An Electrochemical Understanding of Extraction of Silver Picrate by Benzo-3m-Crown-m Ethers (m = 5, 6) into 1,2-Dichloroethane and Dichloromethane

Two extraction constants (Kex± and Kex) for extraction of silver picrate (Ag+Pic) by benzo-15crown-5 ether (B15C5) and benzo-18-crown-6 one (B18C6) into 1,2-dichloroethane (DCE) and dichloromethane (DCM) were determined at 298 K and given values of ionic strength. Here, Kex± and Kex were expressed as [AgL+]o[Pic]o/[Ag+][L]o[Pic] and [AgLPic]o/[Ag+][L]o[Pic], respectively: L symbolizes B15C5 or B18C6 and the subscript “o” denotes the organic phase composed of DCE or DCM. Individual distribution constants (KD,Pic) of picrate ion, Pic, into the two diluents were also determined with the determination of Kex. From comparison of these KD,Pic values with those standardized, interfacial potential differences (∆φeq) at extraction equilibria were evaluated. Then, using these ∆φeq values, relations of the experimentally-determined logKex± or logKex values with their electrochemically-standardized ones were precisely discussed. Consequently, it was indicated that logKex± should be expressed as a function of ∆φeq.


Introduction
Recently, individual distribution constants (K D,A ) of single anions (A − ), such as picrate ion (Pic − ) and 4 MnO − , into various diluents or organic (o) phases have been determined in course of determination of extraction constants (K ex ) for the extraction of some salts, M I A and M II A 2 , by crown compounds (L) [1]- [4].Here, K D,A and K ex have been defined as [A − ] o /[A − ] and [MLA z ] o /[M z+ ][L] o [A − ] z with z = 1 or 2, respectively.For example, the logK D,Pic values were reported to be −2.9 1 for a benzene (Bz) system, −1.89 for 1,2-dichloroethane (DCE), and −0.94 for nitrobenzene (NB) by PbPic 2 extraction experiments with 18-crown-6 ether (18C6) [3].Also, the values were −6.1 2 for Bz and −4.3 5 for DCE from CdPic 2 extraction experiments with 18C6 [2].The logK D,A values were −0.65 for A − = Pic − and −2.137 for 4 MnO − in the CsA extraction by dibenzo-24-crown-8 ether derivatives into DCE [4].Such differences in logK D,Pic between these extraction experiments may be due to those between experimental conditions, such as kinds of the metal ion, M z+ , and L employed, the values of ionic strength (I) of the aqueous solutions and their pH values.Furthermore, the experimental logK D,Pic values have been different from the values [5]- [8] standardized by electrochemical measurements at the water (w)/DCE and w/NB interfaces.These differences seemed to be beyond the range of experimental errors.The electrochemically standardized values, which should be compared to the above logK D,Pic ones, were S D,Pic log K = −1.01 1 [6] for the distribution into DCE and +0.05 for that into NB [6].Similar results have been observed in NaMnO 4 extraction experiments with Benzo-15-crown-5 ether (B15C5) and benzo-18C6 (B18C6) into DCE and NB [1]; as examples, the 4 D,MnO log K values were −3.3 for the extraction system with B15C5 and −2.5 for that with B18C6 into DCE [1], while 4 S D,MnO log K was −3.3 3 [6].Why are the above logK D,A values much different from the S D,A log K ones?Are the logK ex values also different from their standardized ones?Does an extraction constant (K ex± ) for the extraction of ML z+ with A − differ from its standardized value?Here, K ex± has been expressed as In the present paper, we determined the K D,Pic and K ex values by the silver picrate (AgPic) extraction-experiments with B15C5 and B18C6 into less-polar DCE and dichloromethane (DCM), in order to examine the deviations of the logK D,Pic values from the S D,Pic log K ones.In course of this examination, the differences were discussed by introducing interfacial potential differences (∆φ eq ) at extraction (and distribution) equilibria [9] in an extraction model.Also, it was considered how the extraction constants, K ex and K ex± , were expressed by these ∆φ eq values.Here, the K ex± values were calculated from the K ex values and other equilibrium constants determined in this study.

Expression of Overall Extraction Processes by Potential Differences
The following two overall extraction-processes [1] were considered in this study: and Here, species with and without the subscript "o" denote those in the organic and w phases, respectively.
(A) To the process (1), ideas of electrochemical potentials ( ) j µ can be applied as follows.
This equation was rearranged using the properties [10] of j µ .
( ) Here, a j,α , 0 , j α µ and ′φ j (or φ j ) denote the activity of species j {=M(I), A(−I), L, MLA}, the standard chemical potential of j in a phase α (=o) and the inner potential of j, respectively; ∆′φ eq and ∆ ) refer to the potential difference at an extraction equilibrium in the single phase or between the o and w phases and the potential difference for a process k, such as the overall extraction (k = ex, ex±) and an individual distribution {A(−I), M(I), ML(I)}, respectively.Then, we can obtain from Equation (4) the following equation with and The symbols, 0 ex φ ∆ and 0 ex K , in Equation ( 5) can be also expressed in a molar concentration unit, where the "ex" term in shows the process corresponding to its potential difference.
, where y M and y A refer to activity coefficients of M + and A − in water, respectively, and both y L,o and y MLA,o were assumed to be unity.In Equations ( 5) and (5a), ∆′φ eq must equal zero [10], because M + and A − are present in the same phase.Therefore, logK ex (see Introduction) is expressed as follows and then becomes independent of ∆′φ eq .
(B) Similarly, the process (2) was treated with j µ .Its results were and From Equation (10), we can easily see that this ∆φ eq value is an interfacial potential difference at an extraction equilibrium [9] and its form corresponds to a general definition, φ(w phase) − φ(o phase) [5] [8], for the iontransfer potential difference occurred at the w/o interface.So, it was assumed that the ∆φ eq value in Equation ( 9) does not become zero, except for an accidental case (see Table 2 for these examples).Thus, the logK ex± values determined by extraction experiments were expressed as ( ) This equation clearly shows that logK ex± is the function of ∆φ eq .

Evaluation of ∆φ eq
Such ∆φ eq values can be experimentally obtained as a result of the K D,A determination.In this study, we de- [1].Regression analysis of the [1] gives the K D,A value which is dependent on experimental conditions, such as initial concentrations of AgNO 3 , HPic, and L, the ionic strength estimated from their concentrations and pH in the w phases.
According to our previous papers [2] [9], the logK D,A value has been related to an interfacial potential difference, ∆φ, as Putting ∆φ = ∆φ eq into this equation, we can immediately obtain the ∆φ eq value from a difference between the S D,A log K value, the standardized one, and the experimental logK D,A value, that is, ( ) (at ∆φ eq = 0 V) and . This is due to the idea that the ∆φ eq value should be uniform on the interface of a given extraction system [9].The where a combination of

For Expression of Component Equilibrium Constants by ∆φ eq
As described in (A) and (B) of the Section 2.1, we can see that the ∆φ eq (or ∆′φ eq ) dependences of logK ex± and logK ex are different.So, the derivations of standard formal potentials corresponding to the extraction constants from thermodynamic cycles are tried.From the processes ( 1) and ( 2), the following cycles can be obtained as examples.
Here, K D,M and K ML,o are defined as the o phase, K ML,o called a complex formation constant for ML + in the o phase and K MLA,o called an ion-pair formation constant for ML + A − in it.
We will derive the standard formal potentials for the complex formation and then the ion-pair formation in the single phase from the properties [10] This equation can be rearranged in the same manner as that described in the Section 2.2.
( ) ( ) Similarly, the ∆′φ eq value equals zero [10], because all species are present in the same phase (see above).Therefore, logK ML,o becomes The same is true of the ion-pair formation for MLA in the o phase: Introducing Equations ( 8), ( 13), (17) and

Proofs of
and then rearrange it as Thus, the interfacial potential differences, ∆φ eq , were canceled out in the cycle (1a).The same is also true of the other cycle [13] of logK ex = logK ML K MLA K D,MLA /K D,L because of ∆′φ eq = 0 and accordingly we can obtain The definition of the component equilibrium constants were As a result ∆′φ eq = 0 in Equation (5a) was proved, because all species are either present in the same phase or neutral compounds [10].
For the cycle (2a), a similar treatment can be performed.
Rearranging this equation, we easily obtain Consequently, the interfacial potential difference, ∆φ eq , was not canceled out in the cycle (2a).That is, in this cycle, the experimental potential difference, , by ∆φ eq .This difference should be considered to be that in numeral between electrochemically-standardized extraction or distribution data and extraction-experimental data.This is not in conflict with the consideration described in our previous paper [9].

Chemicals
Concentrations of aqueous solutions of AgNO 3 (>99.8%,Kanto Chemical Co., Inc., Tokyo) were determined by a precipitation titration with NaCl (standard for the volumetric analysis, Wako Pure Chemical Industries, Tokyo); for example, 98.8% was obtained as a purity of AgNO 3 .Commercially-available B15C5 (>98%, Tokyo Chemical Industry Co. Ltd., Tokyo) and B18C6 (>96%, TCI Co. Ltd.) were dried at room temperature for more than 20 h under reduced pressures.Their purities were checked by measurements of the melting points: as examples, 79.0 -80.5˚C for B15C5 and 39.0 -40.0 for B18C6.The concentrations of their solutions were obtained from weighed amounts.Although the melting-point range of B15C5 was a little larger than unity, its purity was calculated as 100%.Concentrations of aqueous solutions of picric acid {HPic, guaranteed pure reagent (GR): > 99.5% after drying, Wako P.C.I.} were determined by 0.1 mol⋅L −1 NaOH solutions standardized by acid-base titrations with potassium hydrogen phthalate (GR: 99.8% -100.2%,Wako P.C.I.).Commercially-available DCE (GR: 99.5%, Kanto C.C.) and DCM (GR: 99.5%, Kanto C.C.) were washed three-times with water and kept at water saturated conditions.Other chemicals were of GR grades and used without further purifications.A tap water was distilled once with a still of the stainless steel and then was purified by passing through the Autopure system (type WT101 UV, Yamato/Millipore).This water was employed for preparing all the aqueous solutions.

Instruments
Mixtures of the w phase with the o phase in stoppered glass tubes were agitated at 298 K for 2 h with an Iwaki shaker system, a water bath (type WTB-24) equipped with a driver unit (SHK driver) and a thermoregulator (type CTR-100).Then, the mixtures were centrifuged by a Kokusan centrifuge (type 7163 -4.8.20).Total amounts of species with Ag(I) extracted into the o phase were also determined at 328.1 nm by a Hitachi polarized Zeeman atomic absorption spectrophotometer (type Z-6100) equipped with a hollow cathode lamp (type 139-3614, Mito-rika Co. under the license of Hitachi Ltd.) for Ag.The calibration-curve procedure was employed here for the determination of Ag(I) extracted.Besides, some pH values of the w phases centrifuged were measured at 298 K by using a Horiba pH/ion meter (type F-23) with a commercial glass electrode.
The organic solutions containing L were mixed with aqueous ones containing AgNO 3 and HPic in the stoppered glass-tubes of about 30 mL, these tubes were vigorously shaken up for 1 minute with hand, and then agitated at 298 ± 0.2 K for 2 h in the water bath (see the Section 3.2).After these operations, the mixtures were centrifuged for 5 minutes.The o phases were separated from the w phases and then the pH values of the latter were measured.The o phases were transferred in part into the glass tubes, aqueous solutions of 0.1 mol⋅L −1 HNO 3 were added in their tubes, and then their mixtures were mechanically agitated for 2 h in the bath.The w phases with HNO 3 were separated from the mixtures and then total amounts of Ag(I) in the separated w phases were determined by AAS (see the Section 3.2).The extraction of Ag(I) into the o phases was not detected in blank experiments without L in the both phases.

Data Analysis
Procedures were essentially the same as those reported previously [1] [14] except for an addition of the dissociation of MLA in the o phase: see Appendix.In computations of [Ag + ], [L] o and [Pic − ] by the successive approximation [1] [14], K AgLPic , K AgPic [14] and K HPic values [15] were evaluated as the functions of activity coefficients from the I values.2) × 10 −2 and I DCM = (2.1 -6.9) × 10 −7 for B15C5 and 3.3 × 10 −3 and I DCM = 1.9 × 10 −6 for B18C6.The symbols, I DCE and I DCM , denote ionic strength for the DCE phase and that for DCM, respectively.Also, the dissociation of HPic in the DCE or DCM phase was neglected.Namely, this means that a contribution of the distribution of H + to the ∆φ eq value is negligible.Besides, the formation of AgLNO 3 , HLNO 3 and HLPic and their distribution into the o phase were neglected.[1].An experimental plot analyzed by this equation is shown in Figure 1.Regression lines of the other systems were of a correlation coefficient (R) = 0.196 for the B15C5/DCM system, 0.969 for B18C6/DCM and 0.823 for B15C5/ DCE.From these regression analyses [1], curve fittings of the plots, we obtained the K D,A and K ex values.The logK ex± values were also calculated from the logarithmic form of Equation ( 14).The thus-obtained values were listed in Table 1.

Results and Discussion
The experimental logK D,Pic values in Table 1 were much smaller than those standardized on the extra-thermodynamic assumption of 4 4 Ph As BPh . These facts enable us to examine a presence of the ∆φ eq values.So, it was assumed from Equation (2a) that the potential difference, ∆φ eq , occurred at the w/o interface is the same for the distribution of Ag + , Pic − , and AgL + into the o phase [9], because these ions are simultaneously present in the extraction process.Here, the distribution of H + into the DCE or DCM phase was neglected (see the Section 3.4).Details for ∆φ eq are discussed in the next section.
Also, from the logK Ag/AgL values in Table 1, we can see that the values satisfy the relation of B15C5 ≤ B18C6, because the K D,Ag values are constants for given diluents.Here, K Ag/AgL is expressed as the product [16] of K AgL,o and K D,Ag .Moreover, the logK AgLPic,o values which are logarithmic equilibrium constants for the AgLPic formation in the o phases saturated with water were calculated from the relation, , described in the Section 2.2: logK AgLPic,DCM = 8.0 8 ± 0.2 7 at I DCM,av = 4.5 × 10 −7 mol⋅L −1 for L = B15C5, 5.9 1 ± 0.1 9 at I DCM,av = 1.9 × 10 −6 for B18C6, logK AgLPic,DCE = 5.5 7 ± 0. × 10 −5 for B15C5, and 6.0 5 ± 0.6 7 at I DCE,av = 6.4 × 10 −6 for B18C6.Here, these I DCM,av and I DCE,av values show those on the average; see the Section 3.4 for their original values.The relation of logK AgLPic,DCM between L is in agreement with that of logK AgLPic at 298 K and I → 0 in water [14].Considering this agreement, the dielectric constant of pure DCM < that of pure DCE and a ring size of B15C5 < that of B18C6, these results show that a major interaction of Ag(B15C5) + with Pic − in the o phases or of AgL + in DCM saturated with water is coulombic force at least.

∆φ eq Values Evaluated from Differences in logK D,Pic between the Electrochemical and Extraction Experiments
As can be seen from Table 1, the experimental logK D,Pic values deviate between the B15C5 and B18C6 systems for a fixed diluent.Also their values are different from the S D,Pic log K ones.Using Equation ( 13), the ∆φ eq values corresponding to the differences with S D,Pic log K were evaluated.Here, the 0 Pic φ ′ ∆ values employed for the ∆φ eq evaluation were −0.0598V [6] for the w/DCE system and −0.040 2 [11] for the w/DCM one; these standard formal or ion transfer potentials [8] have been directly or indirectly determined based on the extra-thermodynamic assumption for 4 4 Ph As BPh φ ′ ∆ values.Thus, the ∆φ eq values were different with each system.Also, using Equation (9a) with the experimental logK ex± values (Table 1) and the ∆φ eq ones, we reduced the experimental potentials ( ) . These values were 0.12 V for the B15C5/DCE system, 0.13 for B18C6/DCE, 0.4 3 for B15C5/DCM, and 0.20 for B18C6/DCM.At the same time, The ∆φ eq and logK ex± values (listed in Table 2) for the NaPic extraction by L into NB were evaluated from Equations (21) and (9a), using the logK D,Na and logK NaL,NB values: logK D,Na = −5.18[6] and logK NaL,NB = 6.9 2 [16] for L = B15C5 and 7.91 [17] for B18C6.The logK ex± values evaluated were larger than the S ex log K ± ones (at ∆φ eq = 0).The ∆φ eq values evaluated for the two Ls were in agreement with each other within calculation errors; we suppose this agreement to be other accidental cases.The validity of these evaluations will be examined in future.
Then, we obtained ( ) ( ) S ex 4 log CsLMnO 0.17 K ± = − at ∆φ eq = 0 V for L = TB24C8.These relations between S ex log K ± and logK ex± were similar to those in Table 2; see Figure 2 for ref- erence.   2 were essentially used for preparing this plot.A broken line for the circles was a regression one with the slope of 1.1 0 ± 0. Table 2).This fact indicates that interactions of Pic − with the diluent molecules increase with this order; namely Pic − is easy to more transfer from water to NB than does to DCE.On the other hand, a relation of  This reverse between the AgPic/DCM and NaMnO 4 /DCE systems for B18C6 suggests that the logK ex± value of the NaMnO 4 /DCE system is so small or that of the AgPic/DCM one so large, although the authors cannot now shows its cause, except for the differences of the ∆φ eq values related to their systems.The

Conclusion
It was demonstrated that the ∆φ eq values of the MA extraction systems with L are not necessarily zero in some cases.The logK ex± values determined by the solvent-extraction experiments fairly reflected the S ex log K ± ones standardized on the electrochemical measure at the w/o interface.The ∆φ eq (or ∆′φ eq ) term disappeared in the extraction constant such as K ex , namely, the constant expressing the system without apparently ion transfer at the w/o interface.The same was true of reactions occurred in the single phase.Also, the above results will be applied to the M II A 2 extraction systems with L. Besides, the introduction of ∆φ eq in the extraction systems can solve problems with respect to deviations in logK D,j , Here, K AgPic and K HPic are defines as [AgPic]/[Ag + ][Pic − ] and [HPic]/[H + ][Pic − ], respectively.On the other hand, it was assumed that other component equilibrium-constants are independent of I or I o , since experimental ranges of I and I o were narrow in many cases or ratios of activity coefficients for K AgL and K AgL,o (see the Section 4.1 for the definition) were close to unity.The experimental data were I = (3.4-5.8) × 10 −3 mol⋅L −1 and I DCE = (1.0 -1.1) × 10 −5 for L = B15C5, (3.2 -4.0) × 10 −3 and I DCE = (6.3-6.6) × 10 −6 for B18C6; I = (0.3 5 -1.

4. 1 .
Determination of K D,Pic , K ex and K ex± The experimental data of [AgLPic] o + [AgL + ] o , [Ag + ], [L] o and [Pic − ] were analyzed using a logarithmic form of the equation described in the Section 2.2:

Figure 2
Figure 2. Plot of 3 3 and the intercept of −0.05 5 ± 0.04 2 at R = 0.802.The triangles and squares show the points for the NaPic extraction [1] by B15C5 and B18C6 into NB and those for the CsPic and CsMnO 4 extraction [4] by TB24C8 into DCE, respectively.
DCE (<0).These findings suggest that these interfacial formal or ion transfer potentials reflect the interactions of the diluent molecules with A −[8].The ∆φ eq values were in the orders of NaMnO 4 /DCE (≈0 V) ≤ -/NB and NaPic/NB < AgPic/DCE < -/DCM for L = B15C5 and NaMnO 4 /DCE < (0 V<) -/NB and NaPic/NB < AgPic/DCE < -/DCM for B18C6.There are tendencies of DCE ≤ NB for the NaMnO 4 system and NB < DCE < DCM for MPic. the orders of (NaPic/NB < 0 V <) NaMnO 4 /NB < AgPic/DCE < NaMnO 4 / DCE < AgPic/DCM for B15C5 and (NaPic/NB < 0 V <) NaMnO 4 /NB < NaMnO 4 /DCE < AgPic/DCE < Ag-Pic/DCM for B18C6.We can easily see from these facts that there is a tendency of NB < DCE < DCM in kinds of MA and L. In other word, these tendencies mean that MA is more-effectively extracted with L into NB or DCE than into DCM.In a potential scale, the more the formal (or ion transfer) potentials0 j φ ′ ∆are negative, the more cations transfer from water to an o phase, while the more they are positive, the more anions transfer to the o phase.Probably, the tendency of = B15C5 ≥ B18C6 for the AgPic/DCE system and B15C5 < B18C6 for AgPic/DCM, in S ex log K ± are a little difference from those, B15C5 < B18C6 for AgPic/DCE and -/DCM, in logK ex± determined experimentally ( S ex log K ± values were in the orders of NaPic/NB > NaMnO 4 /NB > AgPic/DCE > NaMnO 4 /DCE > AgPic/ DCM for L = B15C5 and NaPic/NB > NaMnO 4 /NB > NaMnO 4 /DCE > AgPic/DCE > AgPic/DCM for B18C6.Except for the NaMnO 4 /DCE system with B18C6, these orders were in agreement with those (see above) of the experimental logK ex± values.This fact indicates that the experimental logK ex± values are usually reflected into the S ex log K ± ones (at ∆φ eq = 0).Therefore, in many cases, we can expect that a comparison among the logK ex± values has the same meanings as that among the S ex log K ± ones.This expectation is also shown in Figure 2, together with the data (see the Section 4.3) of the CsPic and CsMnO 4 extraction [4] by TB24C8 into DCE.K ± versus logK ex± , gave a positive correlation with R = 0.802.The potentials employed for the plot are essentially based on the

Table 2
lists these ∆φ eq and

Table 2 .
[1]]rfacial potentials, ∆φ eq , at equilibra and standardized formal potentials, Values were evaluated from the differences between the experimental and standardized logK D,A values and essentially based on the ex-Values standardized with Equation (9).dRef.[1].eRef.[12].fValuesestimatedfromTable2for the other values.The same calculations were also performed for the NaMnO 4 or NaPic extraction[1]by B15C5 and B18C6 into DCE and/or NB (see the Section 4.3 for the NaPic-L system).On the other hand, the experimental logK ex values are equal to the a V unit.+ − .b Refs.[5]-[7].c

Table 2 )
. Also, the relations, DCE and -/NB, are the same as those in the experimentally-determined logK ex± values.These results show that properties of the DCE system with AgPic and L are a little different with those of the others.The logK ex± values in Table 2 (or