On the Interfacial Potential Differences for the Extraction of Alkaline-Earth Metal Picrates by 18-Crown-6 Ether Derivatives into Nitrobenzene

Copyright: © 2014 Yoshihiro K, et al. This is an open-access 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.


Introduction
Recently one of the authors has reported an expression by an interfacial potential difference (∆φ eq ) of an extraction constant on silver picrate extraction with crown ethers (L) into 1,2-dichloroethane (DCE) or dichloromethane (DCM) [1]. In this study, its extraction constant has been defined as [ , where the subscript "o" and Pic − denote an organic (o) phase, such as DCE and DCM, and picrate ion, respectively. An introduction of ∆φ eq in extraction experiments also gave an answer for a problem of the deviation between the electrochemically-determined K D,A values and extraction-experimentally-determined values [1,2]. Here, the symbol K D,A refers to an individual distribution constant (= [A − ] o /[A − ]) of A − into the o phase. Similar problems have been observed in the extraction of divalent metal salts, such as CdPic 2 , PbPic 2 and CaPic 2 , by L into various diluents [3][4][5].
In the present paper, we determined at 298 K the K D,Pic values for the extraction of alkaline-earth metal picrates (MPic 2 : M = Ca, Sr, Ba) by 18-crown-6 ether (18C6) or benzo-18C6 (B18C6) into nitrobenzene (NB) which shows the higher polarity. Then, the ∆φ eq values were evaluated from differences between the K D,Pic values electrochemicallydetermined and those determined by the present extractionexperiments. Here, the electrochemically-determined constant was expressed as K D,Pic S , showing the equilibrium constant standardized at ∆φ eq = 0 V [1,6,7]. Moreover, the functional expressions of K ex± , K ex2± and K ex by ∆φ eq were examined; the symbols, K ex± , K ex2± and K ex , refer to [ 2 ), respectively [3,4,8]. On the basis of the above values determined, the M II Pic 2 extraction system with L into NB was characterized.

Theory Derivation of a potential difference at the water/o interface
Using properties of electrochemical potentials j µ [9,10], we had reported relations between ∆φ eq and the constants expressing overall extraction equilibria, such as M + + L o + A − MLA o and M + + L o + A − ML + o + A − o [1]. The same handling [1,11] was applied for the present extraction equilibria. For example, the authors will apply it to the process: Rearranging this equation for the K ex± definition, then we obtained

Abstract
Individual distribution constants (K D,A ) of picrate ion (Pic − ) into nitrobenzene (NB) were determined at 298 K and given values of ionic strength, together with the determination of an extraction constant (K ex ) for the extraction of alkaline-earth metal picrates, MPic 2 , by 18-crown-6 ether (18C6) and benzo-18C6 (B18C6). Here, K D,A and K ex were defined as 2 , respectively: A − shows Pic − , L does either 18C6 or B18C6 and the subscript "NB" refers to the NB phase. Interfacial potential differences (∆φ eq in a V unit) at extraction equilibria were evaluated from differences between the experimental log K D,Pic and its standardized values (log KD , Pic S ) which have been determined by electrochemical measurements at a water/NB interface. By a combination with the K ex values, other extraction constants, 2 , were also determined. Electrochemicallystandardized log K ex± values, log K ex± S ones, were calculated from the relation of log K ex± = (∆φ eq /0.05916) + log K ex± S at 298 K. Using the log K ex± S values, their correlation with the log K ex± ones was discussed. Additionally, ion-pair formation constants (K 1,NB & K 2,NB ) for the stepwise reactions of ML 2+ with Pic − in the NB phase were evaluated from K ex , K ex± and another constant (K ex2± ) reported before at ∆φ eq = 0. Here, K 2,NB was evaluated from K ex /K ex± and K 1,NB is defined as [MLPic + ] NB /[ML 2+ ] NB [Pic − ] NB , which was evaluated from the relation of K 1,NB = K ex± /K ex2± . Moreover, reproductions of the electrochemically-standardized K ex± and K ex2± values were tried, using the ∆φ eq values and relations between K ex± or K ex2± and component equilibrium constants constituting their extraction ones. Consequently, a functional expression of K ex± with ∆φ eq was extended into the MPic 2 -L extraction systems, in addition to the AgPic-L extraction ones reported previously. Therefore, the following equations were derived:

Journal of Thermodynamics & Catalysis
Here,φ j,α and a j,α denote an inner potential for species j in the phase α (= o) and an activity of j in the α phase, respectively; the symbols without α mean those to the water (w) phase, although there is an exception to this rule. From Equation (3), the interfacial potential difference ∆φ eq at an equilibrium was defined [1,11]; in principle, ∆φ eq has been defined as φ(w phase) − φ(o phase). Then, rearranging Equation (3) 2 ). Here, y j,α refers to an activity coefficient of the ionic species j {= MLA(I), A(−I), M(II)} in the α phase; the symbol y without α shows the coefficient for the w phase; ∆φ k 0′ means a standard formal potential. Similarly, equilibrium constants of other processes were expressed as functions of potential differences. These results are listed in Table 1. The condition of ∆φ eq = 0 V was applied for some processes from their properties: namely, ∆φ eq essentially becomes zero, when all species relevant to the inner potentials are present in a single phase [1,9].
Using thermodynamic cycles and the various equilibrium constants in Table 1, we can express the overall extraction processes [1]. Thereby, it becomes possible that we express the overall extraction constants as functions of some formal potentials with ∆φ eq . As an example, K ex2± (see Introduction for its definition) is expressed as K D,M (K D,A ) 2 K ML,org . Taking logarithms of both sides in this equation and rearranging it based on the corresponding relations in Table 1, we easily obtain ∆φ ex2± 0′ = ∆φ M 0′ − ∆φ A 0′ + ∆φ ML,org 0′ + ∆φ eq (4) from ∆φ eq − ∆φ ex2± 0′ = (∆φ eq − ∆φ M 0′ ) − (∆φ eq − ∆φ A 0′ ) − ∆φ ML,org 0′ . The same was true of K ex and K ex± , where the condition of ∆φ eq = 0 V was satisfied for K ex , since all species relevant to the inner potentials were present in the single phase [1,9]. Table 2 summarizes these results. According to the previous paper [1], when the log K D,A values are determined experimentally and the ∆φ A 0′ ones are available, we immediately can calculate the ∆φ eq values from the relation in Table 1.

For an analytical handling of extraction processes
The extraction-constant parameter, K ex mix , has been employed for the determination of K D,A and K ex [3][4][5] In this study, the regression analyses with Equation (5a) were performed at a fixed condition of the K ex value which was determined in terms of the analysis of Equation (5) and accordingly the thus-obtained K ex± value was checked by calculating it from each experimental point ( Table 3).

Evaluation of stepwise ion-pair formation constants for MLA 2 in the o phase
Stepwise ion-pair formation constants for MLA 2 in the watersaturated o phase for given I org,av values were evaluated from the following relations. (7) Here, the symbol, I org,av , was defined as (ΣI org )/N with a number (N ) of run and ionic strength (I org ) for the o phase. Table 3 lists the five equilibrium constants determined with the above procedures. The K ex2± S values which were available from references [8] were actually used as K ex2± in the K 1,NB -calculation with Equation (6). Strictly speaking, there Hence, 1/f = 0.05916 V at 298 K. b ∆φ ML,w 0 ′ shows a standard formal potential for the ML 2+ formation in the w phase. c β ip,org = K 1,org K 2,org . Accordingly, the relation of 2∆φ ip,org 0 ′ = ∆φ 1,org 0 ′ + ∆φ 2,org 0 ′ holds Table 1: Relations between the potential differences, ∆φ eq , ∆φ k 0 ′ or ∆φ j 0 ′, and log K k values in an extraction system.   (6) and (7). See Appendix for this details.

Extraction procedures
Alkaline-earth metal nitrates M(NO 3 ) 2 , HPic and L were mixed with 0.002 mol dm −3 HNO 3 in a stoppered glass-tube of about 30cm 3 and then the same volume of NB was added in its solution. Their total concentrations were [Ca( The thus-prepared glass tube was shaken for 1 minute by hand and was agitated at 298 ± 0.2 K for 2 h in a water bath (Iwaki, type WTE-24) equipped with a driver unit (Iwaki, SHK driver) and a thermoregulator (Iwaki, type CTR-100). After this operation, its mixture was centrifuged with a Kokusan centrifuge (type 7163-4.8.20) for 7 minutes.
A portion of the separated NB phase was transferred into another stoppered glass-tube and then 0.1 mol dm 3 HNO 3 was added in this tube. By shaking the tube, all M(II) species in the NB phase were backextracted into the HNO 3 solution. If necessary, the operation for this back extraction was repeated. An amount of all the M(II) species in the aqueous HNO 3 solution was determined by a Hitachi polarized Zeeman atomic absorption spectrophotometer (type Z-6100) with a hollow cathode lamp of Ca (type 10-020, Mito-rika Co. under the license of Hitachi, Ltd.; measured wavelength: 422.7 nm) or Sr (type 10-038, Mito-rika Co.; 460.7 nm). A calibration-curve method was employed for the determination of the M(II) concentration by AAS. For the Ba(II) determination, a >0.1 mol dm −3 NaOH solution was added in the back-extracted solution with Pic − and then its Ba(II) solution was measured at 355 nm based on the Pic − absorption and 298 K by a spectrophotometer (Hitachi, type U-2001). The Ba(II) concentration was determined with a calibration curve which had been prepared at 355 nm. On the other hand, the pH value in the separated w phase was measured at 298 K with the same electrode and pH/ion meter [1,4,5].

Determination of K ex mix
We used here the same extraction model as that [5] [11], where the symbol HX shows a strong acid, such as HNO 3 and HCl, in water. In particular, the two reactions, 7) and 8), indirectly yielded the process 5). Also, the parentheses with the asterisks show that their equilibrium constants at 298 K have been already determined by several methods (see below for some values).
The equilibrium constants for the reactions 1) and 9) were estimated taking account of the ionic strength, I, for the w phases in a successive approximation [3,5]. Here, the formation constants (K MA ) for MA + = MPic + (M = Sr, Ba) in the w phase were determined by the same method as that [4] reported before: as the log K MPic values at 298 K and I → 0 mol dm −3 , 2.1 8 for M = Sr and 2.0 8 for Ba were obtained. While the K CaPic value was estimated with the value available from reference [12].
The procedure for the calculation of K ex mix values by the successive approximation was essentially the same as that [3] [3][4][5]. Except for the SrPic 2 -18C6 system, the compositions of M(II):L:Pic(−I) were assumed to be 1:1:2 in the determination of K D,Pic , K ex and K ex± [3][4][5]. The slope's values less than unity indicate dissociations of MLPic 2 in the NB phases [4]. Figures 1 and 2 show the plots for the BaPic 2 -18C6 extraction system based on Equations (5) and (5a), respectively, yielding the K D,Pic , K ex and K ex± values ( Table 3). The less correlation coefficient (R) of the plot in Figure 2 may reflect the defect in the sub-analytical extraction model   [4,5], that is, the absence of the ion-pair formation for MLPic 2 in the w phase. Also, the other extraction systems yielded similar plots, from which we got similarly these three kinds of values (Tables 3).
In the determination of K D,Pic , K ex and K ex± for the BaPic 2 -L extraction system, it was assumed that a total amount, [Ba(II)] NB

Results and Discussion
Tendencies of K D,Pic , K ex , K ex± and K n,NB at n = 1, 2 As can be seen from Table 3, the log K D,Pic values are different from each other in spite of the same definition. These are in the orders of Ca < Sr < Ba for a given L. Also, the orders are B18C6 < 18C6 for a given M(II). Thus, these K D,Pic orders are influenced by sizes [14,15] of M 2+ and L, not cavity sizes of L; molar volumes of L were reported to be 214 cm 3 mol −1 for L = 18C6 and 252 for B18C6 [15].
The values of both log K ex and log K ex± were in the orders of Ca < Sr < Ba (Table 3). These tendencies are similar to those for log K D,M S and log K ML,NB (see below for these values). Such facts suggest the presence of these equilibrium constants in the thermodynamic cycles (Table  2). Also, two procedures for evaluating the log K ex± values in Table  3 well agreed within calculation errors. These facts support that the regression analyses based on Equation (5a) are essentially valid under the conditions of constant K ex values.
Orders of the log K 1,NB values were Ca > Sr > Ba for the both L, when we neglected differences in I NB among the extraction systems (see Table 3 for I NB ). On the other hand, the log K 2,NB values were Ca < Sr > Ba. These differences suggest that sizes of M(II) are more-effectively reflected to stability of the 1st-step ion-pair formation than to that of the 2nd-step formation. In other words, these results seem to be due to differences in a size and/or charges, such as the formal and net charges, between ML 2+ and MLPic + as reaction species in NB saturated with water. Also, such effects may be reduced in the more-bulky SrPic 2 -and BaPic 2 -B18C6 systems.
As another explanation for the K 2,NB orders, it can be considered that the I NB values of the Ca(II) system are largest of all the systems. The I NB orders were of M = Ca > Sr < Ba for L = 18C6 and Ca > Sr ≥ Ba for B18C6 (  [16]. From Table 3, the larger the h values [17] [17,18]) < 1 and p > 0, the equation becomes log K 1,NB = log K 1,NB ′ + 0.750p. Therefore, the log K 1,NB values basically increase with an increase in p and consequently can increase with that in h ( Table 3). The above results suggest the existence of the reaction (9) with H 2 O molecules in NB phase, as reported before on the process of M + + L NB + A − ML + NB + A − NB [8].

Calculation of the ∆φ eq values from the experimental log K D,Pic values
Using the relation of log K D,A = −(∆φ eq − ∆φ A 0 )/0.05916 at 298 K (Table 1) Table  4. The ∆φ eq range for the 18C6 system was a little smaller than that for B18C6 one. From a comparison with the log K ex± values in Table 3, the smaller the ∆φ eq values are, the larger the log K ex± ones become. This trend is similar to that reported previously for the extraction of AgPic by B18C6 and benzo-15-crown-5 ether B15C5 into DCE or DCM [1].
As can be seen from Table 4, the log K ex± S values calculated from the relation in Table 1 are equal or close to those calculated from that in Table 2. Especially, a little larger deviations for the BaPic 2 -L systems may be due to the approximation of [Ba(II)] NB,t ≈ [Pic − ] NB,t (see Materials and Methods). On the other hand, the log K ex2± S values calculated from the relation in Table 2 are very small, compared to those [8] reported before, although the order in magnitude of the calculated values is the same as that of the reported ones [8]. A correlation between these two orders was expressed by the following equation While the overall process, M 2+ + L NB + 2Pic − MLPic + NB + Pic − NB , has been included in the model [3][4][5] {see Equation (5a)}. However, it is unclear whether the two above facts, (i) and (ii), cause the negative errors of log K ex2 S or not. Figure 3 shows a plot of log K ex± versus log K ex± S (found) for all the MPic 2 -L systems. Here, the former logarithmic values are listed in Table  3, while the latter values in Table 4. The plot gave a good correlation between both the values: log K ex± = (0.81 ± 0.03)log K ex± S (found) + (2.0 7 ± 0.1 3 ) at R = 0.998. This fact indicates that the experimental log K ex± values clearly reflect the log K ex± S ones at ∆φ eq = 0. The result is the same as that [1] reported before for the AgPic extraction by B15C5 and B18C6 into DCE or DCM. On the other hand, in this study, we were not able to obtain the log K ex2± values which are comparable to the above log K ex± ones.

Conclusion
Expressions of the extraction constants by ∆φ eq were extended into K ex± , K ex2± and K ex of the M II Pic 2 extraction systems with L, in addition to K ex± and K ex of the AgPic-L systems [1]. These expressions were summarized in Tables 1 and 2. However, the matters for precision of the values in the analyses have been present for the determination of K ex2± S . Also, there may be self-inconsistency for the estimation of the K n,NB values. It was demonstrated that the log K ex± values well reflect the log K ex± S ones. So, one can see markedly the relation between K ex± obtained from an extraction experiment and K ex± S from an electrochemical one. This result fundamentally enables us to discuss the extraction-ability and -selectivity of L against M 2+ from both the values. Moreover, it was shown that the expressions of K ex± , K D,ML and K D,Pic by ∆φ eq do not conflict with data obtained from the electrochemical measurements.
In practice, we have calculated the values of log K ex± − log K ex2± S = f(∆φ eq − ∆φ ex± 0 ′) − log K ex2± S (A1) from Equation (6) and the relation in Table 1. Rearranging this equation, the following equation can be easily obtained log K ex± − log K ex2± S = log K ex± S − log K ex2± S + f∆φ eq . (A2) Also, Equation (7) gave log K ex − log K ex± = log K ex S − log K ex± = log K ex S − f(∆φ eq − ∆φ ex± 0 ′) = log K ex S − log K ex± S − f∆φ eq (A3) Log K 1,NB and log K 2,NB in Table 3 are equal to Equations (A2) and (A3), respectively. As examples, the log K 1,NB and log K 2,NB values for the SrPic 2 -B18C6 system were calculated from these equations to be 4.7 3 and 5.0 7 , respectively. These values were in good accord with those listed in Table 3.
Why do Equations (A2) and (A3), the functions expressing log K 1,NB and log K 2,NB , contain ∆φ eq ? This question comes from the fact that log K n,NB (n = 1, 2) in Table 1 were derived from the condition of ∆φ eq = 0 V. Also, the above results are self-consistent to the fact that all the log K n,NB values in Table 3 are conditional equilibrium-constants, such as K n,NB fixed in an I NB value. Unfortunately, the authors cannot now explain these inconsistencies.