Brief Determination of Standard Formal Potentials for the Transfers of Several Pairing Anions across the Nitrobenzene/Water Interface by Na(I) Extraction with 18-Crown-6 Ether

Individual distribution constants (K_D,M and K_D,A) of cations {M^z+ with the formal charge of z (= 1, 2)} and monovalent anions (A⁻) are generally important for the determination of equilibrium constants, such as complex formation (or stability) constants (KML,org) for ML^z+ and acid dissociation ones of HA in organic (o or org) phases, in electrochemistry at water/o solution interfaces [1-5]. With respect to these distribution constants, the authors have proposed the presence of interfacial equilibrium potentials (Δφ_eq) in solvent extraction processes with such interfaces and determined so far many Δφ_eq values by applying this idea to the monovalent or divalent metal extraction with crown compounds (L) [6-10]. Here, the Δφ_eq values have been obtained from the relation [2,8], Δφ_eq = Δφ_Pic^0′− 0.05916log KD,Pic at 298 K, based on the standardized formal potentials (Δφ_Pic^0′) for the transfer of picrate ion (Pic⁻) across the nitrobenzene/water (NB/w) [7-9,11], benzene (Bz)/w [10], dichloromethane (DCM)/w [6,11] or 1,2-dichloroethane (DCE)/w interface [6,8]. On the other hand, there are systematic studies for many A⁻ distribution from water into DCE or NB in the K_D,A determination, using the CsA extraction with 24-crown-8 ether derivative [12] or the extraction of single salts [1,13], MA or MA₂. However, the no relation between K_D,A and Δφ_eq had been reported in these extraction studies [1,12,13]. Therefore, it is difficult to check whether the K_D,A values experimentally-obtained are equivalent to those standardized at Δφ_eq = 0 V (namely the K_D,A^S {= exp(Δφ_A^0′/0.02569) at 298 K [2,8]} values) or not. According to our previous paper [14], K_D,A^S has been electrochemically derived at Δφ_eq =0 V from the equation

      (1)

being the same as that [2] described above. Here, the minus sign of the right hand side (rhs) of this equation comes from the formal charge of A⁻ [11,14].

In order to clarify the presence of Δφ_eq for the transfers of other A⁻ at the NB/w interface, as well as its presence for that of Pic⁻, we performed here extraction experiments of sodium salts, NaA, by 18-crown-6 ether (18C6) into NB at A⁻ = MnO₄⁻, ReO₄⁻, F₃CCO₂⁻ and 2,4-dinitrophenolate ion (Dnp⁻). For increasing the actual distribution efficiency of A(−I) and Na(I) as much as possible, 18C6 was used in the above extraction systems as the more effective L, compared with benzo- 18C6 and dibenzo-18C6 [15]. This idea had been actually employed by Levitskaia et al. [12]. Also, NB was used as a diluent for facilitating the dissociation of the ion-pair complex Na(18C6)⁺A⁻ extracted in the o phase and then this caused totally an increase in extraction-ability of Na(I). Moreover, the ion-pair formation constants, K_MAM⁰ and K_MLA⁰, for NaDnp and Na(18C6)⁺Dnp⁻ in water at I → 0 mol dm⁻³ were determined at 298 K by potentiometry [16] with a commercial Na⁺- selective electrode (Na⁺-SE). Here, the symbol I refers to ionic strength of the aqueous solution with Na⁺Dnp⁻ or Na(18C6)⁺Dnp⁻.

Materials and reagents

Purities of Na(I) in commercial F₃CCO₂Na (Aldrich, 98%) and NaReO₄ (Aldrich, 99.99%) were checked by AAS measurements at 589.0 nm, while those of NaDnp⋅H₂O (Tokyo Chemical Industries, >98.0%) and NaPic⋅H₂O (Wako Pure Chemical Industries, >90%) absorption of 358 nm and the Pic⁻ one of 355, respectively. Water contents of the former three Na(I) salts and commercial 18C6 (Wako Pure Chemical Industries, 98.0%) were determined by a Karl- Fischer titration: F₃CCO₂Na⋅0.0392H₂O (0.517%); NaReO₄⋅0.018H₂O (0.12); NaDnp⋅0.505H₂O (4.23); 18C6⋅0.0309H₂O (0.210). Purity of NaMnO₄⋅H₂O (Aldrich, ≥ 97%) was determined by a redox titration with Na₂C₂O₄ (Wako, 99.96%). The concentration of a basic aqueous solution with commercial HDnp (Tokyo Chemical Industries, >98.0%) was determined spectrophotometrically at 358 nm. Nitrobenzene (Kanto Chemical Co., min. 99.5%) was washed three-times with pure water and then was kept at a state saturated with pure water. Other reagents used here were of guaranteed reagent grades. Tap water was distilled once with a stainless steel-still and purified through the Autopure system (type WT 101 UV, Millipore).

Extraction experiments

Extraction experiments were essentially the same as those [17-19] reported before for the NaMnO₄, NaO₂CCF₃ and NaReO₄ extraction by 18C6 into DCE or NB. Amounts of Na(I) extracted into the NB phases were determined by the AAS measurements, where the same atomic absorption spectrophotometer (Hitachi, Japan) as that described previously [9] was used with the same accessories; Na(I) extracted into the NB phase was two-times back-extracted into an acidic aqueous solution. All the D values were less than unity, where D denotes a distribution ratio of Na(I) species extracted into the NB phase. A stock solution of 0.02 mol dm⁻³ NaMnO₄ for the extraction experiments was diluted immediately before use and its diluted solution was used up within about 8 h [17].

Total concentrations, [NaA, HDnp or L]_t, for the extraction experiments were [NaMnO₄]_t = 3.2 × 10⁻³ mol dm⁻³ with [L]_t = 4.2 × 10−5-6.1 × 10⁻³ mol dm⁻³; [NaReO₄]_t = 9.0 × 10⁻³ with [L]_t = 4.4 × 10−5- 4.4 × 10⁻³; [NaO₂CCF₃]_t = 3.0 × 10⁻³ with [L]_t = 4.4 × 10⁻⁴-3.6 × 10⁻²; [NaOH]_t = 3.2 × 10⁻⁴-2.7 × 10⁻³, [HDnp]_t or [NaDnp]_t = (1.2-9.1) × 10⁻⁴ with [L]_t = 1.4 × 10⁻⁴-2.9 × 10⁻²; see the x-axis in Figure 1 as a reference of [L]_t. In particular, the total concentrations of mixtures of NaOH with HDnp or NaDnp were determined by the AAS measurements.

Figure 1: Plots of 2log D vs. log [18C6]_NB for the NaA extraction by 18C6 into NB at A−=MnO₄⁻ (triangle), Dnp⁻ (circle), ReO₄⁻ (diamond) and F₃CCO₂⁻ (square). See the text for the regression lines.

Data analysis

An extraction model for the data analysis was shown in Appendix A, supplementary information. In the [A⁻] calculation, the KHA values were neglected by assuming that HA is strong acids in water for A⁻= MnO₄⁻, ReO₄⁻ and F₃CCO₂⁻. Similarly, K_D,HA or K_{ex, HA} (= KHA⋅KD,HA) value was neglected. Therefore, the following equation was used: [A⁻] ≈ ([A]_t − Ab)/(1 + {K_NaA + (K_NaLK₁/K_D,L)[L]_NB}[Na⁺]) (see Appendix A) instead of the more-exact equation [A⁻] = ([A]_t − Ab)/(1 + {K_NaA + (K_NaLK₁/K_D,L)[L]_NB}[Na⁺] + (K_HA + K_ex,HA)[H⁺]). Here, K HA</⁻¹, K_D,HA and K_ex,HA denote the acid dissociation constant of HA in water, the distribution one of HA into and an extraction one (mol⁻¹ dm³) for HA into the NB phase, respectively, and see Appendix A for the other equilibrium constants and the symbol Ab.

Similarly, the experiments for the NaDnp extraction system were almost performed in the pH range of more than 10. This pH value means the condition of [HDnp]/[Dnp⁻] ≤ 10⁻⁶ (≈ [H⁺]K_HDnp = 10^−10.8⋅10^4.1 [20]). Hence, the K_HA, K_D,HA and K_ex,HA values were neglected in the calculation.

Emf measurements

The following cell was used for the determination of the K_MA⁰ and K_MLA⁰ values: Ag|AgCl|3.3 mol dm⁻³ KCl|0.1 mol dm⁻³ (C₂H₅)4NCl|test solution|Na⁺-SE. Here, the test solutions were aqueous solutions of NaCl for preparing calibration curves and those of NaDnp and its solutions with 18C6 for the K_MA⁰ - and K_MLA⁰-determination, respectively. Experimental slopes of the calibration curves were in the ranges of 59-74 mV/decade for the NaDnp system, 57-62 for NaPic, 69-76 for NaDnp-18C6 and 65-76 for NaPic-18C6.

The emf values of the above cell were measured at 25 ± 0.3°C using a Horiba pH/ion meter (type F-23) equipped with a Horiba Na⁺-SE (type 1512A). Liquid junction potentials (ΔE_LJ) at the 0.1 mol dm^-3 (C₂H₅)4NCl|test solution interface in the cell were not corrected. An effect of this treatment was examined by determining the the K_MA⁰ and K_MLA⁰ values at MA = NaPic and MLA = Na(18C6)Pic, respectively (see below).

Potentiometric determination of ion-pair formation constants for NaDnp and Na(18C6)Dnp in water

The following equations were used for the determination of the K_MA⁰ and K_MLA⁰ values [16].

       (2)

      (3)

with K_MLA⁰ = [MLA]/(a_ML⋅a_A). Here, y_± and a_j denote a mean activity coefficient and an activity (mol dm⁻³) of species j (= M⁺, A⁻, ML⁺) in water, respectively. Also, we assumed that the activity coefficients of MA and MLA are unity. Figures 2a and 2b show a plot of log (K_MA/y_± 2) versus (aM)2 for MA = NaDnp and that of log (KMLA/y± 2) versus a_ML⋅a_A for MLA = Na(18C6)Dnp, respectively. Regression analyses of these plots at 298 K yielded K_NaDnp⁰ = 8.1 ± 1.2 mol⁻¹ dm³ with b_s = (1.7 ± 0.2) × 10⁻³ mol dm⁻³ at (correlation coefficient)² (R²) = 0.741 and K_Na18C6Dnp⁰ = 78 ± 18 with b = (1.5 ± 0.5) × 10⁻³ at R² = 0.801. The symbols bs and b refer to empirical parameters for curve fittings [16]. Solid lines shown in Figures 2a and 2b were the regression ones based on the curve fittings of the plots into Equations (2) and (3).

Figure 2a: Plot of log (K_MA/y_±²) vs. (a_M)² for the NaDnp (= MA) system.

Figure 2b: Plot of log (K_MLA/y_±²) vs. a_ML⋅a_A for the Na (18C6) Dnp (= MLA) system.

In order to check the accuracy of these values, the K_NaPic⁰ and K_Na18C6Pic⁰ values were determined potentiometrically: K_NaPic⁰ = 7.7 ± 0.5 mol⁻¹ dm³ with bs = (5.1 ± 0.5) × 10⁻⁴ mol dm⁻³ at R² = 0.941 and K_Na18C6Pic⁰ = 136 ± 15 with b = (6.8 ± 0.5) × 10⁻⁴ at R² = 0.960. The former value is close to that (= 4.2 mol⁻¹ dm³ [16]) reported before. On the other hand, the latter value is two-times larger than the literature one (= 62 [16]). These facts indicate that the K_NaDnp0 value which was thus determined is essentially reliable, while the K_Na18C6Dnp⁰ value is an approximate (see below for the analyses of extraction data). Additionally, it can be important that we obtained to a certain degree the reliable K_MA⁰ and K_MLA⁰ values without troublesome corrections of the ΔE_LJ values in the emf measurements. Hence, the two values were used for the calculation [17-19] of the [Na⁺], [18C6]_NB, and [Dnp⁻] values in the analyses on the extraction experiments (see Appendix A). Moreover, we think that this simple procedure has a possibility for the K_MA⁰ - and K_MLA⁰ - determination, namely can become the procedure without the troublesome ΔE_LJ corrections.

Determination of composition of the extracted species

Procedures for determining the composition of Na(I):L:A(−I) at L = 18C6 were the same as those [11,17-19] reported before. That is, plots of log (D/[A⁻]) (call this procedure plot I) and 2log D (call it plot II) versus log [L]_NB are useful for the composition determination of both the ion-pair (NaL⁺A⁻) extraction and the NaL⁺ extraction with the pairing (or counter) anion A⁻ into the NB phase, respectively. Also, the intercepts of the plots I and II correspond to the approximate values of log K_ex and log K_ex±, respectively [6,8,11,17-19]: K_ex is defined as [MLA]_o/P and K_ex± as [ML₊]_o[A⁻]_o/P with P = [M₊][L]_o[A⁻]. Figure 1 shows their plots for the NaA extraction by 18C6 into NB. Basic data for the systems employed were a slope of 1.07 and an intercept of 1.76 at R² = 0.990 in the plot II for the MnO₄⁻ system, 0.96 and −0.37 at R² = 0.942 in that for ReO₄⁻, 0.96 and −1.38 at R² = 0.755 in that for F₃CCO₂⁻ and 0.97 and 0.17 at R² = 0.832 in that for Dnp⁻. The above slopes being in the range of 0.9 to 1.1 [11] indicate the extraction of species with Na(I):18C6:A(−I) = 1:1:1 into the NB phase at least. In this study, all the slopes of the plots I were less than 0.9, indicating the detectable dissociation of NaL⁺A⁻ in the NB phase [17].

Determination of the K_D,A, K_ex± and K_ex values

The K_D,A, K_ex± and K_ex values were determined by the same methods as those [6,8,10,11,17] reported before, together with the K_1,org (= K_ex/ K_ex±) value. That is, the following extraction constants parameters (K_ex^mix) [6,8,10,11,17] were fundamentally used for the determination:

     (4)

    (4a)

with under the condition of [MLA]_o + [ML⁺]_o >> [M⁺]_o + … in the o phase. Non-linear regression analyses based on Equations (4) and (4a) yield the K_D,A and K_ex± values, together with the K_ex one, respectively [6,8,10,11,17]. Figures 3 and 4 show the plots based on Equations (4) and (4a), respectively; the figures were examples of the F₃CCO₂ and Dnp⁻ systems. The R² values of the regression lines obtained from Equations (4) and (4a) were 0.910 and 0.773 for A⁻ = MnO₄⁻, 0.884 and 0.689 for ReO₄, 0.721 and 0.701 for F₃CCO₂⁻and 0.884 and 0.933 for Dnp⁻, respectively.

Figure 3: Plot of log K_ex ^mix vs. −log ([Na⁺][18C6]_NB) for the NaA-18C6 system at A−=F₃CCO₂⁻ (square) and Dnp⁻ (circle). See the K_D,A and K_ex values in Table 1 about the data of the regression lines.

Figure 4: Plot of log K_ex ^mix vs. − (1/2)log P for the NaA-18C6 system at A−=F₃CCO₂⁻ (square) and Dnp⁻ (circle). See the K_ex± and K_ex values in Table 1 about the data of the regression lines.

The K_1,org value is easily calculated from the above relation [6,8,10,11,17]. Also, the K_D,NaL (= [NaL⁺]NB/[NaL⁺]) values at L = 18C6 were estimated from the relation, I_NBK_D,L/(K_NaL[Na⁺][L]_NB), in each run. Here, K_D,NaL, K_D,L and K_NaL denote the individual distribution constant of NaL⁺, that (= [L]_NB/[L]) of L into the NB phase and the complex formation constant (= [NaL⁺]/[Na⁺][L]) for NaL⁺ in water, respectively (see Appendix A): these latter two values were available in references. Table 1 lists the above equilibrium constants determined at 298 K.

Table 1: Fundamental data for the NaA extraction with L = 18C6 into NB at 298 K.

The log K_ex and log K_ex± values were in the orders A⁻ = F₃CCO₂⁻ < ReO₄⁻ < Dnp⁻ < MnO₄⁻ < Pic⁻. The log KD,NaL values were in the same order as those for log K_ex and log K_ex±. Also, the log K_D,A values were in the order F₃CCO₂⁻ ≤ ReO₄⁻ < Pic⁻ < MnO₄⁻ < Dnp⁻.

The order of the log K_1,NB values was F₃CCO₂⁻ ≤ Dnp⁻ ≤ MnO₄⁻ < ReO₄⁻ < Pic. Ionic radii [21] of A⁻ are assumed to be H₃CCO₂ (2.32 Å) ≤ F₃CCO₂⁻ < MnO₄⁻ (2.40) < ReO₄⁻ (2.60) < Dnp⁻ < Pic⁻. On the other hand, the ion size parameters [16,22] in aqueous solutions were in the order MnO₄⁻ (3.5) < ReO₄⁻ (3.9) < H₃CCO₂ − and H2ClCCO₂ − (4.5 Å) ≤ F₃CCO₂⁻ < Dnp⁻ < Pic⁻ (7). Here, the positions for F₃CCO₂⁻, Dnp⁻ and Pic⁻ in the both orders were predicted empirically. Hence, the log K_1,NB order suggests there are two groups: MnO₄⁻ and ReO₄⁻; F₃CCO₂⁻, Dnp⁻ and Pic⁻. Unfortunately, we cannot now explain a reason about the K_1,NB order.

Happily, the difference in a set of K^NaPic0 and K_Na18C6Pic⁰ (mol⁻¹ dm³) between 4.2 and 62 [16] and 7.7 and 136 did not affect the main results of the data analyses in the NaPic extraction by 18C6 into NB, as follows. The K_ex, K_D,Pic or K_1,NB value well agreed with each other and the K_ex± one calculated from 7.7 and 136 mol⁻¹ dm³ was in agreement with its corresponding value in Table 1 within the experimental error of ± 0.5. Their logarithmic values were 7.19 ± 0.07 at K_ex, −2.5₀ ± 0.3₉ at K_D,Pic, 1.4₇ ± 0.5₃ at K_ex± and 5.7₂ ± 0.5₃ at K_1,NB. These results suggest that the extraction data for the NaDnp system with 18C6 are also reliable.

Estimate methods of the K_D,A S, Δφ_eq and K_D,ML^S values at the NB/w interfaces

When the K_D,M^S value, K_D,M at Δφ_eq = 0 V, is available from some references and the K_ex± value was obtained from the present extraction experiment, the K_D,A^S value can be easily calculated from the following thermodynamic relation:

     (5)

Similarly, K_ML,org is introduced as the reference value in this equation: log = 7.7 [23] at L = 18C6 and 298 K; log K_D,Na^S (= −Δφ_Na^0′/0.05916 = −16.90Δφ_Na ^0′) = −5.18 [13] (see Appendix A).

Also, the thus-obtained K_D,AS value is introduced in

    (1a)

with

   (1b)

So we can immediately obtain the Δφ_eq and ΔφA^0′ values from Equations (1a) and (1b), respectively. Of course, the K_D,A values can be determined experimentally (Table 1).

Furthermore, the K_D,ML^S values averaged were calculated from two procedures as follows. (A): procedure estimated from a thermodynamic cycle. Its cycle is

   (6)

Except for the K_D,L and K_ML values, the other values were determined here. For the two values, we adopted log K_NaL = 0.73 [15] and log KD,L = −1.00 [24] at L = 18C6 (see Appendix A) and accordingly log (K_D,L/ K_NaL) becomes −1.73.

(B): procedure estimated from the Δφ_eq and K_D,ML values. Its equation is

   (6a)

which is derived from Δφ_eq = ΔφML^0′ + (2.303RT/F)log K_D,ML with log K_D,ML^S = −(F/2.303RT)ΔφML^0′ at z = 1. The experimental K_D,ML values were individually calculated from the relation K_D,ML ≈ [A⁻]_NB/[ML⁺] (= I_NBK_D,L/K_ML[M⁺][L]_NB) under the approximate condition (see the footnote f in Table 1) of [A⁻]_NB ≈ [ML⁺]_NB, which comes from the charge balance equation [A⁻]_NB = [M⁺]_NB + [ML⁺]_NB {see Equation (B1) in Appendix B, supplementary information}, and then their values were averaged. Here, the fact that the Δφ_eq value is in common for a given extraction system was over-interpreted in the mean calculation {see Equation (1a)}. The above procedures, (A) and (B), are described as fundamental ones in the calculations, although other procedures were able to be considered practically and were tried. The K_D,A^S, Δφ_eq and K_D,NaL^S values obtained from the above are listed in Table 2, together with the ΔφA^0′ values.

Table 2: Log K_D,A^S, Δφ_A^0′, Δφ_eq and log K_D,Na ^S values for the NaA extraction with L = 18C6 into NB at 298 K.

The log K_D,A^S order was F₃CCO₂⁻ < ReO₄⁻ < Dnp⁻ < MnO₄⁻ < Pic⁻; this means that the ΔφA ^0′values were in the same order. This order was reflected to the log K_ex and log K_ex± orders. The K_D,A^S values for A⁻ = MnO₄⁻ and Dnp⁻ were close to those [13,23] reported before. Also, the log K_D,NaL^S order was Pic⁻ < F₃CCO₂⁻ ≈ MnO₄⁻ ≈ ReO₄⁻ ≤ Dnp⁻. Especially, the latter four values (0.7-0.8 = log K_D,NaL^S) were in agreement with that (0.7 [25]) at the NB/w interface directly-determined by iontransfer- polarographic measurements. These facts suggest that 0.7 is appropriate to the log K_D,NaL^S value.

Correlation between log K_ex± and Δφ_eq

A plot of log K_ex± versus Δφ_eq gave a positive correlation: log K_ex± = (13.2 ± 2.9)Δφ_eq + (0.3₈ ± 0.2₇) at R² = 0.748 (Figure 5); the point of MnO₄⁻ due to ref. [13] was removed from the regression calculation because of uncertainty of the Δφ_eq value. This plot can come from Equation (5). For example, by adding the Δφ_eq term in the both sides of Equation (5), Equation (5) can be modified as

Figure 5: Plot of log K_ex± vs. Δφ_eq for the NaA extraction by 18C6 into NB. The regression line was log K_ex± =(13.2 ± 2.9) Δφeq+(0.38 ± 0.27) at R²=0.748, except for the triangle point of MnO₄⁻. See Tables 1 and 2 for the plot data.

 (5a)

with log K_D,A = −16.90Δφ_eq + log K_D,A^S {see Equation (1a) and Appendix B} at 298 K and the rhs of Equation (5a) becomes 16.90Δφ_eq + log K_D,A + 2.5₂. Also, the log K_D,A values for the five extraction systems were in the range of −2.8 to −1.3. Therefore, the value of log K_D,A + 2.52 can be estimated at −0.3 to 1.2. This range which corresponds to the intercept of the plot includes the experimental intercept (= 0.4). This fact indicates that the plot is essentially based on Equation (5a), namely Equation (5).

Moreover, the log K_D,A values can cause the larger deviation of the plots from the regression line (Figure 5), because their values are not constant among A⁻ employed. This is proved by the plot of log (K_ex±/K_D,A) versus Δφ_eq. The regression analysis of this plot yielded the equation, log (K_ex±/K_D,A) {= log ([NaL⁺]NB/[Na⁺][L]NB)} = 15.3Δφ_eq + 2.4 at R² = 0.896. This improvement on R² clearly shows a variance effect of log K_D,A.

Similar correlations have been observed in the plots of log K_ex± versus Δφ_eq for the NaPic extraction with the four L into the two diluents [10,11]. These plots are based on the other modified form of Equation (5a): log K_ex± = 16.90(-Δφ_eq) + log K_D,Na+ log (K_D,Pic^S⋅K_NaL,org) [11] at org = DCM and DCE. For the Bz extraction system, a similar plot has been obtained, but its slope (= 84 V⁻¹ [10]) was much larger than the theoretical value, 16.90 (= F/2.303RT) at 298 K. These facts also support that Equation (5a) is effective for an explanation of the above correlation.

Correlation between log K_D,NaLA and log K_D,A^S

The log K_D,NaLA {= log ([NaLA]_NB/[NaLA])} value was calculated from the thermodynamic relation [15,17].

(7)

since NaLA is a neutral ion pair, its distribution constant naturally satisfies the condition of Δφ_eq = 0 V [26]. Here, the symbol K₁ is defined as [NaLA]/[NaL⁺][A⁻] (see Appendix A) and its values slightly changed with changes of I. The log K_D,NaLA values obtained were 1.01 for A⁻ = MnO₄^-, −0.44 for ReO₄^-, −0.97 for F₃CCO₂⁻ and 0.96 for Dnp⁻; its value for Pic⁻ was reported to be 3.68 [11]. Figure 6 shows a plot of log K_D,NaLA versus log K_D,A^S for the present extraction systems with A⁻. There was a good linear correlation between them at R² = 0.974. This result indicates that a distribution property of Na(18C6)A into the NB phase reflects that of A⁻. In other words, it means that the following relation holds in the present extraction systems: log K_D,NaLA = log K_D,A^S + log (K_NaL,NB/K_NaL) + log (K_D,NaS⋅KD,18C6) + log (K_1,NB/K₁) ≈ log K_D,A^S + 0.72 + log (K_1,NB/K₁), although the coefficient of log K_D,A^S was somewht larger than unity. Here, this relation is derived from log K_ex = log K_ex± + log K_1,NB {see Equations (6) and (7)}. The average values of K₁/mol⁻¹ dm³ were 101.77 for A⁻ = Pic⁻, 10^2.31 for MnO₄⁻, 10^2.43 for ReO₄⁻, 10^1.86 for Dnp⁻and 10^2.51 for F₃CCO₂⁻. Therefore, an estimate of the intercept, 0.7₂ + log(K_1,NB/K₁), becomes in the range of 2.1 to 4.7. Its experimental value was 3.3₂ ± 0.2₃ (see the caption in Figure 6), overlapping this estimate. On the other hand, a plot of log K_D,NaLA versus log K_D,A at Δφ_eq ≠ 0 V did not yield the correlation (R² = 0.038).

Figure 6: Plot of log K_D,NaLA vs. log K_D,A^S at L=18C6 and A−=MnO₄⁻ (2 data), ReO₄⁻, F₃CCO₂⁻, Dnp⁻ (2 data) and Pic⁻. The regression line was log K_D,NaLA=(1.15 ± 0.09)log K_D,A^S+(3.3₂ ± 0.2₃) at R²=0.974, except for the triangle point of MnO₄⁻.

The authors clarified the presence of Δφ_eq at the NB/w interfaces in the NaA extraction systems with 18C6, as well as the NaPic extraction one. Also, the positive correlation of log K_ex± to Δφ_eq among A⁻ was observed in a given combination of Na⁺, NB, and 18C6. This fact makes the previously-reported correlation among L in given combinations of NaPic and diluents more-sure. Moreover, it was demonstrated that this method makes the ΔφA^0′- or K_D,A^S-determination of a single A⁻ having the lower extraction-ability easier. In particular, using the more general L, such as 18C6, is important for the present method, because this promises the high versatility of the method.