Journal of Analytical & Bioanalytical Techniques
Open Access

Crown compounds (L), such as 18-crown-6 ether (18C6) and benzo-18C6 (B18C6), have extracted Cd²⁺ and Pb²⁺ (= M²⁺) with Cl⁻, Br⁻ and picrate ion (Pic⁻) into various diluents [1-6]. In such M²⁺ extraction systems with L, four component equilibrium-constants, K_D,A, K_D,MLA, K_D,MLA2 and K_2,org, have been determined so far [1-5]. Here,the symbols, K_D,A, K_D,MLA, K_D,MLA2 and K_2,org, refer to the conditional distribution constant (=[A⁻]_org/[A⁻]) of A⁻ (=Cl⁻, Br⁻ and Pic⁻), that (=[MLA⁺]org/[MLA⁺]) of MLA⁺ with the distribution equilibrium-potential difference (dep; φ_eq as its symbol employed for equations), the distribution constant (=[MLA₂]_org/[MLA₂]) of MLA₂ with dep=0 V into an organic (org) phase or diluent and the ion-pair formation one {=[MLA₂]_org/[MLA⁺]org[A⁻]_org, see Eq. (4)} for MLA₂ in the org phase, respectively [1-5]. Recently, the approximate determination method for the 5^th component equilibrium-constant, that is K_1,org=[MLA⁺] org/[ML²⁺]_org[A⁻]_org {see Eq. (9)}, was developed [6,7]. So, these five-component equilibrium-constants let us expect an evaluation of general characteristics for the above overall extraction-systems.

In order to evaluate the possibility as the method studying such extraction systems, we examined the present extraction experiments of CdPic₂ with B18C6 by using various diluents, as which nitrobenzene (NB), 1,2-dichloroethane (DCE), o-dichlorobenzene (oDCBz), dichloromethane (DCM), chlorobutane (CBu), chlorobenzene (CBz), bromobenzene (BBz), chloroform (CF), dibutylether (DBE), toluene (TE) and m-xylene (mX) were used. These diluents were selected as the group of the high polarity, NB, that of the medium one, DCE to BBz, and that of the low one, CF to mX with benzene (Bz). In course of such evaluations, the K1,org values were determined more precisely than those [6] reported previously and also comparisons among the K_D,Pic, K_D,CdLPic2, K_D,CdLPic and K_D,CdL values were performed. In addition to the above evaluations, standard distribution constants (K_D,j^S) of j=Pic⁻, C_dLPic⁺and CdL²⁺into the NB, DCE, oDCBz and DCM phasesunder the condition of dep=0 V were calculated from their conditional distribution constants, K_D,j, with dep [6,7]. Besides, the regular-solution theory (RST) plot [3-6,8] based on the data of the K_D,L and K_ex,ip values was examined, where the symbols K_D,L and K_ex,ip denote a distribution constant (=[L]_org/[L]) of L between the water and org phases and an ion-pair extraction constant (=[CdLPic₂]_org/[CdL²⁺][Pic⁻]₂) for CdLPic₂ into the org phase, respectively [8]. Application to the estimation of the potentiometric selectivity coefficient for ISE [9,10] based on K_M/ML {=[ML²⁺]_org/[M²⁺][L]_org, see Eq. (8)} was tried by using 18C6 as L.

Determination of the Cd(II):L composition of extracted species

In the present systems, slopes of the plots of log (D/[Pic⁻]²) versus log [L]_org give compositions of Cd(II):L for species extracted into the various diluents [1-7]. Here, the symbol D refers to an experimental distribution ratio {see Eq. (5)}. Figure 1 shows some examples for such plots. The obtained slope values were 0.92 for the NB system, 1.0₆ for DCE, 1.0₀ for oDCBz (Figure 1), 0.93 for DCM, 0.998 for CBu (Figure 1), 0.95 for CBz (Figure 1), 0.96 for BBz (Figure 1), 1.0₄ for CF, 0.08 for DBE (Figure 1), 1.0₂ for TE (Figure 1) and 0.99 for mX. Except for the DBE system, we concluded the compositions of the mainly extracted species to be Cd(II):L=1:1 on the basis of these values which are about unity. Also, the compositions of Cd(II):Pic(−I)=1:2 for the extracted species were speculated by considering the principle of electroneutrality in the org phases [3-7].

Figure 1: Plots of log (D/[Pic−]2) vs. log [B18C6]_org for the CdPic₂ extraction with B18C6 into some diluents. Org=oDCBz (square), CBu (full circle), CBz (circle), BBz (diamond), DBE (full triangle) and TE (triangle).

The slope being less than unity in the experimental [B18C6]_DBE range suggested the dissociation [3-7] of Cd(B18C6)Pic₂ or Cd(B18C6) Pic⁺ in the DBE phases. So, the following analyses of this system were performed by essentially assuming the extraction of the species composed of Cd(II):B18C6:Pic(−I)=1:1:2 into the DBE phase.

Determination of K_ex, K_ex±, K_D,Pic, K_2,org, K_Cd/CdL and K_1,org

For the determination of K_D,Pic, K_ex and K_ex±, the extraction constant parameter (K_ex^mix) has been used [3-7].

(1)

Here, assuming [CdLPic₂]^_org+[CdLPic⁺]^org >> [CdL²⁺]_org+ …, this equation changes into

(2)

with [CdLPic⁺]org/[Pic⁻] ≈ K_D,Pic at the approximation [Pic⁻]_org ≈ [CdLPic⁺]_org (>>2[CdL²⁺]_org+2[Cd²⁺]_org+…) on the charge balance equation, [Pic⁻]_org=2[Cd²⁺]_org+2[CdL²⁺]_org+[CdLPic⁺]_org+[CdPic⁺]_org for the org phase. Also, the following equation has been derived [3-7].

(3)

Hence, Eq. (2) gives K_D,Pic and K_ex from the plot of log K_ex mix versus −log ([Cd²⁺][L]_org[Pic⁻]) and Eq. (3) does K_ex± and K_ex from that of log K_ex ^mix versus −log P1/2 [3-7].. Examples of these plots are shown in Figures 2 and 3. A regression line was log K_ex^mix=log [(1.7₁ ± 0.2₁) × 10³+{(1.0₉ ± 0.2₅) × 10⁻⁵/[Cd²⁺][L]_mX[Pic⁻]}] at the square of correlation coefficient (R )=0.521 in Figure 2, while a line was log K_ex ^mix=log [(6.₅ ± 4.₂) × 10²+{(1.1₅ ± 0.5₁) × 10⁻³/P}^1/2] at R²=0.520 in Figure 3. In this mX system, the analyses of both Eqs. (2) and (3) yielded somewhat different K_ex values over the experimental errors. Similar results were obtained for the other ten diluent systems. As log K_ex values, the analyses based on Eq. (3) gave 4.48 ± 0.03 for the NB system, 2.45 ± 0.10 for DCE, 2.48 ± 0.15 for oDCBz, 2.26 ± 0.08 for DCM, 3.05 ± 0.04 for CBz, 2.54 ± 0.09 for BBz and 2.82 ± 0.28 for mX (Figure 3).

Figure 2: Plot of log K_ex^mix vs. -log ([Cd²⁺][L]_mX[Pic⁻]) for the mX extraction system with L=B18C6.

Figure 3: Plot of log K_ex^mix vs. −log P^1/2 for the mX extraction system with L=B18C6.

The (K_2,org/mol⁻¹ dm³) values for given ionic-strength ones (I_org/mol dm⁻³) of the org phases were calculated from the relation.

K_2,org=K_ex/K_ex± (4)

Here, I_org was derived approximately to be [Pic⁻]_org {=(1/2)(4[Cd²⁺] _org+4[CdL²⁺]_org+[CdLPic⁺]_org+ [CdPic⁺]_org+[Pic⁻]_org)=(1/2)(2[Cd²⁺] _org+2[CdL²⁺]_org+2[Pic⁻]_org)=[Cd²⁺]_org+[CdL²⁺]_org+[Pic⁻]_org} from the charge balance equation for the org phase (see above) under the condition of [Pic⁻]_org >> (obviously 2[CdL²⁺]_org >) [Cd²⁺]_org+[CdL²⁺]_org {see the derivation of Eq. (2)}. The four basic constants determined above are listed as common logarithmic values in Table 1.

Table 1: Fundamental data of CdPic₂ extraction with B18C6 into various diluents at 298 K.

According to our previous papers [6,7], moreover, K_Cd/CdL has been defined as [CdL²⁺]_org/[Cd²⁺][L]_org (see Introduction) and the firstapproximately equals D/[L]_org. Of course, this constant can be reflected to be the 3^rd extraction constant [6,7], K_ex2±=[CdL²⁺]_org([Pic⁻]_org)²/ P=K_Cd/CdL(K_D,Pic)². Here, the experimental distribution ratio D is exactly expressed as:

D=[CdL²⁺]_org{1+([CdLPic⁺]_org+[CdLPic₂]_org+[CdPic⁺]_org+…)/ [CdL²⁺]_org}/[Cd²⁺]{1+([CdL²⁺]+[CdLPic⁺]+[CdLPic₂]+[CdPic⁺]+ …)/ [Cd²⁺]}=f × [CdL²⁺]_org/[Cd²⁺] (5)

Rearranging this f term, we can easily obtain

f ={1+K_1,orgK_D,Pic[Pic⁻](1+K_2,orgK_D,Pic[Pic⁻])+(K_ex,CdPicK_D,L/K_D,CdLK_CdL) ([Pic⁻]/[L]_org)+…}/

[1+[Pic⁻]{(K_CdL/K_D,L)[L]_org(K₁+K₁K₂[Pic⁻])+K_CdPic}+…] (6)

with K_ex,CdPic=[CdPic⁺]_org/[Cd²⁺][Pic⁻] and K_CdL/K_D,L=[CdL²⁺]/[Cd²⁺] [L]_org. Then, this equation was approximately expressed as:

f ≈ {1+K_1,orgK_D,Pic[Pic⁻](1+K_2,orgK_D,Pic[Pic⁻]) }/[1+[Pic⁻]{(K_CdL/K_D,L) [L]_org(K₁+K₁K₂[Pic⁻])+K_CdPic}], (7)

because of a lack of the K_ex,CdPic value. For the symbols, K_CdL, K_D,CdL, K₁ and K₂, see Eq. (12) to (15). The f values for all the systems were evaluated. The average values of the evaluated f were in the range of 1.2 to 2.6 for the present diluent systems and the the K_Cd/CdL values were corrected with the f terms.

K_Cd/CdL ≈ D/f [L]_org. (8)

So, this equation becomes the second approximation. In the f calculation with Eq. (7), we assumed that K_2,org is independent of I_org, while we calculated K₁, K₂ and K_CdPic as functions of I (see below). Also, K_D,Pic and K_D,CdL terms were used as constant values which consist of their averaged values in the f calculation. Besides, we can calculate easily K_1,org from the thermodynamic relation of

K_1,org=K_ex±/K_Cd/CdL(K_D,Pic)²=K_ex±/K_ex2± [11] (9)

These K_Cd/CdL and K_1,org values are summarized in Table 1, as well as the above four constants.

On amounts of dominant species distributed into org phases

Considering differences among the extraction constants, K_ex, K_ex± and K_Cd/CdL, we can compare distribution (or population) of CdLPic₂⁰, CdLPic⁺ and CdL²⁺ in the org phases [6,7]. The D₀, D₊ and D₂₊ values can be calculated from the following equations:

(2a)

(3a)

and

(8a)

Figure 4 shows the representative example of the log D₀, log D₊ and log D₂₊ plots against log [B18C6]_CF for the CF (=org) extraction system. Obviously, the distribution or population profiles were in the order [CdLPic₂⁰]_CF>[CdLPic⁺]_CF ≥ [CdL²⁺]_CF at L=B18C6. Similar profiles were obtained for the other ten diluent systems. Their profiles were +>0>2+ for the NB system, 0 ≥ 2+=+ for DCE, +≥ 0>2+ for oDCBz, 0 >+> 2+ for DCM, +≥ 0 ≥ 2+ for CBu, 0>+>2+ for CBz, +>0>2+ for BBz, +>2+≥0 for DBE, 0>2+ >+for TE and +>0>2+ for mX. Here, the symbols 0, + and 2+ denote the concentrations at equilibrium of the extracted species CdLPic₂⁰, CdLPic⁺ and CdL²⁺, respectively. There is no diluent system that CdL²⁺ is most extractable. These profiles can be classified to two cases that CdLPic₂⁰ is most extractable, while CdLPic⁺ is most extractable. The DCE, DCM, CBz, CF and TE systems belong to the former cases and the NB, oDCBz, CBu, BBz, DBE and mX systems do to the latter ones. Except for TE, the former diluents contain the Cl group in their molecules. On the other hand, the diluent molecules without the Cl group are major in the latter [8-11].

Comparison of distribution properties of the complexes

The three distribution constants, K_D,MLA2, K_D,MLA and K_D,ML, for the complexes can be calculated from the following thermodynamic cycles:

(10)

(11)

and

(12)

with

(13)

(14)

and

(15)

Here, the two distribution constants, K_D,MLA and K_D,ML, are the conditional equilibrium constants with dep and the evaluations of K₁ and K₂ were performed from the I-dependence of the K₁⁰ and K₂⁰ values [2] (the values at I → 0 mol dm⁻³), respectively. Thus calculated constants are listed in Table 2, with log K_D,Pic.

Table 2: Data derived from the distribution of some species into the various diluents at 298 K.

Figure 5 shows a general tendency for their distribution properties. The log K_D,Pic values were smallest of these log K_D,j values. There was the order of K_D,CdLPic2<K_D,CdLPic<K_D,CdL, except for the TE system (No. 10 in Figure 5). For meanings of the order, the attention should be needed, because its order does not necessarily reflect amounts of the species extracted into the org phase (Figure 4).

Figure 4: Relative concentration profiles of CdPic₂⁰ (circle and D⁰), CdLPic⁺ (triangle & D⁺) and CdL²⁺ (square and D²⁺) for the CF extraction with L=B18C6.

Figure 5: Comparison among the log K_D,Pic (circle), log K_D,CdLPic2 (full triangle), log K_D,CdLPic (square) and log K_D,CdL (diamond) values in the various diluents. See Table 1 or 2 for the numbering of the diluents.

The log K_D,CdL values were positive for the NB (No. 1), DCE (2), DCM (4), CBz (6), BBz (7), CF (8) and TE (10) systems, indicating that interactions of CdB18C6²⁺ with the diluent molecules are larger than those with water molecules. Interestingly, the order, K_D,Pic<K_CdLPic2<K_{D, CdLPic}<K_D,CdL, holds except for the TE system (No. 10), being dependent on the formal charges (−1, 0, +1 and +2) of their species.

On the standardized distribution constants of the complex ions

Generally the dep value is related to the conditional distribution constant K_D,j of an ion (j) as follows [6,7]:

(16)

where the symbols z_j and Δφ_j^0′ denote the formal charge of the ion j with its sign and the standard formal potential (V unit) for the j-ion transfer across the org/water (w) interface, respectively. Also, the following relation with the standard distribution constant KD,j S holds: [4]. The log K_D,Pic^S values have been reported to be 0.05 [12] for the NB/w system, −1.01₁ [12] for DCE/w, −2.278 [13] for oDCBz/w and −0.68 [14] for DCM/w at 298 K. From these values, we were immediately able to calculate the φ_eq values (Table 2) using the modified form of Eq. (16) or the Nernst-Donnan equation [15]:

at 298 K.

Similarly, the log K_D,CdLPic^S and log K_D,CdL^S values were calculated from the experimentally-obtained log K_D,j ( j=CdLPic⁺ & CdL²⁺) and Δφ_eq values. As can be seen from Table 2, the actual (or conditional) K_D,CdLPic and K_D,CdL orders were NB>DCM>oDCBz>DCE and NB>DCM>DCE>oDCBz, respectively. On the other hand, the calculated log K_D,j^S orders were NB>oDCBz>DCM>DCE for j=CdLPic⁺ and NB>oDCBz>DCE>DCM for CdL²⁺ (Table 2). These orders indicate those standardized at dep=0 V, namely, the orders that the dep effects on log K_D,j was lost. So, this fact shows that the occurrences of dep based on the extraction systems affect the more negative effects on CdLPic⁺ and CdL²⁺ in interactions with oDCBz molecules than in those with the other molecules at the present time. On the other hand, DCM molecules have positive effects.

Comparison of K_1,org with K_2,org

There was the relation of K_1,org>K_2,org for the NB, oDCBz, DCM, CBu, CBz, BBz, DBE and mX systems. The authors think that this is a formal case [6,16]. On the other hand, the relation, K_1,org ≤ K_2,org, holds for the other three diluent systems. This relation suggests a structural chance around Cd(II) in the reaction of Cd(B18C6)Pic⁺_org+Pic⁻_org Cd(B18C6)Pic^2,org. Relevantly, it has been reported that the crystals of Cd(B18C6)X₂ at X=Cl(−I) and Br(−I) have a hexagonal bipyramidal structure [17] {although these examples are not ones in solution and of X=Pic(−I)}.

The log K_1,org values were in the order org=NB(log K_1,org=5.3)oDCBz ≤ mX ≤ BBz (8.1) ≤ DBE (Table 1). Also, the log K_2,org values were in the order NB (log K_2,org=4.44)<mX (6.2) ≤ DCM ≤ BBz ≤ oDCBz ≤ CBu ≤ DCE (7.0) ≤ DBE ≤ CBz ≤ CF ≤ TE (9.7) (Table 1). The NB and DCM systems were relatively in the lower range, while the CBz, CF and DBE ones in the higher range. The orders were independent of polarities of the diluents (see the footnote a described in Table 1).

RST plot for the CdPic₂-B18C6 system

The RST plot can be obtained from the data (Table 2) of log K_ex,ip (or log K_D,CdLPic2) and log K_D,B18C6, where the log K_ex,ip values were calculated from the thermodynamic relation [1,18] of log K_ex,ip=log K_ex+log (K_D,L/ K_CdL). The data set, reported before [2], of the Bz system was added in the plot (Table 2). Figure 6 shows its plot for the CdPic₂-B18C6 extraction system. The regression analysis of the plot gave the straight line of log K_ex,ip=(0.9₉ ± 0.1₆)log K_D,B18C6+(2.56 ± 0.21) at R²=0.825. In this equation, the slope means a molar volume ratio (V_CdLPic2/V_L) of C_dLPic2 against L [3-6,8]. The points of the NB and CF extraction systems in Figure 6 were neglected from the calculation of the regression line, because of its high polarity [6] and its hydrogen-bonding ability [6,8], respectively. From the data [18] of VB18C6=252 ± 28 cm³ mol⁻¹, we were able to calculate to be V_CdLPic2=249 ± 49 at L=B18C6. The V_j values were in the order j=Cd(18C6)Pic₂ (about 200 cm³ mol⁻¹ [4]) ≤ 18C6 (214 [8]) ≤ Cd(B18C6)Pic² ≤ B18C6. At least, the V_j relation, Cd(18C6) Pic² ≤ Cd(B18C6)Pic², seems to be reasonable, as well as 18C6 ≤ B18C6.

Figure 6: RST plot based on log K_ex,ip and log K_D,B18C6 for the 12 diluent systems with Bz (Table 2). The symbols with triangle show the NB and CF systems which were neglected from the regression analyses of the plots. See the text for their reasons.

On the other hand, the intercept generally means the term expressing solute-solvent interactions with the ion-pair formation in the w phase [6,8]: that is, (intercept)=(solute-solvent interaction term)+log K₁K₂. The common logarithmic values of the averaged K₁K₂ were in the range of 6.84-7.01. Obtaining K₁K₂=106.93 mol⁻² dm⁶ as average K₁K₂ value, we estimated −4.4 as the interaction term from the intercept. This negative sign indicates that the interaction between water molecules and Cd(B18C6)Pic₂ is larger than that between those and B18C6, assuming that there are little differences between B18C6 and Cd(B18C6)Pic₂ in the interaction with the diluent molecules employed [6]. This result is in good agreement with that in the log K_D,CdLPic2 values of which all are smaller than zero (namely K_D,CdLPic2<1, Table 2 and Figure 5).

Possibility for estimation of potentiometric selectivity coefficients

According to previous papers [9,10], a potentiometric selectivity coefficient of M^z+ against M^′z+ at an org/w interface for ISE had been expressed as:

(17)

where M^′z+ shows an interfering cation in a test solution. From the extraction data [3-5] of the MPic₂-18C6 systems with M=Cd(II) and Pb(II) reported by us and Eq. (8) without the f correction, we can immediately calculate the log K_Cd/Cd18C6 and log K_Pb/Pb18C6 values. The log K_Cd/Cd18C6 values were calculated here to be 2.95 for the NB/w extraction system, −0.1₃ for DCE/w, −0.2₅ for oDCBz/w and −0.68 for DCM/w [6], while the log K_Pb/Pb18C6 values were 6.6₀ ± 0.17 for NB/w, 4.92 ± 0.06 for DCE/w, 6.309 ± 0.009 for oDCBz/w and 4.74 ± 0.05 for DCM/w. Therefore, the log kpot PbCd values based on 18C6 were obtained to be −3.7 for the NB/w interface, −5.1 for DCE/w, −6.6 for oDCBz/w and −5.4 for DCM/w. The oDCBz/w interface shows the highest Pb²⁺ selectivity of the four diluent/w interfaces. Similarly, if the K_Pb/PbB18C6 values are determined, then one can easily estimate the k^pot_PbCd values based on L=B18C6.

On the other hand, the logarithmic ratios of K_ex±,Cd/K_ex±,Pb with L=18C6 were calculated to be −7.5 for the NB system, −7.3 for DCE and −8.5 for oDCBz based on the data [3-5] reported before and its selectivity order is oDCBz >> NB>DCE. Similarly the log (K_ex,Cd/K_ex,Pb) were −7.72 for NB (calculated here from the data [4,5]), −8.08 for DCE, −8.03 for oDCBz and −8.4 for DCM [5] and its order is DCM>DCE>oDCBz>NB. These both orders are not accord with the K_pot^PbCd order, oDCBz >> DCM>DCE >> NB (see above for the evaluated values). This fact indicates that the K_pot^PbCd values are not simply predicted by the ratios of the experimental K_ex± or K_ex values without dep. So, this emphasizes the effect of the conditional K_M/ML value on the estimation of k^pot _MM′ for ISE, because the relation, log K_M/ML=log K_D,M+log K_ML,org=(2F/2.303RT) (Δφ_eq−Δφ_M ^0′)+log K_ML,org, is derived from Eq. (16). In other words, K_{M/ ML} or K_M´/M´L is the function of dep [6,7].

Materials and reagents

Preparation procedures of CdPic₂⋅xH₂O, B18C6 and the 11 diluents were the same as those reported before [3].

Extraction experiments

Operational procedures and analytical methods of the Cd(II) species extracted into the org phases were the same as those reported before [2-4,6]. Experimental initial concentrations were [Cd(II)]₀=0.015 mol dm⁻³, [Pic(−I)]₀=0.031 mol dm⁻³ and [B18C6]₀=0.00070-0.0074 mol dm⁻³ for the NB system, 0.0053 and 0.012, 0.011 & 0.024 and 0.0017- 0.013 for DCE, 0.017, 0.034 and 0.00077-0.0051 for oDCBz, 0.017, 0.034 and 0.00077-0.015 for DCM, 0.020, 0.041 and 0.043 and 0.00074- 0.0095 for CBu, 0.037, 0.075 and 0.00024-0.0028 for CBz, 0.016&0.034, 0.034&0.072 and 0.00013-0.047 for BBz, 0.017, 0.034 and 0.0015-0.015 for CF, 0.020, 0.040 and 0.0018-0.0046 for DBE, 0.037, 0.075 and 0.00042-0.0056 for TE and 0.017, 0.034 and 0.00060-0.0053 for mX. Some results in the extraction experiments obtained from these initial concentrations are shown in Figure 1. The pH values for the w phases after the extraction operations were in the range of 5.34 to 6.87, except for the DBE system of which the lowest value was 4.26. Even such pH value shows that its [Pic⁻]/[HPic] ratio was about 10^3.8 (=10^−pKa/10^{− pH}=10^−0.49/10^−4.26), because pK_a,HPic=0.49 at I=0.03₄ mol dm⁻³ (Table 1) for the DBE extraction system [19].

Data analyses

The data analyses were essentially the same as those reported before [6,7]. In the present study, the following component equilibria were basically employed for the analyses:

(i) Cd²⁺+L CdL²⁺ [1], CdL²⁺+Pic⁻ CdLPic⁺ [2,20], CdLPic⁺+Pic⁻ CdLPic² [2,20], Cd²⁺ +Pic⁻ CdPic⁺ [20] and H⁺+Pic⁻ HPic [19] in the w phase;

(ii) Pic⁻ Pic⁻_org, CdLPic₂ CdLPic_2,org, CdLPic⁺ CdLPic⁺ _org, CdL²⁺ CdL²⁺_org, L Lorg [8] and HPic HPic_org [4,21] between the two phases;

(iii) CdL²⁺_org+Pic⁻_org CdLPic⁺_org and CdLPic⁺_org+Pic⁻_org CdLPic²,_org, in the org phase at L=B18C6. In order to avoid the unnecessary complexity in the overall extraction equilibrium, the equilibria of H⁺ H⁺ NB and Cd²⁺ Cd²⁺ NB were neglected, because their distribution data had been reported so far [11,22,23].

The K_1,org values were determined precisely in terms of evaluating the f coefficients. By comparing these values with the K_2,org ones, the structural changes around Cd(II) in the ion-pair complexes were speculated, as well as the CdA₂-18C6 extraction systems with A=Cl(−I), Br(−I) and Pic(−I). The conditional K_D,CdL values were smoothly estimated from the thermodynamic cycle, in addition to the K_D,Pic, K_D,CdLPic2 and K_D,CdLPic determination at L=B18C6. So, the determination of these actual distribution constants made a systematic study of their distribution properties possible. The results in such a study were not in conflict with those based on the RST plot. Moreover, it was suggested that the evaluation of the K_Cd/CdL values with dep has a possibility in the prediction of the K_pot ^PbCd values for ISE. The above results promise us a systematic procedure for the study of the actual M(II) extraction with L.