slopes of k e and k R vs [H ÷] lines with changes in [Eu 3 +] and [ E u E D T A - ] Am 3+ + E u E D T A - ~ E u 3+ + A m E D T A [acetate] = 0.02 M ; # = 0.1 M ; 25°C [EuEDTA-] [Eu3+]
0.04 0-02 0.06 0.10 0-07 0-09 0.06 1.87 ± 0.19
1.83 ± 1-83 ± 1.68 ± 2.23 ± 1-70 ± 1.81 ± 2-00 +
(M -1 sec -1 x 10 -z)
k~l = kA :-
to +
T~
I
-q
e~
O
4260
G. R. CHOPPIN and K. R. WILLIAMS 20"0¢
15'00 x •
I 0'00
/ J o• •
/
5.00
0
2"100
4.00'
'
6'-00
[Eu 3+] or [Eu EDTA-], MxlO 3 Fig. 3. Plots ofke vs [EuEDTA-] and ko vs [Eu3+].
These results for the acid-dependent terms indicate that the forms of the rate equations are: k r = k~
[EuEDTA - ] [H +] [Eua+] + k8
k g = kcEH +] .-[-.ko.
(5) (6)
Now, let us consider the acid-independent terms. Figure 3 shows that reasonably good straight lines are obtained when the values of kB vs [ E u E D T A - ] and of kD vs [Eu 3÷ ] are plotted. This indicates that the acid-independent term is first-order with respect to EuEDTA - for the forward reaction and first-order with respect to Eu 3 + for the reverse reaction. Values of kB/[EuEDTA-] ( = k~) and kD/[Eu a +] (=k~) are given in Table 2. The respective values for k~ and k~ overlap one another within one standard error and the average Values are uncertain by about 16 per cent. As we mentioned above, the reaction was studied as a function of hydrogen ion concentration for three different concentrations of acetate buffer. Table 3 lists the values of k'a, k'B, kc and k'D for each acetate concentratiori. The rate constants for the acid-dependent mechanism (k~ and kc) increase with an increase in acetate concentration but the rate constants for the acid-independent mechanism (k~ and kb) decrease. The order of the reaction with respect to total acetate could be determined accurately only for k~ and kc. Figure 4 shows plots of k~ and k c vs total acetate concentration. The linear plots both have large intercepts. Thus, k~ and k c are given by: kat = k~[acetate] + kcm
kc = kc[acetate] + k~
ks [EuEDTA ]
± + + ± + + ±
0.76 0.23 0-44 0.35 0.57 0-64 0.41
4.54 ± 0.65
3.92 3.51 5-35 4.67 4-81 5-13 4.38
(M - I sec-l x 102)
k~
2.53 ± 0.02 1,87 _ 0.19 1.56 ± 0.09
0.04 0.02 0.008
0.798 + 0.386 4.54 + 0.65 7.57 + 1.92
k'n (M I sec-I x 102)
k'a
( M - i s e c -1 × 10 2)
[Total acetate] M
1.818 ___ 0.001 1-39 + 0.13 1.18 4- 0.07
( M - l sec -~ × 10 -2)
kc
Table 3. The effect of acetate buffer concentration on the slopes and intercepts of k e and k R vs [H +] plots Am 3+ + E u E D T A - ~ - E u 3+ + A m E D T A [Eu 3+] = 1.20 x 10 -3 M; [ E u E D T A - ] = 1,04 x 10 -3 M; tt = 0-1 M; 25°C
Average values
+ 0-63 + 0,37 + 0-46 + 1.9 ± 0.47 + 0,82 -4- 0-93
3-62 2.93 6.53 16-2 5-15 6.41 6.15
0.79 0.16 0.31 0-50 1-21 1-15 0-36
4-08 2.51 3.82 6.68 10-3 9-19 3.91
1.04 0,714 0.714 1.43 2.14 1.79 0.893
1.20 1.27 1,67 4,60 1.50 1.91 2.19
+ + + + + + ±
(sec-~ x 105)
(sec -~ x 105)
(M x 103)
(M x 103)
lntcp, k R
k O =
kn = lntcp, k F
[EuEDTA-]
[EU3+]
Table 2. Variation of intercepts of ke and k R vs [H +] lines with changes in [Eu 3 +] and [ E u E D T A - ] Am 3+ + E u E D T A - ~ E u 3+ + A m E D T A [acetate] = 0.02 M; ,u = 0,1 M; 25°C
+ ± ± + _ + _
0.53 0-29 0.28 0-41 0.32 0.43 0.43
0.663 + 0.016 3-19 + 0.53 5.64 + 1.40
( M - I sec -1 × 102)
k'D
3.19 _+ 0-53
3.02 2.31 3.91 3,53 3.43 3.35 2.81
(M - l s e c - t x 102)
ko k~ = [Eu3+~
t-.
e~
+
,-t
4262
G . R . CHOPPIN and K. R. WILLIAMS 3-0C
'o x 2.00
I'00
,'o
2%
3)0
[Acetofe]
,!oo
'
5"00
M x 10 2
,
Fig. 4. Plots of k~ and kc vs total acetate concentration.
where k a = 3.06 _+ 0.19 x 10 3 M - 2 sec- 1 ; ka 1.29 + 0.05 x 102 M- 1sec- 1, kc 2.01 __+0.10 x 1 0 3 M - 2 s e c - 1 and k~ = 1.01 ___0.03 × 102 M -1 sec -1. vv
tvv
-~
.
!
DISCUSSION
The results indicate that in the pH range of 5.5-6-5 and at constant acetate buffer concentration, the exchange of trivalent americium with EuEDTA- obeys the following overall rate law : Rate=
{
k~
[EuEDTA-][Am3+]_kc[AmEDTA-~}[H+ ] [Eu3+]
(7)
+ {k~[EuEDTA-] [Am a +] - kb[Eu 3 +] [AmEDTA-]}. This expression correlates with a reaction which proceeds via two pathways; the first set of brackets can be associated with an acid-catalyzed mechanism while the second set represents an acid-independent reaction path.
Acid-independent mechanism For exchange reactions of the transition metals with transition metal-aminopolycarboxylate complexes, Margerum has proposed that an acid-independent (i.e. direct) pathway involves the formation of a binuclear intermediate, M'EDTAM[10]. It would seem reasonable that such a mechanism is also involved in the EDTA exchange between lanthanide and actinide ions. NMR data[13] on LnEDTA- complexes indicate that the carboxylate groups of the ligand are rapidly coordinating with and dissociating from the metal ion. It seems probable that in the first step of the acid-independent mechanism the free americium ion approaches the EDTA complex and forms a bond to a carboxylate group which is momentarily uncoordinated (Eqn. 8). The bond between the americium ion and the ligand should be very labile and dissociate readily. However, if the americium ion bonds to another carboxylate group before it dissociates from the 13. T. H. Siddall, III and W. E. Stewart, Inorg. nucl. Chem. Lett. 5, 421 (1969).
Kinetics of exchange for Am 3 ÷ and E u E D T A -
4263
first, a binuclear complex with two carboxylate groups bonded to each metal ion, E w - E D T A = A m 2+, is formed as in Eqn (9). This complex would react to form either E u = E D T A - - A m 2+ or a complex with three bonds to the americium A m ~ E D T A - - E u ~+ species. The steps in such a mechanism m a y be written: kl
E u E D T A - + Am 3+ ~-- E u ~ E D T A - - A m 2+
(8)
k2
Eu~--EDTA--Am2 * ~-2 E u = E D T A = A m 2 +
(9)
k3
E u = E D T A = A m 2 ~ ~---3E u - - E D T A ~ A m 2 +
(10)
k4
E u - - E D T A ~ A m 2 + kL--~Eu3+ -r- A m E D T A .
(11)
The rate of formation of the binuclear intermediate, E u = E D T A = A m : +, from E u E D T A - and Am 3 ÷ is the rate of formation of E u = E D T A - - A m 2+ times the probability that the latter would form Eu-----EDTA=Am 2 ÷ instead of returning to the reactants. Therefore, the rate of formation of E u = E D T A = A m 2 ÷ from Am 3 + and E u E D T A - would be :
= kl[EuEDTA-][Am3+~ (k2 +k2k_I ) (12a)
-- klk2 [ E u E D T A - ] [Am 3 +1 k_l
k2).
(since k_ 1 >> Likewise, the rate of formation o f E u - - E D T A = A m 2 ÷ from Eu 3 + and A m E D T A is: _ k_ 4k_ 3 [ A m E D T A - ][Eu 3 + ]. k4
(12b)
The rate of dissociation of E u = E D T A = A m 2 + to A m E D T A - and Eu 3 ÷ is the rate of reaction to form E u - - E D T A ~ A m 2 ÷ times the probability that this complex would dissociate to the products rather than form Eu=EDTA-----Am 2 ÷ again. The rate of dissociation of E u = E D T A = A m 2 ÷ to A m E D T A - and Eu 3 + can be written as
k4
= k3[Eu=EDTA=Am2÷](k-3 + kf~)
(13)
= k 3[E u = E D T A = A m 2 * (since k4 >> k_ 3)Similarly the rate of dissociation of E u = E D T A = A m E u E D T A - is = k_ 2 [ E u = E D T A = A m 2 +].
2+ into Am 3÷ and (14)
In the forward direction only the A m E D T A - which is formed from E u E D T A and Am 3 ÷ should be considered. Thus, the rate of the forward reaction is the rate of
4264
O . R . CHOPPIN and K. R. WILLIAMS
formation of Eu--=--EDTA--Am2÷ from EuEDTA- and Am 3 ÷ times the probability that Eu-----EDTA=Am 2÷ reacts to form AmEDTA- and Eu 3 ÷ instead of EuEDTAand Am a+. kl Thus, the forward rate can be expressed, since K 1 = ~-~-1' by Forward rate = K1 "k2. k3 [EuEDTA- ] JAm3 +]. k3 +k--2
(15)
By an analogous treatment the rate of the reverse reaction is given by k_ 3. k_ 2 [Eu 3+] [AmEDTA-]. Reverse rate = K-4. k 3 + k_2
(16)
The overall rate of reaction by the acid-independent pathway is given by the difference between equations (15) and (16): Rate = KI" k2" k3 [EuEDTA-] JAm 3+] - K - 4 " k-3" k-2 [Eu 3+] [AmEDTA-]. (17) k3 + k-2 k3 + k-2 This expression shows that the mechanism is consistent with the experimental data since it is the same as that in the second set of brackets in Eqn (7), where
k~--- /(1 • k2. k3 k3 + k-2
and
(18)
k'D= K_a.k_3.k_2 k3 + k-2 An increase in the concentration of acetate results in a decrease in the reaction rate by the acid-independent mechanism. The rate may be affected by acetate complexation of both the free metal ions and the EDTA complexes. Complexation of the free metal ions should occur to a greater extent than mixed complex formation, and it is expected that the formation of the europium and americium acetate complexes has the more pronounced effect on the reaction rate. Formation of the acetate complexes results in an effective decrease in the concentrations of the free metal ions. Because the metal ion acetate species do not have as great a positive charge as the free metal ions, the acetate complexes will not be attracted to the EDTA complex as strongly as the uncomplexed metal cations. Thus, the effects of replacing free Eu a ÷ and Am a ÷ by their acetate complexes are reductions in K1 and K_ ~, the equilibrium constants for the formation of the first carboxylate bond to the metal ion. The decreases in K1 and K-4 may be modified somewhat by the presence of mixed EDTA + acetate complexes, which have an increased negative charge and would be attracted better to the free metal ions. However, because the concentration of mixed complexes should be very small, their effect on the reaction rate should not be appreciable.
Acid-dependent mechanism There has been disagreement in the literature on the nature of the acid-catalyzed
Kinetics of exchange for Am 3÷ and EuEDTA
4265
pathway. The kinetic results have been used to support both a slow protonation step followed by rapid dissociation and, conversely, a rapid protonation equilibrium followed by slow dissociation. Nyssen and Margerum[141 used a stopped flow technique to measure the rate of formation of LaDCTA- from La 3 ÷ and H2DCTA 2-. Their results indicated that the metal and ligand reacted very rapidly to release the first proton and form the metastable complex *HLaDCTA, which deprotonated at a measurable rate. Thus the slow step in the formation of LaDCTA- is the release of the last proton. It is likely, then, that the slow step in the formation of EDTA complexes of the lanthanide and actinide ions also involves deprotonation. By the principle of microscopic reversibility it can be argued that the protonation of LnEDTA- must be the slow step in the dissociation reaction. That protonation is a slow step is surprising, because as Eigen et a/.[15] have indicated, proton transfer reactions are usually very rapid. The proton passes along hydrogen bonds which bridge the hydration spheres of the protonated species and the base. It is likely, therefore, that protonation actually involves two steps. In the first step there is a rapid protonation equilibrium. This equilibrium is followed by a second, slow step, in which the protonated complex is converted to a form which rapidly dissociates to the free metal and free protonated EDTA. It is necessary first of all to consider the protonation equilibrium itself. In free EDTA the nitrogens are the most basic atoms and are protonated before the carboxyl groups. Because the lanthanide and actinide ions form complexes primarily with oxygen donors, it is likely that the nitrogens are coordinated very weakly to the metal ion. Thus, the nitrogens should be better proton acceptors than the carboxylate oxygens. However, in the lanthanide or actinide EDTA complexes the bond angles are such that the proton cannot become attached to a nitrogen. Thus, it is necessary to assume that the rapid protonation equilibrium involves carboxylate oxygen protonation. There are two possibilities for the second, slow step: (1) the other carboxylate group in the same iminodiacetate moiety as the protonated carboxylate group may become dissociated while the proton still remains on the complex. The remaining two carboxylate groups should then be able to dissociate rapidly from the metal ion. (2) Once a carboxylate group has dissociated from the metal ion the nearest nitrogen is exposed to attack by a proton. The second step may, therefore, involve the transfer of the proton from the carboxylate oxygen to the nitrogen. This process may be a proton transfer or may involve the formation of a hydrogen bond in which the proton is attached to both the nitrogen and the carboxylate oxygen. The formation of hydrogen bonds in free EDTA between the proton on nitrogen and the carboxylate groups has been proposed by Chapman et al.[16] to explain their P M R and infrared data. In either case, once the nitrogen is protonated, reformation of the metal ioncarboxylate chelate ring is blocked and the ligand can dissociate rapidly. In both 14. G. A. Nyssen and D. W. Margerum, lnorg. Chem. 9, 1814 (1970). 15. M. Eigen, W. Kruse, G. Maass and L. DeMaeyer, In Progress in Reaction Kinetics (Edited by G. Porter) Vol. 2, Chapter 6. Macmillan, New York (1964). 16. D. Chapman, D. R. Lloyd and R. H. Prince, J. chem. Soc. 3645 (1963).
4266
G.R.
CHOPPIN
a n d K . R. W I L L I A M S
mechanisms (1) and (2) the ligand picks up the additional protons which it requires as it leaves the metal ion. The first step in the reverse reaction would for both possible mechanisms be the rapid complexation of the two carboxylate groups on one of the iminodiacetate moieties. For mechanism (1) formation of the third carboxylate bond would be ratedetermining. Deprotonation then would occur rapidly. In mechanism (2) the formation of the third carboxylate bond would also be rapid. The rate-determining step would be the transfer of the proton from the nitrogen to the oxygen. Final deprotonation would occur rapidly. It is difficult from our data to decide between mechanisms (1) and (2). However, both cases can be represented by the following mechanism, in which *HEuEDTA and *HAmEDTA represent the metastable protonated complexes. k-lE
EuEDTA- + H + ~
HEuEDTA
(19)
k - 2n
HEuEDTA k~ *HEuEDTA
(20)
k- 3E
*HEuEDTA + (x - 1)H + k~ Hx EDTA4-x + Eu3+
(21)
k3a
Ama+ + H~EDTA4-x k-~A *HAmEDTA + (x - 1)H +
(22)
k2A
*HAmEDTA k-~-~aHAmEDTA
(23)
klA
HAmEDTA k_'7~AmEDTA- + H +.
(24)
The rate of formation of HxEDTA 4-x from EuEDTA- is the rate of formation of HEuEDTA [Eqn (19)] times the probability of forming *HEuEDTA from HEuEDTA [Eqn (20)] all times the probability of forming H~EDTA 4-x from *HEuEDTA [Eqn (21)]. Rate of formation of HxEDTA 4-x from EuEDTA= k_,E[EuEDTA-] [H +] k_2g +
k,E]/k_ 3e-~H+]._---------q ~ k2r]
(25)
= K_ ~ek_ 2~.[EuEDTA- ] [H +] because klE >> I.n.-2E,k - 3 E l -r H + l/X - 1 >> k2m and K_,4 = k-lEl" kl e j Likewise the rate of formation of H,EDTA 4-* from AmEDTA= K_ l ak- 2a [AmEDTA] [H +].
(26)
The rate of formation of AmEDTA- from H,EDTA 4-x and Am 3 ÷ is the rate of formation of *HAmEDTA [Eqn (22)] times the probability of forming HAmEDTA from *HAmEDTA [Eqn (23)], all times the probability of forming AmEDTA- from
Kinetics of exchange for Am3+ and EuEDTA
4267
HAmEDTA. Thus the rate
+ k-3A k2A "
+ k-2A'/ (27)
[HxEDTA 4- x] = K3Ak2A[Am 3+ ]
[H-~Y
(because k_aA[I2I+] ~-l >> k2A,kl.4 >> k_2a , and K3A = _~3~ k_3A I. l In a similar manner the rate of formation of E u E D T A - from HxEDTA 4-* and Eu 3 +
[Eu 3 + ] [HxEDTA 4- ~] = K3Ek21 ~
(28)
[H+]X_ 1
The rate of formation of A m E D T A - from E u E D T A - and Am 3 + is the rate of formation of H~EDTA 4-x from E u E D T A [Eqn (25)] times the probability that the free HxEDTA '~-x will react with Am 3 + [Eqn (27)] instead of with Eu 3 ÷ [Eqn (28)]. Rate of formation of A m E D T A - from E u E D T A - and Am 3 + .....
/~3AK2ALA m
3+ . , / [ H x E D T A 4 - q l J]~
~
)
= K_ 1Ek - 2E[ E u E D T A - ] [H + ] (K3ek2~[Eu3+] + = K_ 1EK_ 2I~K_ 3EK3,1k2A
K
k ~A 3+"[[H*EDTA4-X]/ 34 2AL m 9 / [H---~i~ ]
[ E u E D T A - ] [H+] [Am 3 + ] [Eu3 +]
(29)
(because K3~k2~[Eu a+] >> K3Ak2A[Am 3+] and K_2~ -- -*-2~/ k2~ ]" Likewise, the rate of formation of E u E D T A - from A m E D T A - and Eu 3 + is the rate of formation of HxEDTA 4-x from A m E D T A - [Eqn (26)] times the probability that the free HxEDTA 4-~ will react with Eu 3+ [Eqn (28)] instead of with Am 3÷ [Eqn (27)]. Rate of formation of E u E D T A - from A m E D T A - and Eu 3 ÷ K = K_ l a k - 2A[ A m E D T A - ] [H + ]
'
~" 3+~/[H~EDTA4-~]/
~2~u ~/ EN---~ J E D T A 4 - x)) ,~3~AL~m3 + ~J'/, / [ H x~_~
(Kaek2E[Eu 3+] + . . . . .
= K_ 1Ak_2~[AmEDTA-1 [H +]
(30)
(because Kaek2e[Eu a +] ;> K3Ak2,4[Am 3 +]). The overall rate by the acid-dependent pathway is the difference between Eqn (29) and Eqn (30).
4268
G.R. CHOPPIN and K. R. WILLIAMS Rate = K_ 1EK_ 2EK_ aEK3Ak2A
[EuEDTA-] [H +] JAm 3+] [Eu3 +] (31)
-
K_ 1Ak_ 2A[H+] [AmEDTA- ].
This expression is the same as the first term in Eqn (7) where k'a = K_ 1EK_ 2EK- 3EKaAk2A
(32)
and kc = K-1Ak-2A.
Thus, the proposed mechanism is found to agree with the experimentally determined rate law. From our data it is possible to calculate that the ratio of the rate by the aciddependent mechanism to that by the acid-independent mechanism. F o r b o t h the forward and reverse reactions this ratio has a value of approximately 40 at pcH 5, 4 at pcH 6 and 0.4 at pcH 7. The two mechanisms have approximately equal rates and hence equal probability at a pcH of approximately 6.4 under our experimental conditions. The effect of buffer concentration on the rate of the acid-dependent pathway is opposite to that by the independent mechanism; an increase in buffer concentration results in an increase in the reaction rate. This result was also obtained by Briicher et al.[17] and by Glentworth et al.[5] who also studied the effects of buffer concentration on the acid-dependent mechanism. The rate increase may be caused by either: (1) complexation of the free metal ions by the buffer anions, (2) complexation by the buffer anions of the LnEDTA- complexes (i.e. mixed complex formation), or (3) catalysis by the undissociated buffer acid. In our proposed mechanism for the acid-dependent pathway only the formation of the first three carboxylate bonds to the metal ion can be affected by acetate complexation of the free metal ions. The equilibrium constants K3A and K_3E both appear in k~. However, the effects on K_ 3Eand K3Aa r e expected to offset one another and to produce no significant change in k~. Thus, neither kc, which contains no contribution from these two equilibria, nor k~ is affected by the formation of acetate complexes with the free metal ion. Neither the data of Briicher for the Cu2+/TbEDTA - system nor those of the present study exclude the possibility of catalysis by the undissociated buffer acid. However, Glentworth et al. have compared the effects of acetate on the rates of isotopic exchange of Ce 3+ with CeHEDTA, CeEDTA- and CeDCTA-. The increase in rate by the acid-dependent pathway is ten times greater for CeHEDTA than for CeEDTA- and 2.7 times greater for CeEDTA- than for CeDCTA-. It is difficult to rationalize the relative magnitudes of the acetate effect by consideration of catalysis by undissociated acetic acid. The importance of mixed complex formation on the rate of the acid-dependent pathway has been discussed by Briicher and Glentworth and we also favor this 17. E. Briicherand M. Szihlgyi,In Proceedingsof the Third Symposium on Coordination Chemistry (Edited by M. T. Beck)p. 323. AkademiaiKiado,Budapest(1970).
Kinetics of exchange for Am 3+ and EuEDTA-
4269
explanation. In our proposed mechanism the increased negative charges of the Eu(EDTA)(OAc) 2- and Am(EDTA)(OAc) 2- complexes should cause the protonation equilibrium constants K_I~ and K-IA to increase. Unfortunately, it is not possible to differentiate between the two possibilities for the slow reaction step. The extra acetate ligand on the EDTA complex should cause a general loosening of the metal ion-EDTA bonds. Thus, in proposed mechanism (1) the second carboxylate bond should dissociate more readily. Also, the nitrogens should be located farther from the metal ion and should be more available to attack by a proton as in mechanism (2). As Glentworth has already indicated, the different increases in rate for the three systems studied by his group can also be explained in terms of mixed complex formation. HEDTA has only three carboxylate groups; EDTA and DCTA each have four. Because CeHEDTA contains fewer chelate rings and is neutrally charged, formation of the mixed complex Ce(HEDTA)(OAc)- may be less hindered than formation of Ce(EDTA)(OAc) 2- or Ce(DCTA)(OAc) 2-. The fact that t h e Ce 3÷/CeDCTA- system is relatively insensitive to acetate catalysis may be due to the different steric requirements of that ligand. Acknowledgement--This research was supported by the USAEC under Contract AT-(40-1)-1709. KRW wishes to acknowledge the assistance of NSF and NDEA predoctoral fellowships.
THE KINETICS OF EXCHANGE BETWEEN AMERICIUM(III) A N D EUROPIUM ETHYLENEDIAMINETETRAACETATE G. R. CHOPPIN and K. R. WILLIAMS Department of Chemistry, Florida State University, Tallahassee, Florida 32306 (Received 15 February 1973) Abstract--The kinetics of exchange has been studied for Am a+ and EuEDTA- in an aqueous solution of 0"1 M total ionic strength with acetate buffer. It was found that the kinetic equation involved both acid dependent and acid independent terms, Possible mechanisms consistent with the complete rate equations of the two (acid dependent and acid independent) paths are proposed. The two paths have approximately equal probability at pH 6-4. An increase in the acetate buffer concentration increases the rate of the acid dependent pathway but decreases that of the acid independent one. The effects of buffer concentration can be explained in terms of complexation by acetate of either the free metal ions or the metal-EDTA complex. INTRODUCTION
THE KINETICS of the exchange reactions between lanthanide cations and lanthanide ethylenediaminetetraacetate complexes have been studied by a number of groups [ 1-9]. The kinetic expressions are consistent with a mechanism which involves the decomposition of the complex by protonation. This is followed by a rapid complexation of the ligand by the incoming metal ion. In contrast to this acid dependent mechanism, Asano et al.[2] found that the kinetics for the exchange of LuEDTA- and XVTLu3+ above pH 6 were consistent with an acid independent mechanism involving direct attack of the complex by a cation to form a binuclear intermediate. Glentworth et a/.[5] were not able to find support for such an acid independent mechanism for the reaction between CeEDTA- and 144Cea+, although the system CeDCTA- + 144CeS + did provide evidence for this mechanism. An investigation of the exchange of LaEDTA- with 152-4EuS+, 144Ce3+ and 24XAm3+ in this laboratory[9] gave data consistent with the acid dependent mechanism. Margerum[10] has discussed the evidence for both an acid dependent and an acid independent mechanism in the 1. R. H. Betts, O. F. Dahlinger and D. M. Munro, In Radioisotopes in Scientific Research (Edited by R. C. Extermann) Vol. II, p. 326. Pergamon Press, New York (1958). 2. T. Asano, S. Okada, K. Sakamoto, S. Taniguchi and Y. Kobayashi, Radioisotopes 14, 363 (1965); J. inorg, nucl. Chem. 31, 2127 (1969). 3. P. Szarvas and E. Briicher, Mh. Chem. 101, 1321 (1970). 4. E. Briicher and P. Szarvas, lnorg. Chim. Acta 4, 632 (1970). 5. P. Glentworth, B. Wiseall, C. L. Wright and A. J. Mahmood, J. inorg, nucl. Chem. 30, 967 (1968). 6. P. Glentworth and D. A. Newton, J. inorg, nucl. Chem. 33, 1701 (1971). 7. T. Shiokawa and T. Omori, Bull. chem. Soc. Japan 38, 1892 (1965). 8. W. D'Olieschlager, G. R. Choppin and K. R. Williams, J. inorg, nucl. Chem. 32, 3605 (1970). 9. W. D'Olieschlager and G. R. Choppin, J. inorg, nucl. Chem. 33, 127 (1971). 10. D.W. Margerum, Rec. Chem. Prog. 24, 237 (1963). 4255
4256
G. R. CHOPPIN and K. R. WILLIAMS
exchange reaction of transition metal ions and their aminopolycarboxylate complexes. In this paper we report the results of a study of the kinetics of exchange between EuEDTA- and 241Am3+. EXPERIMENTAL
Materials Europium chloride. A slight excess of Eu20 a (>99.9 ~ purity) from American Potash and Chemical Corporation was boiled in hydrochloric acid until the pH was neutral. The solution was filtered and the pH adjusted to about 2.5 with HCI. The europium concentration was determined by complexometric titration with standard disodium ethylenediaminetetraacetate, Na2EDTA, using a pH 5 acetate buffer and xylenol orange as indicator. Chelating agent. Na2EDTA. 2H20, from J. T. Baker Chemical Company, was dried at 85°C, checked for purity by potentiometric titration with standard NaOH, and used without further purification. A weighed amount of the disodium salt was dissolved in two equivalents of standard NaOH and diluted to a known volume. Acetate buffers. Acetic acid (1.00 N) was prepared from an Acculute from Anachemia Chemicals, Inc. according to the accompanying instructions. A 50 ml aliquot of this solution was brought to the required pH with 10 M NaOH, and the resulting solution was diluted to 250 ml. The concentration of total acetate in these stock solutions was 0-20 M. Sodi,m dlloridt'. Reagent grade NaCI from Matheson, Coleman and Bell was dried at 110°C, weighed, and diluted without further standardization. Radiotracer. Americium-241 was obtained from Oak Ridge National Laboratory. Chemical impurities were removed by ion exchange techniques. The purified solutions were evaporated to dryness and the residue redissolved in 0.01 M HC1. The Am-241 was checked by alpha spectroscopy for purity from other actinide elements. Reaction mixture. Appropriate aliquots of the Eu 3 ÷ and EuEDTA- solutions, 5.0 ml acetate buffer, and enough standard NaC1 to obtain a total ionic strength of 0.1 M (assuming complete dissociation of acetic acid) were placed in a small beaker. The pH was adjusted to the approximate desired value with dilute NaOH, and the solution was transferred and diluted to 50-0 ml. Ion exchange resin columns. Rapid, quantitative separation with a small eluant volume was provided by use of a column of cation exchange resin. A set of nine glass columns of 1.2 cm i.d. were filled to a depth of 1.7 cm with CGC-240 cation exchange resin, 100-200 R (J. T. Baker Chemical Co.) in the sodium form. Each column had a capillary of 5.7 cm length below the wide section. A 1 ml sample was passed through the resin bed in 10 sec and three 1 ml additions were required (also 10 sec passage time each) for complete rinsing of the bed (4 ml total collected volume). Before a run each column was equilibrated with 0-02 M acetate buffer of the same pH (+ 0.1 pH unit) as the reaction solution. Procedure Kinetics run. A stopwatch was started when the tracer (~ 250,000 counts/min) was added to the reaction solution. At fixed time intervals a 1 ml aliquot was withdrawn and passed through a column which was then rinsed with three 1 ml portions of acetate buffer. The eluant fractions were caught in a liquid scintillation vial containing scintillator solution. The aliquots were withdrawn from the reaction mixture for a time corresponding to two reaction half-life periods. (The half-lives ranged from about 15 min to about 40 min.) After a period equal to at least eight half-lives two equilibrium samples were taken. One was passed through a column, the other (the "total activity sample") was transferred directly to a scintillation vial which contained scintillator plus three ml of acetate buffer. Radioactivity measurements. All samples were counted on a Packard No. 3320 Liquid Scintillation Counter. The dioxane-cellosolve scintillator "cocktail" solution was prepared according to Bruno and Christian[l 1], except for the omission of the POPOP (1,4-bis[2-(5-phenyloxazolyl)]-benzene), which tended to precipitate in the present work. A slight shift ( < 0.2 per cent) in the spectral peak was noted for the total-activity sample because of the greater total ionic concentration, but this could usually be ignored. 11. G. A. Bruno and J. E. Christian, Analyt. Chem. 33, 1216 (1961).
Kinetics of exchange for A m 3 ÷ and E u E D T A -
4257
Determination oJ pH. In order to avoid problems caused by precipitation of KCIO4 in the frit of the reference electrode, a 0.1 M ionic m e d i u m was used with NaCI rather t h a n N a C 1 0 4 as the inert electrolyte. Measurements were made with an A. H. T h o m a s No. 4858-Q 15 combination electrode a n d a Beckmann Research p H Meter. Before each p H reading the electrode was standardized with an NBS phthalate buffer prepared according to Bates[12]. Since concentrations were used for all species, it was necessary to know the concentration of hydrogen ion (pcH) rather than its activity (pH). The combination electrode was calibrated as follows : a solution of 0-00100 N HC1 (# = 0.1 NaCI) was titrated potentiometrically with 0.00100 N N a O H (# = 0.1 M NaC1); the calculated pcH was plotted vs the measured p H and the straight line between pH ~ 3 and 4 was extrapolated to the region of interest (pH ~ 5.5-6.5). Results from two such runs were averaged to give an equation relating pcH to pH. This resulted in an estimated error in pcH of + 3 per cent. RESULTS
The overall equation for the exchange reaction is : EuEDTA-
+ A m 3÷ ~--~---Eu 3÷ + A m E D T A - .
(1)
D u r i n g each experiment the concentrations of E u E D T A - and Eu 3 + were constant and only the concentrations of A m 3 ÷ and A m E D T A - vary. Figure 1 s h o w s that the exchange obeys a reversible first-order rate law : Rate = k r [ A m 3÷] - k R [ A m E D T A - ].
(2)
The slope of this plot gives the first-order rate constant, k 1, which equals the sum of the forward and reverse rate constants (i.e. kl = kF + kR). 2.00
1-50
1-00
0"5
,
0
I
Time,
Fig. l. Plot
xe of In xe-x,
I
,
2000
I000
,
d
3000
sec
vs time for the exchange of A m 3 + and E u E D T A - at 25°C, 0.1 M
ionic strength, 0 . 0 2 M acetate, 2.51 x 1 0 - 6 M H +, 1.04 × 1 0 - a M E u E D T A - and 1.20 x 10- 3 M Eu 3 +. X e = specific activity of A m E D T A - at equilibrium and X~ = specific activity of A m E D T A - at time t. 12. R. G. Bates, J. Res. natn. Bur. Stand. A66, 179 (1962).
4258
G. R. CHOPPIN and K. R. WILLIAMS
I0"00f
O-04M/j
/// /// 0
8'00 r
/
~0 x 6.0C
//
/,//
/" "~"
4.00
2.00
0
I
I
1.00
I
I
2"00
,
I
3.00
,
!
4 O0
[H*], MxlO6 Fig. 2. Plot of kF vs [H÷] for Am3+/EuEDTA- systemstudied at three differentacetate concentrations(1.20 x 10-3 M Eu3+, 1.04 x 1 0 - 3 M EuEDTA-). Figure 2 shows the variation of k~ with hydrogen ion concentration for three different concentrations of acetate buffer. (Plots of kR give analogous results.) For each buffer concentration the data fit a straight line, indicating that the reaction is first-order with respect to hydrogen ion. Results of previous studies on the Am(III)/ EuEDTA- system[8, 9] have been shown to obey a rate law containing only aciddependent terms. However, Fig. 2 shows that the kl versus [H +] lines have measurable non-zero intercepts. The equations for kr and kR must contain, therefore, both aciddependent and acid-independent terms: kF = kA[H ÷] + kB
(3)
k R = k c[H + ] + k o.
(4)
In order to determine the dependency with respect to free and to complexed europium of both the acid-dependent and acid-independent terms, seven sets of concentrations of Eu 3+ and EuEDTA- were studied as a function of [H ÷] ([acetate] = 0.02 M; /~ = 0-1 M). Least squares slopes and intercepts were determined for each of the kr and kR vs [H +] lines. Table 1 lists the reaction conditions and the slopes. The data indicate that kc, the slope of the k R vs [H ÷] line, is independent of [Eu a÷] and [EuEDTA-]. Most of the values overlap within one standard error, and all overlap within + 2a. The average value of k c has an uncertainty of about 10 per cent. Likewise, when the slopes of the kF vs [H +] lines (i.e. ka) are divided by [EuEDTA-]/ [Eu 3+], constant values are obtained. Again, all the values overlap within + 2a, and the uncertainty in the average is 10 per cent.
[EuEDTA-]
(M x 10 3)
1.04 0.714 0-714 1.43 2.14 1.79 0-893
[Eu 3 +]
(M x 10 ~)
1-20 1.27 1.67 4-60 1.50 1.91 2.19 1.15 1-78 2.34 3.22 0.701 1.07 2.45
[EuEDTA-]
jell 3 +]
_ ± ± ± ± ± ±
0.04 0-01 0.026 0.031 0.10 0.09 0.025
I × 10-z)
Average values
1-60 1.03 0.716 0.691 2.42 1.69 0-816
(M-lsec
k A = slope kF
+ 0.03 ± 0.03 _+ 0.04 ± 0.12 +_ 0-04 ± 0.06 ± 0.06
1 x 10 -2)
1.39 ± 0.13
1.34 1.38 1.23 1.55 1-25 1.43 1.53
(M-lsec
k c = slope k R
Table 1. Variation of slopes of k e and k R vs [H ÷] lines with changes in [Eu 3 +] and [ E u E D T A - ] Am 3+ + E u E D T A - ~ E u 3+ + A m E D T A [acetate] = 0.02 M ; # = 0.1 M ; 25°C [EuEDTA-] [Eu3+]
0.04 0-02 0.06 0.10 0-07 0-09 0.06 1.87 ± 0.19
1.83 ± 1-83 ± 1.68 ± 2.23 ± 1-70 ± 1.81 ± 2-00 +
(M -1 sec -1 x 10 -z)
k~l = kA :-
to +
T~
I
-q
e~
O
4260
G. R. CHOPPIN and K. R. WILLIAMS 20"0¢
15'00 x •
I 0'00
/ J o• •
/
5.00
0
2"100
4.00'
'
6'-00
[Eu 3+] or [Eu EDTA-], MxlO 3 Fig. 3. Plots ofke vs [EuEDTA-] and ko vs [Eu3+].
These results for the acid-dependent terms indicate that the forms of the rate equations are: k r = k~
[EuEDTA - ] [H +] [Eua+] + k8
k g = kcEH +] .-[-.ko.
(5) (6)
Now, let us consider the acid-independent terms. Figure 3 shows that reasonably good straight lines are obtained when the values of kB vs [ E u E D T A - ] and of kD vs [Eu 3÷ ] are plotted. This indicates that the acid-independent term is first-order with respect to EuEDTA - for the forward reaction and first-order with respect to Eu 3 + for the reverse reaction. Values of kB/[EuEDTA-] ( = k~) and kD/[Eu a +] (=k~) are given in Table 2. The respective values for k~ and k~ overlap one another within one standard error and the average Values are uncertain by about 16 per cent. As we mentioned above, the reaction was studied as a function of hydrogen ion concentration for three different concentrations of acetate buffer. Table 3 lists the values of k'a, k'B, kc and k'D for each acetate concentratiori. The rate constants for the acid-dependent mechanism (k~ and kc) increase with an increase in acetate concentration but the rate constants for the acid-independent mechanism (k~ and kb) decrease. The order of the reaction with respect to total acetate could be determined accurately only for k~ and kc. Figure 4 shows plots of k~ and k c vs total acetate concentration. The linear plots both have large intercepts. Thus, k~ and k c are given by: kat = k~[acetate] + kcm
kc = kc[acetate] + k~
ks [EuEDTA ]
± + + ± + + ±
0.76 0.23 0-44 0.35 0.57 0-64 0.41
4.54 ± 0.65
3.92 3.51 5-35 4.67 4-81 5-13 4.38
(M - I sec-l x 102)
k~
2.53 ± 0.02 1,87 _ 0.19 1.56 ± 0.09
0.04 0.02 0.008
0.798 + 0.386 4.54 + 0.65 7.57 + 1.92
k'n (M I sec-I x 102)
k'a
( M - i s e c -1 × 10 2)
[Total acetate] M
1.818 ___ 0.001 1-39 + 0.13 1.18 4- 0.07
( M - l sec -~ × 10 -2)
kc
Table 3. The effect of acetate buffer concentration on the slopes and intercepts of k e and k R vs [H +] plots Am 3+ + E u E D T A - ~ - E u 3+ + A m E D T A [Eu 3+] = 1.20 x 10 -3 M; [ E u E D T A - ] = 1,04 x 10 -3 M; tt = 0-1 M; 25°C
Average values
+ 0-63 + 0,37 + 0-46 + 1.9 ± 0.47 + 0,82 -4- 0-93
3-62 2.93 6.53 16-2 5-15 6.41 6.15
0.79 0.16 0.31 0-50 1-21 1-15 0-36
4-08 2.51 3.82 6.68 10-3 9-19 3.91
1.04 0,714 0.714 1.43 2.14 1.79 0.893
1.20 1.27 1,67 4,60 1.50 1.91 2.19
+ + + + + + ±
(sec-~ x 105)
(sec -~ x 105)
(M x 103)
(M x 103)
lntcp, k R
k O =
kn = lntcp, k F
[EuEDTA-]
[EU3+]
Table 2. Variation of intercepts of ke and k R vs [H +] lines with changes in [Eu 3 +] and [ E u E D T A - ] Am 3+ + E u E D T A - ~ E u 3+ + A m E D T A [acetate] = 0.02 M; ,u = 0,1 M; 25°C
+ ± ± + _ + _
0.53 0-29 0.28 0-41 0.32 0.43 0.43
0.663 + 0.016 3-19 + 0.53 5.64 + 1.40
( M - I sec -1 × 102)
k'D
3.19 _+ 0-53
3.02 2.31 3.91 3,53 3.43 3.35 2.81
(M - l s e c - t x 102)
ko k~ = [Eu3+~
t-.
e~
+
,-t
4262
G . R . CHOPPIN and K. R. WILLIAMS 3-0C
'o x 2.00
I'00
,'o
2%
3)0
[Acetofe]
,!oo
'
5"00
M x 10 2
,
Fig. 4. Plots of k~ and kc vs total acetate concentration.
where k a = 3.06 _+ 0.19 x 10 3 M - 2 sec- 1 ; ka 1.29 + 0.05 x 102 M- 1sec- 1, kc 2.01 __+0.10 x 1 0 3 M - 2 s e c - 1 and k~ = 1.01 ___0.03 × 102 M -1 sec -1. vv
tvv
-~
.
!
DISCUSSION
The results indicate that in the pH range of 5.5-6-5 and at constant acetate buffer concentration, the exchange of trivalent americium with EuEDTA- obeys the following overall rate law : Rate=
{
k~
[EuEDTA-][Am3+]_kc[AmEDTA-~}[H+ ] [Eu3+]
(7)
+ {k~[EuEDTA-] [Am a +] - kb[Eu 3 +] [AmEDTA-]}. This expression correlates with a reaction which proceeds via two pathways; the first set of brackets can be associated with an acid-catalyzed mechanism while the second set represents an acid-independent reaction path.
Acid-independent mechanism For exchange reactions of the transition metals with transition metal-aminopolycarboxylate complexes, Margerum has proposed that an acid-independent (i.e. direct) pathway involves the formation of a binuclear intermediate, M'EDTAM[10]. It would seem reasonable that such a mechanism is also involved in the EDTA exchange between lanthanide and actinide ions. NMR data[13] on LnEDTA- complexes indicate that the carboxylate groups of the ligand are rapidly coordinating with and dissociating from the metal ion. It seems probable that in the first step of the acid-independent mechanism the free americium ion approaches the EDTA complex and forms a bond to a carboxylate group which is momentarily uncoordinated (Eqn. 8). The bond between the americium ion and the ligand should be very labile and dissociate readily. However, if the americium ion bonds to another carboxylate group before it dissociates from the 13. T. H. Siddall, III and W. E. Stewart, Inorg. nucl. Chem. Lett. 5, 421 (1969).
Kinetics of exchange for Am 3 ÷ and E u E D T A -
4263
first, a binuclear complex with two carboxylate groups bonded to each metal ion, E w - E D T A = A m 2+, is formed as in Eqn (9). This complex would react to form either E u = E D T A - - A m 2+ or a complex with three bonds to the americium A m ~ E D T A - - E u ~+ species. The steps in such a mechanism m a y be written: kl
E u E D T A - + Am 3+ ~-- E u ~ E D T A - - A m 2+
(8)
k2
Eu~--EDTA--Am2 * ~-2 E u = E D T A = A m 2 +
(9)
k3
E u = E D T A = A m 2 ~ ~---3E u - - E D T A ~ A m 2 +
(10)
k4
E u - - E D T A ~ A m 2 + kL--~Eu3+ -r- A m E D T A .
(11)
The rate of formation of the binuclear intermediate, E u = E D T A = A m : +, from E u E D T A - and Am 3 ÷ is the rate of formation of E u = E D T A - - A m 2+ times the probability that the latter would form Eu-----EDTA=Am 2 ÷ instead of returning to the reactants. Therefore, the rate of formation of E u = E D T A = A m 2 ÷ from Am 3 + and E u E D T A - would be :
= kl[EuEDTA-][Am3+~ (k2 +k2k_I ) (12a)
-- klk2 [ E u E D T A - ] [Am 3 +1 k_l
k2).
(since k_ 1 >> Likewise, the rate of formation o f E u - - E D T A = A m 2 ÷ from Eu 3 + and A m E D T A is: _ k_ 4k_ 3 [ A m E D T A - ][Eu 3 + ]. k4
(12b)
The rate of dissociation of E u = E D T A = A m 2 + to A m E D T A - and Eu 3 ÷ is the rate of reaction to form E u - - E D T A ~ A m 2 ÷ times the probability that this complex would dissociate to the products rather than form Eu=EDTA-----Am 2 ÷ again. The rate of dissociation of E u = E D T A = A m 2 ÷ to A m E D T A - and Eu 3 + can be written as
k4
= k3[Eu=EDTA=Am2÷](k-3 + kf~)
(13)
= k 3[E u = E D T A = A m 2 * (since k4 >> k_ 3)Similarly the rate of dissociation of E u = E D T A = A m E u E D T A - is = k_ 2 [ E u = E D T A = A m 2 +].
2+ into Am 3÷ and (14)
In the forward direction only the A m E D T A - which is formed from E u E D T A and Am 3 ÷ should be considered. Thus, the rate of the forward reaction is the rate of
4264
O . R . CHOPPIN and K. R. WILLIAMS
formation of Eu--=--EDTA--Am2÷ from EuEDTA- and Am 3 ÷ times the probability that Eu-----EDTA=Am 2÷ reacts to form AmEDTA- and Eu 3 ÷ instead of EuEDTAand Am a+. kl Thus, the forward rate can be expressed, since K 1 = ~-~-1' by Forward rate = K1 "k2. k3 [EuEDTA- ] JAm3 +]. k3 +k--2
(15)
By an analogous treatment the rate of the reverse reaction is given by k_ 3. k_ 2 [Eu 3+] [AmEDTA-]. Reverse rate = K-4. k 3 + k_2
(16)
The overall rate of reaction by the acid-independent pathway is given by the difference between equations (15) and (16): Rate = KI" k2" k3 [EuEDTA-] JAm 3+] - K - 4 " k-3" k-2 [Eu 3+] [AmEDTA-]. (17) k3 + k-2 k3 + k-2 This expression shows that the mechanism is consistent with the experimental data since it is the same as that in the second set of brackets in Eqn (7), where
k~--- /(1 • k2. k3 k3 + k-2
and
(18)
k'D= K_a.k_3.k_2 k3 + k-2 An increase in the concentration of acetate results in a decrease in the reaction rate by the acid-independent mechanism. The rate may be affected by acetate complexation of both the free metal ions and the EDTA complexes. Complexation of the free metal ions should occur to a greater extent than mixed complex formation, and it is expected that the formation of the europium and americium acetate complexes has the more pronounced effect on the reaction rate. Formation of the acetate complexes results in an effective decrease in the concentrations of the free metal ions. Because the metal ion acetate species do not have as great a positive charge as the free metal ions, the acetate complexes will not be attracted to the EDTA complex as strongly as the uncomplexed metal cations. Thus, the effects of replacing free Eu a ÷ and Am a ÷ by their acetate complexes are reductions in K1 and K_ ~, the equilibrium constants for the formation of the first carboxylate bond to the metal ion. The decreases in K1 and K-4 may be modified somewhat by the presence of mixed EDTA + acetate complexes, which have an increased negative charge and would be attracted better to the free metal ions. However, because the concentration of mixed complexes should be very small, their effect on the reaction rate should not be appreciable.
Acid-dependent mechanism There has been disagreement in the literature on the nature of the acid-catalyzed
Kinetics of exchange for Am 3÷ and EuEDTA
4265
pathway. The kinetic results have been used to support both a slow protonation step followed by rapid dissociation and, conversely, a rapid protonation equilibrium followed by slow dissociation. Nyssen and Margerum[141 used a stopped flow technique to measure the rate of formation of LaDCTA- from La 3 ÷ and H2DCTA 2-. Their results indicated that the metal and ligand reacted very rapidly to release the first proton and form the metastable complex *HLaDCTA, which deprotonated at a measurable rate. Thus the slow step in the formation of LaDCTA- is the release of the last proton. It is likely, then, that the slow step in the formation of EDTA complexes of the lanthanide and actinide ions also involves deprotonation. By the principle of microscopic reversibility it can be argued that the protonation of LnEDTA- must be the slow step in the dissociation reaction. That protonation is a slow step is surprising, because as Eigen et a/.[15] have indicated, proton transfer reactions are usually very rapid. The proton passes along hydrogen bonds which bridge the hydration spheres of the protonated species and the base. It is likely, therefore, that protonation actually involves two steps. In the first step there is a rapid protonation equilibrium. This equilibrium is followed by a second, slow step, in which the protonated complex is converted to a form which rapidly dissociates to the free metal and free protonated EDTA. It is necessary first of all to consider the protonation equilibrium itself. In free EDTA the nitrogens are the most basic atoms and are protonated before the carboxyl groups. Because the lanthanide and actinide ions form complexes primarily with oxygen donors, it is likely that the nitrogens are coordinated very weakly to the metal ion. Thus, the nitrogens should be better proton acceptors than the carboxylate oxygens. However, in the lanthanide or actinide EDTA complexes the bond angles are such that the proton cannot become attached to a nitrogen. Thus, it is necessary to assume that the rapid protonation equilibrium involves carboxylate oxygen protonation. There are two possibilities for the second, slow step: (1) the other carboxylate group in the same iminodiacetate moiety as the protonated carboxylate group may become dissociated while the proton still remains on the complex. The remaining two carboxylate groups should then be able to dissociate rapidly from the metal ion. (2) Once a carboxylate group has dissociated from the metal ion the nearest nitrogen is exposed to attack by a proton. The second step may, therefore, involve the transfer of the proton from the carboxylate oxygen to the nitrogen. This process may be a proton transfer or may involve the formation of a hydrogen bond in which the proton is attached to both the nitrogen and the carboxylate oxygen. The formation of hydrogen bonds in free EDTA between the proton on nitrogen and the carboxylate groups has been proposed by Chapman et al.[16] to explain their P M R and infrared data. In either case, once the nitrogen is protonated, reformation of the metal ioncarboxylate chelate ring is blocked and the ligand can dissociate rapidly. In both 14. G. A. Nyssen and D. W. Margerum, lnorg. Chem. 9, 1814 (1970). 15. M. Eigen, W. Kruse, G. Maass and L. DeMaeyer, In Progress in Reaction Kinetics (Edited by G. Porter) Vol. 2, Chapter 6. Macmillan, New York (1964). 16. D. Chapman, D. R. Lloyd and R. H. Prince, J. chem. Soc. 3645 (1963).
4266
G.R.
CHOPPIN
a n d K . R. W I L L I A M S
mechanisms (1) and (2) the ligand picks up the additional protons which it requires as it leaves the metal ion. The first step in the reverse reaction would for both possible mechanisms be the rapid complexation of the two carboxylate groups on one of the iminodiacetate moieties. For mechanism (1) formation of the third carboxylate bond would be ratedetermining. Deprotonation then would occur rapidly. In mechanism (2) the formation of the third carboxylate bond would also be rapid. The rate-determining step would be the transfer of the proton from the nitrogen to the oxygen. Final deprotonation would occur rapidly. It is difficult from our data to decide between mechanisms (1) and (2). However, both cases can be represented by the following mechanism, in which *HEuEDTA and *HAmEDTA represent the metastable protonated complexes. k-lE
EuEDTA- + H + ~
HEuEDTA
(19)
k - 2n
HEuEDTA k~ *HEuEDTA
(20)
k- 3E
*HEuEDTA + (x - 1)H + k~ Hx EDTA4-x + Eu3+
(21)
k3a
Ama+ + H~EDTA4-x k-~A *HAmEDTA + (x - 1)H +
(22)
k2A
*HAmEDTA k-~-~aHAmEDTA
(23)
klA
HAmEDTA k_'7~AmEDTA- + H +.
(24)
The rate of formation of HxEDTA 4-x from EuEDTA- is the rate of formation of HEuEDTA [Eqn (19)] times the probability of forming *HEuEDTA from HEuEDTA [Eqn (20)] all times the probability of forming H~EDTA 4-x from *HEuEDTA [Eqn (21)]. Rate of formation of HxEDTA 4-x from EuEDTA= k_,E[EuEDTA-] [H +] k_2g +
k,E]/k_ 3e-~H+]._---------q ~ k2r]
(25)
= K_ ~ek_ 2~.[EuEDTA- ] [H +] because klE >> I.n.-2E,k - 3 E l -r H + l/X - 1 >> k2m and K_,4 = k-lEl" kl e j Likewise the rate of formation of H,EDTA 4-* from AmEDTA= K_ l ak- 2a [AmEDTA] [H +].
(26)
The rate of formation of AmEDTA- from H,EDTA 4-x and Am 3 ÷ is the rate of formation of *HAmEDTA [Eqn (22)] times the probability of forming HAmEDTA from *HAmEDTA [Eqn (23)], all times the probability of forming AmEDTA- from
Kinetics of exchange for Am3+ and EuEDTA
4267
HAmEDTA. Thus the rate
+ k-3A k2A "
+ k-2A'/ (27)
[HxEDTA 4- x] = K3Ak2A[Am 3+ ]
[H-~Y
(because k_aA[I2I+] ~-l >> k2A,kl.4 >> k_2a , and K3A = _~3~ k_3A I. l In a similar manner the rate of formation of E u E D T A - from HxEDTA 4-* and Eu 3 +
[Eu 3 + ] [HxEDTA 4- ~] = K3Ek21 ~
(28)
[H+]X_ 1
The rate of formation of A m E D T A - from E u E D T A - and Am 3 + is the rate of formation of H~EDTA 4-x from E u E D T A [Eqn (25)] times the probability that the free HxEDTA '~-x will react with Am 3 + [Eqn (27)] instead of with Eu 3 ÷ [Eqn (28)]. Rate of formation of A m E D T A - from E u E D T A - and Am 3 + .....
/~3AK2ALA m
3+ . , / [ H x E D T A 4 - q l J]~
~
)
= K_ 1Ek - 2E[ E u E D T A - ] [H + ] (K3ek2~[Eu3+] + = K_ 1EK_ 2I~K_ 3EK3,1k2A
K
k ~A 3+"[[H*EDTA4-X]/ 34 2AL m 9 / [H---~i~ ]
[ E u E D T A - ] [H+] [Am 3 + ] [Eu3 +]
(29)
(because K3~k2~[Eu a+] >> K3Ak2A[Am 3+] and K_2~ -- -*-2~/ k2~ ]" Likewise, the rate of formation of E u E D T A - from A m E D T A - and Eu 3 + is the rate of formation of HxEDTA 4-x from A m E D T A - [Eqn (26)] times the probability that the free HxEDTA 4-~ will react with Eu 3+ [Eqn (28)] instead of with Am 3÷ [Eqn (27)]. Rate of formation of E u E D T A - from A m E D T A - and Eu 3 ÷ K = K_ l a k - 2A[ A m E D T A - ] [H + ]
'
~" 3+~/[H~EDTA4-~]/
~2~u ~/ EN---~ J E D T A 4 - x)) ,~3~AL~m3 + ~J'/, / [ H x~_~
(Kaek2E[Eu 3+] + . . . . .
= K_ 1Ak_2~[AmEDTA-1 [H +]
(30)
(because Kaek2e[Eu a +] ;> K3Ak2,4[Am 3 +]). The overall rate by the acid-dependent pathway is the difference between Eqn (29) and Eqn (30).
4268
G.R. CHOPPIN and K. R. WILLIAMS Rate = K_ 1EK_ 2EK_ aEK3Ak2A
[EuEDTA-] [H +] JAm 3+] [Eu3 +] (31)
-
K_ 1Ak_ 2A[H+] [AmEDTA- ].
This expression is the same as the first term in Eqn (7) where k'a = K_ 1EK_ 2EK- 3EKaAk2A
(32)
and kc = K-1Ak-2A.
Thus, the proposed mechanism is found to agree with the experimentally determined rate law. From our data it is possible to calculate that the ratio of the rate by the aciddependent mechanism to that by the acid-independent mechanism. F o r b o t h the forward and reverse reactions this ratio has a value of approximately 40 at pcH 5, 4 at pcH 6 and 0.4 at pcH 7. The two mechanisms have approximately equal rates and hence equal probability at a pcH of approximately 6.4 under our experimental conditions. The effect of buffer concentration on the rate of the acid-dependent pathway is opposite to that by the independent mechanism; an increase in buffer concentration results in an increase in the reaction rate. This result was also obtained by Briicher et al.[17] and by Glentworth et al.[5] who also studied the effects of buffer concentration on the acid-dependent mechanism. The rate increase may be caused by either: (1) complexation of the free metal ions by the buffer anions, (2) complexation by the buffer anions of the LnEDTA- complexes (i.e. mixed complex formation), or (3) catalysis by the undissociated buffer acid. In our proposed mechanism for the acid-dependent pathway only the formation of the first three carboxylate bonds to the metal ion can be affected by acetate complexation of the free metal ions. The equilibrium constants K3A and K_3E both appear in k~. However, the effects on K_ 3Eand K3Aa r e expected to offset one another and to produce no significant change in k~. Thus, neither kc, which contains no contribution from these two equilibria, nor k~ is affected by the formation of acetate complexes with the free metal ion. Neither the data of Briicher for the Cu2+/TbEDTA - system nor those of the present study exclude the possibility of catalysis by the undissociated buffer acid. However, Glentworth et al. have compared the effects of acetate on the rates of isotopic exchange of Ce 3+ with CeHEDTA, CeEDTA- and CeDCTA-. The increase in rate by the acid-dependent pathway is ten times greater for CeHEDTA than for CeEDTA- and 2.7 times greater for CeEDTA- than for CeDCTA-. It is difficult to rationalize the relative magnitudes of the acetate effect by consideration of catalysis by undissociated acetic acid. The importance of mixed complex formation on the rate of the acid-dependent pathway has been discussed by Briicher and Glentworth and we also favor this 17. E. Briicherand M. Szihlgyi,In Proceedingsof the Third Symposium on Coordination Chemistry (Edited by M. T. Beck)p. 323. AkademiaiKiado,Budapest(1970).
Kinetics of exchange for Am 3+ and EuEDTA-
4269
explanation. In our proposed mechanism the increased negative charges of the Eu(EDTA)(OAc) 2- and Am(EDTA)(OAc) 2- complexes should cause the protonation equilibrium constants K_I~ and K-IA to increase. Unfortunately, it is not possible to differentiate between the two possibilities for the slow reaction step. The extra acetate ligand on the EDTA complex should cause a general loosening of the metal ion-EDTA bonds. Thus, in proposed mechanism (1) the second carboxylate bond should dissociate more readily. Also, the nitrogens should be located farther from the metal ion and should be more available to attack by a proton as in mechanism (2). As Glentworth has already indicated, the different increases in rate for the three systems studied by his group can also be explained in terms of mixed complex formation. HEDTA has only three carboxylate groups; EDTA and DCTA each have four. Because CeHEDTA contains fewer chelate rings and is neutrally charged, formation of the mixed complex Ce(HEDTA)(OAc)- may be less hindered than formation of Ce(EDTA)(OAc) 2- or Ce(DCTA)(OAc) 2-. The fact that t h e Ce 3÷/CeDCTA- system is relatively insensitive to acetate catalysis may be due to the different steric requirements of that ligand. Acknowledgement--This research was supported by the USAEC under Contract AT-(40-1)-1709. KRW wishes to acknowledge the assistance of NSF and NDEA predoctoral fellowships.