# Extraction of Sodium Picrate by 3m-Crown-m Ethers and Their Monobenzo Derivatives (m = 5, 6) into Benzene: Estimation of Their Equilibrium-Potential Differences at the Less-Polar Diluent/Water Interface by an Extraction Method

Authors: Yoshihiro Kudo; Tsubasa Nakamori; Chiya Numako
Journal: Journal of Chemistry
 (2016)

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## Abstract

Individual distribution constants (KD,A) of picrate ion (Pic−) and extraction constants (Kex±) of NaPic by some crown ethers (L) into benzene (Bz) at 25°C were calculated from data reported previously. These constants were defined as KD,Pic=Pic-o/[Pic-] and Kex±=NaL+oPic-o/(Na+Lo[Pic-]), respectively. Here, the subscript “o” denotes an organic (o) phase and practically o = Bz. 15-Crown-5 ether (15C5), 18-crown-6 one (18C6), and their monobenzo (B) derivatives (B15C5 and B18C6) were selected as L. Interfacial equilibrium-potential differences (Δϕeq) at extraction were estimated at 298 K. A plot of log⁡Kex± versus -Δϕeq for the four L extraction systems gave a straight line with slope = 84 V−1. This slope was compared with those, reported before, of the dichloromethane (DCM), 1,2-dichloroethane (DCE), and nitrobenzene (NB) extraction systems. The slopes of the regression lines were in the order NB < DCM ≤ DCE < Bz. Also, the individual distribution constants of the complex ion NaL+ and an ion-pair complex (NaL+Pic-) into Bz phase were calculated from the above extraction data. At least, a comparison between these values suggests that Bz molecules mainly interact with NaL+ moiety of NaL+Pic-.


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## Body

## 1. Introduction

A presence of interfacial equilibrium-potential differences (Δϕeq) at extraction processes with polar diluents, such as dichloromethane (DCM), 1,2-dichloroethene (DCE), and nitrobenzene (NB), has been clarified [1, 2]. For example, crown compounds (L) extract silver picrate into DCE [1, 2] or alkaline-earth metal (Ca-Ba) picrates [1] into NB. In these studies [1, 2], an individual distribution constant (KD,A) of a pairing anion (A−), such as picrate ion (Pic−), has been determined in the course of Kex determination. Here, KD,A and Kex have been defined as A-o/[A-] and MLAzo/P with P=Mz+LoA-z, respectively; the symbols MLAz, Mz+ and the subscript “o” denote an ion-pair complex, a metal ion with the formal charge z (=1,2), and an organic (o) phase, respectively. The Δϕeq values have been determined by using the experimental KD,A values and the electrochemical equation of log⁡KD,A=-(F/2.303RT)(Δϕeq-ΔϕA0′) [1], where ΔϕA0′ refers to a standard formal potential for an A- transfer across the o/water (w) interface and F, R, and T have usual meanings. Thus the presence of Δϕeq at the polar diluent/w interfaces has been examined and proved experimentally [1, 2]. Also, Δϕeq presence had been already described in the distribution study of protonated amino acids into NB [3]. However, the presence of Δϕeq has not been clearly considered for the extraction of simple salts into NB [4], that of metal salts by extractants, such as calix[4]arene and dibenzo-24-crown-8 ether derivative, into NB [5] or DCE [6], and that of R4N+A− into DCE [7] in the field of extraction chemistry and for electrochemical extraction studies [8–10] at the liquid/liquid interfaces. Besides, the presence of Δϕeq at less-polar diluent/w interfaces has not been clarified so far. Its cause seems to be the lower concentrations of ions present in the less-polar diluents, compared with their concentrations in the polar diluents. Additionally, the correlation between the extraction chemistry and the electrochemistry at the liquid/liquid interfaces had not been reported, except for our studies [1–3] and a description [11] with respect to the distribution of a simple salt, such as Bu4NBr.In the present paper, selecting benzene (Bz) as the representative less-polar diluent, we determined from available extraction data [12–15] Δϕeq values at the Bz/w interface. Also, the thus-determined values at 25°C were compared with Δϕeq ones for the DCM, DCE, and NB extraction systems. For the comparison, 15-crown-5 ether (15C5), 18-crown-6 one (18C6), benzo-15C5 (B15C5), and B18C6 were selected as L and NaPic was done as an extract. Moreover, individual distribution constants of the ion-pair complexes NaL+Pic− and the complex ions (NaL+), which constitute parts of the complexes, into the four diluents were estimated from the above results and then their properties for solute-solvent interaction were discussed.


## 2. Experimental Section

This study was performed by reusing the extraction data [12–16] reported previously at 25°C. Also, analytic procedures were the same as those [12–16] described before. Hence, experiments for the extraction into Bz have not been newly performed here at all; see Takeda et al.’s studies [12–16] for the experimental details.The fundamental data of [Na+], LBz, and [Pic−] were calculated from the extraction data in successive approximations [12–16]. In the analysis of an overall extraction equilibrium, the following component equilibria were considered [2, 16]: L⇌LBz (the equilibrium constant for this equilibrium: KD,L; see Section 3.5); Na++L⇌NaL+ (KNaL; see Section 3.5); NaL++Pic⇌NaLPic (K1; see Section 3.5); NaLPic⇌NaLPicBz (KD,NaLPic; see Section 3.5); NaLPicBz⇌NaL+Bz+Pic-Bz (K1,Bz-1; see Section 3.2); and Na++Pic-⇌NaPic. In addition to these equilibria, one can understand the presence of other component equilibria: NaL+⇌NaL+Bz (KD,NaL; see Section 3.2 and Table 1) and Pic-⇌Pic-Bz (KD,Pic; see Section 1 and Table 1).Table 1
Extraction data of the NaPic systems with L into Bz at 25°C.
L log ⁡ K D , A a (Δϕeq/V)b log ⁡ K e x ± c (I)d log ⁡ K e x a , c log ⁡ K 1 , B z e (IBz)d log ⁡ K D , N a L f (ΔϕNaL0′/V)g 15C5 −4.11 ± 0.27(−0.24) −3.14 ± 0.22,−4.11 ± 0.38h (0.0060) 3.909 ± 0.007a, 3.889 ± 0.008c, 4.67 [12–15] 7.0 ± 0.2(3.5 × 10−7) −1.51 ± 0.38,−1.3i (−0.15)  B15C5 −4.7 ± 3.4(−0.21) −5.99 ± 6.7,−6.50 ± 0.39h (0.023) 3.178 ± 0.008a, 3.18 ± 0.01c, 3.378 [12–15] 9.7 ± 0.4j (1.3 × 10−7) −1.13 ± 0.39,−0.6i (−0.1)  18C6 −4.21 ± 0.16(−0.24) −3.18 ± 0.31,−3.73 ± 0.23h (0.010) 3.45 ± 0.02a, 3.40 ± 0.03c, 3.84 [12–15] 6.6 ± 0.3(5.3 × 10−7) −1.55 ± 0.24,−1.6i (−0.14)  B18C6 −5.2 ± 3.7(−0.18) −7.8 ± 15.5,−8.03 ± 0.38h (0.010) 3.062 ± 0.002a, 3.060 ± 0.004c, 3.162 [12–15] 11.1 ± 0.4j (2.4 × 10−8) −2.73 ± 0.38,−2.7i (−0.0) aValues obtained from the analyses of the log⁡Kexmix  versus -log⁡([Na+][L]Bz) plots. bSee the text for the evaluation. cValues obtained from the analyses of the log⁡Kexmix  versus -1/2log⁡P plots. dMean values of ionic strength for the w or the Bz phase. eValues calculated from the thermodynamic relation, log⁡K1,Bz=log⁡Kexa-log⁡Kex±c. fMean values calculated from the relation, KD,ML≈IBzKD,L/KML[M+][L]Bz. gMean values calculated from the relation, ΔϕML0′=Δϕeq-0.05916log⁡KD,ML at 25°C. hMean values calculated from the relation, Kex±≈IBz2/P. iValues calculated from the thermodynamic relation, log⁡KD,ML=log⁡Kex±+log⁡(KD,L/KML)-log⁡KD,A. jValues calculated from the values of footnote h for convenience, because the Kex± values of footnote c showed the larger calculation errors.


## 3. Results and Discussion

### 3.1. Redetermination of Compositions of the Ion-Pair Complexes Extracted into Bz

Plots [16] for redetermining a Na(I) : L : Pic(−I) composition in the four extraction systems yielded regression lines of a slope = 0.997 and an intercept = 3.89 (≈log⁡Kex at z=1) at a correlation coefficient (R) = 0.998 for the 15C5 system, of 0.999 and 3.17 at R=0.9999 for the B15C5 one, of 0.903 and 3.04 at R=0.996 for the 18C6 one, and of 1.02 and 3.09 at R=0.999 for the B18C6 one; see log⁡(D/[Pic-]) versus log⁡LBz plots in Figure 1, where D denotes a distribution ratio of species with Na(I) into the Bz phase.Figure 1
Plots oflog⁡(D/[Pic-]) versus log⁡LBz for the 15C5 (square), B15C5 (diamond), 18C6 (circle), and B18C6 (triangle) extraction systems. See the text for regression results of the solid lines. The symbol of 1 mol dm−3 = 1 M was used.These slopes of about unity obviously indicate that the compositions of extracted species, mainly ion-pair complex, are Na(I) : L : Pic(−I) = 1 : 1 : 1 [16]. These results were in good agreement with those [12–15] described previously.


### 3.2. Determination of Extraction Constants and Their Several Component Equilibrium Constants

TheKD,A and Kex values at A = Pic(−I) and z=1 were determined by the plot of log⁡Kexmix versus -log⁡Na+LBz (Figure 2) based on the equation (1)log⁡Kexmix≈logKex+KD,ANa+LBz,where Kexmix has been defined as (MLAo+ML+o+M+o+⋯)/P [1, 2, 16]. Also, Kex± values were determined by the plot of log⁡Kexmix versus -1/2log⁡P (Figure 3) based on the equation (2)log⁡Kexmix≈log⁡Kex+Kex±P1/2,where the symbol Kex± has been defined as ML+oA-o/P [1, 2, 6] at z=1.Figure 2
Plot of logKexmix versus -log⁡(Na+LBz) for the NaPic extraction with L = 15C5. The KD,Pic and Kex values obtained from a nonlinear regression analysis with (1) were (7.7 ± 4.8) × 10−5 and 8115 ± 133 M−2, respectively.Figure 3
Plot oflog⁡Kexmix versus -1/2log⁡P for the NaPic extraction with L = 15C5. The Kex± and Kex values were obtained to be (7.3±3.8) × 10−4 M−1 and 7747 ± 149 M−2 from the nonlinear regression analysis with (2).The thus-determined values at 25°C are listed in Table1 (see Appendix A for reference), together with their component equilibrium constants, KD,Pic, KD,NaL (= NaL+Bz/[NaL+] [1]), and K1,Bz (= Kex/Kex±=NaLPicBz/NaL+BzPic-Bz [1, 2, 16]). Kex values were in the order B18C6 < B15C5 < 18C6 < 15C5, although the ionic strength (I) for the water phase of the 15C5 system is somewhat smaller than those of the other systems. This order was in accord with those [12–15] reported before (Table 1) and reflected the order of the (intercept/slope) values for the plots of log⁡(D/[Pic-]) versus log⁡LBz (see Section 3.1). Similarly, Kex± values showed the order B18C6 ≤ B15C5 < 18C6 ≤ 15C5, although the values of the benzo derivatives have large errors. This order agreed with that of Kex. These facts indicate that the present analyses are essentially valid.


### 3.3. OnΔϕeq Estimation and Its Correlation with log⁡Kex±

We can formally calculate theΔϕeq values from the relation (3)Δϕeq=ΔϕA0′-2.303RTFlog⁡KD,A[1, 2, 21] (see Table 1), when ΔϕA0′ values are available. Fyles had evaluated the free energy of the Pic− transfer from w to Bz [22]; then, ΔϕPic0′ value at the Bz/w interface was estimated from its free energy to be −0.486 V at 25°C. The thus-estimated Δϕeq values are listed in Table 1. Δϕeq values were in the order 15C5 ≈ 18C6 < B15C5 ≈ B18C6, although their experimental errors were large. Also, one can see that Δϕeq values for the Bz system with L are negative, indicating that KD,Pic values are larger than KD,PicS ones which are defined as exp⁡(ΔϕPic0′/0.02569) [1–3] at 25°C. On the other hand, the values reported before for the DCM, DCE, and NB systems have been accidentally all positive [1, 2].As Figure4 shows, a plot of log⁡Kex± versus -Δϕeq yielded the straight line: log⁡Kex±=84±12-Δϕeq-(23.6±2.6) at R=0.981. Similar lines were observed in NaPic extraction by L into DCM and DCE. Adding the data of NB systems, these slope values at Δϕeq (not -Δϕeq) were in the order Bz (slope = −84 V−1) < DCE (−26) ≤ DCM (−21) < NB (3). This order was close to that of dielectric constants (εr) [23] of the pure diluents at 298.15 K: Bz (εr=2.27) < DCM (8.93) < DCE (10.23) < NB (34.82), although these diluents were saturated with water. These results can be explained in terms of a model like a parallel-plate capacitor at the diluent/w interface [24]. Namely, its capacitance (C) is expressed as the following equation [24]: (4)C=qE≈εrSd.Here, the symbols q, E, S, and d refer to a charge stored on the capacitor, a potential across the capacitor, an area of the plate, and an interplate spacing, respectively [24].Figure 4
Plot oflog⁡Kex± versus -Δϕeq for the NaPic extraction with L into Bz. See the text for the regression line.So assuming that the slopes in V−1 of log⁡Kex± versus -Δϕeq plots correspond to C terms, then their values have to be proportional to εr ones under the condition of a fixed S/d in (4). The symbol S can be considered to be the area of the o/w interface and S value corresponding to its area in test tubes which had been used for the extraction experiments into the four diluents was estimated to be 2.4 cm2 from their mean inner diameter (=1.750 cm). A plot of slope versus εr showed a positive correlation. From this fact, as an example, it can be considered that d value for Bz is smaller than those for others. Unfortunately, we have no experimental ground with respect to this consideration.


### 3.4. On Some Tendencies of theKD,Pic and K1,Bz Values

The experimentallog⁡KD,Pic values of the Bz systems agreed with each other within experimental errors among L listed in Table 1. At least, the values for L = 15C5 and 18C6 were much larger than log⁡KD,PicS one (= −8.208 [22] = ΔϕPic0′/0.05916 at 25°C) without L. This fact indicates that the presence of L, namely, the distribution of NaL+, in the extraction largely facilitates Pic− transfer at Bz/w interfaces.A plot oflog⁡(IBz/I) (=y) versus log⁡KD,Pic (=x) gave a straight line with a slope of 1.45±0.23 and an intercept of 1.7±1.1 at R=0.975. Although the slope value is larger than unity, this linear relation is similar to those reported before for the extraction systems of CdPic2 [21] and PbPic2 [25] with 18C6 into various diluents containing Bz. Such a similarity also suggests that the present analysis is valid.log ⁡ K 1 , B z values were in the order L = 18C6 ≤ 15C5 < B15C5 < B18C6 (Table 1). This order is close to 18C6 < 15C5, B18C6 < B15C5, which was predicted from a combined parameter, B+M′+V, of basicity of the donor O atoms (parameter: B), selectivity of L against Na+ (M′) with a molecular volume (V); see Table 3 and Appendix B for the parameters. Also, an addition of a benzo group to the ring skeletons is causing an increase in K1,Bz: 15C5 < B15C5 and 18C6 < B18C6. That is, its addition which spontaneously changes the parameters B, S, and V of L (see Table 3 and Appendix B for S) has a positive effect on K1,Bz.K 1 , B z value at L = 15C5 was larger than K1,DCE, K1,DCM, and K1,NB ones; K1,DCM=106.2M-1 at average IDCM=3.0×10-6M, K1,DCE=106.5 at 1.7×10-6, and K1,NB=105.3 at 3.1×10-6. Also, the same is true for K1,org values for the other L. These facts indicate that although NaL+Pic- in Bz phases are less dissociable than those in DCM, DCE, and NB phases, the ions are present even in Bz phases. In other words, it suggests that the occurrence of Δϕeq is possible at Bz/w interface.


### 3.5. On the Distribution ofNaL+ and NaL+Pic- into Bz

The following relation can be used forKD,NaLS evaluation: (5)log⁡KD,MLS=log⁡KD,ML-Δϕeq0.05916at25°C[1, 3] and the symbol KD,NaLS denotes the distribution constant, KD,NaL, of NaL+ into the Bz phase at Δϕeq=0V. As can be seen from Table 2 (see the values of footnote d and Appendix A for reference), log⁡KD,NaLS values were in the orders DCE < DCM < NB < Bz for L = 15C5, DCE < DCM < Bz < NB for B15C5, NB < DCM < DCE < Bz for 18C6, and DCM < Bz < DCE < NB for B18C6. These orders indicate that the addition of the benzo group to the ring skeleton causes an increase in an interaction between NaL+ and NB molecules.Table 2
Individual distribution constants of NaL+ and NaL+Pic− into some diluents at 25°C.
(a) L log⁡KD,NaLSa (log⁡KD,NaL)b o = Bz DCM DCE NB 15C5 2.6 (−1.5) −1.14 (1.0) −1.54 (0.3) 0.0, −0.3d, 0.62e (1.7) B15C5 2 (−1.1) −0.34 (2.3) −0.54 (2) 2.2, 3.7d, 2.1e (4.1) 18C6 2.4 (−1.6) −0.44 (0.77) 0.47 (0.84) −0.3, −1.4d, 0.7e (1.1) B18C6 0.3 (−2.7) 0.19 (2.62) 1.16 (2.47) 1.5, 2.0d, 2.1f, (3.7) Without L —g −5.73h −6.09i, −4.38 [17] −5.18i, −5.95 [17] (b) L log⁡KD,NaLPic Bz DCMc DCEc NBc 15C5 0.94 2.87 2.47 3.82 B15C5 1.29 (1.42 [13]) 3.01 (3.13 [13]) 2.61 (2.73 [13]) 3.75 18C6 −0.26 1.88 1.16 3.68 B18C6 0.48 (1.18 [13, 15]) 2.47 (3.36 [13, 15]) 2.06 (2.97 [13, 15]) 3.71 Without L aStandard values calculated from the thermodynamic relation, log⁡KD,MLS=log⁡Kex±+log⁡(KD,L/KML)-log⁡KD,AS. bSee footnote f in Table 1. cUnpublished data by Kudo. dStandard values calculated from (5). eValues determined by ion-transfer polarographic measurements at the presence of 0.05 M (C4H9)4N+B(C6H5)4- in the NB phase. See [18]. fValues determined by the ion-transfer polarographic measurements at the presence of 0.05 M (C4H9)4N+B(C6H5)4- in the NB phase. See [19]. gNot determined. hThe values are a logarithmic individual distribution-constant of a single Na(I) ion into the DCM, DCE, or NB phase and are standardized at Δϕeq=0 V. iSee [20] and footnote h.Table 3
A measure of basic parameters for a comparison between Ls.
L Cavity size (parameter:C) Molecular volume (V) Number of donor O atoms (N) Basicity of donor O atoms (B) Softness of ring skeleton (S) Na+ selectivity (M′) 15C5 1 0 5 2 2 2 B15C5 1 2 5 1 1 2 18C6 2 1 6 2 2 0 B18C6 2 3 6 1 1 0 DB18C6 2 4 6 0 0 0The largerKD,NaLS values for Bz systems (Table 2) do not necessarily show surprising results. Consider KD,NaLS value, using the thermodynamic relation, log⁡KD,MLS=log⁡Kex±+log⁡(KD,L/KML)-log⁡KD,AS. Here, KD,L and KML refer to the distribution constant (=Lo/[L]) of L into the o phase and a complex formation one (=[ML+]/[M+][L]) of M+ with L in water, respectively.Comparing Bz system with NB one at L = 15C5, for example, a difference betweenlog⁡Kex±,Bz and log⁡Kex±,NB was -5.27=log⁡Kex±,Bz/Kex±,NB=-3.91-1.36. Similarly, log⁡KD,15C5Bz/KD,15C5(NB) and -log⁡KD,PicS(Bz)/KD,PicS(NB) were −0.15 = −0.81 [12] − (−0.66 [18]) and +8.258=-(−8.208 − 0.05 [20]), respectively. Therefore, log⁡KD,NaLS(Bz)/KD,NaLS(NB) value becomes 2.83. From such handling, we can see that the difference (=+8.26) in log⁡KD,PicS between these diluents greatly contributes the positive difference (=2.8) in log⁡KD,NaLS between them. Also, the same is true for other L’s systems with Bz. The same explanation holds in comparison with DCM or DCE system because log⁡KD,PicS values have been reported to be −1.011 [20] for DCE and −0.68 [23] for DCM. In other words, accuracy of KD,PicS value for Bz system can become important for the discussion of the above larger KD,NaLS values; Fyles had estimated log⁡KD,NaLS value for DCM at −0.44 [22], compared to −0.68 [23].On the other hand, the orders of the actualKD,NaL values, the values at Δϕeq≠0, were Bz < DCM < DCE < NB for L = 18C6 and Bz < DCE < DCM < NB for the other three (Table 2). Also, the log⁡KD,NaLPic (=log⁡KD,NaLPicS in practice [1]) orders were Bz < DCE < DCM < NB for all the Ls employed. Here, the thermodynamic relation log⁡KD,MLA=log⁡Kex+log⁡(KD,L/KML)-log⁡K1, was used for the calculation [12–16] and the symbol K1 denotes the ion-pair formation constant in M−1 for ML+A− in water. The orders of KD,NaLPic determined in the benzo derivatives systems were in agreement with the corresponding orders [13, 15] reported before. This agreement shows a validity of such KD,NaLPic evaluations. For 15C5 and 18C6 systems, log⁡KD,NaLPic values were not cited here because of limitations [26] of their analytic procedures. Both orders of KD,NaL and KD,NaLPic essentially agreed with each other (see Table 2). These facts suggest that an interaction of the diluent molecules with NaL+Pic− is fundamentally similar to that with NaL+. Again, its main interaction with Bz molecules occurs around NaL+ moiety of the ion-pair complex.


## 3.1. Redetermination of Compositions of the Ion-Pair Complexes Extracted into Bz

Plots [16] for redetermining a Na(I) : L : Pic(−I) composition in the four extraction systems yielded regression lines of a slope = 0.997 and an intercept = 3.89 (≈log⁡Kex at z=1) at a correlation coefficient (R) = 0.998 for the 15C5 system, of 0.999 and 3.17 at R=0.9999 for the B15C5 one, of 0.903 and 3.04 at R=0.996 for the 18C6 one, and of 1.02 and 3.09 at R=0.999 for the B18C6 one; see log⁡(D/[Pic-]) versus log⁡LBz plots in Figure 1, where D denotes a distribution ratio of species with Na(I) into the Bz phase.Figure 1
Plots oflog⁡(D/[Pic-]) versus log⁡LBz for the 15C5 (square), B15C5 (diamond), 18C6 (circle), and B18C6 (triangle) extraction systems. See the text for regression results of the solid lines. The symbol of 1 mol dm−3 = 1 M was used.These slopes of about unity obviously indicate that the compositions of extracted species, mainly ion-pair complex, are Na(I) : L : Pic(−I) = 1 : 1 : 1 [16]. These results were in good agreement with those [12–15] described previously.


## 3.2. Determination of Extraction Constants and Their Several Component Equilibrium Constants

TheKD,A and Kex values at A = Pic(−I) and z=1 were determined by the plot of log⁡Kexmix versus -log⁡Na+LBz (Figure 2) based on the equation (1)log⁡Kexmix≈logKex+KD,ANa+LBz,where Kexmix has been defined as (MLAo+ML+o+M+o+⋯)/P [1, 2, 16]. Also, Kex± values were determined by the plot of log⁡Kexmix versus -1/2log⁡P (Figure 3) based on the equation (2)log⁡Kexmix≈log⁡Kex+Kex±P1/2,where the symbol Kex± has been defined as ML+oA-o/P [1, 2, 6] at z=1.Figure 2
Plot of logKexmix versus -log⁡(Na+LBz) for the NaPic extraction with L = 15C5. The KD,Pic and Kex values obtained from a nonlinear regression analysis with (1) were (7.7 ± 4.8) × 10−5 and 8115 ± 133 M−2, respectively.Figure 3
Plot oflog⁡Kexmix versus -1/2log⁡P for the NaPic extraction with L = 15C5. The Kex± and Kex values were obtained to be (7.3±3.8) × 10−4 M−1 and 7747 ± 149 M−2 from the nonlinear regression analysis with (2).The thus-determined values at 25°C are listed in Table1 (see Appendix A for reference), together with their component equilibrium constants, KD,Pic, KD,NaL (= NaL+Bz/[NaL+] [1]), and K1,Bz (= Kex/Kex±=NaLPicBz/NaL+BzPic-Bz [1, 2, 16]). Kex values were in the order B18C6 < B15C5 < 18C6 < 15C5, although the ionic strength (I) for the water phase of the 15C5 system is somewhat smaller than those of the other systems. This order was in accord with those [12–15] reported before (Table 1) and reflected the order of the (intercept/slope) values for the plots of log⁡(D/[Pic-]) versus log⁡LBz (see Section 3.1). Similarly, Kex± values showed the order B18C6 ≤ B15C5 < 18C6 ≤ 15C5, although the values of the benzo derivatives have large errors. This order agreed with that of Kex. These facts indicate that the present analyses are essentially valid.


## 3.3. OnΔϕeq Estimation and Its Correlation with log⁡Kex±

We can formally calculate theΔϕeq values from the relation (3)Δϕeq=ΔϕA0′-2.303RTFlog⁡KD,A[1, 2, 21] (see Table 1), when ΔϕA0′ values are available. Fyles had evaluated the free energy of the Pic− transfer from w to Bz [22]; then, ΔϕPic0′ value at the Bz/w interface was estimated from its free energy to be −0.486 V at 25°C. The thus-estimated Δϕeq values are listed in Table 1. Δϕeq values were in the order 15C5 ≈ 18C6 < B15C5 ≈ B18C6, although their experimental errors were large. Also, one can see that Δϕeq values for the Bz system with L are negative, indicating that KD,Pic values are larger than KD,PicS ones which are defined as exp⁡(ΔϕPic0′/0.02569) [1–3] at 25°C. On the other hand, the values reported before for the DCM, DCE, and NB systems have been accidentally all positive [1, 2].As Figure4 shows, a plot of log⁡Kex± versus -Δϕeq yielded the straight line: log⁡Kex±=84±12-Δϕeq-(23.6±2.6) at R=0.981. Similar lines were observed in NaPic extraction by L into DCM and DCE. Adding the data of NB systems, these slope values at Δϕeq (not -Δϕeq) were in the order Bz (slope = −84 V−1) < DCE (−26) ≤ DCM (−21) < NB (3). This order was close to that of dielectric constants (εr) [23] of the pure diluents at 298.15 K: Bz (εr=2.27) < DCM (8.93) < DCE (10.23) < NB (34.82), although these diluents were saturated with water. These results can be explained in terms of a model like a parallel-plate capacitor at the diluent/w interface [24]. Namely, its capacitance (C) is expressed as the following equation [24]: (4)C=qE≈εrSd.Here, the symbols q, E, S, and d refer to a charge stored on the capacitor, a potential across the capacitor, an area of the plate, and an interplate spacing, respectively [24].Figure 4
Plot oflog⁡Kex± versus -Δϕeq for the NaPic extraction with L into Bz. See the text for the regression line.So assuming that the slopes in V−1 of log⁡Kex± versus -Δϕeq plots correspond to C terms, then their values have to be proportional to εr ones under the condition of a fixed S/d in (4). The symbol S can be considered to be the area of the o/w interface and S value corresponding to its area in test tubes which had been used for the extraction experiments into the four diluents was estimated to be 2.4 cm2 from their mean inner diameter (=1.750 cm). A plot of slope versus εr showed a positive correlation. From this fact, as an example, it can be considered that d value for Bz is smaller than those for others. Unfortunately, we have no experimental ground with respect to this consideration.


## 3.4. On Some Tendencies of theKD,Pic and K1,Bz Values

The experimentallog⁡KD,Pic values of the Bz systems agreed with each other within experimental errors among L listed in Table 1. At least, the values for L = 15C5 and 18C6 were much larger than log⁡KD,PicS one (= −8.208 [22] = ΔϕPic0′/0.05916 at 25°C) without L. This fact indicates that the presence of L, namely, the distribution of NaL+, in the extraction largely facilitates Pic− transfer at Bz/w interfaces.A plot oflog⁡(IBz/I) (=y) versus log⁡KD,Pic (=x) gave a straight line with a slope of 1.45±0.23 and an intercept of 1.7±1.1 at R=0.975. Although the slope value is larger than unity, this linear relation is similar to those reported before for the extraction systems of CdPic2 [21] and PbPic2 [25] with 18C6 into various diluents containing Bz. Such a similarity also suggests that the present analysis is valid.log ⁡ K 1 , B z values were in the order L = 18C6 ≤ 15C5 < B15C5 < B18C6 (Table 1). This order is close to 18C6 < 15C5, B18C6 < B15C5, which was predicted from a combined parameter, B+M′+V, of basicity of the donor O atoms (parameter: B), selectivity of L against Na+ (M′) with a molecular volume (V); see Table 3 and Appendix B for the parameters. Also, an addition of a benzo group to the ring skeletons is causing an increase in K1,Bz: 15C5 < B15C5 and 18C6 < B18C6. That is, its addition which spontaneously changes the parameters B, S, and V of L (see Table 3 and Appendix B for S) has a positive effect on K1,Bz.K 1 , B z value at L = 15C5 was larger than K1,DCE, K1,DCM, and K1,NB ones; K1,DCM=106.2M-1 at average IDCM=3.0×10-6M, K1,DCE=106.5 at 1.7×10-6, and K1,NB=105.3 at 3.1×10-6. Also, the same is true for K1,org values for the other L. These facts indicate that although NaL+Pic- in Bz phases are less dissociable than those in DCM, DCE, and NB phases, the ions are present even in Bz phases. In other words, it suggests that the occurrence of Δϕeq is possible at Bz/w interface.


## 3.5. On the Distribution ofNaL+ and NaL+Pic- into Bz

The following relation can be used forKD,NaLS evaluation: (5)log⁡KD,MLS=log⁡KD,ML-Δϕeq0.05916at25°C[1, 3] and the symbol KD,NaLS denotes the distribution constant, KD,NaL, of NaL+ into the Bz phase at Δϕeq=0V. As can be seen from Table 2 (see the values of footnote d and Appendix A for reference), log⁡KD,NaLS values were in the orders DCE < DCM < NB < Bz for L = 15C5, DCE < DCM < Bz < NB for B15C5, NB < DCM < DCE < Bz for 18C6, and DCM < Bz < DCE < NB for B18C6. These orders indicate that the addition of the benzo group to the ring skeleton causes an increase in an interaction between NaL+ and NB molecules.Table 2
Individual distribution constants of NaL+ and NaL+Pic− into some diluents at 25°C.
(a) L log⁡KD,NaLSa (log⁡KD,NaL)b o = Bz DCM DCE NB 15C5 2.6 (−1.5) −1.14 (1.0) −1.54 (0.3) 0.0, −0.3d, 0.62e (1.7) B15C5 2 (−1.1) −0.34 (2.3) −0.54 (2) 2.2, 3.7d, 2.1e (4.1) 18C6 2.4 (−1.6) −0.44 (0.77) 0.47 (0.84) −0.3, −1.4d, 0.7e (1.1) B18C6 0.3 (−2.7) 0.19 (2.62) 1.16 (2.47) 1.5, 2.0d, 2.1f, (3.7) Without L —g −5.73h −6.09i, −4.38 [17] −5.18i, −5.95 [17] (b) L log⁡KD,NaLPic Bz DCMc DCEc NBc 15C5 0.94 2.87 2.47 3.82 B15C5 1.29 (1.42 [13]) 3.01 (3.13 [13]) 2.61 (2.73 [13]) 3.75 18C6 −0.26 1.88 1.16 3.68 B18C6 0.48 (1.18 [13, 15]) 2.47 (3.36 [13, 15]) 2.06 (2.97 [13, 15]) 3.71 Without L aStandard values calculated from the thermodynamic relation, log⁡KD,MLS=log⁡Kex±+log⁡(KD,L/KML)-log⁡KD,AS. bSee footnote f in Table 1. cUnpublished data by Kudo. dStandard values calculated from (5). eValues determined by ion-transfer polarographic measurements at the presence of 0.05 M (C4H9)4N+B(C6H5)4- in the NB phase. See [18]. fValues determined by the ion-transfer polarographic measurements at the presence of 0.05 M (C4H9)4N+B(C6H5)4- in the NB phase. See [19]. gNot determined. hThe values are a logarithmic individual distribution-constant of a single Na(I) ion into the DCM, DCE, or NB phase and are standardized at Δϕeq=0 V. iSee [20] and footnote h.Table 3
A measure of basic parameters for a comparison between Ls.
L Cavity size (parameter:C) Molecular volume (V) Number of donor O atoms (N) Basicity of donor O atoms (B) Softness of ring skeleton (S) Na+ selectivity (M′) 15C5 1 0 5 2 2 2 B15C5 1 2 5 1 1 2 18C6 2 1 6 2 2 0 B18C6 2 3 6 1 1 0 DB18C6 2 4 6 0 0 0The largerKD,NaLS values for Bz systems (Table 2) do not necessarily show surprising results. Consider KD,NaLS value, using the thermodynamic relation, log⁡KD,MLS=log⁡Kex±+log⁡(KD,L/KML)-log⁡KD,AS. Here, KD,L and KML refer to the distribution constant (=Lo/[L]) of L into the o phase and a complex formation one (=[ML+]/[M+][L]) of M+ with L in water, respectively.Comparing Bz system with NB one at L = 15C5, for example, a difference betweenlog⁡Kex±,Bz and log⁡Kex±,NB was -5.27=log⁡Kex±,Bz/Kex±,NB=-3.91-1.36. Similarly, log⁡KD,15C5Bz/KD,15C5(NB) and -log⁡KD,PicS(Bz)/KD,PicS(NB) were −0.15 = −0.81 [12] − (−0.66 [18]) and +8.258=-(−8.208 − 0.05 [20]), respectively. Therefore, log⁡KD,NaLS(Bz)/KD,NaLS(NB) value becomes 2.83. From such handling, we can see that the difference (=+8.26) in log⁡KD,PicS between these diluents greatly contributes the positive difference (=2.8) in log⁡KD,NaLS between them. Also, the same is true for other L’s systems with Bz. The same explanation holds in comparison with DCM or DCE system because log⁡KD,PicS values have been reported to be −1.011 [20] for DCE and −0.68 [23] for DCM. In other words, accuracy of KD,PicS value for Bz system can become important for the discussion of the above larger KD,NaLS values; Fyles had estimated log⁡KD,NaLS value for DCM at −0.44 [22], compared to −0.68 [23].On the other hand, the orders of the actualKD,NaL values, the values at Δϕeq≠0, were Bz < DCM < DCE < NB for L = 18C6 and Bz < DCE < DCM < NB for the other three (Table 2). Also, the log⁡KD,NaLPic (=log⁡KD,NaLPicS in practice [1]) orders were Bz < DCE < DCM < NB for all the Ls employed. Here, the thermodynamic relation log⁡KD,MLA=log⁡Kex+log⁡(KD,L/KML)-log⁡K1, was used for the calculation [12–16] and the symbol K1 denotes the ion-pair formation constant in M−1 for ML+A− in water. The orders of KD,NaLPic determined in the benzo derivatives systems were in agreement with the corresponding orders [13, 15] reported before. This agreement shows a validity of such KD,NaLPic evaluations. For 15C5 and 18C6 systems, log⁡KD,NaLPic values were not cited here because of limitations [26] of their analytic procedures. Both orders of KD,NaL and KD,NaLPic essentially agreed with each other (see Table 2). These facts suggest that an interaction of the diluent molecules with NaL+Pic− is fundamentally similar to that with NaL+. Again, its main interaction with Bz molecules occurs around NaL+ moiety of the ion-pair complex.


## 4. Conclusions

The compositions of the ion-pair complexes, NaLPic, extracted into the Bz phases were clarified again and their few dissociations were shown from the magnitudes oflog⁡K1,Bz values. The Δϕeq values at the Bz/w interfaces were easily calculated from the experimentally obtained log⁡KD,Pic values. Namely, the presence of Δϕeq at a less-polar diluent/w interface was clarified, as well as those at the polar diluents/w interfaces. Also, log⁡Kex± values for the NaPic extraction with L into Bz were proportional to the -Δϕeq ones and the slope of its regression line was about 84 V−1. The order of the slopes is NB < DCM ≤ DCE < Bz, although its meaning is not still clear. Besides, by comparing the actual KD,NaL with KD,NaLPic values, it was suggested that the main interaction site of Bz molecules with NaL+Pic− is NaL+ moiety in their ion pairs. The authors hope that the present study will become a topic which connects the extraction chemistry with the electrochemistry at the o/w interfaces.



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