Distribution of Ag(I), Li(I)-Cs(I) Picrates, and Na(I) Tetraphenylborate with Differences in Phase Volume between Water and Diluents

Ionic strength conditions in distribution experiments with single ions are very important for evaluating their distribution properties. Distribution experiments of picrates (MPic) with M = Ag(I) and Li(I)-Cs(I) into o-dichlorobenzene (oDCBz) were performed at 298 K by changing volume ratios (Vorg/V) between water and oDCBz phases, where “org” shows an organic phase. Simultaneously, an analytic equation with the Vorg/V variation was derived in order to analyze such distribution systems. Additionally, the AgPic distribution into nitrobenzene (NB), dichloromethane, and 1,2-dichloroethene (DCE) and the NaB(C6H5)4 (=NaBPh4) one into NB and DCE were studied at 298 K under the conditions of various Vorg/V values. So, extraction constants (Kex) for MPic into the org phases, their ion-pair formation constants (KMA,org) for MA = MPic in the org ones, and standard distribution constants ( S D,M K ) for the M(I) transfers between the water and org bulk phases with M = Ag and Li-Cs were determined at the distribution equilibrium potential (dep) of zero V between the bulk phases and also the Kex(NaA), KNaA,org, and S D,A K values were done at 4 A BPh − − = . Here, the symbols Kex, KMA,org, and S D,M K or S D,A K were defined as [MA]org/[M][A], [MA]org/[M]org[A]org, and [M]org/[M] or [A]org/[A] at dep = 0, respectively. Especially, the ionic strength dependences of Kex and KMPic,org were examined at M = Li(I)-K(I) and org = oDCBz. From above, the conditional distribution constants, KD,BPh4 and KD,Cs, were classified by checking the experimental conditions of the I, Iorg, and dep values.


Introduction
In electrochemistry at liquid/liquid interfaces, such as water/nitrobenzene (w/NB) and w/1,2-dichloroethane (w/DCE) ones, formal potentials ( 0 dep j ′ ) for the transfer of single ions j across the interfaces have been determined [1] [2]. These potentials have been obtained at 298 K from standardized potentials of cations or anions based on the extra-thermodynamic assumption for the distribution of tetraphenylarsonium tetraphenylborate ( 4 4 Ph As BPh + − ) and so on [1] [2] [3] in many cases. In these studies, there are many data for the potentials 0 dep j ′ in the w/NB and w/DCE systems [1] [2] [3] [4], while there are some data [5] [6] for w/o-dichlorobenzene (oDCBz) one. Especially, the data [6] for the metal ions (M z+ at z = 1) seems to be very few. Also, the In this study, we determined the standard distribution constants,

Chemicals
The procedures for the preparation of MPic, except for NaPic, were the same as those [13] [14] reported before. Commercial NaPic (monohydrate, extra pure reagent: ≥95.0%, Kanto Chemical) and NaBPh 4 {guaranteed pure reagent (GR): ≥95.0%, Kanto} were dissolved into pure water and then recrystallized by concentrating their aqueous solutions with a rotary evaporator. The thus-obtained crystals were filtered and then dried for > 20 h in vacuum. Amounts of the water of crystallization in these picrates were determined with a Karl-Fischer titration: 7.34 3 % for M(I) = Li; 6.23 2 for Na; 1.23 0 for K; 2.76 7 for Rb; 0.414 for Cs. Water was not detected for the AgPic crystal [14].

Experiments for the MPic and NaBPh 4 Distribution
Aqueous solutions of MPic or NaBPh 4 were mixed with some diluents in the various r org/w (see Table 1 & Table 2 for their ratios) in stoppered glass tubes of about 30 mL and then they were shaken for 3 minutes (in the experiments with the AgPic and NaBPh 4 distribution) or one minute (in those with the LiP-ic-CsPic one) by hand. After this operation, these tubes were mechanically agitated at 25˚C ± 0.3˚C for 2 h and centrifuged for 5 minutes in order to separate the two phases. The separated diluent phases were taken into the glass tubes and treated as follows. The diluent phases of AgPic, NaPic, and NaBPh 4 distribution systems were back-extracted by using 0.1 mol/L HNO 3 , pure water, and 0.02 mol/L HCl, respectively. For the NaPic system, the w phases back-extracted were separated, transferred to 5 mL tubes produced by polypropylene, and then their separated phases were diluted with the HCl solution. Total amounts of Ag(I) and Na(I) in these aqueous solutions were analyzed at 328.1 nm for Ag and 589.0 for Na with a Hitachi atomic absorption spectrometer (type Z-6100). In addition to American Journal of Analytical Chemistry

Derivation of Analytic Equation under the Conditions of Different Phase Volumes
Under the condition that V org is different from V in the MA distribution into the org phase, we considered the following equation as a total mass balance at mol unit:  K . This dep practically means a total energy which is necessary for the M + or A − transfer across the interface between the two bulk phases at equilibrium. Equation (3) is the modified form of the Nernst equation [16]; this expression has a little problem in its definition (see ref. [17]). As similar to Equation (3), the following equation can hold (see Appendix A for its derivation).   Figure 1 shows an example of the AgPic extraction into DCE. The straight line was

Reproducibility of the Experimental Values in Equation (4)
 at correlation coefficient (R ) = 0.997. From these intercept and slope, the logK D,± value was evaluated to be −3.8 5 ± 0.1 6 , while the logK ex one was to be −1.0 2 ± 0.3 9 . In the latter K ex evaluation, the K ex values were obtained from ex DCE / w ex  Table   1). The broken line is a regression one based on Equation (4) (see the text). calculated one (= −1.83): see Table 1. The deviation of the latter value (=logK ex − logK AgPic , see the section 3.4 for K AgPic ) can depend on the error of logK ex . Table 1 lists the results for the AgPic and NaBPh 4 distribution into several diluents and Table 2 does results for the LiPic-CsPic distribution into oDCBz.
In the relation of ( ) , the pair of the

Comparable Validity of Equation (4)
For K D,± and K ex determination, another simple analytic equation was derived from Equation (4) as follows.
As examples, these common logarithmic K D,± and K ex values for the AgPic distribution into DCE were −3. (see Table 1) reported before, compared with the values determined in terms of Equation (4).
The form of Equation (5) was simpler than that of Equation (4). Although the difference in reproducibility between the two equations was few, we did not adopt here Equation (5) (4) for the determination of the K D,± and K ex values. Table 1 showed the order of org = NB > DCE ≥ DCM > oDCBz for the K D,± values at I and I org → 0 mol/L, that for K ex in the I range of 0.020 to 0.044, and that for K D,AgPic . Here, the K D,AgPic value was calculated from the thermodynamic relation of K D,AgPic = K ex /K AgPic with K AgPic = [AgPic]/[Ag + ][Pic − ], which was evaluated from the 0 AgPic K value (=2.8 L/mol [19]) reported at I → 0 and 298 K. On the other hand, the K AgPic,org values showed the reverse order: org = NB < DCE ≤ DCM ≤ oDCBz in the I org range of 1.3 × 10 −6 to 1.6 × 10 −4 mol/L (Table 1). These orders seem to reflect polarities of the diluents, except for K D,AfPic . Also, the S D,Ag K values were in the order NB > oDCBz ≥ DCE > DCM (see Table 1), al-though the value for the oDCBz system was calculated from S D,Pic K [5] reported at T = 295 ± 3 K and K D,± obtained here at 298 K. Moreover, it was assumed that the logK D,Pic values for the oDCBz and DCM systems satisfy the conditions of I and I org → 0 and dep = 0; for the former system, that of I and I org → 0 or an activity expression was cleared as described in Appendix B.

On Features of the AgPic Distribution Systems
Considering the experimental errors of K D,± (or S D,M K ) in Table 2, except for the oDCBz system of Table 1, we can suppose that the differences in S D,M K between T = 295 ± 3 [5] and 298 K are negligible. However, the S D,Pic K determination at 298 K will be necessary for the determination of the more-exact Here, the symbol, the both phases, respectively. As the description of the superscript % (or u t //x t ), its numerator shows the condition of I org → 0 (or the left hand side of // does the total concentration, u t , of an electrolyte in the org phase), while its denominator does that of I → 0 (or its right hand side does the total one x t in the w phase).
According to Equation (6) Table 1 & Table 2). The S% D,M K values were in the order M = Li < Na < K > Rb < Cs. This order is the same as that of the distribution with the neutral MPic. The log K D,MPic order was M = Li (log K D,MPic,av = −4.6 ± 0.2) < Na (−2.8 ± 0.4) < K (−1.0 ± 0.6)  Rb (−3.5) < Cs (−3.2) (see Table 2). Here the symbol K D,MPic,av refers to the average value of K D,MPic . These orders for   M = Li-K are in agreement with those for the MPic distribution into NB [3,8] and DCE; that is, the order increases in going from M = Li to K (monotonically to Cs the deviation of about 0.1 in log(y + /y +,oDCBz ) seems to be effective for deviations in the NB and DCE distribution systems.  with the intercept (= 0.1) of the plot within both the errors, ±2 for the estimated value and ±0.3 for the intercept. These results indicate that the regression line is essentially based on Equation (7). Also, from the above, it can be seen that the dep term is included in log K ex at least. The same is also true of the plot of logK ex versus Additionally, the symbols, y − and y −,org , refer to the activity coefficients of A − in the w and org phases, respectively; y ± and y ±,org show their mean activity ones. The corresponding regression line with the MPic system was 2log(y ± /y ±,org ), this improvement of the intercept suggests log(y ± /y ±,org ) < 0. Similarly, from this result, it can be seen that the S% D,M K term is included in log K ex .

On the I Dependence of logK ex
In this section, using the data in Table 2, we tried to examine a dependence of logK ex on the I values at 298 K. In general, it is empirically known that the Davies equation [12] is effective for analyzing the I dependences of equilibrium constants in the I ranges of less than 1 mol/L. Defining 0 ex K as K ex based on the activity expression, we can obtain

On the I org Dependence of logK MA,org
As similar to the I dependence of logK ex , we considered 0 MA,org K based on an  Table 2). This order recalls that (Li > Na ≤ K) of 0 MPic K [19] in water potentiometrically-determined at 298 K to us. The difference in order between Na (=M) and K may reflect that between the water and oDCBz phases in the hydration to M + .  Table 1) were much smaller than the values reported from the distribution [3] [8] [18] and electrochemical experiments [20]. Their values have been reported to be 6.3 [3] at I = x and 5.6 [8] at I → 0 for the NB systems; 5.396 [20] (3) and (6), we can immediately derive the following basic equation:  Table 3  Based on Equation (10)

Conclusions
The logK ex and logK MA,org values were well expressed by Equation (8a) with I and Equation (9a) with I org , respectively. Now, it is unclear why the experimental A and A org values are much larger than their theoretical ones. Also, the MA distri-