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Ascending water electrode studies of metal extractants 4-acyl-5-pyrazolones and selected tervalent lanthanide ions. Lin. Sinru, and Henry. Freiser. An...
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Anal. Chem. 1987,59,2834-2838

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Ascending Water Electrode Studies of Metal Extractants. 4-Acyl-5-pyrazolones and Selected Tervalent Lanthanide Ions Lin Sinru' and Henry Freiser* Strategic Metals Recovery Research Facility, Department of Chemistry, University of Arizona, Tucson, Arizona 85721

The polarographic and chronopotentlometrlcbehavior of the chelating extractants 1-phenyl-3-methyl-4-trifiuoroacetyl-5pyrazoione (HTFP) and I-phenyl-3-methyl-4-benzoyl-5pyrazolone (HBP) In the dlchloroethane (=E)-aqueous systems have been characterized at the ascending water electrode (AWE) and the stationary water electrode (SWE). The nature of the phase transfer processes both In the absence and presence of tervalent lanthanide metal ions has been elucidated. Self-adduct and mixed ligand chelate formations have been deduced (the latter when trlocytylphosphine oxide (TOPO) Is present). The reverslbiiity, transfer coefficlents, and transfer rate constants of the band anions were deduced. This electrochemical approach Is shown to provide novel insights into solvent extraction processes.

It has been demonstrated in this laboratory (1-5) that the investigation of faradaic ion transfer across an externally polarized interface of an aqueous-immiscible organic solvent pair provides powerful insights into the mechanisms of liquid-liquid mass transfer processes, such as those involved in solvent extraction, biomembrane processes, and the like. By use of current scan polarography a t the ascending water electrode (AWE) and chronopotentiometry at the stationary water electrode (SWE), the nature and sequence of steps involved in heterogeneous acid-base chemistry of 1 , l O phenanthroline (phen) and several of its derivatives ( I ) have been tracked in detail, as have the kinetics and mechanism of the formation of phen complexes with several transitionmetal ions and their manner of extraction (2). With this approach, the behavior of 0-containing "neutral carriers", e.g., valinomycin (3) and crown ethers ( 4 , 5 )and their potassium ion complexes, has also been investigated. On the strength of these earlier studies, it is now opportune to investigate the more widely used weakly acidic chelating extractants which form neutral metal chelates. Inasmuch as these electrochemical techniques focus on ion transfer, evidence will be obtained about charge species, such as chelating extractant anions and chelate intermediates, and, indirectly, of the neutral species themselves. In this report, we report the behavior of the acylpyrazolones (I) which, like the 0-diketones (11)they formally resemble, are capable of extracting a wide range of metal ions, but at significantly lower pH ranges (6). In particular, 1-phenyl-3-methyl-4-trifluoroacetyl-5H3C-C

I

3 R-C-CH-

-R'

$

R-

C-C n

O

~

2

1

cb

i

H I

I1

pyrazolone (where R = CF,) (HTFP), one of the extractants On study leave from the Shanghai Institute of Metallurgy, Academy of Sciences of China, Shanghai, People's Republic of China 200050. 0003-2700/87/0359-2834$01.50/0

applied to the separation of tervalent lanthanide ions (7), and, for comparison, 1-phenyl-3-methyl-4-benzoyl-5-pyrazolone (R = C6H5) (HBP), both alone and in the presence of an adductant, tri-n-octylphosphine oxide, with representative lanthanides, La3+, Gd3+,and Yb3+will be described.

EXPERIMENTAL SECTION Current scan polarography at the ascending water electrode (AWE), chronopotentiometry, and current reversal chronopotentiometry at the stationary water electrode (SWE) involved apparatus and procedures that have been described earlier ( I , 5-8).

The electrolytic cell was slightly modified in order to improve the stability of the organic reference electrode. The elimination of tetramethylammoniumchloride from both aqueous and organic reference solutions (which contain 1 M LiCl and 0.01 M tetraheptylammonium tetraphenylborate,respectively) of the electrode resulted in readings that were stable for at least a month, whereas the earlier organic reference electrode had to be replaced at least weekly. The potential of the modified organic reference electrode is largely determined by the charge of the double layer, inasmuch as there is no common ion transferring across the aqueous/organic interface. As long as no charge flows through the electrode, i.e., no charging or discharging occurs, the potential is reproducible. The net effect is a shift in the @E of 106 mV (standard deviation 7 mV) in the positive direction, compared to the reference electrode containing TMA+Cl-. HPMBP (Beijing Chemicals Factory, China) was used as received. HPMTFP was synthesized by Dr. S. Umetani in this laboratory (7). DCE (Aldrich Chemical Co., Inc.) was used without further purification. The electrolyte used in the DCE phase was 0.01 M THA'TPB-, prepared by mixing THA+Br-dissolved in DCE and aqueous Na'TPB- in stoichiometric proportions (1). The lanthanide oxides, La203,Gd203,and Yb203(Alfa Products), were used as received to prepare solutions of their acetate salts. Tri-n-octylphosphineoxide (Eastman Kodak Co.), TOPO, was used without further purification.

RESULTS AND DISCUSSION Behavior of Acylpyrazolones. A typical polarogram, seen in Figure 1,was obtained by using 1 M Na2S04at pH 4.0 as aqueous supporting electrolyte with 4.0 X M HTFP in DCE having 0.01 M THA+TPB- as supporting electrolyte. The potential difference, A S , is defined as the electrical potential of the aqueous phase with respect to the potential of the organic phase. Following the terminology in conventional polarography, the polarographic wave in Figure 1,which corresponds to the flow of negative charge from the aqueous to the organic phase (or positive charge in the opposite direction), is referred to as a cathodic wave. Figures 2 and 3 show the chronopotentiogram and that for current reversal chronopotentiometry, for the same electrolysis system as described above for Figure 1. Distinct polarographic waves were observed for HTFP a t pH values above 2, but for HBP no wave was observed until the pH was above 4,where pH adjustment was accomplished with 0.02 M Na acetate and H2S04 When Na2S04was replaced by 0.4M sodium acetate, the minimum pH values at which the cathodic waves appear rose to 4 and 6 for HTFP and HBP, respectively. That the cathodic wave arises from a transfer process that is essentially controlled by diffusion of the neutral acyl1987 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 59, NO. 24, DECEMBER 15, 1987

.

I

I -

'

2835

*l

ld Q 0

a

01.

-1001: 2

; ;*

8

0

l*!

10

PH Figure 4. Dependence of half wave potential on pH of aqueous phase: aqueous phase, Na2S0, 1 M; DCE phase, THA-TPB 0.01 M and HPMTFP 0.4 mM (0)or HPMBP 0.4 mM (0).

Figure 1. Current scan polarogram at AWE aqueous phase, Na,SO, 1 M, pH 4.9; DCE phase, THAoTPB 0.01 M and HPMTFP of (1) 0 mM, (2) 0.3 mM.

I

f

the transfer process within the time scale of the experiment. Values of the diffusion coefficient, D, of HPMTFP and HPMBP in DCE, determined from the values of i ~obtained ~ / ~ at various currents under our experimental conditions, are 4.4 (f0.3)X lo4 and 3.5 (f0.3)X 104/s, respectively. These findings indicate clearly that the transferring species from the aqueous phase into the organic phase is a singly charged anion. Since the cathodic waves can be obtained at relatively low pH values, hydroxide ion may be ruled out. They must arise from the pyrazolone anion transferring electrochemically from the aqueous phase into the organic phase following the diffusion of the neutral compound into the aqueous solution and its subsequent dissociation. The half wave potential undergoes a positive shift with increasing pH (nearly 59 mV/pH unit) below pH 5 (see eq 5) and above pH 10 (see eq 3) but is independent of pH in the range of 5-10 (see eq 4) (Figure 4). These observations conform to the following scheme: The cathodic wave represents the transfer of the pyrazolonate anion, P, from the aqueous to the organic phase. Thus, P- P(o) (by electrochemicaltransfer). The aqueous anion concentration [P-] can be calculated from the reasonable assumption that the phase distribution and aqueous acid dissociation equilibria are sufficiently rapid to be established within the time frame of the electrochemical transfer

-

HP&H+

Figure 3. Current reversal chronopotentlogram at SWE: aqueous phase, Na2S041 M, pH 4.3 DCE phase, THAaTPB 0.01 M and HPMTFP 0.3 mM; current: 8 MA; area of electrode, 0.4 om2.

pyrazolone in DCE solution is supported by the following findings: 1. The limiting current, or the wave height, is directly proportional to the DCE concentration of pyrazolone and is essentially independent of the aqueous pH in the range studied. 2. The wave height exhibits a half order dependence on the hydrostatic head of the aqueous solution in the AWE. 3. The logarithmic analysis of this wave results in a straight line of slope 64 mV, very close to the theoretical value for the transfer of a singly charged species. 4. Analysis of the chronopotentiograms reveals that the transition time constant, i d 2 / C 0 ,is independent of i, signifying that no adsorption or chemical reaction is observed in

+ P-

where H P stands for the pyrazolone, o denotes the organic phase, KD the distribution constant, and Ka the acid dissociation constant of HP, and from which (9)

For the potential difference between two phases in the cathodic process, we have

By use of the self-dissociation equilibrium for water [P-] = K a [OH-][HP] K&d

A t the higher pH values, [OH-] is sufficiently high so that its diffusion need not be considered in relation to that of the pyrazolone in the organic phase (IO, 11). The half-wave po-

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ANALYTICAL CHEMISTRY, VOL. 59, NO. 24, DECEMBER 15, 1987

tential of the cathodic wave shown in Figure 1 can then be expressed by

(3)

At intermediate pH values, the half wave potential can be given by eq 4. Since [HP], > [OH-] ASll2

1 1

w 1 / 2=

=

(4) At lower pH values, the half wave potential of the wave can be given by the expression

w u 2= RT

DHP(~)

RT

KD RT

A@”p- - - ln -- - In - - - In [H+] (5) 2F DpF K, F The current reversal chronopotentiogram shown in Figure 3 was obtained when the reverse current is equal to the “forward” current, if. As may be seen, the reverse transition time, 7,, is equal to one-third of the forward transition time, tf, signifying that the electrochemical process involved is not irreversible. Further, the anodic and cathodic curves are slightly separated, indicating a small overpotential is required to reverse the electrochemical process. This separation increases with pH, indicating that the electrochemical process under investigation is quasi-reversible at higher pH values. It is well-known that current reversal chronopotentiometry provides not only a qualitative estimation of reversibility of an electrode process but, by examination of the ratio of 7f/7,, a quantitative evaluation of the kinetic parameters of the process, as well. The transfer coefficient, a, can be determined from the potential vs. time behavior of the reverse process. For a quasi-reversible process, a plot of E against In [(7 + 1)ll2 - 2t1i2]was constructed. This plot should be linear with a slope of RTInF(1 - a) (12). (Here t is the electrolysis time in the reverse process and 7 is the transition time of the forward electrolysis process.) The apparent transfer coefficient, a , for transport of the TFP- between sodium solution at pH 8 and the DCE solution, 0.47, was calculated from the slope of the line obtained. The transfer rate constant can be obtained by the method developed by Anderson and Macero (13)and Beyerlein and Nicholson (14), briefly described below. The pyrmlone anion is present only in the aqueous solution before the applied current flows through the system. It is assumed that DF,o= Dp-. If lifl = li,l and cy is within 0.3-0.7, k, can be measured by the expression

K = if/nFC,k,

(6)

where C, is the initial bulk DCE concentration of pyrazolone expressed in millimoles per liter, if is given in mA/cm2, and n and F have their usual meaning. The kinetic parameter K can be determined from the plot of the equation

x 59 a =2 log [(P + l ) ’ / 2 + K]2 n

(7)

where AE, in mV, is the difference between E, and Ef ( E , occurs at 0.2157, in the reverse step and Ef at t , / = ~ 0.25 ~ in the forward step), 7f and 7, are the transition times in the forward and reverse process, respectively, tf is the electrolysis time in the forward step. This method holds when A E is

Figure 5. Current scan polarograms at AWE: aqueous phase, NaOAc 0.2 M and La3+(1 and 2) 0.01 M and (3) 0 M, pH (1) 6.9 and (2 and 3)6.5; DCE phase, THA-TPB 0.01 M and (1) HTFP 0.5 mM and (2and

3) HPMBP 1 mM.

between 10 and 100 mV. The error is not more than lo%, an acceptable uncertainty for a rate constant. The transfer rate constants of HTFP at the interface between the DCE solution containing 0.01 M THA+TPB- and the 1 M sodium sulfate solution at pH 4.3 and 8 determined and 1.4 X by the method described above are 5.4 X cm/s (lid = li,l = 19.3 FA/cm2), respectively. The reversibility of an electrode process depends on the nature of the electrochemical experiment. Transport rate values in an electrolysis system can change with different types of electrochemical perturbations. A process will appear reversible when it is examined by methods in which the charge transfer rate constant is much larger (ca. 10 times larger) than the transport rate value, but it appears to be irreversible when examined by methods in which the transport rate of the species is much higher (14-17). In the present work, the transport rate of HTFP is 6.3 X cm/s for chronopotentiometry. Obviously,the transfer process can be regarded as reversible, at low pH values, e.g., 4.3, when it is predominantly controlled by diffusion, but as quasi-reversible, i.e., controlled by both diffusion and transfer rate a t the higher pH, since here the transfer rate constant is only twice the transport rate. This explains the increase in separation between anodic and cathodic curves in the current reversal chronopotentiogram as the pH increases. Behavior of Acylpyrazolones in the Presence of Metal Ions. When the aqueous phase in the system under polarographic observation contains metal ions such as lanthanides, cadmium,zinc, cobalt, nickel, etc., an additional cathodic wave appears. Polarogram 1in Figure 5 was obtained for a 0.5 mM HTFP solution in DCE in contact with an aqueous phase that is 0.2 M NaOAc and 0.01 M La(OAc)* In addition to the dissociated anion wave of height id, there is an additional cathodic wave of height i, corresponding to the electrochemicaltransfer of an anionic La chelate complex from the aqueous into the DCE phase. Polarograms 2 and 3 in Figure 5 were obtained when HBP in the DCE phase was in contact with an 0.2 M NaOAc solution with and without La(OAc)* The cathodic background current in the polarograms arises from the transfer of BPanion. Characteristics of i,. The anionic La complex wave can be observed at pH values higher than 4.5 for both HBP and HTFP. When La3+is in large excess, i, increases somewhat with pH. When HBP is in excess, however, i, is a maximum at a pH of about 6. When La3+is in large excess, i, is proportional to the concentration of the pyrazolone. The sum of id and i, is almost equal to id(,$, obtained in the absence of La3+,provided the pyrazolone concentration is the same in both cases. Figure 6 shows the dependence of i, and i d on the concentration of La3+in the aqueous phase: i, increases while

ANALYTICAL CHEMISTRY, VOL. 59, NO. 24, DECEMBER 15, 1987

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50. B

1

30.0

i0.0 . [Laa 1 . q . b M )

30.0

50.0 .

'

70.0

CHPMBPlJmM

Figure 6. Dependence of i' on concentration of Las+ In aqueous phase: aqueous phase, NaOAc 1 M and La3+,pH 8.6; DCE phase, THA.TPB 0.01 M and HPMTFP 0.5 mM, i,," obtained without La3+.

Figure 7. Dependence of i' on concentrationof HPMBP in DCE phase: aqueous phase, NaOAc 0.2 M and La3+ 0.16 mM ph 6 . 4 DCE phase, THA-TPB 0.01 M and HPMBP.

id decreases with increasing La3+at lower La3+concentrations. Both wave heights are almost independent of [La3+],however, as La3+becomes stoichiometrically in excess. The sum of id and i, remains equal to id,o throughout the range of the [La3+] used. These findings indicate that i, results from a singly charged anion, in which one pyrazolone is involved, transferring into the DCE phase from the aqueous phase, because id,o corresponds to the transfer of the dissociated singly charged pyrazolone anion (v.s.). Thus it would appear that the species which transfers results in i, is La(OAc),P- (where P refers to a dissociated pyrazolone anion) when sodium acetate is used as aqueous electrolyte. The observation of current reversal chronopotentiometry that there is no reverse wave for i, can probably be attributed to the formation of the neutral complex Lap3 in the DCE phase after La(OAc),P- transfers there. Effect of Pyrazolone Concentration. Although i, increases with pyrazolone concentration when La3+is in large excess, it decreases with increasing pyrazolone concentration when the pyrazolone is in large excess (Figure 7). The decrease of i, can be attributed to the reduction of the concentration of complex anion, L ~ ( O A C ) ~ by P - ,the formation of neutral complex, LaP3,in the aqueous phase. Shortly before i, reachea its maximum value, the aqueous droplets rising from the AWE through the DCE phase start to appear turbid. The turbidity becomes more pronounced as the concentration of HBP increases. Most probably this turbidity is caused by the neutral complex precipitation. Neutral complex formation can proceed according to the equation

part of the parabolic curve of i, vs. [HPMBP]@ At the top of the parabolic curve, we have

+

L ~ ( O A C ) ~ P -n H P

P

LaP3(HP),-2

+ 30Ac- + 2H+ (8)

where 0, the equilibrium constant, is given by

P=

[L~P,.HP,-,][OAC-]~[H+]~ [La(OAc),P-] [H P ] fl

(9)

The concentration ratio of the neutral complex to the complex anion can be expressed as [L*~.HP~-zI [La(0Ac)3P-]

--

[HPI" [O Ac-I [H+l

(10)

The concentration ratio in the left side of eq 10 can be obtained from the dependence of i, on [HPMBPl0,i.e., the falling

ia(max)

= K[LdOAc)3P-lm,

(11)

where K is the current constant. Due to neutral complex formation, ia decreases from ia(-). At the falling part we have

i, = K{[La(OAc),P-],,

- [LaP,(HP),-,]) = K [ L ~ ( O A C ) ~ P(12) -]

Substituting the current for the concentration ratio of the left side of eq 10 leads to log [(ia(max)- ia)/41 = log (~/KD[OAC-]~[H+]~) + n log [HP], (13) where

KD = [HP]O/ [HP]

(14)

with a value of 102.sfor both pyrazolones (18). From eq 13, the variation of log - i,)/i,] with log [HBP],, keeping the aqueous phase composition constant, must be linear with a slope of n, i.e., the number of pyrazolone ligands involved in the neutral complex. The values of n from lines constructed from data a t pH values of 6.4,7.6, and 8.5 are 3.1,3.3, and 2.2, respectively, indicating that there are three ligands when the pH is 8 or less, but that only two are present in the complex at higher values. Thus, the neutral complex formed in the aqueous phase when [HBP], >> [La3+] is a self-adduct chelate complex, LaP3.HP, at moderate pH values. At higher pH values, however, the neutral species formed in the aqueous phase is the simple chelate, LaP3, reflecting that at higher pH values, the HBP exists entirely in its dissociated form in this phase. Equation 8 predicts that the formation of the neutral complex will be inhibited by increasing acetate, i.e., i, will increase with [OAc-] if HBP remains constant (provided it is in large excess over [La3+])until it reaches a maximum where further increases in [OAc-] have no further effect. The experiments are in accord with the prediction. Let the value of i, obtained at the [OAc-] at which it is maximum be called I. It can be considered that no neutral complex is present in the aqueous phase at this point. A t lower [OAc-1, the decrease in wave height (I- i,) will be proportional to the concentration of the neutral complex formed. With eq 9, we then have log [i,/(Z - i,)] = log ([H+]2/p[HP],,n)

+ 3 log [OAC-] (15)

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ANALYTICAL CHEMISTRY, VOL. 59, NO. 24, DECEMBER 15, 1987

The plot of log [i,/(I- i,)] against log [OAc-] obtained at pH 6.5 with [HP], constant is linear with a slope of almost 3 (2.8). This finding unequivocally demonstrates that the complex anion whose transfer gives rise to this wave contains three acetate anions, since all of them are released by formation of the neutral Lap,. Effect of Trioctylphosphine Oxide (TOPO). TOPO is an excellent extractant for some metals and is widely used in conjunction with an acidic extractant to get a “synergistic” enhancement of extraction. It was found that i, is suppressed when TOPO is present in the DCE phase, decreasing with increasing [TOPO],. The plot of i, vs. [HBPIowith TOPO present gives the same shape as that without TOPO (Figure 7). Also, a turbidity in the aqueous phase can be observed as the concentration of HBP is higher than that at which i, is close to its maximum. From these findings, it may be concluded that the suppression of i, is due to the formation of a neutral complex involving TOPO. The number of TOPO molecules attached to the neutral complex can also be evaluated by an analysis of the dependence of i, on [TOPOlowhen [HBPIo> [La3+]. If the formation of the neutral complex containing TOPO proceeds according to the equation L ~ ( O A C ) ~+P nTOPO + 2P- P1 LaP,(TOPO), 30Ac- (16)

-

+

When TOPO is absent in the DCE phase, we have

ioa = K[La(OAc),P-]’

(17)

with TOPO present

i, = K{[L~(OAC)~P-]’ - [LaPJTOPO),]]

(18)

from eq 16, 17, and 18, the following expression can be obtained:

log [(io” - ia)/ia] = log (Pl[p-]2/K~’[OAC-]3) + log [TOP010 (19) where

KD’ = [TOPO],/[TOPO]

(20)

with a value of >IO5 (19). A plot of log [(ioa- i,)/iOa]vs. log [TOPOlo made when [HBPIo = 15 mM and pH 8.5 is linear with a slope of 0.9, indicating that one TOPO is incorporated into the neutral complex, i.e., that at higher pH (>8) an adduct complex with TOPO, LaP3.TOP0, is formed, though no self-adduct complex forms. One would expect that an adduct

with TOPO can also be formed at lower pH (C8). It follows from the suppression in i, by TOPO present in the DCE phase that the synergic enhancement is caused by the formation of the more extractable neutral species in the presence of an adductant. It was observed that gadolinium and ytterbium behave in the same manner as lanthanum does in the above series of experiments. The results obtained by polarographicinvestigations in the present work indicate strongly that those extractable neutral species, LaP3, LaP3.HP, or LaP,.TOPO, can be formed in the aqueous phase; otherwise i, could not be reduced by the formation of those neutral species in the organic phase. Finally, this work demonstrates the high utility of current scan polarography and its associated chronopotentiometric techniques in the study of intimate details of metal extraction systems. Registry No. HTFP, 1691-93-6; HBP, 4551-69-3; DCE, 1300-21-6;TOPO, 78-50-2;THA’TPB-, 22560-28-7;Gd, 7440-54-2; Yb, 7440-64-4;La, 7439-91-0;HzO,7732-18-5;Na2S04,7757-82-6; NaOAc. 127-09-3.

LITERATURE CITED Yoshida. Z.; Freiser, H. J . Electroanal. Chem. 1984, 762,307. Yoshida, 2.; Freiser, H. Inorg. Chem. 1984, 23. 3931-3935. Yoshida, Z.; Freiser, H. J . Electroanal. Chem. 1984, 779, 31-39. Lin, S.; Frelser, H. J . Electroanal. Chem. 1985, 797, 437-439. Lin, S.; Zhao. 2 . ; Freiser, H. J . Electroanal. Chem. 1986. 210, 137- 146. Zolotov, Y. A. Extraction of Chelate Compounds; Humphrey Science Publishers: Ann Arbor, MI, 1970. Umetani, S.; Freiser, H. Inorg. Chem. in press. Cunningham, L.; Freiser, H. Langmuir 1985, 7 , 537-541. Morrison, G. H.; Freiser, H. Solvent Extraction in Analytical Chemistry; Wiley: New York, 1957. Homolka, D.; Hung, L.; Hofmanova, A.; Khalil, M. W.; Koryta, J.; M a r s cek, V.; Samec, Z.; Sen, S. K.; Vanysek, P.; Weber, J.; Brezina, M.; Janda, M.; Stibor. I. Anal. Chem. 1980, 52, 1606. Vanysek, P.: Ruth, W.; Koryta, J. J . Electroanal. Chem. 1983, 748, 117. Berzins, T.; Delahay, P. J . Am. Chem. SOC. 1953, 75,4205. Anderson, L. B.; Macero, D. J. Anal. Chem. 1985, 37,322. Beyerlein, F. H.; Nicholson. R. S. Anal. Chem. 1988, 4 0 , 286. Galus, 2. Fundamentals of Electrochemical Analysis ; Ellis Horwood, Ltd.: New York, 1976; Chapter 3. Sinru, L.; Qiangsheng, F. Anal. Chem. 1981, 53, 1006. Sinru, L.; Qiangsheng, F. Anal. Chem. 1982, 5 4 , 1362. Huang, C.; Freiser, H. Solvent Extr. Ion Exch. 1986, 4(1), 41. IUPAC Equilibrium Constants of Liquid-Liquid Distribution Reactions ; Marcus, Y., Kertes, S., Yanir, Y., Eds.; Butterworths: England, 1974; Part 1.

REED for review January 27,1987. Accepted July 10,1987. This research was supported from a grant by the National Science Foundation.