Extraction of Several Divalent Metal Picrates by 18-Crown-6 Ether Derivatives into Benzene: A Refinement of Methods for Analyzing Extraction Equilibria

Three kinds of extraction constants, Kex, Kex, and Kex+, were evaluated from the improved model that the following three component-equilibria were added to a previously-proposed model for an overall extraction: M + A MA, MLABz + ABz MLA2,Bz, and A ABz. Here, Kex, Kex, and Kex+ were defined as [MLA2]Bz/([M][L]Bz[A]), [MLA]Bz[A]Bz/([M][L]Bz[A]), and [MLA]Bz/([M][L]Bz[A]), respectively; the subscript “Bz” denotes benzene as an organic phase. The symbols correspond to M = Ca and Pb, L = 18-crown-6 ether (18C6) and dibenzo-18C6 (DB18C6), and A = picrate ion. The ion-pair formation constant for M + A MA at M = Pb in an aqueous phase was also determined at 298 K and ionic strength of zero by an extraction of HA into 1,2-dichloroethane and Bz with the presence of Pb in the aqueous phase. The Kex values re-evaluated from the present model were in agreement with those determined by the previous extraction model. Individual distribution constants of A into Bz were almost constant irrespective of kinds of M and L employed. Furthermore, the composition-determination method of the ion pairs, MLA2, extracted into Bz was re-examined. Similar analyses were performed in the SrA2-, BaA2-18C6, and SrA2-DB18C6 systems without considering the formation of MA in the aqueous phases.

into DCE and nitrobenzene saturated with water (Kudo et al., 2011).Additionally, the extraction of CdBr 2 or CdPic 2 by 18C6 into various diluents with lower polarities, such as Bz, chloroform, dichloromethane, and DCE, has been studied (Kudo et al., 2013).However, these papers (Kudo, Harashima et al., 2011;Kudo, Horiuchi et al., 2013) did not verify what kind of effect changes of M 2+ and L give on magnitudes of the individual distribution constants (K D,A ) of A  .
In the present paper, we re-analyzed the MPic 2 -L extraction data into Bz for M = Ca, Sr, Ba, and Pb and L = 18C6 and DB18C6 by adding the above two equilibria, namely ion-pair formation of MLPic + with Pic  in the organic phase and the distribution of Pic  between the two phases, and an ion-pair formation for CaPic + or PbPic + in the aqueous phase to the previously-proposed model (Takeda & Kato, 1979) (see the section 3.2).However, the accuracies of the equilibrium analyses were obviously less than those of the analyses reported previously for the Cd(II) systems (Kudo et al., 2013).In the course of such analyses, the authors discussed a determination-method of the ion-pair formation constant (K MA ) between divalent metal ions, M 2+ , and A  in aqueous solutions saturated with DCE or Bz based on an extraction procedure, instead of potentiometric one (Kudo, 2013), and then determined the K PbPic value at 298 K. Also, the composition-determination (Kudo et al., 2013;Takeda & Kato, 1979;Takeda, 1979;Takeda & Nishida, 1989;Katsuta et al., 2000) of species with M(II) extracted into Bz was precisely re-examined, because its procedure has been based on some limitations, such as the presences of an excess of M 2+ in the aqueous phase and an excess of MLA 2 in the organic one.Moreover, properties of the above extraction systems were briefly re-discussed on the basis of three kinds of extraction constants (K ex , K ex , and K ex+ ) (Kudo et al., 2013), in which the latter two constants were newly determined for the present systems.
This study was mainly carried out for clarifying effects of introduction of these component equilibria on overall extraction equilibrium.Speaking more clearly, (i) does the introduction of their constants to the extraction model (Takeda & Kato,1979) proposed before largely change the magnitude of the extraction constant, K ex ?Also, (ii) we would like to clarify whether the introduced K D,Pic value becomes a constant or not for an employed diluent.Moreover, (iii) does the limitations described above really hold for the composition-determination in the extraction model presented here?These questions were examined using the above MPic 2 and L. At least, the authors have not encountered a detailed discussion on the question (iii).Benzene was selected as a representative among less-polar diluents and expected to be a standard diluent against other ones which will be treated in future.

Chemicals
Picric acid (HPic; hydrate, 99.5%) was purchased from Wako Pure Chemical Industries, Japan.Its purity was checked by acid-base titration.Aqueous solutions of lead nitrate {guaranteed reagent (GR) grade: 99.5%, Kanto Chemical Co. Ltd., Japan} were titrated by di-sodium salt of EDTA.Nitric acid was GR grade (60 to 61%, Kanto Chemical Co.Ltd.) and used without any purification.Both diluents, DCE (99.5%, Kanto Chemical Co.Ltd.) and Bz (>99.5%,Wako Pure Chemical Industries), were GR grades; these were washed three-times with water and then saturated with water (Kudo et al., 2013).Other chemicals were of GR grade.A tap water was distilled once and then was purified by passing through Autopure system (Yamato/Millipore, type WT101 UV) (Kudo & Takeuchi, 2013).This water was employed for preparation of all aqueous solutions.

HPic Extraction into DCE in the Presence of Pb(NO 3 ) 2 in the Aqueous Phase
First, mixtures composed of (0.3 to 1.3)  10 3 mol L 1 solution of HPic, (0.1 to 1.1)  10 2 mol L 1 one of HNO 3 , and (0.1 to 5.5)  10 3 mol L 1 one of Pb(NO 3 ) 2 were prepared in stoppered-glass tubes of about 30 mL, next an equivalent volume of DCE was added to each of these mixtures, and then shaken by hand during 1 minute.These glass tubes thus-obtained were agitated for 2 h by an Iwaki shaker system (a driving unit: SHK driver; a thermo regulator: type CTR-100) equipped with water-bath (type WTB-24, Iwaki) kept at 298 K.After the mixtures reached equilibrium in the tubes, they were centrifuged for 7 minutes by using a Kokusan centrifuge (type 7163-4.8.20), in order to separate them into the two phases.Then, the pH values in the resulting aqueous phases were measured using a Horiba pH/ion meter (type F-23) with a Horiba electrode (LAQUA, type 9615).Also, portions of the DCE phases were separated by pipettes, set in other glass-tubes, aqueous solutions of 1 mol L 1 NaOH were added to them, and then HPic extracted into the DCE phases were back-extracted into the aqueous phases with NaOH.Total amounts of Pic  in these aqueous phases were determined at the Pic  absorption of 335.0 nm spectrophotometrically using a Hitachi U-2001 spectrophotometer and then symbolized as [HPic] DCE .Furthermore, blank experiments were performed for the extraction of HPic into DCE without Pb 2+ , in order to determine D Pic values (see Equation 3 for a meaning of this symbol).
An experimental distribution ratio ( Pb D Pic ) for Pic  in the presence of Pb(NO 3 ) 2 in the aqueous phase were calculated from Pb D Pic = Pb [HPic] DCE /([HPic] t  Pb [HPic] DCE ).Here, [HPic] t denotes a total concentration of HPic, of which the concentrations were in the range of (0.3 to 1.3)  10 3 mol L 1 (see above).Also, Pb [HPic] DCE shows a molar concentration of HPic in the DCE phase and then the superscript "Pb" means experimental data for the HPic extraction under the presence of Pb 2+ in the aqueous phase (see the section 3.1).
Similarly, the Pb D Pic and D Pic values were determined for the HPic extraction into Bz with and without Pb(NO 3 ) 2 , respectively.
A commercial Pb 2+ -selective electrode with a solid membrane was employed for the determination of Pb 2+ in aqueous solutions of PbPic 2 .However, its electrode did not clearly respond Pb 2+ , as similar to the case (Kudo, 2013) of a Cd 2+ -selective electrode described before.That is, the electrode slightly responded Pic  in the solutions.

Re-calculation of the Extraction and Other Constants for the MPic 2 -L Extraction Systems
The K ex , K ex , K ex+ , and K D,Pic values were calculated using the same original data as those obtained before by Takeda & Kato (1979) : see the section 3.2 about details of these symbols.That is, extraction experiments with M(NO 3 ) 2 , HPic, and 18C6 or DB18C6 were not performed anew.Other procedures for calculation were similar to those (Kudo, Harashima et al., 2011;Kudo, Horiuchi et al., 2013;Kudo, Kobayashi, Katsuta, & Takeda, 2009) described before.

Determination of K MA for M 2+ in the Aqueous Phase by Extraction Experiments
In order to determine the first-step ion-pair formation constant (K MA ) in the case of an abnormal respose of the Pb 2+ electrode or lack (Kudo et al., 2013) of commercial ISE, such as Sr 2+ -and Ba 2+ -selective electrodes, we first considered the following equilibria.
To this HA extraction system, the distribution ratio (D A ) of A  is expressed as where the subscript "o" of HA o or [HA] o and lack of the subscript denote the organic and aqueous phases, respectively, and HA means an organic acid.Next, a divalent metal salt (MX 2 ) is added to this system.If MX 2 almost dissociates and then M 2+ associates with A  : Here, M [ ] (or M [ ] o ) denotes the molar concentration at equilibrium in the aqueous (or organic) phase for the HA extraction system with M 2+ .Equation 5 holds under the conditions that the formation of MA 2 in the aqueous phase and the distribution of M 2+ or MA + into the organic phase are negligible: namely, Rearranging Equations 3 and 5, the following equations were given. [ with and Then, subtracting Equation 3a from Equation 5a, we can immediately obtain Here, the conditions of K ex,HA  M K ex,HA and K D,HA  M K D,HA were employed.From Equation 6, we can easily derive Since we can determine  7; in computation, the K D,HA and K HA values (see below) for a given ionic strength (I ) in the aqueous phase were determined by a successive approximation.Mass-balance equations are expressed as a total concentration of species with A  : and as that of species with M 2+ : Therefore, we obtain from Equations 8, 9, and 3d and Here, we employed 1.9 5 mol 1 L (Kortüm, Vogel, & Andrussow, 1961) at 298 K and ionic strength ( M I or I ) of 0.1 in water as K HPic .Hence, Equations 7, 9a, and 10 yield K MA for a given I in the aqueous phase.
for Equations 1, 2, and 4 Equations 1 and 2 (12) Strictly speaking, although a difference between M I and I is present, the M I value was used for practical extraction experiments.

Analysis of Overall Extraction Equilibria Based on Added Component Equilibria
To component equilibria expressing an overall extraction equilibrium described by Takeda et al. (Takeda & Kato, 1979;Takeda & Nishida, 1989) HA o , and Equation 1, the following three component equilibria were added.
Using component equilibrium constants and an ion-pair extraction one (K ex,ip ), these constants are expressed as (Takeda & Kato, 1979) and (Kudo et al., 2013), where these component-equilibrium constants are ).Unfortunately, these K 1 , K 2 , and K D,MLA2 values have not been reported systematically, except for their values of the CdBr 2 and CdPic 2 extraction systems with 18C6 or benzo-18C6 (Kudo et al., 2013;Kudo et al., 2009).Hence, we could not use these values as the component equilibrium constants in this study.
We assumed that [MLA n (2n)+ ] o values at n = 1, 2 were obtained experimentally and then defined (Kudo et al., 2013) and the value at n = 0 was neglected because of low polarities of Bz.Here, the [MLA n (2n)+ ] o values, total amounts of species with M(II) in the organic phases, had been determined by AAS (Takeda & Kato, 1979;Takeda, 1979;Kudo et al., 2013).From this definition, we can easily derive the following equations.
So, one can obtain immediately the K ex and K D,A or K ex values from plots of log (Kudo et al., 2013), respectively, in a given range of I in the aqueous phase by using a non-linear regression analysis to these plots.Here, [M 2+ ], [L] o , and [A  ] have been expressed as the functions of and h([M 2+ ], [L] o , some K), respectively, and then determined by the successive approximation (Kudo, Horiuchi et al., 2013;Kudo, Kobayashi et al., 2009).
By Equation 16, the relation

Determination of Ion-Pair Formation Constants of PbPic + in the Aqueous Phase
Figure 1 shows a plot of log K PbPic versus ( M I ) 1/2 for the extraction of HPic into DCE in the presence of Pb(NO 3 ) 2 in the aqueous phase.These experimental ionic strength values, Pb I/mol L 1 , of ionic species in the aqueous phases were in the range of 0.003 to 0.017.A broken line is a line with a correlation coefficient (R) = 0.751 due to a non-linear regression analysis to the equation, log (Kudo, 2013), where K MA 0 refers to K MA at M I  0 and we assumed that the activity coefficient of PbPic + in water equals that of Pic  .The curve fitting of the plot in Figure 1 to the other equation like log ), but it is difficult to explain the numerical value of its parameter, C. Therefore, the authors gave up the curve fittings to other equations, although the R values of the fittings to the Davies and extended Debye-Hückel equations were smaller than that to the other.Their smaller R values may mean that the above assumption of activity coefficients between PbPic + and Pic  is not effective.
The regression analysis yielded log K PbPic 0 = 2.00  0.02 in water saturated with DCE (see Figure 1); 2.00  0.02 from the extended Debye-Hückel equation (Kudo, 2013) with an ion size parameter of 4.5 Å for Pb 2+ (Kielland, 1937).Similarly, the analysis for the HPic extraction into Bz gave log K PbPic 0 = 1.97  0.07 in water saturated with Bz at R = 0.462 and a number (N) of run = 5; 1.96  0.07 was obtained from the Debye-Hückel equation.In spite of a difference between the diluents, both the log K PbPic 0 values agreed with each other within experimental errors.The experiments for confirming the K MPic values at M = Ca and Cd are in progress, in order to establish the present K MA -determination method; we are now obtaining the finding that its value (= about 100 mol 1 L) for CdPic + determined by this method is in accord with that (= 108, 107) (Kudo, 2013) done by potentiometry with ISE.Strictly speaking, these values may not be the thermodynamic equilibrium constant but it has no problem that we ordinarily use their values for an equilibrium analysis in solvent extraction.

For the Experimental Determination of Composition of Species Extracted into Benzene
For the present extraction systems, compositions of their extracted species have been determined by the plot of log (D M expl.(Takeda & Kato, 1979;Takeda, 1979;Takeda & Nishida, 1989).Here, D M expl. is a distribution ratio of species with M(II), obtained from experiments:
The experimental mean-values of f with a standard deviation were calculated to be 0.98  0.03 for the CaPic 2 -18C6 extraction system, 0.99  0.04 for SrPic 2 -18C6, 0.51  0.04 {estimated from the data in Kudo et al. (2013)} for CdPic 2 -18C6, 1.8  0.6 for PbPic 2 -18C6, 1.3  0.1 for CaPic 2 -DB18C6, 1.1  0.1 for SrPic 2 -DB18C6, and 0.95  0.01 for PbPic 2 -DB18C6.Although deviations of the f values from unity for the Cd(II)-, Pb(II)-18C6, and Ca(II)-DB18C6 systems are larger than the others, the above results demonstrate validity of the above condition, f in the present data analysis and consequently effectiveness of such plots determining the composition.Therefore, one may suppose that an accuracy on the composition-determination of the extracted species based on the relation (Takeda & Kato, 1979;Takeda, 1979;Takeda & Nishida, 1989) for M 2+ to bA  } primarily depends on the magnitude of the f value, namely a degree of the deviation of a (or b) from 1 (or 2).Here, log K ex inter.denotes the intercept of the plot and the relation of log K ex inter.
However, a comparison of the a values with the f ones suggests that when f is in the range of 0.5 to 1.8 at least, the a values do not largely deviate from 1; see above for the a value of the Pb(II)-18C6 system and the a value evaluated for the CdPic 2 -18C6 system was 1.0 8 at R = 0.966 (Kudo et al., 2013).From rearranging the experimental equation, log (0. /0.51), we can easily see that the f value is less sensitive to the slope a than to the intercept log K ex inter.
. In other words, an effect of f is directed to log K ex inter.but its effect is limited to the composition a.The same is true of rearranging the equation, log /1.3).These results are supported by the fact that a plot of a versus f for the above M(II)-L systems, except for the Ba(II)-18C6 one, gave the R value of 0.089.
The plots yield log fK ex as the intercepts (Kudo et al., 2013).This fact indicates that the intercepts deviate from the true log K ex values by log f.On this ground, obtaining the log K ex value from the intercepts of the plots is not preferable in general.

Determination of Fundamental Equilibrium Constants
After the composition-determination of the extracted species, we can determine next the extraction constants by using Equations 20 and 20a.Figures 3 and 4 show the plots of log K ex mix versus log for the PbPic 2 -18C6 extraction system, respectively.Both the plots yielded curves which rose with increases in the prameters of the x-axises.The regression analyses of these plots gave (K ex /mol 3 L 3 ) = (1.9 1.2)  10 11 with K D,Pic = (2.4 9  0.4 9 )  10 2 (Figure 3) and (K ex /mol 3 L 3 ) = (4.4 3  0.9 1 )  10 11 with (K ex /mol 2 L 2 ) = (2.6  1.3)  10 6 (Figure 4).The same plots for other MPic 2 -L extraction-systems as those for the PbPic 2 -18C6 one yielded the same kinds of constants.
Table 1 lists logarithmic values of the fundamental equilibrium constants determined in this study, together with the log K ex values (Takeda & Kato, 1979) reported previously.Marked differences between the present log K ex values and the previously-reported ones (Takeda & Kato, 1979) were not observed.The log K ex values were in the order M = Cd << Ca < Sr  Ba < Pb for L = 18C6 and Ca < Sr < Pb for DB18C6.The same seems to be true of log K ex orders.The log K D,Pic values were almost a constant within experimental errors, except for the Cd(II) extraction system.This fact suggests validity of the present procedure, although the experimental I values are different from each other (see Table 1).At the same time, this suggests that there is an individual value for the distribution constant of single Pic  into Bz (see Figure 5).The large deviation from the log K D,Pic value of the Cd(II) system shows that the other log K D,Pic values are apparent ones which depend on distribution-abilities of MLPic + (or ML 2+ ) into Bz (Kudo et al., 2013).That is, considering an electroneutrality between ionic species in the Bz phase, Pic  has to distribute into Bz in the process such as Pic  + MLPic + Pic  Bz + MLPic + Bz .

For Component Equilibrium and Ion-Pair Extraction Constants
The component equilibrium constants and K ex,ip relevant to K ex and K ex are summarized in Table 2.As can be seen from this table, the reported log K ML values (Takeda & Kato, 1979;Høiland, Ringseth, & Brun, 1979;Shchori, Nae, & Jagur-Grodzinski, 1975) are in the order M = Cd << Ca << Sr < Ba < Pb for L = 18C6 and Ca < Sr < Pb for DB18C6.The log K ex,ip values were also in the order Cd << Ba < Ca < Sr < Pb for 18C6; their values were close to those (Takeda & Kato, 1979) reported before (see Table 2).Except for the BaPic 2 -18C6 system, both the orders of log K M18C6 and log K ex,ip control the log K ex one at L = 18C6.This result is the same as that reported before (Takeda & Kato, 1979).Moreover, comparing the present log K ex,ip and log K MDB18C6 values with the previously-reported ones (Takeda & Kato, 1979) at DB18C6, their orders reflect the log K ex order.The same is true of the log K ex orders for both the L.
The K 2 org value at I o , I in the organic phase, can be easily calculated from the relation of K ex /K ex = K 2 org (Kudo et al., 2013).Here, the I o value at o = Bz was estimated from the charge balance equation (see Table 2 and the theoretical section 3.2) by assuming Bz values in Table 2 were in the order M = Pb < Ca  Sr < Cd for L = 18C6 and Ca  Sr  Pb for DB18C6.The R IR values of these metal ions at a coordination number of 6 were 1.00 Å for Ca(II), 0.95 for Cd(II), 1.19 for Pb(II), and 1.18 for Sr(II), where R IR refers to an effective ionic radius (Shannon, 1976).In comparison with R IR , a coulombic force around M(II) seems to be ineffective for the order of log K 2 Bz .If the constants K 2 Bz satisfy a general tendency, K 1 > K 2 , such as stepwise complex-formation constants, their overall constants, K 1 Bz K 2 Bz , can become very large.This suggests the condition of [MLPic + ] Bz < [MLPic 2 ] Bz at least.Except for Pb(18C6)Pic + , the following results were consistent with this suggestion.
The log K MPic values determined at I  0 were in the order M II = Ca (1.9 4 ) (Kudo, Takeuchi, Kobayashi, Katsuta, & Takeda, 2007)  Pb  Cd (2.03) (Kudo et al., 2007).The same was true of the log K MPic values evaluated at the I values in Table 2.The order is not in accord with that of the coulombic force around M(II): Pb < Ca < Cd.On the other hand, hydration free energies (Marcus, 1997) (ΔG h /kJ mol 1 ) are in the order Pb 2+ (1434) < Ca 2+ (1515) < Cd 2+ (1763).These facts suggest incomplete dehydration around these M 2+ in water (Kudo et al., 2007;Rudolf & Irmer, 1994;Kudo, 2013).There was no large difference among the log K HPic values of the extraction systems employed (see log K HA in Table 2).This fact obviously comes from the small I range of 0.0030 to 0.016 in the extraction experiments.

For Other Extraction Constant K ex+
We can define K ex+ as (Kudo et al., 2013) and relate it to K ex .According to their thermodynamic cycle, K ex is expressed as Using this equation, the log K ex+ values were estimated from Table 1 to be 3.8 for the CaPic 2 -, 5. 9 for SrPic 2 -, 1.4 for CdPic 2 -, and 8.0 for PbPic 2 -18C6 systems and 1.4 for the CaPic 2 -, 1.8 for SrPic 2 -, and 3. 4 for PbPic 2 -DB18C6 systems.Therefore, if Equation 22 holds for the Bz extraction systems, then a plot of log K ex versus log K ex+ will yield a straight line with a slope of unity and an intercept of log K D,A .Figure 5 shows such a plot for all the extraction systems analyzed.Except for the points of the CdPic 2 -and PbPic 2 -18C6 systems, the plot gave a straight line with the slope of 0.98 4 and the intercept of 3.20 at R = 0.980.These values are in good agreement with those described above: for example, the geometric mean-value of the log K D,Pic values was estimated to be 3.1 2  0.7 3 at N = 7 in Table 1, except for the Cd(II) system.Similarly, a plot for the relation of log (K ex /K ex+ ) = log K 2 org + log K D,A was examined.However, a correlation between the log (K ex /K ex+ ) and log K 2 org values was not obtained.

Conclusion
(i) The introduction of the three equilibria, expressed by K MPic , K D,Pic , and K 2 Bz , to the extraction model of MPic 2 by L into Bz did not show large deviations from the reported values (Takeda & Kato, 1979) about K ex and K ex,ip .Consequently, their values seemed not to be sensitive to the K MPic and K 2 Bz ones.The higher mole fractions of MLPic 2 than those of MLPic + in the Bz phases were verified experimentally in this regard; the smaller fractions of the ionic species can be presumed by the larger standard deviations of K ex compared with those of K ex .Also, (ii) among the extraction of alkaline-earth metal picrates by L employed, the evaluated log K D,Pic values agreed with each other.This fact suggests at least that the individual K D,A value at a fixed diluent is constant.Moreover, (iii) it was demonstrated that, regardless of the f range of 0.5 to 1.8, the composition-determination method (Takeda & Kato, 1979;Takeda, 1979)  L 3 ) 3. 9  1. 5 a Calculated ionic strength in the aqueous phase.Here, 1 L was defined as 1 dm 3 .b Takeda and Kato (1979).c Not determined because of their larger experimental errors.d Kudo et al. (2013).e Values evaluated by the procedure reported in Takeda and Kato (1979).Takeda and Kato (1979);Høiland et al. (1979);and Shchori et al. (1975).b Calculated ionic strength/mol L 1 in the organic phases.c Ion-pair formation constant of Pb 2+ or Cd 2+ with Pic  in the aqueous phase (see the text) and values evaluated from log K CaPic = 1.9 4 determined by potentiometry with ISE (Kudo et al., 2007) at I  0 and 298 K. d See Table 1.e Protonation constant of Pic  in water.f Distribution constant of L between the aqueous and Bz phases.See Takeda, 2002.g Takeda and Kato (1979).h Not determined because of lack of the K MA values.i Kudo et al. (2013).j Katsuta et al. (2000).k Value calculated at (I/mol L 1 ) = 0.014.See Kudo et al. (2013) and the footnote e in Table 1.
equation in the organic phase.Using this relation and the experimental data of [MLA n (2n)+ ] o and K ex , we will evaluate a mole fraction, [MLA + ] o /[MLA n (2n)+ ] o , as described below.

Figure 1 .Figure 3 .
Figure 1.Plot of log K PbPic versus ( M I ) 1/2 for the extraction of HPic into DCE in the presence of Pb(NO 3 ) 2 in the aqueous phase.A broken line is a regression one with R = 0.751 based on the equation, log K MA = log K MA 0  40.511{(M I ) 1/2 /[1 + ( M I ) 1/2 ]  0.3 M I} at MA + = PbPic +

Figure 5 .
Figure 5. Plot of log K ex versus log K ex+ for the MPic 2 -L extraction systems employed.A broken line is a linear regression one based on the equation, log K ex = log K ex+ + log K D,Pic , without the two triangles which show the points of the CdPic 2 -and PbPic 2 -18C6 systems broken line is a non-linear regression one with R = 0.778 based on Equation20aTable1.Fundamental extraction and distribution constants for the MPic 2 -L extraction systems into benzene at 298 K  0.06, 5.38 b 1.1 8  0.4 5 2.9 7  0.6 1

Table 2 .
Ion-pair extraction (K ex,ip ) and component equilibrium constants for the MPic 2 -L extraction systems into benzene at 298 K a See