18-Crown-6 ether (18C6) extracts CdBr₂, cadmium picrate (CdPic₂), or alkaline-earth metal picrates into various diluents [1-3]. In the previous study [1], the authors clarified that the extracted ion-pair complex, Cd(18C6)Br₂, very weakly interacts with water molecules and also the diluents ones and they also suggested that another complex Cd(18C6)Pic₂ strongly interacts with water molecules. In addition to this, it has been suggested that the latter ion-pair complex has a more polar structure than the former does [1]. However, kinds of the diluents used for the CdPic₂ extraction experiments with 18C6 were fewer, compared with kinds of the diluents for the CdBr₂ extraction ones.

In the above studies, furthermore, component equilibria which constitute overall extraction equilibria have been considered to be at least 6-10 ones [1,3,4]. For example, the component equilibria are L L_o, CdPic⁺ Cd²⁺+Pic^-, H⁺+Pic^- HPic, L+Cd²⁺ CdL²⁺, CdL²⁺+Pic^- CdLPic⁺, CdLPic⁺+Pic^- CdLPic², CdLPic² CdLPic_2,o , CdLPic_2,o CdLPic⁺_o+Pic⁻_o, Pic Pic⁻_o, and CdLPic⁺ CdLPic⁺_o at L=18C6 [1] where the subscript “o” denotes an organic phase. Unfortunately, except for several studies of the M(II) extraction with dibenzo-18C6 into nitrobenzene (NB) [5,6] the authors have not been able to find out studies based on such precise equilibrium analyses. Also, it is very difficult to criticallyevaluate equilibrium constants determined in the studies of the NB systems, because the corresponding component equilibrium-constants experimentally-obtained from other methods are few.

In the present paper, by employing o-dichlorobenzene (oDCBz), bromobenzene (BBz), dibutylether (DBE), and NB, we added new data in the CdPic₂ extraction by 18C6 and then re-discussed extraction characteristics of 18C6 against CdPic₂. Also, extraction constants (K_ex and K_ex±) for the same extraction into benzene (Bz) were re-determined, because the data of its Bz system abnormally deviated from the plot [1,4] of log K_ex,ip versus log K_D,L. Here, K_ex, K_ex±, K_ex,ip, and KD,L were defined [MLA₂]_o/([M²⁺][L]_o[A⁻]²),[MLA⁺]_o[A⁻]_o/([M²⁺][L]_o[A⁻]²), [MLA₂]_o/[ML²⁺][A⁻]², and [L]_o/[L] [1,3,4], respectively, with M²⁺=Cd²⁺ and A⁻=Pic. In the above discussion, an interfacial equilibrium-potential difference (Δφ_eq) at the transfer of Cd²⁺, CdL²⁺, CdLPic⁺, and Pic⁻ from water into the o phase, in particular NB or oDCBz, was introduced, as described previously [3]. Furthermore, an extraction constant of picric acid, HPic, into DBE was determined spectrophotometrically at 25°C, in order to precisely analyze extraction data for the Cd(II) extraction by 18C6 into DBE.

Chemicals

The preparation method of CdPic₂·nH₂O was essentially the same as that reported before [1]: this n value was determined by a Karl-Fischer titration to be 5.67 ± 0.23 at number (N) of run of 3. This finding was in good agreement with that (n=5.65) obtained from an EDTA titration of Cd(II) in the aqueous solution which contains CdPic₂·nH₂O. Also, spectrophotometric analysis of Pic (−I) in the aqueous solution at 355.0 nm showed the molar ratio of Cd(II):Pic(−I)=1:2.1 (see below). Water amount of used 18C6 (>98.0%, Wako) was determined by the Karl- Fischer titration to be 0.062 ± 0.029% at N=4. The H(I) amount of an aqueous solution prepared from a commercial HPic (>99.5%, Wako) was determined by an acid-base titration [7]. Other reagents were the same as or similar to those employed previously [1,4].

Extraction procedures

The experimental procedures for the CdPic₂ extraction by 18C6 were essentially the same as those described before [1,4] although the experiments were performed with the prepared CdPic₂ for the oDCBz (>99.0%, Kanto), DBE (>99.0%, Kanto), NB (>99.5%, Kanto), and Bz (>99.5%, Wako) systems and with mixtures of CdSO₄{>99.0%: (3/8) hydrate, Kanto} with HPic for the oDCBz and BBz (>98.0%, Kanto) systems. Here, the mixture was prepared by mixing an aqueous CdSO₄ solution with a mixture between Ba(OH)₂ (>98.0%: 8 hydrate, Wako) and an excess amount of HPic and then that with the precipitate was filtered. Total amounts of Cd(II) back-extracted from the o phases into aqueous solutions of the 0.1 mol dm^-3 HNO₃ were determined at the wavelength of 228.8 nm by a Hitachi atomic absorption spectrophotometer (type Z-6100) equipped with a Hitachi hollow cathode lamp (Mitorika Co., under the license of Hitachi Ltd.) of Cd in an air-acetylene flame [1]. Total concentrations employed for the experiments were (0.79-1.7) × 10⁻² mol dm^-3 for the prepared CdPic₂ and 1.1 × 10⁻⁵ -0.22 for 18C6; (0.79-1.5) × 10⁻² mol dm^-3 Cd(II), 0.012- 0.030 Pic(−I), and 0.0017 SO₄^2- for the mixture and (0.051-5.1) × 10^-2 for 18C6. Also, the procedures for the HPic extraction into DBE were the same as those reported before [7]. Total amounts of Pic(−I) extracted into DBE were back-extracted into aqueous solutions with 0.1 mol dm^-3 NaOH from the DBE phases and then were determined at the wavelength of 355.0 nm spectrophotometrically [7]. Total concentrations of the aqueous HPic solutions employed were in the range of (0.50-3.4) × 10^-2 mol dm^-3.

Data analysis

Data analysis for the extraction experiments was essentially the same as that described before [1,3,4]. The extraction constant parameter, K_ex^mix, has been introduced, where K_ex^mix is defined as ([MLA₂]_o+[MLA⁺]_o)/([M²⁺][L]_o[A⁻]²) by assuming that [MLA₂]_o+[MLA⁺]_o>> [MA⁺]_o+[ML²⁺]_o+[M²⁺]_o [1,3,4]. Its numerators were determined by AAS measurements (see above) and were expressed as “Ab” here. Also, the [M²⁺], [L]_o, and [A⁻] values were calculated from the following equations by a successive approximation method:

(1)

(2)

(3)

With a=2K_MLK₁K₂ [M²⁺][L]_o/KD,L, (3a)

b=1+2K_MA[M²⁺](K_HA+K_ex,HA)[H⁺], (3b)

and c=2Ab− [A]_t. (3c)

Here, K_MA, K_ML, K₁K₂, K_HA, and K_ex,HA in the above equations denote an ion-pair formation constant (mol⁻¹ dm³ unit) for MA⁺ in water, a complex formation one (mol^-1 dm³) for ML²⁺ in water, overall ionpair formation one (mol⁻² dm⁶) between ML²⁺ and 2A^- in water, an association one(mol^-1 dm³) for an acid, HA, in water, and an extraction one (mol⁻¹ dm³) for HA into the o phase, respectively. These values were either available from a reference [8] or evaluated from those [1,9,10] reported previously. Also, [j]_t shows the total concentration of species with j=M(II), L, or A(−I). In the computation, the K_MA, K₁K₂, and K_HA values were calculated taking account of the ionic strength (I ) of ionic species in water: I=(1/2)(4[M²⁺]+4[ML²⁺]+[MLA⁺]+[MA⁺]+[A⁻]) [1,3,4]which was changed into I=[M²⁺]+[ML²⁺]+[A⁻] fundamentally based on the charge balance equation, 2[M²⁺]+2[ML²⁺]+[MLA⁺]+[M A⁺]=[A⁻] (see below).

On the determination of fundamental extraction data

Compositions of extracted complexes were determined by plotting log (D/[Pic⁻]²) against log [18C6]_o at o=BBz, oDCBz, DBE, NB, and Bz [1-4,11]. Here, D refers to an experimental distribution ratio of Cd(II) into the o phases and the [Pic⁻] and [18C6]_o values were calculated from Equations (3) and (2), respectively. Regression lines of the plots were lines with slope (a)=0.81 and intercept (b)=3.90 at a correlation coefficient (R)=0.976 and N=11 for the BBz system, a=1.13 and b=4.65 at R=0.972 and N=7 for oDCBz with the mixture, a=0.76 and b=3.39 at R=0.944 and N=18 for oDCBz with the prepared CdPic₂, a=1.02 and b=4.61 at R=0.712 and N=23 for DBE, a=0.55 and b=4.80 at R=0.992 and N=15 for NB, and a=0.95 and b=4.28 at R=0.995 and N=15 for Bz. These results indicate that the species composed of M:L:A=1:1:2 are extracted into oDCBz from the mixture, DBE, and Bz, where the ratios of Pic(−I)=A were speculated from the charge balance to Cd(II) (see above) [1,3,4,11]. Also, the intercepts, b of these systems approximately show their log Kex values, when a equals unity [11]. On the other hand, dissociations of the species extracted are suggested for the BBz, NB systems, and oDCBz one with the prepared salt. The difference in a between the two oDCBz systems is caused by that between the experimental log [18C6]_oDCBz ranges which were -3.02 to -2.53 for the mixture and -6.73 to -3.09 for the prepared salt. That is, Cd(18C6) Pic₂ in the oDCBz phase dissociates in the lower log [18C6]_oDCBz range and its ion-pair formation is facilitated in the higher range: the former case causes a < 1, while the latter one does a ≥ 1. Therefore, further data analyses were performed by assuming the extraction of CdLPic₂ into the three diluent-systems [3,4,11]. Next, we determined the Kex, KD,A, and K_ex± values in terms of the following equations:

logK_ex^mix≈ log {K_ex+K_D,A/([M²⁺][L]_o[A⁻])} (4)

and ≈ log {Kex+(K_ex±/[M²⁺][L]_o[A⁻]²)1/2} (4a)

under the electroneutrality condition of [MLA⁺]_o≈ [A⁻]_o[3,4,11]: see Data Analysis. The non-linear regression analyses of plots [1,3,4,11] of log K_ex^mix versus −log ([M²⁺][L]_o[A⁻]) {from Equation (4)} and −log {([M²⁺][L]_o)1/2[A⁻]} {from Equation (4a)} yielded these values. The latter plots were analyzed here by introducing the Kex values, obtained from the former plots, in Equation (4a). As examples, Figures 1 and 2 show the plots for the extraction of the prepared CdPic₂ with 18C6 into oDCBz. Lastly, the log K_2,org, log K_D,MLA2, and log K_ex,ip were evaluated from the following thermodynamic cycles: log K_2,org = log (Kex/K_ex±), log K_D,MLA2 = log ([MLA₂]_o/[MLA₂])=log (KexKD,L/K_MLK₁K₂) (see the introduction for the KD,L definition), and log K_ex,ip = log (K₁K₂K_D,MLA2)=log (K_exK_D,L/K_ML), respectively [3,4]. Table 1 summarizes the thus determined fundamental values.

Table 1: Fundamental data for the CdPic₂ extraction by 18C6 into oDCBz, BBz, DBE, and NB at 25°C.

Figure 1: Plot of log K_ex^mix versus−log ([Cd²⁺][L]_oDCBz[Pic⁻])for the Cd(II) extraction with L=18C6 into oDCBz.The dotted line shows a regression one based on Equation (4): log K_ex ^mix=log {2.04 × 10⁴+(3.22 × 10⁻⁶/[Cd²⁺][L] oDCBz[Pic⁻])} at R=0.838.

Figure 2: Plot of log K_ex^mix versus−log {([Cd²⁺][L]_oDCBz[Pic⁻])}for the Cd(II) extraction with L=18C6 into oDCBz. The dotted line shows a regression one based on Eq. (4a): log K_ex^mix =log {2.04 × 10⁴+(9.40 × 10^-4/[Cd²⁺][L]_oDCBz[Pic⁻]²)^1/2} at R=0.761.

In Table 1, there were no large differences in log K values between the 18C6 extraction from the prepared salt, CdPic₂·5.7H₂O, and that from the mixture into oDCBz, except for logK_D,Pic. These facts fundamentally show that the BBz system is comparable with the oDCBz, DBE, and NB systems. The difference in log K_D,Pic can come from that in I_oDCBz, because its value is proportional to the log (I_org/I ) one in some cases [4]; see below for another detailed explanation.

The log Kex values were in the order DBE ≤ oDCBz ≤ BBzTable 1). Similar tendencies were observed in the log K_ex±, log K_D,Pic, and log _KD,CdLPic2 values. The log K_2,org values were in the order DBE ≥ oDCBz ≥ BBz > NB. Although there are differences in I_org and amounts of water saturated into the diluents, these three orders seem to fundamentally reflect the diluent’s polarity except for the KD,Pic order; the authors were not able to find the data of amount of water into DBE in reference: (H₂O)NB=0.178 mol dm⁻³ at 25°C [12]; mole fractions of water in the o phases were 0.0025 for o=oDCBz, 0.0021 for BBz, and 0.0149 for NB [13]. The log K_D,MLA2 order was DBEex,ip one, because the average log K₁K₂ values are in the range of 6.86-7.04 (Table 1); that is, differences in K₁K₂ among the diluents employed are very small.

Plot of log K_ex,ip versus log K_D,L

Figure 3 shows the re-plot of log K_ex,ip versus log K_D,L for the various diluent systems [1,4,14] at L=18C6. A point of the NB extraction system seemed to largely deviate from other points. Its regression line in Figure 3 was log K_ex,ip=(0.80 ± 0.13)log K_D,L+(4.13 ± 0.18) at R=0.894 and N=12 except for the NB system, where the two sets of data were employed for the oDCBz system in the calculation. In CdLX2 crystals at L=18C6 with X=Cl, Br, and I [15,16] and at B18C6 with Cl and Br [17] the two X(−I) bind directly to the central Cd(II) and their positions are perpendicular to the mean plane composed of the donor oxygen atoms in L. These complexes have the hexagonal bi pyramidal geometry. One can easily suppose its structure is kept in o phases with less polarities, except for the NB phase; see the caption in Figure 1 about the o phases. From comparing the log K_ex,ip versus log K_D,L plot of the Cd(18C6)Pic₂ system with that of Cd(18C6)Br₂ one (log K_ex,ip=1.16log K_D,L+5.27 at R=0.993 and N=11 [1,4]), we can immediately see that the plots of the both systems largely differ from each other at the R and slope values. The R value of the Pic⁻ system suggests that the extracted ion-pair complex Cd(18C6)Pic₂ has the higher polar structure, compared with Cd(18C6)Br₂, and also its slope (=VMLA₂/VL) suggests that the complex with Pic(−I) has relatively a compact shape [1,4]. Here, V denotes a molar volume (cm³ mol^-1) of the species corresponding to the subscript, MLA₂ or L. The VCdLPic₂ value was estimated to be 1.7 102 cm³ mol^-1from V18C6=214 cm³ mol^-1 [14]. This value is in accord with that (=about 200) reported before [1].

Figure 3: Plot of log K_ex,ip versus log K_D,L at L=18C6. The circles show points of the oDCBz, BBz, DBE, Bz, 1-chlorobutane [1], chloroform [1], 1,2-dichloroethane [1], dichloromethane [1], chlorobenzene [1], toluene [1], and m-xylene [1] extraction systems andthedotted line shows a regression one based on log K_ex,ip=(V_MLA2/V_L)log K_D,L+log K₁K₂+[the constant term] (see text). The triangle shows the point of the NB extraction system.

Since the intercept is expressed as log K₁K₂+[a term based on interactions between solutes and solvent molecules] [1,14], we can immediately evaluate this latter term from the average log K₁K₂ value among the extraction systems. This interaction term was calculated to be -2.7, when log K₁K₂=6.86 was used. This negative sign suggests a strong interaction between water molecules and the ion-pair complex Cd(18C6)Pic₂ and/or a weak one between diluent molecules and the complex (see below), compared with the interaction of 18C6 with both the solvent molecules. This suggestion is in agreement with the finding speculated from the R value [1]. The same discussion can be satisfied for the plot of log KD,Cd(18C6)Pic₂ versus log KD,18C6 [1].

For the CdPic₂ extraction by 18C6 into Bz, we easily obtained from the analysis described in the above section log K_ex=4.39 ± 0.04 {or 4.2± 0.1 from Equation (4a)}, log K_D,Pic=-5.18 ± 0.11, and log K_ex±=-2.97 ± 0.18 {or -2.32 ± 0.20 from Equation (4a) without the fixed Kex}. These values also gave log K_2,Bz (=log K_ex−log K_ex±) =7.4 ± 0.2 at IBz=8.4 × 10⁻⁸ mol dm⁻³ and log K_D,CdLPic2=−3.75{= log K_ex-log K_CdL-log K₁K₂(average)+log K_D,L=4.39 +0.05 − 6.92 (at I=0.019 mol dm⁻³)-1.27, see above} [1,10,14] at L=18C6. The thus determined log K_ex value was used for a recalculation of log K_ex,ip: log K_ex,ip becomes 3.17 (= log K_ex+log K_D,L-log K_CdL). In this study, the authors correct the log K_ex value from 1.98 reported in ref.1 to 4.39 and also do the logarithmic separation factor [4], log (K_ex,Pb/K_ex,Cd), from 9.73 in ref. 4 to 7.32; the revised log (K_ex±,Pb/ K_ex±,Cd) value became 7.1. By the re-determination of K_ex, the authors will eliminate a problem on the large deviation [1] of the Bz system from the plot of log K_ex,ip versus log K_D,18C6.

Determination of equilibrium constants for the HPic extraction into DBE

Figure 4 shows a plot of log D_A versus pH for the HPic extraction into DBE. A non-linear regression analysis of this plot gave the log K_ex,HPic value from its intercept: K_ex,HA=[HA]_o/[H⁺][A⁻]. Here, the relation of

logD_A=log K_ex,HA-pH-log (1+K_HA10^-pH) (5) in which the K_HA value averaged in the experimental I range (=0.00043-0.022 mol dm⁻³ at HA=HPic) was introduced, was employed for the analysis [7]. The symbol DA refers to the distribution ratio of species with A⁻. The line seems to be somewhat higher than the plots in the lower range of pH. This deviation may be due to that of the averaged K_HPic. The thus obtained value was log K_ex,HPic=1.06 ± 0.01 at 25°C with the regression line at R=0.997. This value was used for the K_ex calculation {see Equations (3) and (3b)}. Also, using the average log K_HPic value (=0.55 ± 0.03) [8], we evaluated log K_D,HPic to be 0.51 ± 0.03. This log K_D,HPic value was the smallest of those (=0.89-1.97) [7] reported previously by the authors on the HPic extraction into various diluents.

Figure 4: Plot of log D_Pic versus pH for the HPic extraction into DBE. The dotted line shows a regression one based on Equation (5) (see text).

On the interfacial equilibrium-potential difference at extraction

According to our previous papers [3,18], a difference between log K_D,Pic S and log KD,Pic for the NB system shows the presence of an interfacial potential difference,Δφ_eq, at extraction equilibrium. From the relation [1,3,18]

Δφ_eq=Δφ_A ^0′−(2.303RT/F)log K_D,A (6)

for the univalent anion A^-, we can easily calculate the Δφ_eq value. Here, the symbol, Δφ_A ^0′, refers to the formal potential standardized at Δφ_eq=0 V based on the Ph₄As⁺BPh₄⁻ assumption [19] and is expressed as the function log K_D,A(= FΔφ_A ^0′/2.303RT)=Δφ_A ^0′/0.05916 (defined as log K_D,AS) at 25°C [1,3,18,20]. Also, F, R, and T show usual meanings. From Δφ_Pic^0′=0.030 V [21] and the log K_D,Pic value of the NB extraction system in Table 1, the Δφ_eq value was calculated to be 0.14 V. At the same time, this value indicates that log K_D,Cd, log K_D,CdL, and log K_D,CdLPic values are expressed as 2(Δφ_eqΔφ_Cd^0′)/0.05916, 2(Δφ_eq−Δφ_CdL^0′)/0.05916,and (Δφ_eq−Δφ_CdLPic ^0′)/0.05916 at Δφ_eq=0.14 V, respectively [3,18]:“+2”of the former two terms refer to the formal charges of Cd²⁺ and CdL²⁺ {see Equation (7a)}. The same is essentially true of the other extraction systems, although their Δφ_Pic ^0′ values have not been determined in many cases. For the 1,2-dichloroethane and dichloromethane systems, ΔÏ?_Pic ^0′ available from references [21,22]. The difference between log KD,Pic values (see Table 1) in the oDCBz extraction system can be explained in terms of those between their charge balance equations, namely the difference between the Δφ_eq values and is also relevant to the difference between the I_oDCBz values (see above). The experimental condition with the extraction of the prepared CdPic₂ by L yields the charge balance equation of

2[Cd²⁺]_o+2[CdL²⁺]_o+[CdLPic⁺]_o=[Pic⁻]_o (7)

(or actually [CdLPic⁺]_o≈ [Pic⁻]_o, see above) in the o phase, while the other condition with the extraction of the mixture can yield the equation of 2[Cd²⁺]_o+2[CdL²⁺]_o+[CdLPic⁺]_o+[H⁺]_o+[HL+]_o=[Pic⁻]_o (8)

(or similarly [CdLPic⁺]_o+[H⁺]_o+[HL⁺]_o≈ [Pic⁻]_o). Probably, the [H⁺]_o+[HL⁺]_o term in Equation (8) corresponds to an increase in I_o for the extraction of the mixture with L (see Table 1).

Applying Equiation (6) to Equation (7) and the term in Equation (8), we can rewrite them as

2[Cd²⁺]exp{2F(Δφ_eq−ΔφCd ^0′)/RT}+2[CdL²⁺]exp{2F(Δφ_eq−φCdL ^0′)/ RT}

+[CdLPic⁺]_o=[Pic⁻]exp{−F(Δφ_eq − ΔPic ^0′)/RT} (7a)

and [H+]exp{F(Δφ_eq−ΔφH ^0′)/RT}+[HL+]exp{F(Δφ_eq−ΔφHL ^0′)/ RT},(8b)

respectively [18,23]. The symbol Δφj ^0′ denotes the standard formal potential for the species j {= Cd(II), CdL(II), CdLPic(I), Pic(−I), H(I), and HL(I)}. Defining x=exp(FΔφ_eq/RT) in Equation (7a) or Equation (8a) that Equation (8b) was added to the left-hand side of Equation (7a), then we can easily obtain the cubic equations, ax³+bx+c=0, solve them for x, and also for Δφ_eq [18,23]. For example, a=2[Cd²⁺]exp(- 2Fφ_Cd ^0′/RT)+ 2[CdL²⁺]exp(-2Fφ_CdL ^0′/RT), b=[CdLPic⁺]_o(see below for the NB system), and c=-[Pic⁻]exp(FΔφ_Pic ^0′/RT) in the case of Equation (7a).

One can easily see that this Δφ_eq value is common to all processes of Cd²⁺ Cd²⁺ _o, CdL²⁺ CdL²⁺_o, CdLPic⁺ CdLPic⁺ _o, and Pic⁻ Pic⁻_o or to those of Cd²⁺ Cd²⁺ _o,CdL²⁺ CdL²⁺_o,CdLPic⁺ CdLPic⁺_o, H⁺ H⁺ _o, HL⁺ HL⁺ _o, and Pic Pic⁻_o[18] at o=oDCBz. Thus, these Δφ_eq values solved by the above charge-balance equations are equivalent to those determined from log KD,Pic [18] and accordingly both the Δ_eq values can reflect materials employed in extraction experiments. Therefore, the upper log K_D,Pic value (= -5.49) in Table 1 is different from the lower value (=-4.24) and the increase in the lower value from Equation (7) can be caused by Equation (8b). Unfortunately, we were not able to find out the basic Δj ^0′ data {j=Cd(II), Pic(−I), or H(I)} in references with respect to the oDCBz system.

Estimate of ion-transfer formal potential of CdLPic⁺ at the water/NB interface

On the basis of the above discussion, the Δφ_CdLPic ^0′ value at the water/ NB interface was evaluated at L=18C6. The [CdLPic⁺]_NB values were evaluated from the relation [MLA⁺]_o=(K_ex mix−K_ex)[M²⁺][L]_o[A⁻]² (>0) and then the [CdLPic⁺] ones were calculated from [MLA⁺]=K1[ML²⁺] [A⁻]=(K1K_ML/KD,L)[M²⁺][L]_o[A⁻]. Here, K₁ was evaluated from the relation log K₁{= log K₁⁰-log (y_II+y₋/y_I+)}≈ log K₁⁰-log y_II+ with y₋≈y_I+. The symbols, K₁⁰,y_II+, y₋, and y_I+, denote K₁ at I 0, an activity coefficient of ML²⁺, that of A⁻, and that of MLA⁺ in water at 25°C, respectively [10,24]; K₁ 0=3.4 × 104 mol⁻¹ dm³. From the above calculation, −0.43(± 0.15 at N=8) was obtained as the average log K_D,CdLPic value. Hence, using the equation (Δφ_eq-Δφ_CdLPic ^0′)/0.05916=log K_D,CdLPic and Δφ_eq=0.14 V (see above), we immediately was able to calculate Δφ_CdLPic ^0′ to be 0.17 V at 25°C. This value is much larger than that (Δφ_Pic ^0′=0.003 V) [21] of Pic⁻ in the ion transfer at the water/NB interface. This fact suggests the stronger interaction of CdLPic⁺ than Pic⁻ with water molecules, as described above.

By adding the log K_ex,ip values for the three diluent systems except for the NB one, the plot of log K_ex,ip versus log K_D,L for the present CdPic₂-18C6 extraction system was re-analyzed in the number of data comparable with the plot of the CdBr₂-18C6 extraction one. Although the extraction data for the Bz system were revised, the result for the interaction between Cd(18C6)²⁺(Pic^-)₂ and water molecules, obtained from the former plot, was in agreement with the previously-reported result [1]. Also, the presence of Δφ_eq in the Cd(II) extraction system was shown from the K_D,Pic determination, as well as that in the M(I) extraction ones with L. Moreover, the authors were able to estimate the ion-transfer formal potential of Cd(18C6)Pic⁺ at the water/NB interface.