Silver ( I ) Extraction with Benzo-18-Crown-6 Ether from Water into 1 , 2-Dichloroethane : Analyses on Ionic Strength of the Phases and their Equilibrium Potentials

Extraction constants (Kex & Kex±) for the extraction of silver picrate (AgPic) by benzo-18-crown-6 ether (B18C6) into 1,2-dichloroethane (DCE) were determined at 298 K and various ionic strength (I)-values of a water phase with or without excess HNO3. Here the symbols, Kex and Kex±, were defined as [AgLPic]DCE/P and [AgL]DCE[Pic]DCE/P with P = [Ag][L]DCE[Pic] and L = B18C6, respectively; [ ]DCE refers to the concentration of the corresponding species in the DCE phase at equilibrium. Simultaneously, KD,Pic (= [Pic]DCE/[Pic]) and K1,DCE (= Kex/Kex±) values for given I and IDCE values were determined, where the symbol IDCE shows I of the DCE phase. Also, equilibrium potential differences (∆φeq) based on the Pic− transfer at the water/DCE interface were obtained from the analysis of the KD,Pic [= KD,Pic exp{−(F/RT) ∆φeq}] values; the symbol KD,Pic shows KD,Pic at ∆φeq = 0 V. On the basis of these results, I dependences of logKex and logKex± and IDCE ones of logK1,DCE and logKex± were examined. Extraction experiments of AgClO4 and AgNO3 by B18C6 into DCE were done for comparison. The logKex±-versus-∆φeq plot for the above Ag(I) extraction systems with Pic−, ClO4, and NO3 gave a good positive correlation.


Introduction
It is well known that crown compounds (L) extract alkali and alkaline-earth metal ions (M z+ , z = 1, 2) from water (w) into various diluents [1][2][3][4].In many extraction experiments, extraction constants for L have been determined so far [1][2][3][4][5][6][7][8].For example, the two representative constants, K ex and K ex± , for the extraction of a univalent metal salt (M I A) by L have been defined as [MLA] org /P [2,3] and [ML + ] org [A − ] org /P [1,4] with P = [M + ][L] org [A − ], respectively.Generally, the K ex value is effective for the evaluation of an extraction-ability and -selectivity of L against M + into low-polar diluents, while the K ex± value is for those of L into high-polar ones.Here, the subscript "org" denotes an organic phase and A − does a univalent pairing anion.For the latter K ex± , its thermodynamic equilibrium constants have been reported [4].For the former K ex , its thermodynamic treatment seems to be few.The authors were not able to find out the study with respect to a dependence of logK ex on the ionic strength (I) of the w phase.
Presences of equilibrium potential differences (∆φ eq ) between aqueous and diluent solutions have been recently reported for the extraction of some M + or M 2+ with L [5][6][7].This symbol ∆φ eq was defined as ∑{inner potential (φ ) of ionic species in the w phase} − ∑{φ of those in the org or diluent phase} [8], according to the definition [9,10], φ w − φ org , of an interfacial equilibrium potential-difference in the electrochemistry at liquid/liquid interfaces.In the above studies, an approximation method [5][6][7][8] for the ∆φ eq determination, namely the method with a use of a "conditional" distribution constant (K D,A ) of A − into the org phase, has been described in comparison with its more-precise method with solving higher-degree equations [6].Here the "conditional" is due to the fact that the K D,A values change depending on the ∆φ eq ones, even at fixed pressure and temperature.However, it is still not clarified whether the ∆φ eq values determined by the K D,A values equal those coming from the distribution of M + into the org phases or not.
In the present paper, we determined the K ex , K ex± , and K D,A values [6,8] at 298 K by the extraction experiments into 1,2-dichloroethane (DCE) with silver picrate (AgPic) and benzo-18-crown-6 ether (B18C6), in order to elucidate mainly the above two subjects for I and ∆φ eq .The same experiments were performed under the condition of the presence of excess HNO 3 in the w phases.Then, an ion-pair formation constant (K 1,DCE /mol −1 •dm 3 ) for Ag(B18C6) + Pic − in the DCE phase, DCE saturated with water, and the ∆φ eq values were calculated from the relations, K 1,DCE = K ex /K ex± [6,8] and ∆φ eq = −(2.303RT/F){logKD,A − log(K D,A standardized at ∆φ eq = 0 V)} [11], respectively.Here, R, T, and F are usual meanings.On the basis of these data, the dependences of logK ex and logK ex± on the I values and those of logK 1,DCE and logK ex± on the I values (I DCE ) of the DCE phases were examined.Moreover, a relation between the ∆φ eq values determined by the K D,A ones and the conditional distribution constants (K D,Ag ) of Ag + into the DCE phases was discussed indirectly.For comparison, the K ex± and K ex values were experimentally determined at 298 K for the AgClO 4 -and AgNO 3 -B18C6 extraction into DCE.As basic data, the K D,Ag S value was determined in terms of a simple Ag + Pic − extraction experiment into DCE.The symbol K D,Ag S denotes the distribution constant of Ag + into the DCE phase standardized at ∆φ eq = 0 V, that is, the standard distribution one.

S
According to our previous paper [12], the K D,M S value has been obtained from a plot of D A versus [A − ] based on the equation with and in the org phase.A regression analysis of the plot (see Figure 1) yields a straight line with a slope of K ex,AgPic and an intercept of K D, ± .We call this K D, ± a mean distribution constant.Using the K D,Pic S value (= 10 −1.011 [12]), we immediately can obtain the K D,Ag S one from Equation (2).The thus-determined values were logK D, ± = −3.74± 0.04, logK ex,AgPic = −1.49± 0.05, and logK AgPic,DCE = 5.992 ± 0.008 and then the logK D,Ag S value became −6.47 ± 0.04 from the logarithmic form of Equation (2).This K D,Ag S value was used only for the K AgL,DCE calculation (see Tables 1 and 2).Using the KD,Pic S value (= 10 −1.011 [12]), we immediately can obtain the KD,Ag S one from Equation (2).The thus-determined values were logKD, ± = −3.74± 0.04, logKex,AgPic = −1.49± 0.05, and logKAgPic,DCE = 5.992 ± 0.008 and then the logKD,Ag S value became −6.47 ± 0.04 from the logarithmic form of Equation ( 2).This KD,Ag S value was used only for the KAgL,DCE calculation (see Tables 1 and 2).

Composition Determination of Complex Species Extracted into DCE
Compositions of species extracted into DCE have been determined by a plot of 2logD or log(D/[A − ]) versus log[L]org [2,7,13].When the slope of both plots is in unity, it independently gives the compositions of ML + with A − or MLA as the extracted major species.Among their plots, experimental slopes of all the log(D/[Pic − ])-versus-log[B18C6]org plots were less than unity, suggesting the dissociation of Ag(B18C6)Pic in the DCE phases [13].On the other hand, the 2logD-versuslog[L]org plots were in the slope ranges of 1.01-1.11for the AgPic extraction with L = B18C6, in the slopes of 1.09 for the AgClO4 one and of 1.08 for the AgNO3 one (Figure 2).These results indicate the AgB18C6 + extraction into DCE with A − = Pic − , ClO4 − , or NO3 − .That is, the extraction systems were accompanied with the dissociation process, Ag(B18C6)ADCE ↔ AgB18C6 + DCE + A − DCE (see Appendix).[2,7,13].When the slope of both plots is in unity, it independently gives the compositions of ML + with A − or MLA as the extracted major species.Among their plots, experimental slopes of all the log(D/[Pic − ])-versus-log[B18C6] org plots were less than unity, suggesting the dissociation of Ag(B18C6)Pic in the DCE phases [13].On the other hand, the 2logD-versus-log[L] org plots were in the slope ranges of 1.01-1.11for the AgPic extraction with L = B18C6, in the slopes of 1.09 for the AgClO 4 one and of 1.08 for the AgNO 3 one (Figure 2

Determination of Various Equilibrium Constants for the Extraction Systems
For the determination of KD,A, Kex±, and Kex, the following extraction-constant parameter (Kex mix /mol −2 •dm 6 ) has been employed [7,8,11].
Rearranging this equation, we immediately obtain ≈ log{Kex + (Kex±/P)  3 and 4 show examples for such plots.Additionally, the ion-pair formation constant, K1,org, for MLA in the org phase was calculated from K1,org = Kex/Kex± for a given Iorg on average.

Determination of Various Equilibrium Constants for the Extraction Systems
For the determination of K D,A , K ex± , and K ex , the following extraction-constant parameter (K ex mix /mol −2 •dm 6 ) has been employed [7,8,11].
Rearranging this equation, we immediately obtain under the assumption of [MLA] org + [ML + ] org >> [M + ] org .So we can determine the K D,A and K ex± values from the plots of logK ex mix versus −log([M + ][L] org ) {see Equation (3a)} and −(1/2)logP {see Equation (3b)}, respectively, together with the K ex values.Figures 3 and 4 show examples for such plots.Additionally, the ion-pair formation constant, K 1,org , for MLA in the org phase was calculated from K 1,org = K ex /K ex± for a given I org on average.Similarly, a complex formation constant (KAgB18C6,DCE/mol −1 •dm 3 ) for AgB18C6 + in the DCE phase was estimated from the thermodynamic relation of KAgB18C6,DCE = Kex±/(KD,Ag S •KD,Pic S ).Tables 1 and 2 list the logarithmic KD,A, Kex±, Kex, K1,DCE, and KAgB18C6,DCE values thus-obtained, together with the average I and IDCE values.

Determination of Equilibrium Potential Differences between the Water and DCE Phases
The logKD,A values were obtained from the plots based on Equation (3a).Next, the equilibrium potential differences Δφeq can be evaluated from using the following equation [11]: with Similarly, a complex formation constant (KAgB18C6,DCE/mol −1 •dm 3 ) for AgB18C6 + in the DCE phase was estimated from the thermodynamic relation of KAgB18C6,DCE = Kex±/(KD,Ag S •KD,Pic S ).Tables 1 and 2 list the logarithmic KD,A, Kex±, Kex, K1,DCE, and KAgB18C6,DCE values thus-obtained, together with the average I and IDCE values.

Determination of Equilibrium Potential Differences between the Water and DCE Phases
The logKD,A values were obtained from the plots based on Equation (3a).Next, the equilibrium potential differences Δφeq can be evaluated from using the following equation [11]: with Similarly, a complex formation constant (K AgB18C6,DCE /mol −1 •dm 3 ) for AgB18C6 + in the DCE phase was estimated from the thermodynamic relation of Tables 1 and 2 list the logarithmic K D,A , K ex± , K ex , K 1,DCE , and K AgB18C6,DCE values thus-obtained, together with the average I and I DCE values.

Determination of Equilibrium Potential Differences between the Water and DCE Phases
The logK D,A values were obtained from the plots based on Equation (3a).Next, the equilibrium potential differences ∆φ eq can be evaluated from using the following equation [11]: where the symbols, K D,A S and ∆φ A • , are called the standard distribution constant of A − into the org phase, namely K D,A at ∆φ eq = 0 V, and a standard formal potential for the A − transfer at the w/diluent interface, respectively; see Section 2.1 for the K D,Pic S value.The thus-evaluated values are listed in Tables 1 and 2. Strictly speaking, ∆φ eq and ∆φ A 0 are the equilibrium potential differences between the two bulk phases.However, they can be regarded approximately as the equilibrium potential differences at the liquid/liquid interfaces [9,10].

I Dependences of LogK ex and LogK ex±
The dependences of logK ex and logK ex± on I are considered below.On the basis of their definitions, the K ex value can be dependent on [M + ] and [A − ], while, in addition to these concentrations, the K ex± value can be on [ML + ] org and [A − ] org .Therefore, K ex is mainly a function of I, while K ex± is a function with the two parameters, I and I org ; the relations [14] of [M + ] = a M /y + (I) and [A − ] org = a A,org /y −,org (I org ) hold as examples (see below for the symbols a and y).The I dependence of logK ex± is of an approximate.
Figure 5 shows the logK ex -versus-I plot for the AgPic-B18C6 extraction system with DCE; in the plot, the average value of I was employed as I (x-axis) of each system.Using the extended Debye-Hückel (DH) equation [14], the extraction constant (K ex 0 ) at I → 0 mol•dm −3 is expressed as where the symbols, a j and y, denote the activity of species j (= M + , A − ) and its activity coefficient with I, respectively [14].Rearranging Equation ( 5), the following equation was obtained immediately: Figure 5 shows the logKex-versus-I plot for the AgPic-B18C6 extraction system with DCE; in the plot, the average value of I was employed as I (x-axis) of each system.Using the extended Debye-Hückel (DH) equation [14], the extraction constant (Kex 0 ) at I → 0 mol•dm −3 is expressed as where the symbols, aj and y, denote the activity of species j (= M + , A − ) and its activity coefficient with I, respectively [14].Rearranging Equation ( 5), the following equation was obtained immediately: .There are some cases where the bars were smaller than the points, such as circle and square.Especially, all the bars were smaller than the size of the circles in Figure 5.
The regression analysis of the plot in Figure 5 based on this equation yielded the regression line with log(Kex 0 /mol −2 •dm 6 ) = 5.28 ± 0.25 and Bå = 44 ± 661 mol −1/2 •dm 3/2 Å at r = 0.024 and N (number of data) = 10, the fixed A value (= 0.5114) in pure water, and 298 K. Considering the error of the experimental Bå value, it is difficult to discuss the Bå or å value in this result.When the three parameters, logKex 0 , A, and Bå, had been used for the regression analysis, it gave the results of logKex 0 > 0, A < 0, and Bå < 0. Consequently, we gave up such an analysis.
On the other hand, the log(KAgB18C6,DCE/mol −1 •dm 3 ) values were calculated from the relation logKML,org = logKex± − logKD,M S ⋅KD,A S for a given IDCE.Here, we assumed that, considering the smaller IDCE values, the ratio, yMl,DCE/y+,DCE, of the activity coefficients in the thermodynamic complexformation constant, KML,DCE 0 , equals unity.Accordingly, the approximation that an average value among the KAgB18C6,DCE ones equals the KAgB18C6,DCE 0 value becomes valid.Consequently, as its logarithmic value, 7.77 ± 0.25 was obtained on average (N = 12) at 298 K.

A Trend between LogKD,Pic and Log(IDCE/I)
From a plot of logKD,Pic versus log(IDCE/I), we obtained a theoretical line of logKD,Pic = log(IDCE/I) − (0.09 ± 0.12) at r = 0.398 (Figure 9) under the condition of the fixed slope of unity, except for the points in the I range of 0.024-0.26mol•dm −3 .This trend suggests that the KD,Pic values are basically proportional to the ratios of (IDCE/I), as reported before [16].The deviation of the five points in Figure 9 can come from an effect of the higher I values in (IDCE/I).An answer to this deviation is explained as follows.For the case of only MA (or mixture of MX with small excess organic acid, HA) in w phase with L, we can propose the following equation for I and Iorg.On the other hand, for the present case of mixture of MX with the small excess HA and excess HX (strong acid) in the w phase with L, the corresponding equations are the extraction systems without the presence of excess HNO3 in the w phase (see Tables 1 and 2).The Δφeq,Pic values show the Δφeq ones obtained from the experimental logKD,Pic values.The predictable intercept value was calculated to be 1.30 (= logKD,Ag S + logKAgB18C6,DCE = −6.47+ 7.77) ± 0.25, being in accord with the experimental value.Similarly, the slope value was in good agreement with its theoretical one (= 17).These facts indicate that the Δφeq,Pic values essentially correspond to the Δφeq ones in logKD,Ag {see Equation (10a)}.In other words, the relation of logKAg/AgB18C6 = (slope) × Δφeq,Pic + logKD,Ag S •KAgB18C6,DCE is satisfied.A plot of logKex± versus Δφeq for the A − = Pic − , ClO4 − , and NO3 − systems also gave a regression line with a slope of 19.3 ± 2.0 V −1 and an intercept of −1.23 ± 0.18 at r = 0.974 and N = 7 in the narrow I range (see Table 1 for their basic data).This slope was very close to the theoretical value (= 17).As similar to the previous results [11], these results indicate that the plot satisfies the relation of logKex± = 16.90Δφeq+ logKD,A + logKD,Ag S •KAgB18C6,DCE (= 16.90Δφeq + logKD,A + 1.30).The (logKD,A + 1.3) term corresponds to the intercept [11] within ±0.3 at least.The regression analysis of the plot in Figure 5 based on this equation yielded the regression line with log(K ex 0 /mol −2 •dm 6 ) = 5.28 ± 0.25 and Bå = 44 ± 661 mol −1/2 •dm 3/2 Å at r = 0.024 and N (number of data) = 10, the fixed A value (= 0.5114) in pure water, and 298 K. Considering the error of the experimental Bå value, it is difficult to discuss the Bå or å value in this result.When the three parameters, logK ex 0 , A, and Bå, had been used for the regression analysis, it gave the results of logK ex 0 > 0, A < 0, and Bå < 0. Consequently, we gave up such an analysis.

Evaluation of LogKex± Based on LogKD,A S
Similarly, the extraction constant (K ex± 0 ) at I → 0 is expressed as where the subscript "ML" means the complex ion ML + .Rearranging this equation, we can immediately obtain log where Unfortunately, the analysis of the plot based on Equation (6a) did not yield the suitable result which satisfies the condition of Bå > 0.
On the other hand, using the Davies equation without Bå instead of the extended DH equation [14], logK ex± 0 = 0.60 ± 0.11 and A = 2.05 ± 0.38 mol −1/2 •dm 3/2 were obtained (Figure 6).The Davies [14], where z shows a formal charge of ionic species with a sign (refer to the Introduction).
The analysis of the logK ex -versus-I plot by the Davies equation yielded logK ex 0 = 5.29 ± 0.11 with A = 0.08 ± 0.40 mol −1/2 •dm 3/2 .Within the calculation error of ±0.3, this logK ex 0 value was in accord with 5.3 determined by the DH equation (see above in this section).

I DCE Dependence of LogK ex±
Applying the DH limiting law [14] for the system and rearranging Equation ( 6) at org = DCE, we can easily obtain log Hence, a plot of logK ex± versus I DCE yields logK ex± 0 and A DCE values immediately.Here, K ex± 0 is defined as a ML,DCE a A,DCE /([M + ][L] DCE [A − ]) (=y + y − K ex± 0 ). Figure 7 shows its plot for the AgPic-18C6 extraction systems with DCE.Also the average values of I DCE were used for the plot (see Section 3.1) and the y + y − value in K ex± 0 was estimated on average (N = 10) to be 0.76 ± 0.14.This product was calculated from the ion size parameters, a(Ag + ) = 2.5 and a(Pic − ) = 7 Å, in water [15].A plot analysis gave logK ex± 0 = −0.45± 0.24 and A DCE = 116 ± 46 mol −1/2 •dm 3/2 at r = 0.665.Accordingly, introducing y + y − in logK ex± 0 = logy + y − + logK ex± 0 , the logK ex± 0 value became -0.36 ± 0.24.The experimental A DCE value was much larger than its theoretical one (= 10.6 mol −1/2 •dm 3/2 ) for a pure DCE at 298 K.This difference between these A DCE values may be due to simple errors caused by the narrow experimental I DCE -range of (0.097-2.2) × 10 −5 mol•dm −3 or to the condition where the diluent DCE was saturated with water.

I DCE Dependences of LogK 1,DCE
The thermodynamic ion-pair formation constant (K 1,org 0 ) at I org → 0 is described as logK 1,org 0 = log([MLA] org /a ML,org a A,org ) = logK 1,org − log(y ML,org y −,org ) Rearranging this equation at org = DCE and ML + = AgB18C6 + can give the following equation: A plot of logK 1,DCE versus I DCE is shown in Figure 8.The plot analysis yielded the regression line with logK 1,DCE 0 = 5.89 ± 0.19 and A DCE = 152 ± 37 mol −1/2 •dm 3/2 at r = 0.821 and N = 10.This A DCE value overlaps with the value (= 116) determined above (see Section 3.2), within the calculation error (= 46) and much larger than the theoretical one too.The authors cannot clearly explain the larger experimental A DCE values, as similar to Section 3.2.
On the other hand, the log(K AgB18C6,DCE /mol −1 •dm 3 ) values were calculated from the relation logK ML,org = logK ex± − logK D,M S •K D,A S for a given I DCE .Here, we assumed that, considering the smaller I DCE values, the ratio, y Ml,DCE /y +,DCE , of the activity coefficients in the thermodynamic complex-formation constant, K ML,DCE 0 , equals unity.Accordingly, the approximation that an average value among the K AgB18C6,DCE ones equals the K AgB18C6,DCE 0 value becomes valid.Consequently, as its logarithmic value, 7.77 ± 0.25 was obtained on average (N = 12) at 298 K.

A Trend between LogK D,Pic and Log(I DCE /I)
From a plot of logK D,Pic versus log(I DCE /I), we obtained a theoretical line of logK D,Pic = log(I DCE /I) − (0.09 ± 0.12) at r = 0.398 (Figure 9) under the condition of the fixed slope of unity, except for the points in the I range of 0.024-0.26mol•dm −3 .This trend suggests that the K D,Pic values are basically proportional to the ratios of (I DCE /I), as reported before [16].The deviation of the five points in Figure 9 can come from an effect of the higher I values in (I DCE /I).An answer to this deviation is explained as follows.
For the case of only MA (or mixture of MX with small excess organic acid, HA) in w phase with L, we can propose the following equation for I and I org .
with the charge balance equation of [M + ] + [ML + ] = [A − ].Similarly, the authors can obtain On the other hand, for the present case of mixture of MX with the small excess HA and excess HX (strong acid) in the w phase with L, the corresponding equations are and with the assumptions that , respectively.Therefore, Equations ( 9) and (9a) give the experimental relation of (  3).

∆φ eq Dependences of LogK M/ML and LogK ex±
The logK M/ML , defined as log([ML + ] org /[M + ][L] org ) [8], can be resolved as follows and calculated from logK ex± − logK D,A .logK M/ML = logK D,M + logK ML,org = 16.90∆φeq + logK D,M S •K ML,org (10) at 298 K with logK D,M = (F/2.303RT)∆φeq + logK D,M S (10a) Here, the term of log(K D,M S •K ML,org ) has to be a constant, because these two equilibrium constants are independent of ∆φ eq ; logK ML,org = −(F/2.303RT)(standard formal potential of the ML + formation in the org phase) [8].The magnitude of the K M/ML (or K M/ML S ) value shows an incorporation-ability into the org phase of L against M + .Then, the plot of logK M/ML versus ∆φ eq based on Equation ( 10) can yield a straight line with the slope of 17 V −1 and the intercept of logK D,M S •K ML,org .Figure 10 shows its plot, of which the experimental regression line was logK M/ML = (16.8± 6.1)∆φ eq,Pic + (1.30 ± 0.50) at r = 0.775 and = 7.Here, the three data (the squares in Figure 10) were neglected from the calculation of the line, because their I values were much larger than the values of the extraction systems without the presence of excess HNO 3 in the w phase (see Tables 1 and 2).The ∆φ eq,Pic values show the ∆φ eq ones obtained from the experimental logK D,Pic values.The predictable intercept value was calculated to be 1.30 (= logK D,Ag S + logK AgB18C6,DCE = −6.47+ 7.77) ± 0.25, being in accord with the experimental value.Similarly, the slope value was in good agreement with its theoretical one (= 17).These facts indicate that the ∆φ eq,Pic values essentially correspond to the ∆φ eq ones in logK D,Ag {see Equation (10a)}.In other words, the relation of logK Ag/AgB18C6 = (slope) × ∆φ eq,Pic + logK D,Ag S •K AgB18C6,DCE is satisfied.A plot of logK ex± versus ∆φ eq for the A − = Pic − , ClO 4 − , and NO 3 − systems also gave a regression line with a slope of 19.3 ± 2.0 V −1 and an intercept of −1.23 ± 0.18 at r = 0.974 and N = 7 in the narrow I range (see Table 1 for their basic data).This slope was very close to the theoretical value (= 17).As similar to the previous results [11], these results indicate that the plot satisfies the relation of logK ex± = 16.90∆φeq + logK D,A + logK D,Ag S •K AgB18C6,DCE (= 16.90∆φ eq + logK D,A + 1.30).The (logK D,A + 1.3) term corresponds to the intercept [11] within ±0.3 at least.
by using Equations (10a) and ( 4).It is difficult to accurately determine the K D,M S {or K D,M (∆φ eq ): the function of ∆φ eq , see Equation (10a)} and K ML,org values.On the other hand, it is comparatively easy to determine the K M/ML S value.So, if the logK M/ML S {or logK M/ML (∆φ eq )} value is determined for given ML + and diluent, then the logK ex± values can be calculated from Equation (11) with the logK D,A S {or logK D,A (∆φ eq )} ones.In this study, we determined the logK Ag/AgL S value to be 1.30 from the data (see Table 1) of the AgPic-B18C6 extraction systems with DCE.Calculated logK ex± values for some A − are listed in Table 3, together with several experimental values.The determination of the K ex± values will be experimentally difficult for the Cl − to I − extraction systems, because of the precipitation [18] of their silver salts.The same is true of the SCN − extraction system, because of its low solubility product (= 1.0 × 10 −12 mol 2 •dm −6 [18]) against Ag + in water.Also, AgN 3 , which is a white insoluble crystal, is explosive [19].Therefore, the experimental K ex± values were determined at 298 K for the ClO 4 − and NO 3 − extraction systems (see Table 1).Considering the differences (0.03-0.26) between the logK D,A S values at a fixed A − in Table 3 and the standard deviation in the pH ranges of 1.64 and 1.65 at [HNO 3 ] t = 0.025 mol•dm −3 , 1.34-1.38 at 0.050, 1.06 at 0.10, and 0.62-0.68 at 0.25.Used apparatus, such as the atomic absorption spectrophotometer, UV-V, centrifuge, mechanical shaker, and pH meter with the glass electrode, were the same as those [8,16] described previously.

Conclusions
The versus ∆φ eq,Pic , it was indirectly proved that the ∆φ eq values obtained from the K D,Pic ones is common to those from the K D,Ag values.Moreover, the logK ex± values were predicted from the sum of the logK D,A S and logK Ag/AgB18C6 S ones for given MB18C6 + and DCE at least.At the same time, the order in K ex± reflected that in K D,A S .

3 Figure 5 .
Figure 5.A plot of logKex vs.I for the AgPic extraction with B18C6 into DCE.See the text for the regression line (broken line).Error bars were added for only the present experimental values in Figures 5-10.There are some cases where the bars were smaller than the points, such as circle and square.Especially, all the bars were smaller than the size of the circles in Figure 5.

Figure 5 .
Figure 5.A plot of logK ex vs.I for the AgPic extraction with B18C6 into DCE.See the text for the regression line (broken line).Error bars were added for only the present experimental values in Figures 5-10.There are some cases where the bars were smaller than the points, such as circle and square.Especially, all the bars were smaller than the size of the circles in Figure 5.

Figure 7 .
Figure 7.A plot of logK ex± vs.I DCE for the AgPic extraction with B18C6 into DCE.See the text for the regression line (broken line).

Figure 9 .
Figure 9.A plot of logK D,Pic vs. log(I DCE /I ) for the AgPic extraction with B18C6 into DCE.The broken line shows a theoretical one for the slope fixed at unity: see the text.The plots (square) were of the extraction with the excess addition of HNO 3 in the w phases.

Figure 10 .
Figure 10.A plot of logKAg/AgL vs. Δφeq for the AgPic extraction with B18C6 (= L) into DCE.See the text for the regression line (broken line).

Figure 10 .
Figure 10.A plot of logK Ag/AgL vs. ∆φ eq for the AgPic extraction with B18C6 (= L) into DCE.See the text for the regression line (broken line).
and then its ratio becomes smaller than the K D,Pic value in the case of [NO 3 − ] >> [Pic − ].When [NO 3 − ] nearly equals [Pic − ] in Equation (9b), the log(I DCE /I) value deviates from the logK D,Pic one by +0.3: that is, (I DCE /I) ≈ K D,Pic /2.However, such a deviation is comparable to experimental errors.Thus, Equation (9b) explains well the deviation of the five points from the regression line in Figure 9. Obviously, the deviation becomes larger, when an excess of HX, such as HNO 3 , was added in the w phase and X − less distribute into the org phase than A − does (for example, see the K D,Pic S & K D,NO3 S values in Table

3. 6 .
Evaluation of LogK ex± Based on LogK D,A S Using the logK M/ML S and logK D,A S values, we can immediately evaluate the logK ex± value as follows.A thermodynamic cycle gives logK ex± = logK M/ML S + logK D,A S = logK M/ML + logK D,A I or I DCE dependences of the logK ex± and logK ex values for the present extraction systems were clarified experimentally.Their experimental equations were logK ex = 5.3 -2×0.51 √ I/(1 + 44 √ I) and logK ex± = 0.6 − 2×2.0 √ I/ 1 + √ I − 0.3I = −0.5 + 2×116 √ I DCE .However, the magnitudes of these changes in logK ex± or logK ex with I or I DCE were insignificant in practical separation.It was also suggested that the style of M(I) employed in the extraction experiments with L, either the simple salt MPic or the mixture of MX with HPic and excess HX, largely control whether the logK D,Pic values are dependent on the log(I DCE /I ) ones or not.The logK ex± -versus-∆φ eq plot for the Pic − , ClO 4 − , and NO 3 − systems yielded the good positive correlation.On the basis of the plot of logK Ag/AgB18C6

Table 2 .
Fundamental data for the extraction with AgPic and B18C6 (= L) into DCE in the presence of excess HNO 3 in the water phases at 298 K.

Table 3 .
Log K ex± values evaluated from the logK D,A [17].[17];4Not determinable, probably because of precipitation etc. See the text;5Not determined here;6The K Ag/AgL S value was determined, based on the data of the extraction experiments. Se Table 1; 7 Not evaluated; 8 Average value in the I range of (2.5-3.6)× 10 −3 mol•dm −3 .See Table 1; 9 Value at I DCE → 0. See the text.