Yoshihiro Kudo^{1*}, Shoichi Katsuta^{1}, Yuuki Ohsawa^{2} and Kohei Nozaki^{2}  
^{1}Graduate School of Science, Chiba University, Chiba 2638522, Japan  
^{2}Department of Chemistry, Faculty of Science, Chiba University, Chiba 2638522, Japan  
Corresponding Author :  Yoshihiro Kudo Graduate School of Science Chiba University, 133 Yayoicho, Inageku Chiba 2638522, Japan Tel: +81432902786 Email: [email protected] 
Received May 21, 2015; Accepted June 16, 2015; Published June 26, 2015  
Citation: Kudo Y, Katsuta S, Ohsawa Y, Nozaki K (2015) Solvent Extraction of Cadmium Picrate by 18Crown6 Ether into Several Lesspolar Diluents and Nitrobenzene: Reevaluation of the Corresponding Overall Extraction Systems. J Thermodyn Catal 6:146. doi: 10.4172/21577544.1000146  
Copyright: © 2015 Kudo Y, et al. This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.  
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TCadmium picrate (CdPic2) in water was extracted at 25°C by 18crown6 ether (18C6) into odichlorobenzene (oDCBz), bromobenzene (BBz), dibutylether (DBE), and nitrobenzene (NB). Their extraction constants (Kex and Kex±) were determined, where Kex and Kex± at L=18C6 were defined as (CdLPic2)o/((Cd2+)(L)o(Pic−)2) and (CdLPic+) o(Pic−)o/((Cd2+)(L)o)(Pic−)2), respectively. The subscript “o” denotes an organic phase, such as oDCBz and BBz. The same extraction constants were redetermined for a system with benzene. Also, individual distribution constants (KD,Pic=(Pic−)o/(Pic−)) of picrate ion Pic− into the above o phases were determined with the Kex determination. Properties for the CdPic2 extraction with 18C6 were discussed by using the above constants and those available from the same extraction systems with other diluents. From comparing the experimental log KD,Pic value with the log KD,Pic S one for only the highpolar NB system, an interfacial potential difference (Δφeq) at extraction equilibrium was evaluated, where the symbol, log KD,Pic S, shows the log KD,Pic value standardized at Δφeq=0 V and 25°C. In the course of this study, an extraction constant for an HPic extraction into DBE was determined spectrophotometrically at 25°C.
Keywords 
Extraction constants; Individual distribution constant; Interfacial equilibrium potential; Solutesolvent interaction; At water/ nitrobenzene interface; Cadmium picrate; 18Crown6 ether 
Introduction 
18Crown6 ether (18C6) extracts CdBr_{2}, cadmium picrate (CdPic_{2}), or alkalineearth metal picrates into various diluents [13]. In the previous study [1], the authors clarified that the extracted ionpair complex, Cd(18C6)Br_{2}, very weakly interacts with water molecules and also the diluents ones and they also suggested that another complex Cd(18C6)Pic_{2} strongly interacts with water molecules. In addition to this, it has been suggested that the latter ionpair complex has a more polar structure than the former does [1]. However, kinds of the diluents used for the CdPic_{2} extraction experiments with 18C6 were fewer, compared with kinds of the diluents for the CdBr_{2} extraction ones. 
In the above studies, furthermore, component equilibria which constitute overall extraction equilibria have been considered to be at least 610 ones [1,3,4]. For example, the component equilibria are L L_{o}, CdPic^{+} Cd^{2+}+Pic^{}, H^{+}+Pic^{} HPic, L+Cd^{2+} CdL^{2+}, CdL^{2+}+Pic^{} CdLPic^{+}, CdLPic^{+}+Pic^{} CdLPic^{2}, CdLPic^{2} 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 dibenzo18C6 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 equilibriumconstants experimentallyobtained from other methods are few. 
In the present paper, by employing odichlorobenzene (oDCBz), bromobenzene (BBz), dibutylether (DBE), and NB, we added new data in the CdPic_{2} extraction by 18C6 and then rediscussed extraction characteristics of 18C6 against CdPic_{2}. Also, extraction constants (K_{ex} and K_{ex±}) for the same extraction into benzene (Bz) were redetermined, 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 [MLA_{2}]_{o}/([M^{2+}][L]_{o}[A^{−}]^{2}),[MLA^{+}]_{o}[A^{−}]_{o}/([M^{2+}][L]_{o}[A^{−}]^{2}), [MLA_{2}]_{o}/[ML^{2+}][A^{−}]^{2}, and [L]_{o}/[L] [1,3,4], respectively, with M^{2+}=Cd^{2+} and A^{−}=Pic. In the above discussion, an interfacial equilibriumpotential difference (Δφ_{eq}) at the transfer of Cd^{2+}, CdL^{2+}, 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. 
Materials and Methods 
Chemicals 
The preparation method of CdPic_{2}·nH_{2}O was essentially the same as that reported before [1]: this n value was determined by a KarlFischer 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 CdPic_{2}·nH_{2}O. 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 acidbase titration [7]. Other reagents were the same as or similar to those employed previously [1,4]. 
Extraction procedures 
The experimental procedures for the CdPic_{2} extraction by 18C6 were essentially the same as those described before [1,4] although the experiments were performed with the prepared CdPic_{2} for the oDCBz (>99.0%, Kanto), DBE (>99.0%, Kanto), NB (>99.5%, Kanto), and Bz (>99.5%, Wako) systems and with mixtures of CdSO_{4}{>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 CdSO_{4} 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) backextracted from the o phases into aqueous solutions of the 0.1 mol dm^{3} HNO_{3} were determined at the wavelength of 228.8 nm by a Hitachi atomic absorption spectrophotometer (type Z6100) equipped with a Hitachi hollow cathode lamp (Mitorika Co., under the license of Hitachi Ltd.) of Cd in an airacetylene flame [1]. Total concentrations employed for the experiments were (0.791.7) × 10^{−2} mol dm^{3} for the prepared CdPic_{2} and 1.1 × 10^{−5} 0.22 for 18C6; (0.791.5) × 10^{−2} mol dm^{3} Cd(II), 0.012 0.030 Pic(−I), and 0.0017 SO_{4}^{2} for the mixture and (0.0515.1) × 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 backextracted 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 (0.503.4) × 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 ([MLA_{2}]_{o}+[MLA^{+}]_{o})/([M^{2+}][L]_{o}[A^{−}]^{2}) by assuming that [MLA_{2}]_{o}+[MLA^{+}]_{o}>> [MA^{+}]_{o}+[ML^{2+}]_{o}+[M^{2+}]_{o} [1,3,4]. Its numerators were determined by AAS measurements (see above) and were expressed as “Ab” here. Also, the [M^{2+}], [L]_{o}, and [A^{−}] values were calculated from the following equations by a successive approximation method: 
(!) 
(2) 
(3) 
With a=2K_{ML}K_{1}K_{2} [M^{2+}][L]_{o}/KD,L, (3a) 
b=1+2K_{MA}[M^{2+}](K_{HA}+K_{ex,HA})[H^{+}], (3b) 
and c=2Ab− [A]_{t}. (3c) 
Here, K_{MA}, K_{ML}, K_{1}K_{2}, K_{HA}, and K_{ex,HA} in the above equations denote an ionpair formation constant (mol^{−1} dm^{3} unit) for MA^{+} in water, a complex formation one (mol^{1} dm^{3}) for ML^{2+} in water, overall ionpair formation one (mol^{−2} dm^{6}) between ML^{2+} and 2A^{} in water, an association one(mol^{1} dm^{3}) for an acid, HA, in water, and an extraction one (mol^{−1} dm^{3}) 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}, K_{1}K_{2}, and K_{HA} values were calculated taking account of the ionic strength (I ) of ionic species in water: I=(1/2)(4[M^{2+}]+4[ML^{2+}]+[MLA^{+}]+[MA^{+}]+[A^{−}]) [1,3,4]which was changed into I=[M^{2+}]+[ML^{2+}]+[A^{−}] fundamentally based on the charge balance equation, 2[M^{2+}]+2[ML^{2+}]+[MLA^{+}]+[M A^{+}]=[A^{−}] (see below). 
Results and Discussion 
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 [14,11]. 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 CdPic_{2}, 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) Pic_{2 }in the oDCBz phase dissociates in the lower log [18C6]_{oDCBz} range and its ionpair 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 CdLPic_{2} into the three diluentsystems [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}/([M^{2+}][L]_{o}[A^{−}])} (4) 
and ≈ log {Kex+(K_{ex±}/[M^{2+}][L]_{o}[A^{−}]^{2})1/2} (4a) 
under the electroneutrality condition of [MLA^{+}]_{o}≈ [A^{−}]_{o}[3,4,11]: see Data Analysis. The nonlinear regression analyses of plots [1,3,4,11] of log K_{ex}^{mix} versus −log ([M^{2+}][L]_{o}[A^{−}]) {from Equation (4)} and −log {([M^{2+}][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 CdPic_{2} 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 ([MLA_{2}]_{o}/[MLA_{2}])=log (KexKD,L/K_{ML}K_{1}K_{2}) (see the introduction for the KD,L definition), and log K_{ex,ip} = log (K_{1}K_{2}K_{D,MLA2})=log (K_{ex}K_{D},L/K_{ML}), respectively [3,4]. Table 1 summarizes the thus determined fundamental values. 
In Table 1, there were no large differences in log K values between the 18C6 extraction from the prepared salt, CdPic_{2}·5.7H_{2}O, 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 ≤ BBz<NB (Table 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: (H_{2}O)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 DBE<oDCBz ≤ BBz<NB. This order is strongly reflected into the log K_{ex,ip} one, because the average log K_{1}K_{2} values are in the range of 6.867.04 (Table 1); that is, differences in K_{1}K_{2} among the diluents employed are very small. 
Plot of log K_{ex,ip} versus log K_{D,L} 
Figure 3 shows the replot 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)Pic_{2} system with that of Cd(18C6)Br_{2} 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 ionpair complex Cd(18C6)Pic_{2} has the higher polar structure, compared with Cd(18C6)Br_{2}, and also its slope (=VMLA_{2}/VL) suggests that the complex with Pic(−I) has relatively a compact shape [1,4]. Here, V denotes a molar volume (cm^{3} mol^{1}) of the species corresponding to the subscript, MLA_{2} or L. The VCdLPic_{2} value was estimated to be 1.7 102 cm^{3} mol^{1}from V18C6=214 cm^{3} mol^{1} [14]. This value is in accord with that (=about 200) reported before [1]. 
Since the intercept is expressed as log K_{1}K_{2}+[a term based on interactions between solutes and solvent molecules] [1,14], we can immediately evaluate this latter term from the average log K_{1}K_{2} value among the extraction systems. This interaction term was calculated to be 2.7, when log K_{1}K_{2}=6.86 was used. This negative sign suggests a strong interaction between water molecules and the ionpair complex Cd(18C6)Pic_{2} 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)Pic_{2} versus log KD,18C6 [1]. 
For the CdPic_{2} 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 K_{1}K_{2}(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 redetermination 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 nonlinear 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}pHlog (1+K_{HA}10^{pH}) (5) in which the K_{HA} value averaged in the experimental I range (=0.000430.022 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 (=0.891.97) [7] reported previously by the authors on the HPic extraction into various diluents. 
On the interfacial equilibriumpotential 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 Ph_{4}As^{+}BPh_{4}^{−} 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_{eq}Δφ_{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 Cd^{2+} and CdL^{2+} {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 1,2dichloroethane 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 CdPic_{2} by L yields the charge balance equation of 
2[Cd^{2+}]_{o}+2[CdL^{2+}]_{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[Cd^{2+}]_{o}+2[CdL^{2+}]_{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[Cd^{2+}]exp{2F(Δφ_{eq}−ΔφCd ^{0′})/RT}+2[CdL^{2+}]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 lefthand side of Equation (7a), then we can easily obtain the cubic equations, ax^{3}+bx+c=0, solve them for x, and also for Δφ_{eq} [18,23]. For example, a=2[Cd^{2+}]exp( 2Fφ_{Cd} ^{0′}/RT)+ 2[CdL^{2+}]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 Cd^{2+} Cd^{2+} _{o}, CdL^{2+} CdL^{2+}_{o}, CdLPic^{+} CdLPic^{+} _{o}, and Pic^{−} Pic^{−}_{o} or to those of Cd^{2+} Cd^{2+} _{o},CdL^{2+} CdL^{2+}_{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 chargebalance 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 iontransfer 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})[M^{2+}][L]_{o}[A^{−}]^{2} (>0) and then the [CdLPic^{+}] ones were calculated from [MLA^{+}]=K1[ML^{2+}] [A^{−}]=(K1K_{ML}/KD,L)[M^{2+}][L]_{o}[A^{−}]. Here, K_{1} was evaluated from the relation log K_{1}{= log K_{1}^{0}log (y_{II+}y_{−}/y_{I+})}≈ log K_{1}^{0}log y_{II+} with y_{−}≈y_{I+}. The symbols, K_{1}^{0},y_{II+}, y_{−}, and y_{I+}, denote K_{1} at I 0, an activity coefficient of ML^{2+}, that of A^{−}, and that of MLA^{+} in water at 25°C, respectively [10,24]; K_{1} 0=3.4 × 104 mol^{−1} dm^{3}. 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. 
Conclusion 
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 CdPic_{2}18C6 extraction system was reanalyzed in the number of data comparable with the plot of the CdBr_{2}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 previouslyreported 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 iontransfer formal potential of Cd(18C6)Pic^{+} at the water/NB interface. 
References 

Table 1 
Figure 1  Figure 2  Figure 3  Figure 4 