Anal. Chem. 1993, 65,1510-1516
1510
Simultaneous Characterization of Extraction Equilibria and Back-Extraction Kinetics: Use of Arsenazo I I I To Characterize Lanthanide-Bis(2,4,4-trimethylpentyl)phosphinic Acid Complexes in Surfactant Micelles Kazuho Inaba,+Subramaniam Muralidharan,*and Henry Freiser Strategic Metals Recovery Research Facility, Department of Chemistry, University of Arizona, Tucson, Arizona 85721
A novel “metallochromic indicator method” that simultaneously yields kinetic and extraction equilibrium information for metals has been developed. The use of arsenazo I11 to monitor the kinetics of dissociation of lanthanide-bis(2,4,4-trimethylpenty1)phosphinic acid (HBTMPP) complexes in polyethylene glycol tert-octylphenylether (Triton X-100) micelles is described as an example. The distribution and the dimerization constants of HBTMPP in these micelles resemble its values in the CHC13-H20 system but the extraction equilibrium constants of the lanthanides, K,,, are 4-6 orders of magnitude larger than the values in CHC13-H20. Two series of lanthanide-HBTMPP dimer complexes having ratios of 1:2.5 and 1:3 are extracted into the micelles, and for both series, the K,, values for the heavy lanthanides are higher than for the light lanthanides. The rate-limiting step in the dissociation of these complexes is their attack by H+ and appears to proceed exclusively in the micellar phase under the conditions employed. The rate constants for the dissociation reaction are larger for the lighter lanthanides than those of heavier lanthanides. For a given metal, the 1:2.5 metal-dimer complex dissociates more readily than the 1:3 dimer complex.
and In the course of the separation studies of PGM we found that their CPC efficiencies were limited mainly by slow metal complex dissociation kinetics. Independent kinetic studies of the dissociation of these complexes in micelles, by the direct monitoring of the metal complex absorption bands, enabled us to establish a correlation between the CPC efficiencies and the half-lives of the metal complex dissociation reactions. The separation of tervalent lanthanides by CPC using the heptane-water phase pair and HBTMPP as the ligand also exhibited poor CPC efficiencies.’ It is thus necessary to understand the kinetics of formation and dissociation of the M-HBTMPP complexes in order to understand the influence of such kinetics on the efficiencies of their CPC separations. The direct monitoring of the formation and dissociation kinetics of these complexes is hampered by the lack of characteristic UV-visible absorption bands. This led us to the development of the metallochromic indicator method to characterize the extraction equilibria and the back-extraction kinetics of the M-HBTMPP complexes in Triton X-100 micellar pseudophase. The method reported has several advantages over the previous attempts, using Cu2+, to generate the needed chromophore with the ligand in the lanthanide complexes.4-8 They are as follows: the much greater sensitivity of a metallochromic indicator compared to Cu2+;wider applicability, including to systems involving excess ligand; and the simultaneous determination of equilibrium constants for the ligand and metal complex and kinetics of back-extraction. These are highlighted in this paper.
INTRO DUCT10N
EXPERIMENTAL SECTION Apparatus. A HI-TECH Scientific stopped-flowSHU spectrophotometer and associated HI-TECH software was used for data acquisitionand treatment. A Hewlett-Packard 8452A diode array spectrophotometer was used for measurement of spectra of reagents and complexes. Reagents. The extractant, HBTMPP, was kindly supplied by American Cyanamid as a pale yellow liquid. It was purified accordingto our previouslydescribed procedure,by the formation of its copper(I1)complex and its subsequent dissociation.9 The purified HBTMPP (99 % ) was a clear, viscous liquid. Stock solutions of Pr, Eu, Tb, Ho, and Yb were prepared from their chloride salts (99.9% purity, Alfa Products) by dissolving
The characterization of the equilibrium and kinetics, in homogeneous and heterogeneous media, of metal complex formation and dissociation reactions that have a poor “spectral handle” is a significant and challenging problem. We have developed a novel “metallochromicindicator method” wherein the free metal is complexed by an indicator. Following the kinetics of formation of the metal-indicator complex provides information on the kinetics and equilibrium of metal-ligand complex formation or dissociation reactions. In the current work, this metallochromic indicator method has been applied to the characterization, using arsenazo 111, of the extraction equilibria and back-extraction kinetics of the lanthanide (MIbis(2,4,4-trimethylpentyl)phosphinicacid (HBTMPP; commerical name Cyanex 272)system in polyethylene glycol tertoctylphenyl ether (Triton X-100) micelles. We have recently demonstrated the value of centrifugal partition chromatography (CPC),a multistage liquid-liquid partition technique, for the complete separation of closely related metal ions such as the platinum group metals (PGM) On study leave from the National Institute for Environmental Studies. 16-2 Onogawa, Tsukuba, Iharaki 305 Japan.
(1) Muralidharan, S.; Cai, R.; Freiser, H. J . Liq. Chrornatogr. 1990,13, 3651-3672. ( 2 ) Surakitbanharn. Y.; Muralidharan, S.; Freiser, H. Solvent E r t r . I o n Exch. 1991, 9, 45-49. (3) Surakithanharn,Y.;Muralidharan,S.;Freiser,H. A n a l . Chem. 1991, 63, 2642-2645. (4) Nyssen, G. N.; Margerum, D. W. Inorg. Chem. 1970,9.1814-1820. ( 5 ) Rhyl, T. A c t a Chern. S c a n d . 1972, 26, 3955-3968. (6) Choppin, G. R.; Williams, K. R.J . Inorg. Nucl. Chern. 1973, 35, 4255-4269. ti)De Jonghe, M.; D‘Olieslager, W. Inorg. Chirn. A c t a 1985,109,7-14. (8) Choi, K.: Choppin, G. R. J . Coord. Chem. 1991, 24, 19-28. (9) Komatsu, Y.; Freiser, H. A n a l . Chirn. A c t a 1989, 227, 397-404.
0003-2700/93/0365-1510$04.00/0’c: 1993 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 65, NO. 11, JUNE 1, 1993
in 0.1 M hydrochloric acid. Arsenazo I11 (Aldrich Chemical), Triton X-100 (Fluka, >99%),and the other reagents were used without any purification. Procedure. All the experiments were carried out at 298 K. The ionic strength of experimental solutions was adjusted to 0.1 M with sodium perchlorate. A micellar solution of a nonionic surfactant, polyethylene glycol tert-octylphenyl ether (Triton X-loo),was used in order to solubilizeHBTMPP in the aqueous phase. Neither the extractant nor its complexes in Triton X-100 micelles show appreciable absorption in the visible region, and hence arsenazoI11was used in the dual role of colorimetricreagent and scavenger for the lanthanides. Stopped-flow experiments were conducted in micelles formed from 0.2 to 4% (0.0031-0.063 M) Triton X-100 for the measurement of rate constants and distribution constants. The metal complex formed from (1-4) X M of the respective lanthanide and 6 X 10-5-1 X M HBTMPP (concentrationas dimer) at pH 2.4-4 (succinatebuffer; total succinate 0.0025 M) was mixed with 1.6 X 10-5-7.8 X lo4 M arsenazo I11 solution containing the same concentrations of Triton X-100 and HBTMPP at an appropriate pH (total succinate 0.0025 M) such that the resulting pH of the mixture was 1.6-3.8 (pH jump to dissociate M-HBTMPP). The M-HBTMPP solutions were left at room temperature for 1 h to achieve complexation equilibria. The rate constants and distribution ratios were taken as the average of a minimum of 10 runs. The pH of the metal complex solutions and the solutions after mixing with arsenazo I11 were determined using a Fisher Scientific Accumet 925 pH meter. Data Treatment. The monomeric and dimeric forms of HBTMPP are represented by HL and (HL)2 and the free lanthanide and the total lanthanide (free metal + complexed metal) by M3+and M(III), respectively. The concentrations of species in the micellar phase are denoted by subscript m, those in the bulk aqueous phase by no subscript, and total concentrations by subscript t. The followingequilibrium constants for the ligand are essential for the data analysis. K , = [H+l[L-I/[HLl
(1)
K,, = [HLl,/[HLl
(2)
K,, = [(HL)21,/CHLl,2
(3)
The volume fraction V,, of the micellar phase is defined as
V, = d([Triton X-1001- cmc) (4) where 4 is the molar volume of the micelle (1.29 M-I for Triton X-100)10and cmc, the critical micelle concentration a t 1= 0.1(2.4 X M)." Under our experimental conditions, V , is much smaller than the volume fraction of the bulk aqueous phase, V,. Hence V, can be taken to be 1. The total concentration of the ligand, [HLIt, is given by eq 5. [HL], = 2[(HL),],V, 2KdmKD2Vrn
K,2
+ [HL],V, + [HL] + [L-] = K V [H+l2[L-I2 m [ H + ] [ L - ] + Ka
+
Equation 5 thus yields [L-] at a given [HL], when K,, KDR,and Kdm are known. Even though the total concentration of HBTMPP in the micellar and aqueous phases is small, the local concentration of HBTMPP in the micellar phase, which has a small volume fraction, is high, ca. 0.0003-0.03 M as the dimer. The rate of dissociationof the metal complex,R , can be written as
R = k,b,[com~lexl,irne (6) Here [complexltimerepresents the total concentration of the (10)Hayashi, K.; Sasaki, Y.; Tagashira, S.; Kosaka, E. Anal. Chem. 1986,58,1444-1448. (11)Kalyanasundaram, K.; Thomas, J. K. J.Am. Chem. SOC.1977,99, 2039-2044.
1511
M-HBTMPP complex in the aqueous and micellar phases at any given time during the kinetic run. This can be calculated from the initial concentration of the complex, [cornplex]i,i, and the concentration of the free lanthanide metal ion at a given time during the kinetic run, [M3+ltime, see eqs 10 and 11below. The concentration of the free metal at a given time during the dissociation reaction, [M3+]time, was calculated using the absorbance at that time, Atime,and the molar absorptivity of the M-arsenazo I11 complex. The observed rate constant was determined from the slope of the plot of log [complex],ime(log - [M3+ltime)) as a function of time. ([complexl~,~t
RESULTS AND DISCUSSION Determination of the Concentration of Free M and M-HBTMPP from the Kinetics of the Formation of M-Arsenazo 111. The formation of the M-arsenazo I11 complexes upon dissociation of the M-HBTMPP complexes was monitored a t 654 nm. The molar absorptivities of the M-arsenazo I11 complexes due to dissociable protons in the complexed indicator are sensitive to pH, and in the pH range 2.4-4 are Pr (5.2-5.5) X lo4M-l cm-' and T b and Ho (5.5-5.8 X lo4 M-l cm-1 and in the pH range 1.5-4 are Eu (4.5-5.5) X lo4 M-' cm-l and Yb (4.0-4.8) X lo4 M-l cm-1. The most sensitive pH range for the detection of lanthanides is 2.5-3.5. The molar absorptivities determined here are in excellent agreement with those determined by Sawin.12 We first characterized the complexation of lanthanides by arsenazo I11in the presence of Triton X-100 micelles and in the absence of HBTMPP and its lanthanide complexes. The formation of the M-arsenazo I11 complex involved a two-stage reaction, evidenced as a fast rise in absorbance, reaching a maximum value in less than 0.1 s, followed by a slow decrease, attaining the absorbance value corresponding to the molar absorptivity independently determined by spectrophotometry. The fast rise was independent of the nature of the lanthanide while the slow decrease in absorbance was dependent on the lanthanide, for example, 3 s for Eu and 30 s for Yb. It is well established that the M-arsenazo I11 complexes are dimers.13 Thus the fast step in the formation of the M-arsenazo I11 complex probably corresponds to the formation of the 1:1 M-arsenazo I11monomer and the slowstep to the dimerization reaction. The molar absorptivities of these complexes determined by spectrophotometry correspond to the dimeric species. The difference in the absorbance of the monomeric and dimeric species is not very large, ca. 10%. The kinetics of the complexation of free lanthanide ions by arsenazo I11 were not fully characterized as a function of pH, and the total reaction times quoted above for the fast and slow steps in this complexation reaction are upper limits for the pH range 2-4. As will be seen, the formations of the M-arsenazo I11 complexes are much faster than the dissociation of the M-HBTMPP complexes and the two reactions are well separated. Thus, the pH dependence of the formation of M-arsenazo I11kinetics is not essential for the analysis of the kinetics of dissociation of M-HBTMPP complexes. The relevant equilibria following the pH jump are shown in eqs 7-9. The dissociation of the M(HL2)Scomplex is taken as an example. Further discussion based on the experimental results will indicate that this is not the only kind of complex that exists in the micelles. It may be assumed, as in the case of solvent extraction experiments, that the free M3+ and H+ reside in the bulk aqueous phase and that the (HL)2 and M(HL2)3 reside in the bulk micellar phase. Thus, the concentration of the free M3+at the beginning of the reaction, namely, [M3+]i,it can be calculated from the initial absorbance of the absorbance vs time kinetic trace for the formation of (12)Sawin, S. B. Talanta 1961,8,673-685. (13)Budesinsky, B.2.Anal. Chem. 1964,202,96-101.
1512
ANALYTICAL CHEMISTRY, VOL. 65, NO. 11, JUNE 1, 1993
+
2M3+ 2arsenazo I11 6 (M-arsenazo III), 1
(8)
+ 3(HL),,,, + M(HL,),,,, + 3H' + arsenazo I11 (9)
/,(M-arsenazo 1111,
the M-arsenazo I11 complex. An accurate value ( f 5 % ) of the initial absorbance was obtained by extrapolating the A vs time kinetic trace to zero time. It is evident from eq 7 that [M3+]initand, hence, the initial absorbance should be a function of the pH of the micellar solution containing the M-HBTMPP complex before being mixed with the arsenazo I11 solution to initiate the dissociation reaction. The dissociation of the Eu-HBTMPP complex a t different initial pH values is shown in Figure 1 to illustrate this point. The concentration of the M-HBTMPP complex a t the beginning of the dissociation reaction and at any given time during the dissociation reaction can be determined using eqs 10 and 11, [complexlinit= [M(III)] - [M3+Iinit
(10)
[complexltime= [complexlinit- [M3+ltime (11) where [M(III)] refers to the total initial concentration of the lanthanide ion taken in the micellar phase before the dissociation reaction. The concentration of the free metal at a given time during the dissociation reaction, [M3+ltime, was calculated using the absorbance at that time, Atime,and the molar absorptivity of the M-arsenazo I11 complex. It is evident from eq 7 that the amount of M-HBTMPP complex dissociating is a function of pH and that the dissociation is complete only a t low pH, for example, a t pH 1.6 for Yb. The initial rates of dissociation of M-HBTMPP complexes [log([complexlin~t - [M3+l,i,,) vs time], typically the first half-life, was used to derive the rate constants to minimize the interference from the equilibrium in eq 9. The formation of the M-arsenazo I11 complex was independent of the concentration of arsenazo 111,indicating that the ratelimiting step was the dissociation of the M-HBTMPP complex by H+ and not by arsenazo I11and that the formation of M-arsenazo I11 complexes is fast. Characterization of the Equilibria of Extraction of Lanthanides by HBTMPP into Triton X-100 Micelles. The distribution ratio of the lanthanide defined by eq 12
D = ([M(III)l - [M3+l,nit)/V,[M3+linit
(12)
(ratio of the concentration of the metal in the micellar phase to its concentration in the aqueous phase) can be calculated from the initial absorbance of the kinetic trace and eq 10. We have shown previously that the extraction of tervalent lanthanides by HBTMPP ([HBTMPP] = 0.05-0.1 M as dimer) into CHC13 is given by eq 13 and the corresponding
M3++ 3(HL),,,,
+ M(HL,),,,,
+ 3H+
(13)
extraction equilibrium constant by eq 14.9 We may expect the HBTMPP to be in the dimeric form in the micelle a t high concentration,and the extraction equilibrium in eq 13is most likely at such concentrations and low pH (pH < pK, of HBTMPP). The distribution ratio of Yb a t pH 2.48 and
2r
1
/I
I
0
d I
I
20
10
Time, s
Flgure 1. Formation of Eu-arsenazo I11 as function of time for the dissociation of Eu-HBTMPP complexes in 1 % Triton X-100 following pH jump. Initial conditions a-c: [Eu]~= 2.2 X M; [(HL)?],= 7.5 X M; pH, a = 2.86, b = 3.3. c = 3.96. Final conditions a-c: = 1.1 X [EU]~ M; pH 2.35. Traced is M; [(HL)*], = 7.5 X the blank absorbance due to arsenazo I11 at pH 2.35.
total initial concentration of HBTMPP as dimer of 5 x 10-4 M were used to obtain a first estimate of Kex,susing eq 14. This value of 22 for Kex,sand the distribution ratios were then used to determine the total concentration of HBTMPP as the dimer in the micelle, [ (HL)21t,, from eq 14, at initial concentrations of HBTMPP of 7 X 10-j-5 X M and pH 2.5-4.1 for the Yb system. Thus, the concentration of HBTMPP in the aqueous phase can be determined from eq 15. The term [(HL)2Itrepresents the total initial concentration of HBTMPP taken in the kinetic run
The distribution ratio of the ligand, DHL,is given by eq 16, where the aqueous K , value has been taken from our previous work.14 The plot of D H L (+~ K,/[H+]) vs [HL] yielded a
straight line from which the KDRand K d m values were calculated from the intercept and slope, respectively. These values are KDR= 41 f 9 (43.8 f 1.8)and K d m = 243 f 80 M-' (184.3 f 16.1 M-I) and are similar to the values in the CHCl3HzO system which are given in parentheses. The similarity between the values in the micelle and CHClS-HzO probably indicates that on the average the HBTMPP dimer resides in the polar (oxyethylene) region of the micelle. The KDRand Kdmvalues determined for the micelle using the kinetic data for Yb and the K, from our previous work14 were used to determine [(HL)&, for all the other lanthanides from eq 5. The above type of calculationswas repeated by assuming the lanthanide to be complexed to 2.5 and 2 dimers of HBTMPP. The latter assumption yielded unrealistically small KDR(=2) and large Kdm(=1.8 X lo4)values. The former assumption, even though it yielded reasonable KDR(=30) and Kdm(=170) values, led to log D - 3pH vs log[ (HL)21tmplots that exhibited large deviations from a slope of 2.5 at high [ ( H L ) & ,values (see discussion that follows). (14) Li, K.; Muralidharan, S.; Freiser, H.Solvent Ertr. IonExch. 1985, 3, 895-908.
ANALYTICAL CHEMISTRY, VOL. 05, NO. 11, JUNE 1, 1993
1519
Table I. Extraction Equilibrium Constants for Lanthanide Extraction by HBTMPP in Triton X-100 Micelles and CHClS-HzO micelle
CHClrH90" ~~
metal Ker,z.bb KeJ %ddd Kexc Pr3+ f 0.019 f 6.3 X fO.O1 Eu3+ 0.022 0.64 28.6 2.0 X f0.004 dzO.03 f6.9 Tb3+ f 2.26 f f f0.15 6.12 f 7.8 X Ho~+ f f0.42 Yb3+ 1.27 31.7 24.9 1.5 X f0.07 f5.6 f5.8
.
-10
I PPI
-111
-5
-4
-3
-2
-1
I
0
Log [(HL)*Itm F l ~ w2. r Plots of log 0 3pH vs log [(HL)&, for Pr, Eu, Tb, Ho, and Yb In 1% Trlton X-100.
-
A plot of log D - 3pH vs log[(HL)zItmwas constructed for Pr, Eu, Tb, Ho, and Yb (Figure 2). It may be seen that this plot is not a simple straight line for Yb and Eu (which typify the behavior of lanthanides) in the range of [(HL)2ltm= 10-4-0.02M. At low concentrations of (HL)2in the micelle [[(HL)2ltrn= lo-LlO-3 MI this line has a slope of 2.5,and at higher concentrations [[(HL)&, > 10-3 M)] this line has a slope of 3. Thus, our initial assumption of the formation of M ( H L Z )a~t the initial HBTMPP concentrations of 7 X 10-"5 X 10-4 M is valid. The lanthanide is extracted as a different complex,namely, M(HL2)zLa t smaller [(HL)zltmvalues. The extraction equilibrium a t these low concentrations of (HL)2 and the equilibrium constant, Kex.2.5 are given in eqs 17 and 18. The kinetics of dissociation of the M-HBTMPP com-
M3++ 2.5(HL),(,, Kex,2.5 =
* M(HL,),L(,, + 3H'
-
[M(HL2)&Im[H+l3
DEH+13
[M3+lE(HL)zltm2.5 [(HL)21trn2.5
(17)
(18)
plexes also supporta the formation of the two types of complexes (see section below on kinetics). Peppard made a similar observation on the formation of different types of lanthanide complexesin the extraction of lanthanides by di(nocty1)phosphinicacid into benzene.15 The Kex,2.5values for Eu and Yb and Kex,3values for all the lanthanides were determined from the intercepts of the slope 2.5 and slope 3 lines in Figure 2. These values are given in Table I. The Kex,3values increase from Pr to Yb, similar to the observation we have made in the CHC13-Hz0 system (Table 11.9 It may be seen from Table I that the Kex,3values in the micellar system are much higher than those in the CHC13-HzO system for the individual lanthanides but the difference in the Kax,3values between lanthanides is higher in the CHCls-HzO system. In other words, the two-phase system offers better selectivitybetween adjacent lanthanides but the extractabilityof the lanthanides is orders of magnitude better in the micellar system. The extraction behavior in the (15) Peppard, D. F.; Mason, G. W.; Lewey, S. J.Inorg. Nucl. Chem. 1965,27,2065-2073.
~~
KTOPO~
1.4 X lO-,
2.2
5.5 X
2.8 X lo3
f
f
0.058
740
0.85
560
Reference 9. M0.5.No dimension. M-O5. mined. (I
~
Kex.TOPOe
e M-I. f
X
lo3
Not deter-
micellar system is similar to the behavior in CHC13-HZO in the presence of a ligand such as trioctylphosphine oxide (TOPO),which forms a 1:l adduct with M(HL213.9 The Kex,3 value increases but the difference in the Kex,3values between adjacent lanthanides decreases in the presence of TOPO. The much higher extractibility of lanthanides by HBTMPP into Triton X-100 micelles compared to CHCl3 thus enables the detection of the M(HL&L species at low HBTMPP initial concentrations. The extraction equilibrium constant Kex,3can be expressed in terms of the stability constant ,!Iof the M(HLz)3complex in the aqueous phase, its distribution constant, KDC,~, the distribution constant of the extractant HBTMPP, KDR,and the dimerization constant, Kdrn (eq 19). The ratio of Kex,3
values in micelles and CHC13-HzO varies from 3 X 105 for Pr to 2 X lo4for Yb. It is evident that this difference must be entirely due to the differencein Km,3between the two systems as ,!I is the same and KDRand Kdrnare about the same in the two systems. It is unlikely that the KDCJof Pr-HBTMPP in micelles is about lo5times and that of Yb-HBTMPP 104 times their respective values in the CHC13-HzO system. As mentioned above, the variation of Kex,3values in Triton X-100 micelles between individual lanthanides resembles more closely the variation in the CHCl3-HZ0system in the presence of TOPO. The ratio of Kex,3values in the presence and absence of TOPO in the CHC13-Hz0 system yields the equilibrium constant, KTOPO, for the formation of M(HL&(TOPO) in CHCl3. These values in Table I indicate that the light lanthanides form stronger TOPO adducts than the heavy lanthanides with KTOPOchanging by a factor of 4 between light and heavy lanthanides. A similar ratio of Kex,3values in micelles and the CHC13-HzO system is a product of the ratio of K D Cvalues ,~ and the association equilibrium constant between the oxyethylenechains of Triton X-100 and M(HLz)3, namely, ( K r n ~ , 3 / K s x ~ , 3 ) K ~ r i and b n "SX" represent micelle and solvent extraction system, respectively). This composite value varies from 3 X lo5 for Pr to 2.1 X 104 for Yb and is about 2 orders of magnitude larger than KTOPOfor every lanthanide investigated. This suggests that the higher Kex,3 in Triton x-100 micelles is probably due to larger KDCJin these micelles and larger KTribn. We may expect KTribn to be larger than KTOPOas lanthanides in general have affinity toward oxygen-containing ligands and each Triton X-100 has an average of 10 oxyethylene chains. The encapsulation of the M(HLz)3in the Triton X-100 micelles may provide an additional enhancement to the value. We have conducted preliminary studies on the extraction of lan-
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 11, JUNE 1, 1993
the rate of dissociation of the M-HBTMPP complex as a sum of the rates in the bulk aqueous and micellar phases (eq 21).
R = ka[complexl [H+lVa+ k,[complexl,[H+l
Y"
-1
6
A-
-?
I
\
-2
-3
3
2
4
PH Flguro 3. Plots of log kobsvs pH for the dissociation of HBTMPP complexes of Pr, Eu, Tb, Ho, and Yb in 1% Triton X-100: [M(III)] = 5 X 10-6-1 X M. HBTMPP concentrations, [(HL)&: Pr (A), M; Eu (0)8.7 X M; Eu (0)6.9 X Tb (e),Ho (V) 4 X M; Yb M; Yb (R)3.5 X M; Yb (P)1.6 X M; Eu (0) 5X (0) 8.7 x 10-5 M.
thanides by HBTMPP in the CHCls-H20 system in the presence of Triton X-100 in CHC13. The extractibility of lanthanides increases significantly in the presence of Triton X-100; for example, the K,, in the presence of 0.01 M Triton X-100 is 1 order of magnitude larger than the values in the presence of 0.01 M T O P 0 for Pr, Eu, Ho, and Yb. The complete characterization of the extraction of lanthanides by HBTMPP in the presence of Triton X-100 is underway and will be the subject of a future publication. The Kex,Sand Kex,2,5 values can be utilized to determine the equilibrium constant for the conversion of M(HL2)ZL to M(HL2)sin the micellar phase (eq 20). It is evident that this
M(HL,),L,,j
+ 0.5(HL),(,j
+
M(HLz),(,j
The kinetic experiments were conducted such that the total concentration of the complex, [~ornplex]~, is limiting. Thus, the observed rate constant (quantity in bracket X [H+]) in eq 21 will be independent of V,, if k,/(V,KDc) is negligible k,. Such a situation can be compared to k,; i.e., kobs envisioned in the current studies even if ka >> k,, since KDC can be expected to be large (>lo6by comparisonto the CHC13HzO s y ~ t e m )based ,~ on the large magnitude of Kex. This means that the experimental conditions employed in these studies can only detect dissociation of the M-HBTMPP complexesin the micellar phase. The locus of the dissociation reaction in the micelle is an interesting question and most likely this reaction occurs at the aqueous-micelle interface as the distribution of protons to the bulk of the micelle is expected to be poor. The rate-limiting steps for the dissociation of the M(HL2)s and M(HL2I2Lcomplexes based on the above discussion are given in eq 22 and eq 23, respectively. The k, in eq 21 is a
M(HL,),,,,
+ H+
-
slow
M(HL2I2++ 2HL,,,
(22)
k3m
k2.5m
composite rate constant, comprising the rate constants for the dissociation of M(HLz)3and M(HL2)zLcomplexes. Thus the expression for kobs is eq 24, taking into account the equilibrium between M(HL&L and M(HL2)s (eq 20).
(20)
equilibrium constant Kadd = Ker,3/Kex,2.5.The Kedd values thus calculated for Eu and Yb are almost identical (Table I). We may infer from this that the reaction in eq 20 is equally important for the light and heavy lanthanides. This equilibrium is also evident in the kinetics of dissociation of M(HL&L and M(HL2)3by H+ as discussed in the following section.
Kineticsof Dissociation (Back-Extraction)of M-HBTMPP Complexes. The dependence of the pseudo-first-order rate constant, kobs, on the proton concentration for Pr, Eu, Tb, Ho, and Yb are shown in Figure 3. It is evident that the plot of log kobs vs pH has a slope of -1 at high and low total concentrations of the dimer [[(HL),lt,] in the micelle. This indicates the involvement of one proton in the rate-limiting step of the dissociation of the M(HL2)s and M(HL212L complexes. The observed rate constant was independent of the concentration of Triton X-100 in the range of 0.2-4% Triton X-100 at constant pH and concentration of M and HBTMPP. We have shown in our studies on the complexation of Ni2+ by 8-quinolinolin micelles that the complexation reaction occurs in the bulk aqueous and micellar phases.16 Following the model proposed in this work, we can express (16) Muralidharan, S.; Yu, W.; Tagashira, S.; Freiser, H. Langrnuir 1990, 6, 1190-1196.
V, =
The experimental ksmand k2.5, values are a product of the true rate constant for the reaction in the micelle and the distribution constants of the complexes or proton, depending on the location of the dissociation reaction. If the dissociation reaction occurs at the interface, then K D C Iand , ~ KDCi,2.5,the distribution constants of the M(HL& and M(HL212Lcomplexes between the bulk micelle and interface, will be incorporated in the observedk3, and k2.5mvalues, respectively. The distribution constant of the proton, KDH,between the bulk aqueous and bulk micellar phases will be incorporated in the observed kSmand k2.5mvalues if the dissociation between occurred in the bulk micellar phase. These distribution constants, K D C ~K~ci,2.5, ,~, and KDH,can be expected to be small (
