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Liquid—liquid extraction of alkali metal ions with non-ionic surfactant having a poly(oxyethylene) chain
311
Analytrca Chumca Acta, 256 (1992) 311-318
Elsevler Science Pubhshers B V . Amsterdam
Liquid-liquid extraction of alkali metal ions with non-ionic surfactant having a poly(oxyethylene) chain Yolchl Ikuchl,
Noboru Takahashl, Toshlo Suzuki and IGyoshl Sawada
Laboratory of Analytrcal Chumstry, Faculty of Sccence, Nugata Umuersrty, Nugata 950-21 (Japan)
(Recewed 8th May 1991)
Ah&act The Ion-pau extractlon of poly(oxyethylene) alkylphenyl ether (Tnton X-100) complexes of alkah metal Ions (Mf) wrth plcrate *on (PK-) mto 1,Zdlchloroethane (1,ZDCE) was studied The results of vapour pressure osmometry suggest a partlal dlssoclatlon of the Ion pair m 1,2-DCE Quantitative analysis of the extraction data revealed the extractlon of the Ion pair of Tnton X-10%alkah metal Ion urlth plcrate ion and dissoaatlon of the IOIIpau The thermodynamic constants of the extractlon and the dlssoclation of the Ion pairs were evaluated by takmg mto conslderatlon the actlvlty coefficients of Ionic species m the aqueous and 1,2-DCE phases The extractlon constants of large metal Ions, rubldlum and caesmm, are almost the same as that of potassium Ion, whereas those of sodium and hthmm tons decrease with decrease m the Ion sne The effect of the sue of the alkab metal ions on the Trlton X-100 extractlon system IS less Important than that on the 18-crown-6 extractlon system The dlssoclatlon constants of the Ion pans were almost the same lrrespectlve of the land of alkah metal Ion, and the mterlomc distance of the Ion pair between the catlomc complex and plcrate Ion was estimated to be about 6 k Keywords Alkah metals, ExtractIon, Surfactants
Non-ionic surfactants havmg a non-cyclic poly(oxyethylene) (POE) cham are known to form catlomc complexes with alkali and alkahne earth metal ions slmllarly to crown ethers [l-31 The complexes are extracted into organic solvents by forming ion pan-s mth hpophlllc anions This extraction system has been utdlzed for the determination of non-ionic surfactants 14-81 and of trace metals [g-12] and also for the sensor membrane of ion-selective electrodes [13,141 The extraction mechanism of non-cyclic POE complexes IS not well understood compared with that of crown ether complexes Yanaglda et al [ll investigated the ion-pan extraction of alkali and alkaline earth metal complexes of POE derlvatlves with various amons Yoshlda et al 1151studied the extraction of lanthanold ions with
polfioxyethylene) alkylphenyl ethers Although Yanaglda et al [l] tried to determine the composition of the Ion pairs by usmg a monodisperse POE denvatlve, octa(oxyethylene) monododecyl ether, they could not analyse the results quantltatlvely and attributed the devlatlon from stolchlometry to partial mlcelle formation of POE derivatives Consequently, the mechanism of the extraction of metal ions wrth POE derlvatrves 1s still open to question In this study, the ion-pmr extractlon of polfioxyethylene) alkylphenyl ether complexes of alkali metal ions v&h plcrate ion mto 1,2-dlchloroethane was studied together with vapour pressure osmometry The extraction eqtuhbna were analysed by takmg into conslderatlon the dlssoclatlon of the ion pair
0003-2670/92/$05 Oil 0 1992 - Elsevler Science Pubhshers B V All rights reserved
312
Y KIKUCHI
EXPERIMENTAL
Reagents
Polytoxyethylene) alkylphenyl ether (Trlton X-100) was purchased from Wako and was used as received This surfactant IS a polydlsperse compound whose average number of oxyethylene umts, nav, 1s about 10 Plcrlc acid (Wako) was recrystalhzed twice from dlst1lled water 1,2-D1chloroethane (1,2-DCE) (Wako) was washed three times with dlstllled water Potassmm plcrate was synthesized from potassium hydroMde and plcrlc acid and recrystallized twice from dlstllled water Other chemicals were of analytical-reagent grade Extractton procedure
A portlon of a 1,ZDCE solution (20 ml) contammg Trlton X-100 and an equal volume of an aqueous solution contammg plcr1c acid, alkali metal chloride and alkali metal hydroxide were placed m a centnfuge tube (50 ml) After shakmg m a thermostated water-bath for 30 mm at 25 L0 1 o C, It was centnfuged The pH of the aqueous solution was adjusted to 8-10 with alkah metal hydroxide solution The concentration of plcrate ion 1n the equlhbrated aqueous phase was determined by spectrophotometry (Hltachl U-3400) (E = 14400 1 mol-’ cm-l at 356 nm) A portion of the orgamc phase (5 ml) was transferred mto another centrifuge tube and allowed to evaporate, the residue was dissolved m 1O-3 M sodium hydroxide solution and the plcrate concentration was determmed by spectrophotometry The potassmm ion concentration m the organic phase was determmed by atomic absorption spectrometry (Shlmazu AA-640-01s) The concentration of potasaurn ion m the organic phase agreed with that of plcrate Ion w1thm expenmental error No dlstnbutlon of plcrate 1on to the organic phase m the absence of Trlton X-100 was measured spectrophotometrlcally The followmg expernnents under three sets of condltlons were performed C,,=Ol M, (a) CPK,,=2~10-~-5xlO-~M, Cs,=001M,(b)C,,~,~=1x10-4M,‘C,,=1x 10L3-0 1 M, C,,, = 0 01 M, (c) Cp,e,I= l’x 1O-4 M, C,,, = 0 1 M, Cs,,= 1 x 10-3-5 x 1O-2 M, where Cplcl and C,, refer to the uutlal concen-
ET AL
tratlons of plcrate and alkali metal ion m the aqueous solution respectively, and C,,, refers to the m1tlal concentration of Trlton X-100 m the organic solution Vapour pressure measurements
The vapour pressure measurements were made with a Corona Model 117 osmometer The mean molecular weight of Trlton X-100 was measured over the concentration range 2 5 X 10p3-1 5 X 1O-2 M Potassmm plcrate crystals (0 3-O 5 g) were shaken with 30 ml of 1,ZDCE solutions contammg various concentrations of Trlton X-100 (2 5 x 10e3-1 5 x lop2 M) m 50 ml centrifuge tubes for 30 mm at 25 & 0 1 o C After separation of the crystals, the vapour pressures of the solutions were measured The concentration of PIcrate Ion was determined by spectrophotometry
RESULTS
Llqutd-lrquld
extraction study
By assummg the extraction of the Ion pair of the Trlton X-100 (S) complex of alkah metal Ion (M+) with plcrate ion (PIG-), S,MLPIC;, the extraction equlhbrmm 1s expressed m a general form by mM++pPlc-+
sS,,s + S,MLPlc;,,
(1)
where the subscript org refers to the organic phase The extractlon constant, K,, 1s defined by
Kex=
[wcPl&g [M+l”Plc-lPPl”,r,
(2)
The eqtuhbrmm concentrations of plcrate ion m the organic and aqueous phases are approxlmated by the total concentrations of plcrate m each phase, CP,c,organd CP_,, respectively, that and CPs,.+ = [Plc-I 1% CPICerg=p[S,M~Plc;],, By u&g these relationship, Eqn 2 leads to log C,, 0rg= log K, + log p + m log[M+] +P
log CPlc,aq + s w%r,
(3)
Plots of log CpIc,Orgvs log CP,c,aqunder the conddlons of experiment (a) are shown m Fig la As can be seen from Eqn 3, the plots m Rg la
LIQUID-LIQUID
EXTRACTION
-6
OF ALKALI
METAL
313
IONS
-5 ‘09CPlC
oq
b
0
t
-3
-2 loglH+I
-1
-3
-2
-1
log[Slorg
Fig 1 Ion-pan extractjon of Trlton X-lOO-alkah metal 10”s with plcrate ron mto 1,2-DCE (a) Plots of log CPlcorg vs (a) (b) Plots of log Cplcorg ‘og CP,, aq for experiment (b) (c) Plots of p log CP,, aq vs log[M+] for experiment ‘og CPlC OrB - p log CRcdQ vs log[Sl,, for experiment (c) v LI’, o, Na+, 0, K+, A, Rb+, 0, Csf
should be linear with a slope p, as the concentrations of alkah metal ions, [M+], and Trlton X-100, is1erg, are kept virtually constant By using the value of p obtamed from Fig la, log CP,_,_ p log CP,c,aq is plotted as a function of log[M+] [expenment (b), Fig lb] or log[S],, [experiment cc>, Fig lcl The slopes of these plots should represent the coefficient m or s m Eqn 3 The values of p, m and s should be mtegral, because they correspond to the composltlon of the extracted Ion pair However, fractlonal numbers were obtained for these coefficients, VIZ, p = 0 53-O 62, m = 0 54-O 59 and s = 0 52-O 62 Hence this extraction system cannot be explamed by the eqmhbrmm m Eqn 1
Vapour pressure osmometry The mean molecular weight of Trlton X-100 in 1,ZDCE 1s plotted m Fig 2 as a function of the concentration of Trlton X-100 As can be seen from Fig 2, the molecular weight 1s constant irrespective of concentration over the range 2 5 X 10P3-1 5 x lo-’ M, and It was determined to be 638 7 Hence the average number of oxyethylene units was obtained as IZ, = 9 6 The value obtamed here agrees with the catalogue data, nav = 10 These facts Indicate that Trlton X-100 extsts as a monomeric form m 1,ZDCE and the formation of mlcelles 1s negligible m the concentration range used The vapour pressure of the 1,ZDCE solution of Trrton X-100 (2 5 x 10W3-1 5 x lo-’ M) contaming potassium plcrate was measured The number of solute molecules m the solution was divided by that of Trlton X-100 (the van’t Hoff factor, IJ The value of ls IS plotted as a function of the concentration of Trlton X-100 m Fig 3a As potassium plcrate 1s msoluble m 1,ZDCE m the absence of Trlton X-100, potassmm ion m the organic phase is necessarily reacting with Trlton X-100 Therefore, if s = 1 m Eqn 1, the number of solute molecules in the solution contammg potassium picrate should be equal to that of Trlton X-100, Ie , ts = 1 If the Trlton X-lOOpotassium ion (S-K+) complex contains two or more Trlton X-100 molecules, ls < 1 As can be
700
-
0 0 - “0
EE
on
n ”
“0
Y
0
600 $ ki 2 $
500 -
5 E” LOO-
0
5
10 Cg/10-3M
15
Fig 2 Mean molecular weight of Trlton X-100 as a functron of the total concentration of Trlton X-100
314
Y KIKUCHl
ET AL
By usmg the condltlons of electrical neutral@ and a mass balance of plcrate m 1,2-DCE, [SM+],,
= [Plc-]org
C Pqorg
[SM+Plc-I,,
=
(6) + [Plc-1,
(7)
we obtain the followmg 10 0
2
L
6
6
10
12
0
2
CS/~O+M
L
6
8
&s =
CP,C erg ’ ‘O+M
Rg 3 (a) Van’t Hoff factors, ls, of 1,ZDCE solutions contammg the ion pan of Tnton X-100-K+ with PIG- as a function of the total concentration of Trlton X-100 (b) Van’t Hoff factors ehmmated a contnbutlon of the free Trlton X-100, I~, as a function of the total concentration of picrate m the 1,2-DCE solution Sohd Ime, calculated curve
[Plc-l:,, C P1c,org
-
[PlC-
The van? Hoff factor eliminated a contrrbutlon of free Trlton X-100, zp, IS plotted m Fig 3b as a function of the total concentration of plcrate m the organic phase By consldermg the dlssoclatlon of the ion pair, lp IS given by 1 = [SM+Plc-Ior,
seen from Fig 3a, however, ls > 1, which mdlcates that the number of solute molecules m 1,ZDCE increases m the presence of potassmm prcrate
(8)
lorg
+ [SM+],,
P
+
[Plc-]org (9)
fl
L
P1c.org
Substltutlon of Eqns 6 and 7 m Eqn 9 leads to Ip = 1 +
[pdc-lw3
(10)
P1c,org
DISCUSSION
Substltutlon of Eqn 8 mto Eqn 10 leads to
Analysis of osmometnc data As mentioned above, we obtamed
unreasonable results for the composltlon of the extracted species Yanaglda et al [ll also reported slmllar results and attributed thts devlatlon from stolchlometry to partlal mlcelle formatlon of POE derlvatlves As shown m Fig 2, however, it is evident that Trlton X-100 exists m a monomeric form under these expenmental condltlons As shown m Fig 3a, the number of solute molecules m 1,ZDCE Increases m the presence of potassmm plcrate This suggests partial dlssoclatlon of the Ion pan If It IS assumed that the composltlon of the ion pan 1s 1 1 1 with respect to S M+ PIG-, the dlssoclatlon of the ion pair can be wrltten as SM +PIG& + SM,:, + Plc,
(4)
The dlssoclatlon constant of the ion pair is defmed by K
= dls
[SM+]o,[Plc-lo, [SM+Plc-I,,,
(5)
z,=l+
-&
+ (Ki, + 4Kd,sCPqxg)1’2 2C P1c,org
(11)
The best-fit curve calculated by usmg Eqn 11 1s shown by the sohd line m Fig 3b The good ftttmg of the curve with the experlmental data confirms the dissociation of the Ion pan given by Eqn 4 Although the data were not analysed by a rigorous treatment such as correction of a&v@, the dlssoclatlon constant of the Ion pair was estimated to be roughly Kdls = 1O-34 Analysts of extraction data
As suggested by the osmometrlc study, extraction of an alkali metal plcrate with Trlton X-100 IS interpreted by the extractlon and dlssoclatlon of the ion pair K,, M++ PIG-+ Sorg =+ SM+Plc,
K&s + SM,:, + Plc, (12)
By takmg mto conslderatlon the actlvlty coefflclent of the lomc species, the thermodynamic
LIQUID-LIQUID
EXTRACTION
OF ALKALI
METAL
31.5
IONS
constants of extraction, K$, and dnsoaatlon, K&, of the ion pair are defined as follows
(14)
[SM+Plc-I,,,
where f, IS the mean activity coefficient of M+ and PIG- m the aqueous phase and f, erg IS that m the 1,2-DCE phase, f, of SM,f,, and Plc, were evaluated by using an extended and fho Debye-&kc1 equation The concentrations of lomc species m 1,2-DCE (SM& and Plc;J are low under the experlmental condltlons used Nevertheless, It 1s necessary to correct the actlvlty coefficients of the lomc species because of the low dielectric constant of 1,ZDCE (E = 10 36 at 25°C) The dlstrlbutlon ratlo of picrate, D, is defined as
D = cPlc,org/Glc,aq = [SM+Plc-],,g+ [Plc-lo, (15)
[Plc-]
D =
13 and 14 m Eqn
15 leads
K:‘[M+][S]o,f: x ( 1 + K~,6”[SM+Plc-]~~“f;b,)
From Eqns
14 and 7, we obtam
(16) Eqn
C p,c ,,rg = [SM+Plc-I,, + K~,b/‘[SM+Plc-]~!,f;t,, By solving the quadratic PIG-]A{;, we obtain [SM+Plc-]A;,2
=
[
Eqn
(17) 17 for
[SM+
-K,9,“2f,10,,
1 (18)
+ ( Ka;~org + 4GK,org ) L’2 /2 Substltutlon
of Eqn
L -
1 + (1+ 4Gw,orgf:.or*G,‘)1’2 (20)
KO = [SM+lorg[Plc-]org~:,org
of Eqns
n
(13)
K,9, = [M+][Plc-][S],,,f:
Substitution to
F 1s given by
F=l+
[SM+Plc-]orp
da
where the function
18 m Eqn
16 leads to
log D = log K,9, + log[M+ ] + log[S],,, + 21og f * + log P
(19)
The mltlal concentrations of alkali metal ion CC,, = 0 1 MI and Trlton X-100 CC,, = 0 01 MI are much higher than that of plcrate (C,,J under the condrtlons of expenment (a) Consequently, the free concentrations of alkali metal ion, [M+], and Trlton X-100, [Sl,,, can be approxlmated to CM,, and Cs ,, respectively, and can be taken as constant The change m log D, therefore, depends only on log F under the condltlons of experiment (a> Hence Eqn 19 can be normalized to the function given by 2 Y=log
1+ -1+
X=log
(1+4xy
(21)
x
where x corresponds to CpIc,Orgf &rgKd~-’ The results m Fig la are replotted as log D vs log GlcOrB m Ag 4a The values of the constants Ki,, and Kzx are obtained by means of curve fittmg of the plots m Fig 4a with the normalized curve, Eqn 21, from the dlsplacements of the abscissa and ordinate, respectively As the mean actlvlty coefficient m the 1,2-DCE depends on the concentration of phase, f k,orgr lomc species, I e , on K&, it was corrected by means of a successive approxlmatlon The concentratlons of lomc species m l,ZDCE, [SM+l,,, were calculated by usmg the value and [PO,rgr of the of K,,s obtained wlthout the correction actlvlty coefficient The value of Kdqs m the secondary approxlmatlon was obtamed by curve fittmg with the normahzed curve corrected with the activity coefficient, f, erg Three iterations of this successive approxlmatlon were sufficient to give the converged values of K& and f +org The best-fit curves thus obtained are dep&d m Fig 4a by solid hnes By using the values of Kdqs and K,q, thus obtamed, the expernnental results of experiments (b) and (c) were analysed As can be seen from Eqn 19, the plots of log D-log F - 2 log f +
316
Y KIKUCHI
1 1 1 The values of the constants K& and Kz! were refined with all the expernnental data shown m Fig 4a-c by means of the successtve approxlmatlon with a non-linear regression usmg a mlcrocomputer The dlssoclatlon constants, Kdqs, and extractlon constants, Kz!, thus obtained are summarized m Table 1 These values agreed with the values obtained by curve fittmg to wlthm +02 The good agreement of the value of log K& of Kf thus obtamed with that estimated by osmometry (log Kdls = -3 4) strongly supports the equlhbrnnn proposed here (Eqn 12)
a
I -L
-5 ‘o%c
lag[WI
ET AL
-3 erg
1% [Slorg
Fig 4 (a) Plots of log D vs log Cplcors for experiment (a) Sohd hnes, normahzed cmves (b) Plots of log D -log F - 2 log f vs log[M+ I for expernnent (b) Solid Imes, straight hnes with a slope of umty (c) Plots of log D-log F vs log[S], for expernnent (c) Sohd hnes, strarght hnes with a slope of umty Symbols as m Fig 1
vs log[M+l for experment (b> and log D - log F vs log[S],, for experiment Cc) should give straight hnes with a slope of umty As shown m Fig 4b and c, these plots conform well with the predlction The fact that the results deplcted m Fig 4a-c show good agreement with the calculated lines confirms the extractlon and dissociation of the Ion-pair consistmg of Trlton X-100 M+ PIG-=
Iiktractlon constant A number of studies on the extraction of alkah metals with crown ethers have been reported The selectivity for alkah metal Ions has been explained from the viewpomt of the size-fit concept, 1 e , the confornuty of the sue of metal ion with the cavity size of a crown ether [16-231 The values of log Kzx for the Trlton X-100 system are plotted as a function of the ionic radu of alkali metals m Fig 5, where the results of the extractlon of alkah metal picrates with l&crown-6 into benzene are also deplcted 120,211 With l&crown6, potassium ion, which has the optimum size for the cavity of the ether, shows the largest extraction constant among alkali metal Ions Rubidium and caesmm ions are too large to enter the host cavity and hthmm and sodium ions are too small to fit Moreover, the high dehydration energies of these small size ions 1s unfavourable for the formation of crown ether complexes This selectlvlty for alkali metal ions is high m the l&crown-6 system In the Trlton X-100 system, the central metal ion IS considered to be surrounded by the
TABLE
1
Logarithms of extractlon and mtenomc distances,
constants and dlssoclatlon a, of the Ion pairs
constants
Parameter
LI
Na
K
Rb
Cs
Log K,q, Log Kdqs
1 10 -348
254 -358
3 84 -348
3 86 -349
3 67 -336
60
56
60
60
67
a (A)
LIQUID-LIQUID
EXTRACTION
OF ALKALI
METAL
317
IONS
Dmocuztlon of the ion paw ln 1,2-DCE Ion-pair formation was expressed by Blerrum on the basis of an electrostatic attraction between ions of opposite charges [25] He proposed the followmg theoretical equation to connect the mterlomc distance, a, with the dlssoclatlon constant ’
Q(b)
(22)
where Q(b) = Lbx-” ew(x)
15
10
a5 Iomc
radius
20
IA
Rg 5 Plots of logarithm of extractlon constant as a function of lomc radn Open symbols, extractlon of alkah metal prcrate urlth Triton X-100 mto 1,2-DCE, closed symbols, extractlon of alkah metal plcrate with l&crown-6 mto benzene
poly(oxyethylene) chain of Trlton X-100 with a helical conformation 1241 Because of its shape, the complexes of non-cyclic POE compounds may be called “turban” m contradlstmctlon to “crown” complexes As seen from Fig 5, the extractlon constants of alkali metals with a large ion size, K+, Rb+ and Cs+, are substantially the same These results can be interpreted by a flexible structure of Trlton X-100, 1 e , a free cavity size On the other hand, the extractability of the smaller alkali metal ions decreases with decreasmg lomc radius This might be interpreted m terms of the higher dehydration energy of the smaller ion rather than size flttmg The dlfferences m log Kz! values between the alkali metal ions are smaller than those for the 18-crown-6 system Hence the effect of size fitting on the formation of the flexible “turban” complex 1s less important than that on the formation of the “crown” complex
dx, b =
Iz,z,le2 aCkT
(23)
N IS Avogadro’s number, z, and z, are the charges on ions z and J, E is the dielectric constant of the solvent and T IS absolute temperature In the present system, as 1,ZDCE IS a non-coordinating solvent, ion pan formation between the catlomc “turban” complex and plcrate ion 1s explained predommantly by the electrostatic mteractlon The ionic distances of the extracted ion pairs, a, calculated using BJerrum’s equation, are listed m Table 1 Neither the cation nor the amon 1s spherical and the charges on the complex cation and picrate ion are localized on the central metal ion and the proton-dissociated oxygen of the picrate ion, respectively It is, therefore, difficult to treat the a value obtained here exactly, but It can be tentatively taken as the distance between the Oof plcrate and the central metal ion of the “turban”complex As can be seen from Table 1, the a values are almost the same irrespective of the kmd of alkali metal ion This distance (ca 6 A) 1s about 3 A longer than the sum of the ionic radius of the oxygen ion and alkali metal ion, which indicates that the alkali metal ion IS surrounded by the oxyethylene chain and the O- of the plcrate ion 1s situated outside the oxyethylene chain Yanaglda et al [ll and Lm 131indicated that more than seven oxyethylene units are required for a sufflclent interaction with K+ The number of oxyethylene units in Trlton X-100, nav = 9 6, might be sufficient to surround any kmd of alkali metal ion
Y KIKLJCHI ET AL
318
In the present system, as Trlton X-100 1s a polydlsperse compound, average a values were obtamed Further studies using monodlsperse compounds having different lengths of the poly(oxyethylene) chain wdl provide a detailed mechanism of the ion-pair extraction
REFERENCES S Yanaglda, K Takahashl and M Okahara, Bull Chem Sot Jpn ,50 (1977) 1386 AMY Jaber, G J Moody and J D R Thomas, J Inorg Nucl Chem , 39 (1977) 1689 K J LIU, Macromolecules, 1 (1968) 308 L Favretto, B Stancher and F Tums, Analyst, 103 (1978) 955 L Favretto, B Stancher and F Tums, Analyst, 104 (1979) 241 L Favretto and F Tums, Analyst, 101 (1976) 198 K Toe], S Motomlzu and T Umano, Talanta, 29 (1982) 103 M J Whltaker, Anal Chum Acta, 179 (1986) 459 T Sotobayashl, T Suzuki and S Tonouchl, Chem Lett , (1976) 585
10 T Sotobayashl, T Suzuki and K Yamada, Chem L&t, (1976) 77 11 T Sotobayashl, T Suzuki and H Kudo, J RadIoanal Chem, 36 (1977) 145 12 T Suzuki, N Murakaml and T Sotobayashl, Bull Chem Sot Jpn , 53 (1980) 1453 13 R J Levms, Anal Chem , 43 (1971) 1045 14 D L Jones, G J Moody and J D R Thomas, Analyst, 106 (1981) 439 15 I Yoshlda, R Takeshlta, K Ueno and M Takagl, Anal SCI , 2 (1986) 53 16 C J Pedersen, J Am Chem Sot, 89 (1967) 7017 17 C J Pedersen, J Am Chem Sot, 92 (1970) 386 18 H K Frensdorff, J Am Chem Sot, 93 (1971) 600 19 H K Frensdorff, J Am Chem Sot , 93 (1971) 4684 20 Y Takeda and H Goto, Bull Chem Sot Jpn , 52 (1979) 1920 21 Y Takeda and Y Matsumoto, Bull Chem Sot Jpn, 60 (1987) 2313 22 Y Tdkeda, Bull Chem Sot Jpn, 53 (1980) 2393 23 Y Takeda, T &mura, Y Kudo and H Matsuda, Bull Chem Sot Jpn , 62 (1989) 2885 24 M D Adams, P W Wade and R D Hancock, Talanta, 37 (1990) 875 25 N Bjerrum, Dan Vldensk Selsk Mat Fys Medd , 7 No 9 (1926) 1
Analytrca Chumca Acta, 256 (1992) 311-318
Elsevler Science Pubhshers B V . Amsterdam
Liquid-liquid extraction of alkali metal ions with non-ionic surfactant having a poly(oxyethylene) chain Yolchl Ikuchl,
Noboru Takahashl, Toshlo Suzuki and IGyoshl Sawada
Laboratory of Analytrcal Chumstry, Faculty of Sccence, Nugata Umuersrty, Nugata 950-21 (Japan)
(Recewed 8th May 1991)
Ah&act The Ion-pau extractlon of poly(oxyethylene) alkylphenyl ether (Tnton X-100) complexes of alkah metal Ions (Mf) wrth plcrate *on (PK-) mto 1,Zdlchloroethane (1,ZDCE) was studied The results of vapour pressure osmometry suggest a partlal dlssoclatlon of the Ion pair m 1,2-DCE Quantitative analysis of the extraction data revealed the extractlon of the Ion pair of Tnton X-10%alkah metal Ion urlth plcrate ion and dissoaatlon of the IOIIpau The thermodynamic constants of the extractlon and the dlssoclation of the Ion pairs were evaluated by takmg mto conslderatlon the actlvlty coefficients of Ionic species m the aqueous and 1,2-DCE phases The extractlon constants of large metal Ions, rubldlum and caesmm, are almost the same as that of potassium Ion, whereas those of sodium and hthmm tons decrease with decrease m the Ion sne The effect of the sue of the alkab metal ions on the Trlton X-100 extractlon system IS less Important than that on the 18-crown-6 extractlon system The dlssoclatlon constants of the Ion pans were almost the same lrrespectlve of the land of alkah metal Ion, and the mterlomc distance of the Ion pair between the catlomc complex and plcrate Ion was estimated to be about 6 k Keywords Alkah metals, ExtractIon, Surfactants
Non-ionic surfactants havmg a non-cyclic poly(oxyethylene) (POE) cham are known to form catlomc complexes with alkali and alkahne earth metal ions slmllarly to crown ethers [l-31 The complexes are extracted into organic solvents by forming ion pan-s mth hpophlllc anions This extraction system has been utdlzed for the determination of non-ionic surfactants 14-81 and of trace metals [g-12] and also for the sensor membrane of ion-selective electrodes [13,141 The extraction mechanism of non-cyclic POE complexes IS not well understood compared with that of crown ether complexes Yanaglda et al [ll investigated the ion-pan extraction of alkali and alkaline earth metal complexes of POE derlvatlves with various amons Yoshlda et al 1151studied the extraction of lanthanold ions with
polfioxyethylene) alkylphenyl ethers Although Yanaglda et al [l] tried to determine the composition of the Ion pairs by usmg a monodisperse POE denvatlve, octa(oxyethylene) monododecyl ether, they could not analyse the results quantltatlvely and attributed the devlatlon from stolchlometry to partial mlcelle formation of POE derivatives Consequently, the mechanism of the extraction of metal ions wrth POE derlvatrves 1s still open to question In this study, the ion-pmr extractlon of polfioxyethylene) alkylphenyl ether complexes of alkali metal ions v&h plcrate ion mto 1,2-dlchloroethane was studied together with vapour pressure osmometry The extraction eqtuhbna were analysed by takmg into conslderatlon the dlssoclatlon of the ion pair
0003-2670/92/$05 Oil 0 1992 - Elsevler Science Pubhshers B V All rights reserved
312
Y KIKUCHI
EXPERIMENTAL
Reagents
Polytoxyethylene) alkylphenyl ether (Trlton X-100) was purchased from Wako and was used as received This surfactant IS a polydlsperse compound whose average number of oxyethylene umts, nav, 1s about 10 Plcrlc acid (Wako) was recrystalhzed twice from dlst1lled water 1,2-D1chloroethane (1,2-DCE) (Wako) was washed three times with dlstllled water Potassmm plcrate was synthesized from potassium hydroMde and plcrlc acid and recrystallized twice from dlstllled water Other chemicals were of analytical-reagent grade Extractton procedure
A portlon of a 1,ZDCE solution (20 ml) contammg Trlton X-100 and an equal volume of an aqueous solution contammg plcr1c acid, alkali metal chloride and alkali metal hydroxide were placed m a centnfuge tube (50 ml) After shakmg m a thermostated water-bath for 30 mm at 25 L0 1 o C, It was centnfuged The pH of the aqueous solution was adjusted to 8-10 with alkah metal hydroxide solution The concentration of plcrate ion 1n the equlhbrated aqueous phase was determined by spectrophotometry (Hltachl U-3400) (E = 14400 1 mol-’ cm-l at 356 nm) A portion of the orgamc phase (5 ml) was transferred mto another centrifuge tube and allowed to evaporate, the residue was dissolved m 1O-3 M sodium hydroxide solution and the plcrate concentration was determmed by spectrophotometry The potassmm ion concentration m the organic phase was determmed by atomic absorption spectrometry (Shlmazu AA-640-01s) The concentration of potasaurn ion m the organic phase agreed with that of plcrate Ion w1thm expenmental error No dlstnbutlon of plcrate 1on to the organic phase m the absence of Trlton X-100 was measured spectrophotometrlcally The followmg expernnents under three sets of condltlons were performed C,,=Ol M, (a) CPK,,=2~10-~-5xlO-~M, Cs,=001M,(b)C,,~,~=1x10-4M,‘C,,=1x 10L3-0 1 M, C,,, = 0 01 M, (c) Cp,e,I= l’x 1O-4 M, C,,, = 0 1 M, Cs,,= 1 x 10-3-5 x 1O-2 M, where Cplcl and C,, refer to the uutlal concen-
ET AL
tratlons of plcrate and alkali metal ion m the aqueous solution respectively, and C,,, refers to the m1tlal concentration of Trlton X-100 m the organic solution Vapour pressure measurements
The vapour pressure measurements were made with a Corona Model 117 osmometer The mean molecular weight of Trlton X-100 was measured over the concentration range 2 5 X 10p3-1 5 X 1O-2 M Potassmm plcrate crystals (0 3-O 5 g) were shaken with 30 ml of 1,ZDCE solutions contammg various concentrations of Trlton X-100 (2 5 x 10e3-1 5 x lop2 M) m 50 ml centrifuge tubes for 30 mm at 25 & 0 1 o C After separation of the crystals, the vapour pressures of the solutions were measured The concentration of PIcrate Ion was determined by spectrophotometry
RESULTS
Llqutd-lrquld
extraction study
By assummg the extraction of the Ion pair of the Trlton X-100 (S) complex of alkah metal Ion (M+) with plcrate ion (PIG-), S,MLPIC;, the extraction equlhbrmm 1s expressed m a general form by mM++pPlc-+
sS,,s + S,MLPlc;,,
(1)
where the subscript org refers to the organic phase The extractlon constant, K,, 1s defined by
Kex=
[wcPl&g [M+l”Plc-lPPl”,r,
(2)
The eqtuhbrmm concentrations of plcrate ion m the organic and aqueous phases are approxlmated by the total concentrations of plcrate m each phase, CP,c,organd CP_,, respectively, that and CPs,.+ = [Plc-I 1% CPICerg=p[S,M~Plc;],, By u&g these relationship, Eqn 2 leads to log C,, 0rg= log K, + log p + m log[M+] +P
log CPlc,aq + s w%r,
(3)
Plots of log CpIc,Orgvs log CP,c,aqunder the conddlons of experiment (a) are shown m Fig la As can be seen from Eqn 3, the plots m Rg la
LIQUID-LIQUID
EXTRACTION
-6
OF ALKALI
METAL
313
IONS
-5 ‘09CPlC
oq
b
0
t
-3
-2 loglH+I
-1
-3
-2
-1
log[Slorg
Fig 1 Ion-pan extractjon of Trlton X-lOO-alkah metal 10”s with plcrate ron mto 1,2-DCE (a) Plots of log CPlcorg vs (a) (b) Plots of log Cplcorg ‘og CP,, aq for experiment (b) (c) Plots of p log CP,, aq vs log[M+] for experiment ‘og CPlC OrB - p log CRcdQ vs log[Sl,, for experiment (c) v LI’, o, Na+, 0, K+, A, Rb+, 0, Csf
should be linear with a slope p, as the concentrations of alkah metal ions, [M+], and Trlton X-100, is1erg, are kept virtually constant By using the value of p obtamed from Fig la, log CP,_,_ p log CP,c,aq is plotted as a function of log[M+] [expenment (b), Fig lb] or log[S],, [experiment cc>, Fig lcl The slopes of these plots should represent the coefficient m or s m Eqn 3 The values of p, m and s should be mtegral, because they correspond to the composltlon of the extracted Ion pair However, fractlonal numbers were obtained for these coefficients, VIZ, p = 0 53-O 62, m = 0 54-O 59 and s = 0 52-O 62 Hence this extraction system cannot be explamed by the eqmhbrmm m Eqn 1
Vapour pressure osmometry The mean molecular weight of Trlton X-100 in 1,ZDCE 1s plotted m Fig 2 as a function of the concentration of Trlton X-100 As can be seen from Fig 2, the molecular weight 1s constant irrespective of concentration over the range 2 5 X 10P3-1 5 x lo-’ M, and It was determined to be 638 7 Hence the average number of oxyethylene units was obtained as IZ, = 9 6 The value obtamed here agrees with the catalogue data, nav = 10 These facts Indicate that Trlton X-100 extsts as a monomeric form m 1,ZDCE and the formation of mlcelles 1s negligible m the concentration range used The vapour pressure of the 1,ZDCE solution of Trrton X-100 (2 5 x 10W3-1 5 x lo-’ M) contaming potassium plcrate was measured The number of solute molecules m the solution was divided by that of Trlton X-100 (the van’t Hoff factor, IJ The value of ls IS plotted as a function of the concentration of Trlton X-100 m Fig 3a As potassium plcrate 1s msoluble m 1,ZDCE m the absence of Trlton X-100, potassmm ion m the organic phase is necessarily reacting with Trlton X-100 Therefore, if s = 1 m Eqn 1, the number of solute molecules in the solution contammg potassium picrate should be equal to that of Trlton X-100, Ie , ts = 1 If the Trlton X-lOOpotassium ion (S-K+) complex contains two or more Trlton X-100 molecules, ls < 1 As can be
700
-
0 0 - “0
EE
on
n ”
“0
Y
0
600 $ ki 2 $
500 -
5 E” LOO-
0
5
10 Cg/10-3M
15
Fig 2 Mean molecular weight of Trlton X-100 as a functron of the total concentration of Trlton X-100
314
Y KIKUCHl
ET AL
By usmg the condltlons of electrical neutral@ and a mass balance of plcrate m 1,2-DCE, [SM+],,
= [Plc-]org
C Pqorg
[SM+Plc-I,,
=
(6) + [Plc-1,
(7)
we obtain the followmg 10 0
2
L
6
6
10
12
0
2
CS/~O+M
L
6
8
&s =
CP,C erg ’ ‘O+M
Rg 3 (a) Van’t Hoff factors, ls, of 1,ZDCE solutions contammg the ion pan of Tnton X-100-K+ with PIG- as a function of the total concentration of Trlton X-100 (b) Van’t Hoff factors ehmmated a contnbutlon of the free Trlton X-100, I~, as a function of the total concentration of picrate m the 1,2-DCE solution Sohd Ime, calculated curve
[Plc-l:,, C P1c,org
-
[PlC-
The van? Hoff factor eliminated a contrrbutlon of free Trlton X-100, zp, IS plotted m Fig 3b as a function of the total concentration of plcrate m the organic phase By consldermg the dlssoclatlon of the ion pair, lp IS given by 1 = [SM+Plc-Ior,
seen from Fig 3a, however, ls > 1, which mdlcates that the number of solute molecules m 1,ZDCE increases m the presence of potassmm prcrate
(8)
lorg
+ [SM+],,
P
+
[Plc-]org (9)
fl
L
P1c.org
Substltutlon of Eqns 6 and 7 m Eqn 9 leads to Ip = 1 +
[pdc-lw3
(10)
P1c,org
DISCUSSION
Substltutlon of Eqn 8 mto Eqn 10 leads to
Analysis of osmometnc data As mentioned above, we obtamed
unreasonable results for the composltlon of the extracted species Yanaglda et al [ll also reported slmllar results and attributed thts devlatlon from stolchlometry to partlal mlcelle formatlon of POE derlvatlves As shown m Fig 2, however, it is evident that Trlton X-100 exists m a monomeric form under these expenmental condltlons As shown m Fig 3a, the number of solute molecules m 1,ZDCE Increases m the presence of potassmm plcrate This suggests partial dlssoclatlon of the Ion pan If It IS assumed that the composltlon of the ion pan 1s 1 1 1 with respect to S M+ PIG-, the dlssoclatlon of the ion pair can be wrltten as SM +PIG& + SM,:, + Plc,
(4)
The dlssoclatlon constant of the ion pair is defmed by K
= dls
[SM+]o,[Plc-lo, [SM+Plc-I,,,
(5)
z,=l+
-&
+ (Ki, + 4Kd,sCPqxg)1’2 2C P1c,org
(11)
The best-fit curve calculated by usmg Eqn 11 1s shown by the sohd line m Fig 3b The good ftttmg of the curve with the experlmental data confirms the dissociation of the Ion pan given by Eqn 4 Although the data were not analysed by a rigorous treatment such as correction of a&v@, the dlssoclatlon constant of the Ion pair was estimated to be roughly Kdls = 1O-34 Analysts of extraction data
As suggested by the osmometrlc study, extraction of an alkali metal plcrate with Trlton X-100 IS interpreted by the extractlon and dlssoclatlon of the ion pair K,, M++ PIG-+ Sorg =+ SM+Plc,
K&s + SM,:, + Plc, (12)
By takmg mto conslderatlon the actlvlty coefflclent of the lomc species, the thermodynamic
LIQUID-LIQUID
EXTRACTION
OF ALKALI
METAL
31.5
IONS
constants of extraction, K$, and dnsoaatlon, K&, of the ion pair are defined as follows
(14)
[SM+Plc-I,,,
where f, IS the mean activity coefficient of M+ and PIG- m the aqueous phase and f, erg IS that m the 1,2-DCE phase, f, of SM,f,, and Plc, were evaluated by using an extended and fho Debye-&kc1 equation The concentrations of lomc species m 1,2-DCE (SM& and Plc;J are low under the experlmental condltlons used Nevertheless, It 1s necessary to correct the actlvlty coefficients of the lomc species because of the low dielectric constant of 1,ZDCE (E = 10 36 at 25°C) The dlstrlbutlon ratlo of picrate, D, is defined as
D = cPlc,org/Glc,aq = [SM+Plc-],,g+ [Plc-lo, (15)
[Plc-]
D =
13 and 14 m Eqn
15 leads
K:‘[M+][S]o,f: x ( 1 + K~,6”[SM+Plc-]~~“f;b,)
From Eqns
14 and 7, we obtam
(16) Eqn
C p,c ,,rg = [SM+Plc-I,, + K~,b/‘[SM+Plc-]~!,f;t,, By solving the quadratic PIG-]A{;, we obtain [SM+Plc-]A;,2
=
[
Eqn
(17) 17 for
[SM+
-K,9,“2f,10,,
1 (18)
+ ( Ka;~org + 4GK,org ) L’2 /2 Substltutlon
of Eqn
L -
1 + (1+ 4Gw,orgf:.or*G,‘)1’2 (20)
KO = [SM+lorg[Plc-]org~:,org
of Eqns
n
(13)
K,9, = [M+][Plc-][S],,,f:
Substitution to
F 1s given by
F=l+
[SM+Plc-]orp
da
where the function
18 m Eqn
16 leads to
log D = log K,9, + log[M+ ] + log[S],,, + 21og f * + log P
(19)
The mltlal concentrations of alkali metal ion CC,, = 0 1 MI and Trlton X-100 CC,, = 0 01 MI are much higher than that of plcrate (C,,J under the condrtlons of expenment (a) Consequently, the free concentrations of alkali metal ion, [M+], and Trlton X-100, [Sl,,, can be approxlmated to CM,, and Cs ,, respectively, and can be taken as constant The change m log D, therefore, depends only on log F under the condltlons of experiment (a> Hence Eqn 19 can be normalized to the function given by 2 Y=log
1+ -1+
X=log
(1+4xy
(21)
x
where x corresponds to CpIc,Orgf &rgKd~-’ The results m Fig la are replotted as log D vs log GlcOrB m Ag 4a The values of the constants Ki,, and Kzx are obtained by means of curve fittmg of the plots m Fig 4a with the normalized curve, Eqn 21, from the dlsplacements of the abscissa and ordinate, respectively As the mean actlvlty coefficient m the 1,2-DCE depends on the concentration of phase, f k,orgr lomc species, I e , on K&, it was corrected by means of a successive approxlmatlon The concentratlons of lomc species m l,ZDCE, [SM+l,,, were calculated by usmg the value and [PO,rgr of the of K,,s obtained wlthout the correction actlvlty coefficient The value of Kdqs m the secondary approxlmatlon was obtamed by curve fittmg with the normahzed curve corrected with the activity coefficient, f, erg Three iterations of this successive approxlmatlon were sufficient to give the converged values of K& and f +org The best-fit curves thus obtained are dep&d m Fig 4a by solid hnes By using the values of Kdqs and K,q, thus obtamed, the expernnental results of experiments (b) and (c) were analysed As can be seen from Eqn 19, the plots of log D-log F - 2 log f +
316
Y KIKUCHI
1 1 1 The values of the constants K& and Kz! were refined with all the expernnental data shown m Fig 4a-c by means of the successtve approxlmatlon with a non-linear regression usmg a mlcrocomputer The dlssoclatlon constants, Kdqs, and extractlon constants, Kz!, thus obtained are summarized m Table 1 These values agreed with the values obtained by curve fittmg to wlthm +02 The good agreement of the value of log K& of Kf thus obtamed with that estimated by osmometry (log Kdls = -3 4) strongly supports the equlhbrnnn proposed here (Eqn 12)
a
I -L
-5 ‘o%c
lag[WI
ET AL
-3 erg
1% [Slorg
Fig 4 (a) Plots of log D vs log Cplcors for experiment (a) Sohd hnes, normahzed cmves (b) Plots of log D -log F - 2 log f vs log[M+ I for expernnent (b) Solid Imes, straight hnes with a slope of umty (c) Plots of log D-log F vs log[S], for expernnent (c) Sohd hnes, strarght hnes with a slope of umty Symbols as m Fig 1
vs log[M+l for experment (b> and log D - log F vs log[S],, for experiment Cc) should give straight hnes with a slope of umty As shown m Fig 4b and c, these plots conform well with the predlction The fact that the results deplcted m Fig 4a-c show good agreement with the calculated lines confirms the extractlon and dissociation of the Ion-pair consistmg of Trlton X-100 M+ PIG-=
Iiktractlon constant A number of studies on the extraction of alkah metals with crown ethers have been reported The selectivity for alkah metal Ions has been explained from the viewpomt of the size-fit concept, 1 e , the confornuty of the sue of metal ion with the cavity size of a crown ether [16-231 The values of log Kzx for the Trlton X-100 system are plotted as a function of the ionic radu of alkali metals m Fig 5, where the results of the extractlon of alkah metal picrates with l&crown-6 into benzene are also deplcted 120,211 With l&crown6, potassium ion, which has the optimum size for the cavity of the ether, shows the largest extraction constant among alkali metal Ions Rubidium and caesmm ions are too large to enter the host cavity and hthmm and sodium ions are too small to fit Moreover, the high dehydration energies of these small size ions 1s unfavourable for the formation of crown ether complexes This selectlvlty for alkali metal ions is high m the l&crown-6 system In the Trlton X-100 system, the central metal ion IS considered to be surrounded by the
TABLE
1
Logarithms of extractlon and mtenomc distances,
constants and dlssoclatlon a, of the Ion pairs
constants
Parameter
LI
Na
K
Rb
Cs
Log K,q, Log Kdqs
1 10 -348
254 -358
3 84 -348
3 86 -349
3 67 -336
60
56
60
60
67
a (A)
LIQUID-LIQUID
EXTRACTION
OF ALKALI
METAL
317
IONS
Dmocuztlon of the ion paw ln 1,2-DCE Ion-pair formation was expressed by Blerrum on the basis of an electrostatic attraction between ions of opposite charges [25] He proposed the followmg theoretical equation to connect the mterlomc distance, a, with the dlssoclatlon constant ’
Q(b)
(22)
where Q(b) = Lbx-” ew(x)
15
10
a5 Iomc
radius
20
IA
Rg 5 Plots of logarithm of extractlon constant as a function of lomc radn Open symbols, extractlon of alkah metal prcrate urlth Triton X-100 mto 1,2-DCE, closed symbols, extractlon of alkah metal plcrate with l&crown-6 mto benzene
poly(oxyethylene) chain of Trlton X-100 with a helical conformation 1241 Because of its shape, the complexes of non-cyclic POE compounds may be called “turban” m contradlstmctlon to “crown” complexes As seen from Fig 5, the extractlon constants of alkali metals with a large ion size, K+, Rb+ and Cs+, are substantially the same These results can be interpreted by a flexible structure of Trlton X-100, 1 e , a free cavity size On the other hand, the extractability of the smaller alkali metal ions decreases with decreasmg lomc radius This might be interpreted m terms of the higher dehydration energy of the smaller ion rather than size flttmg The dlfferences m log Kz! values between the alkali metal ions are smaller than those for the 18-crown-6 system Hence the effect of size fitting on the formation of the flexible “turban” complex 1s less important than that on the formation of the “crown” complex
dx, b =
Iz,z,le2 aCkT
(23)
N IS Avogadro’s number, z, and z, are the charges on ions z and J, E is the dielectric constant of the solvent and T IS absolute temperature In the present system, as 1,ZDCE IS a non-coordinating solvent, ion pan formation between the catlomc “turban” complex and plcrate ion 1s explained predommantly by the electrostatic mteractlon The ionic distances of the extracted ion pairs, a, calculated using BJerrum’s equation, are listed m Table 1 Neither the cation nor the amon 1s spherical and the charges on the complex cation and picrate ion are localized on the central metal ion and the proton-dissociated oxygen of the picrate ion, respectively It is, therefore, difficult to treat the a value obtained here exactly, but It can be tentatively taken as the distance between the Oof plcrate and the central metal ion of the “turban”complex As can be seen from Table 1, the a values are almost the same irrespective of the kmd of alkali metal ion This distance (ca 6 A) 1s about 3 A longer than the sum of the ionic radius of the oxygen ion and alkali metal ion, which indicates that the alkali metal ion IS surrounded by the oxyethylene chain and the O- of the plcrate ion 1s situated outside the oxyethylene chain Yanaglda et al [ll and Lm 131indicated that more than seven oxyethylene units are required for a sufflclent interaction with K+ The number of oxyethylene units in Trlton X-100, nav = 9 6, might be sufficient to surround any kmd of alkali metal ion
Y KIKLJCHI ET AL
318
In the present system, as Trlton X-100 1s a polydlsperse compound, average a values were obtamed Further studies using monodlsperse compounds having different lengths of the poly(oxyethylene) chain wdl provide a detailed mechanism of the ion-pair extraction
REFERENCES S Yanaglda, K Takahashl and M Okahara, Bull Chem Sot Jpn ,50 (1977) 1386 AMY Jaber, G J Moody and J D R Thomas, J Inorg Nucl Chem , 39 (1977) 1689 K J LIU, Macromolecules, 1 (1968) 308 L Favretto, B Stancher and F Tums, Analyst, 103 (1978) 955 L Favretto, B Stancher and F Tums, Analyst, 104 (1979) 241 L Favretto and F Tums, Analyst, 101 (1976) 198 K Toe], S Motomlzu and T Umano, Talanta, 29 (1982) 103 M J Whltaker, Anal Chum Acta, 179 (1986) 459 T Sotobayashl, T Suzuki and S Tonouchl, Chem Lett , (1976) 585
10 T Sotobayashl, T Suzuki and K Yamada, Chem L&t, (1976) 77 11 T Sotobayashl, T Suzuki and H Kudo, J RadIoanal Chem, 36 (1977) 145 12 T Suzuki, N Murakaml and T Sotobayashl, Bull Chem Sot Jpn , 53 (1980) 1453 13 R J Levms, Anal Chem , 43 (1971) 1045 14 D L Jones, G J Moody and J D R Thomas, Analyst, 106 (1981) 439 15 I Yoshlda, R Takeshlta, K Ueno and M Takagl, Anal SCI , 2 (1986) 53 16 C J Pedersen, J Am Chem Sot, 89 (1967) 7017 17 C J Pedersen, J Am Chem Sot, 92 (1970) 386 18 H K Frensdorff, J Am Chem Sot, 93 (1971) 600 19 H K Frensdorff, J Am Chem Sot , 93 (1971) 4684 20 Y Takeda and H Goto, Bull Chem Sot Jpn , 52 (1979) 1920 21 Y Takeda and Y Matsumoto, Bull Chem Sot Jpn, 60 (1987) 2313 22 Y Tdkeda, Bull Chem Sot Jpn, 53 (1980) 2393 23 Y Takeda, T &mura, Y Kudo and H Matsuda, Bull Chem Sot Jpn , 62 (1989) 2885 24 M D Adams, P W Wade and R D Hancock, Talanta, 37 (1990) 875 25 N Bjerrum, Dan Vldensk Selsk Mat Fys Medd , 7 No 9 (1926) 1