According to previous papers [1] - [6] , the following equation was employed for the determination of the composition of Cd(II) species extracted into the org phases.

log ( D / [ A − ] 2 ) ≈ log [ L ] org + log K ex (1)

with D defined as [Cd(II)]_org/([Cd(II)]_t − [Cd(II)]_org) at A⁻ = I⁻ and L = 18C6. This equation was derived approximately from the definition of K_ex [7] described in the introduction. Here, the symbols D, [Cd(II)]_org, and [Cd(II)]_t denote an experimental distribution ratio for Cd(II), a measurement concentration of all the Cd(II) species extracted into the org phase determined by AAS, and a total concentration of CdI₂ included in the water phase at the beginning of the extraction experiment, respectively. When slopes obtained from the plots of log (D/[A⁻]²) vs. log [L]_org are unity, they would mean that the extracted species have the composition of Cd(II): L = 1:1 [1] - [7] .

The experimental slopes were 0.95 at correlation coefficient (R) = 0.813 for the NB system, 1.03 at 0.989 for 1,2-dichloroethane (DCE), 0.97 at 0.939 for o-dichlorobenzene (oDCBz), 1.03 at 0.940 and 0.96 at 0.754 for dichloromethane (DCM), 1.07 at 0.883 for chlorobenzene (CBz), 1.08 at 0.959 for bromobenzene (BBz), 1.02 at 0.769 for chloroform (CF), 1.01 at 0.871 for Bz, 0.90 at 0.827 for toluene (TE), and 1.05 at 0.924 for m-xylene (mX). Here, the R values were obtained from the regression lines determined with the log(D/[I⁻]²) vs. log[18C6]_org plots. Also, the composition of I(−I) was speculated from the formal charge of Cd(II). This speculation was based on the experimental data plots of the log(D/[L]_Bz) vs. log [Pic^-] with the slope of two [7] . These results indicated that the complexes composed of Cd(II):18C6:I(−I) = 1:1:2 were extracted into the employed ten diluents.

For the determination of K_D,I, K_ex±, and K_ex, we employed the parameter

K ex mix = [ Cd ( II ) ] org / P (2)

as similar to the previous papers [1] - [6] . Therefore, we can determine the K_D,I and K_ex values from the plot of log K ex mix vs. −log([Cd²⁺][L]_org[I⁻]) based on

K ex mix ≈ K ex + K D , I / ( [ Cd 2 + ] [ L ] org [ I − ] ) (2a)

while can do the K_ex± and K_ex ones from that of log K ex mix vs. −logP^1/2 on

K ex mix ≈ K ex + ( [ CdLI + ] org [ I − ] org / P 2 ) 1 / 2 = K ex + ( K ex ± / P ) 1 / 2 (2b)

at L = 18C6; see the Section 3.3 for the detailed derivation of Equations (2)-(2b). Figure 1 and Figure 2 show examples of these plots for the present Cd(II) extraction systems and logarithmic values of these equilibrium constants were listed in Table 1. The K_ex values determined with Equation (2a) in the 5 diluent systems (Table 1) were in accordance with those with Equation (2b) within their experimental errors.

From the thermodynamic relation of K_ex = K_CdLK_ex,ip/K_D,L [1] - [7] , the K_ex,ip values were evaluated at the same time (see Table 1). Here, the symbols K_CdL, K_ex,ip, and K_D,L denote a complex formation constant (=[CdL²⁺]/[Cd²⁺][L]) [12] for CdL²⁺ in water, an ion-pair extraction constant (=[CdLI₂]_org/[CdL²⁺][I⁻]²) of

a. Abbreviations of the diluents were NB: nitrobenzene; DCE: 1,2-dichloroethane; oDCBz: o-dichlorobenzene; DCM: dichloromethane; CBu: 1-chlorobutane; CBz: chlorobenzene; BBz: bromobenzene; CF: chloroform; Bz: benzene; TE: toluene; mX: m-xylene; b. Ionic strength for the water phases; c. Values determined with Equation (2b); d. Calculated from logK_ex,ip = logK_ex − logK_D,18C6- logK_Cd18C6 = logK_ex - logK_D,18C6 + 0.05. See ref. [12] ; e. Not determined with Equation (2b).

CdLI₂ into the org phase, and a distribution constant (=[L]_org/[L]) [13] [14] of L into the org phase, respectively. As described below, the K_ex,ip and K_D,L values are employed for the RST plot [1] - [6] [13] .

The relation between dep or Δϕ_eq and K_D,A has been reported for these extraction systems [1] - [6] [8] .

Δ ϕ eq = ( 2 . 3 0 3 R T / z A F ) ( log K D , A − log K D , A S ) (3)

= ( 0.0591 6 / z A ) ( log K D , A − log K D , A S ) (3a)

at T = 298 K, where the symbols z_A and K D , A S denote the formal charge of A⁻ with its sign and a standard distribution constant at dep = 0 V for an A^- transfer across the interface between the water and org bulk phases, respectively. The value of K_D,A called a conditional distribution constant of A^- into the org phase changed in depending on species of M(II), L, and diluent molecule [1] - [6] [8] .

Estimated dep values at z_I = -1 were −0.01₀ V for the NB system, −0.06₄ for DCE, and 0.02₄ and 0.02₁ for DCM. Here, the following log K D , I S values at 298 K were used for these calculations: −4.0 [15] for NB, −4.56 [15] for DCE, and −3.790 [16] for DCM. The dep presences were clarified at least for these diluents systems, as similar to the results [1] - [6] [8] reported previously.

Referring to the previous papers [1] - [6] [8] [17] , the K_1,org and K_2,org values were obtained from

K 1 , org = [ CdLA + ] org / [ CdL 2 + ] org [ A − ] org = K ex ± / K ex2 ± ≈ K ex ± / ( K Cd / CdL K D , A 2 ) (4)

and

K 2 , org = [ CdLA 2 ] org / [ CdLA + ] org [ A − ] org = K ex / K ex ± (5)

for a given ionic strength (I_org) in the org phase. Here, the equilibrium constant K_Cd/CdL has been assumed to be equal to D/[L]_org [3] [5] [6] [17] . The thus-calculated values are listed in Table 2, together with the K_Cd/CdL and their corresponding I_org values.

Figure 3 shows the K_1,org and K_2,orgvalues with ten kinds of the diluents described in Table 2. The x-axis indicates the decrease of the diluent’s polarities from No. 1 (NB) to 10 (mX). Except for the DCE and mX systems, there was the relation [3] [5] [6] [17] of K_1,org ³ K_2,org. This trend seems to be similar to that [18] [19] of the complex formation for CdA₂ in water with A^- = Cl^-, Br^-, and I^-. For the two systems, some structural changes around Cd(II) in the second-step reaction, CdLI org + + I org − ⇌ I-CdLI org at L = 18C6, could be suggested [3] [5] [6] .

a.^.See the footnote a in Table 1; b. Average values calculated from experimental D/[L]_org ones; c. Calculated from Equation (4); d. Calculated from Equation (5); e. The values were employed for the plots of Figure 3.

The extraction constant K_ex2± {see Equation (4)} and the two conditional distribution constants, K_D,CdLI and K_D,CdL, were calculated from the following thermodynamic relations [1] [3] [6] .

K ex2 ± = [ CdL 2 + ] org [ I − ] org 2 / P ≈ K Cd / CdL K D , I 2 (6)

K D , CdLA = [ CdLI + ] org / [ CdLI + ] ≈ K ex , ip / ( K 1 K 2 , org K D , I ) (7)

and

K D , CdL = [ CdL 2 + ] org / [ CdL 2 + ] = K ex , ip / ( β 2 , org K D , I 2 ) (8)

with K₁ = [CdLI⁺]/[CdL²⁺][I^-], called the ion-pair formation constant for water, and β_2,org = K_1,orgK_2,org, which is an overall ion-pair formation constant for the org phase. As described in Equation (3a), K_D,CdLI and K_D,CdL are expressed as functions of Δϕ_eq and called the conditional distribution constants: log K D , CdLI = log K D , CdLI S + ( Δ ϕ eq / 0.0 591 6 ) {=(standard distribution constant at Δϕ_eq = 0 V) + (Δϕ_eq term)} at z_CdLI = +1 and log K D , CdL = log K D , CdL S + ( 2 Δ ϕ eq / 0.0 591 6 ) at z_CdL = +2 and 298 K.

Assuming that the relation of K 1 0 = K CdI 0 K CdLBr 0 / K CdBr 0 (=308 × 10^−0.25/118 = 10^0.17 mol^-1∙dm³ [1] [6] [10] [19] at I ® 0 & 298 K) holds, the K₁ values in Equation (7) were estimated approximately from the experimental I (Table 1) and K 1 0 (≈y_II+K₁) values. Here, the K CdA 0 and K CdLBr 0 refer to an ion-pair (or a complex) formation constant [19] of Cd²⁺ with A^- (=I^- & Br^-) and that [10] of Cd18C6²⁺ with Br^- in water at I ® 0, respectively. The activity coefficient (y_II+) of CdL²⁺ in water was evaluated from the Davies equation [20] . These calculated values, with the K_D,18C6 values available from references [13] [14] were listed in Table 3. The logK_ex2± values were energetically (−ΔG˚/2.303RT = logK) the

a. See the footnote a in Table 1; b. Calculated from Equation (6); c. Calculated from Equation (7); d. Calculated from Equation (8); e. Refs. [13] & [14] ; f. The values were employed for the plots of Figure 4.

smallest in the three extraction constants determined: logK_ex2± < logK_ex± < logK_ex (see Table 2 for K_ex & K_ex±). Equations (7) and (8) are related with pseudo-RST plots described in the Section 2.8.

As shown in Figure 4, the K_D,j values were in the order j = I^- (<18C6) < Cd18C6²⁺ < Cd(18C6)I⁺. This order is basically different from that [3] for the CdPic₂-B18C6 extraction system: j = Pic^- { 2 ⁰} < Cd(B18C6)Pic ⁺ < CdB18C6 ²⁺. Equations (7) and (8) predict that a difference between K _D,CdLA and K _D,CdL is proportional to that between K 1 − 1 and (K _1,orgK _D,A) ^{- 1}. The relation of K 1 − 1 > ( K 1 , org K D , I ) − 1 can cause the K _D,j order of j = Cd18C6 ²⁺ < Cd(18C6)I ⁺, while that of K 1 − 1 < ( K 1 , org K D , Pic ) − 1 can do that of CdB18C6 ²⁺ > Cd(B18C6)Pic ⁺. These experimental results of the CdI ₂-18C6 extraction systems were in the -logK ₁ range of -0.0 ₃ to 0.0 ₃ and in the -log(K _1,orgK _D,I) one of −2.6 ₃ to −2.0 ₄. On the other hand, the values of the CdPic ₂-B18C6 systems were evaluated to be in the −logK ₁ range of −4.60 to −4.39 (see Appendix for the calculation of logK ₁ averaged in the Bz system) and in the −log(K _1,orgK _D,Pic) one of −2.7 to −0.1 [3] . These experimental orders are in good agreement with the orders predicted above.

We have defined distribution ratios D₀, D₊, and D₂₊ as described below [3] [5] [6] [17] . Using the experimental data sets of [L]_org and [I^-], these values were calculated from

D 0 = [ CdLI 2 ] org / [ Cd 2 + ] = K ex [ L ] org [ I − ] 2 (9)

D + = [ CdLI + ] org / [ Cd 2 + ] = K ex ± [ L ] org [ I − ] / K D , I (10)

and

D 2 + = [ CdL 2 + ] org / [ Cd 2 + ] ≈ K Cd / CdL [ L ] org (11)

at each experimental point. Here, the K_ex, K_ex±, K_D,I, and K_Cd/CdL values at L = 18C6 in Table 1 and Table 2 were used for the calculations. From the three equations, we can calculate relative concentrations (or molar fractions), such as f₀/% = 100D₀/D_t and f₊ = 100D₊/D_t with D_t = D₀ + D₊ + D₂₊ [5] . The mean values of f₀, f₊, and f₂₊were listed in Table A1 of the Appendix, where the symbols f₀, f₊, and f₂₊ (=100D₂₊/D_t) denote the relative concentrations of CdLI₂, CdLI⁺, and CdL²⁺, respectively.

As can be seen from Figure 5 and Table A1, the f₊ values were the largest in the extraction into the many diluents, except for the values of the DCE and mX systems. Especially, the f₊ values exceeded 50% in the NB, oDCBz, DCM, BBz, CF, and Bz systems. These behaviors in Figure 5 can be explained as follows. Considering a homogeneous reaction defined as K_1,org/K_2,org. ( = [ CdLI + ] org 2 / [ CdL 2 + ] org [ CdLI 2 ] org ) , we can evaluate the formation of CdLI⁺ or CdLI₂ which is dominant about the reaction of CdL org 2 + + CdLI 2 , org ⇌ 2CdLI org + .

From the K_1,org and K_2,org values in Table 2, the log (K_1,org/K_2,org) values were calculated to be negative (namely K_1,org < K_2,org) for the org = DCE and mX systems, while their values to be positive (namely K_1,org > K_2,org) for the other systems. Therefore, we can easily see that the formation of CdLI₂ is dominant, CdL org 2 + + CdLI 2 , org , in the DCE and mX phases, while that of CdLI⁺ is dominant, 2CdLI⁺_org, in the other diluents. The diluent dependence of the f values in Figure 5 reflects mainly the difference between K_1,org and K_2,org (see the Section 2.4). Considering these phenomena from ion-pair-formation point of view [3] [6] , the systems dominant for the distribution of CdLI⁺ can be a major case in the present extraction systems.

According to our previous paper [10] , the complex ions Cd18C6²⁺ and CdB18C6²⁺ in water have been classified as the hard acids in their reactions with A⁻ = Cl⁻, Br⁻, (I⁻,) or Pic⁻. As standards of the HSAB classification, we assumed that 1) trends in the hardness and softness of the anions A⁻ in the org phases are the same as those [9] [10] in water. That is, I⁻ and Br⁻ are soft bases [9] , while Cl⁻ and Pic⁻ are hard bases [9] [10] . 2) The reactions with the halogen ions are primarily employed for the classification. Only when one of the reactions with the three halogen ions lack, the reaction of Pic⁻ was used for it. In the classification, 3) we neglected effects of the I_org values on K_1,org, K_2,org, and β_2,org, because the I_org values were in the lower ranges [1] [2] [3] [6] : see Table 2 as an example.

For example, the K_1,NB and β_2,NB (=K_1,NBK_2,NB) values were in the order Pic⁻ < I⁻ < Cl⁻ (see Table A2 in Appendix). These orders suggested that the Cd18C6²⁺ is a borderline acid in the NB phase, because the order between the hard and soft bases is random. The K_1,oDCBz values were in the order Br⁻ < I⁻ < Cl⁻, while the β_2,oDCBz ones were Cl⁻ < I⁻ < Br⁻ (see Table A2). The former order suggested that Cd18C6²⁺ in the oDCBz phase is a hard acid. On the other hand, the latter one indicated that Cd18C6²⁺ is a soft acid. This discrepancy in the classification between K_1,org and β_2,org can reflect the soft acidity of the intermediate ion-pair complex ion, Cd(18C6)A⁺; namely the effect of K_2,org. A similar trend was observed in the Bz systems: they were classified as the hard acid from K_1,Bz (Br⁻ < I⁻ < Cl⁻) and as the borderline acid from β_2,Bz (I⁻ < Cl⁻ < Br⁻). The Cd18C6²⁺ ions in the other diluents were classified as the soft acids for the DCE, DCM, CBz, BBz, and CF systems, the borderline acid for CBu, and the hard acid for mX and TE: see Table A2 in Appendix. In these systems, the HSAB classifications by K_1,org were in accordance with those by β_2,org.

On the basis of the above results, it could be considered that Cd18C6²⁺ in water almost changes from the hard acid to the soft or borderline acids in the extraction into the org phases. This indicated that the hardness and softness of Cd18C6²⁺might be changed with species of the diluents, according to the criteria of the A⁻ basicity.

The following measure can be also considered for the HSAB classification of Cd(18C6)A⁺ in the each phase, because there were no data for the reactions, such as CdLCl org + + Br org − → Br-CdLCl org and CdLCl org + + I org − → I-CdLCl org . The ratio of K_2,org(A)/K_2,org(Cl) = [CdLA₂]_org[CdLCl⁺]_org[Cl⁻]_org/([CdLCl₂]_org[CdLA⁺]_org[A⁻]_org) at L = 18C6 was proposed and simply expressed as K_2,org(A/Cl). Fixing the ([CdLCl⁺]_org[Cl⁻]_org/[CdLA⁺]_org[A⁻]_org) term or both [CdLCl⁺]_org[Cl⁻]_org and [CdLA⁺]_org[A⁻]_org terms at unity, the ratio virtually can become the [CdLA₂]_org/[CdLCl₂]_org ratio. Hence, we considered that if the logK_2,org(A/Cl) value is positive, the formation of CdLA₂ in the org phase becomes dominant and if it is negative, that of CdLCl₂ does dominant. The former case means the softer complex ion, while the latter one does the harder ion. So, this K_2,org(A/Cl) value gives us a criteria for evaluating the HSAB acidity of Cd(18C6)A⁺ in the org phases (water). Consequently, the order of K_2,org among A⁻ yields the magnitude in the formation of CdLA₂ in the org phase under the assumption for the above ratio.

As an example, the logK_2,oDCBz(A/Cl) values were in the order A⁻ = Cl⁻ = 1.0 < I⁻ < Br⁻ (see Table A2), suggesting that Cd(18C6)A⁺ in the oDCBz phase is the soft acid. Similarly, the Cd(18C6)A⁺ in the other diluents were classified as the soft acid for the org = NB, DCE, DCM, CBz, BBz, CF, TE, and mX systems, the borderline acid for CBu {logK_2,CBu(A/Cl): 1.0 = Cl < Br < Pic} and Bz (I < 1.0 = Cl < Br), and not the hard acid, except for water {logK₂(A/Cl): Br < 1.0 = Cl < Pic}. From the above, all Cd(18C6)A⁺ change from the hard acids in water to the soft and borderline ones in the org phases.

Thus, the changes of the diluents (or the org phases) are reflected into the HSAB acidities of these complex ions in the extraction of Cd18C6²⁺ and Cd(18C6)A⁺. In other words, this means that the HSAB acidity of the complex ion or the ion-pair cation varies with the kinds of the diluents, if the HSAB basicity of the A⁻ can be considered to be the standard. It can be seen that it is easier for the monovalent CdLA⁺ to become the soft acid than for the divalent CdL²⁺ to do it with the extraction into the diluents. This can be supported by the fact that Cd(18C6)A⁺ in the 9 diluents among the 11 ones is classified as the soft acids, compared with Cd18C6²⁺ in the 4 diluents done as the hard acids (Table A2). We can see it particularly from this comparison that the six diluents, DCE, oDCBz, DCM, CBz, BBz, and CF, are the higher effect than the others in softening the acidity of the complex ions. It is interesting that these diluents contain the Cl- or Br-group(s) in their molecules, though CBu, Cl-CH₂CH₂CH₂CH₃, does not clearly show its effect.

We obtained the regression line from the RST plot [1] [2] [3] [6] [13] of logK_ex,ip vs. logK_D,18C6 for the present Cd(II) extraction systems, except for the points of the NB and CF ones [3] [13] : logK_ex,ip = (0.7₅ ± 0.2₁)logK_D,18C6 + (6.8₀ ± 0.2₅) at R = 0.800. Also, using V_18C6 = 214 ± 47 cm³ mol^-1 [13] reported by Takeda, the V_CdLI2 value was calculated to be 160 ± 57 from the slope of the RST plot. Adding the data of previous papers, the V_j values became in order V_CdLI2 ≤ V_CdLPic2 (=171 cm³ mol^-1 [2] ) ≤ V_L [13] ≤ V_CdLBr2 (=248 [1] ) < V_CdLCl2 (=398 [6] ) at L = 18C6. At least, there is a tendency in the order of V_CdLA2 among A = Cl, Br, and I.

In general, the RST plot for the M(II) extraction system is expressed as logK_ex,ip = (V_MLA2/V_L)logK_D,L + C + log β₂ in the form of a linear equation, where the constant C shows solute-solvent (or non-electrostatic) interactions term with cohesive energy densities [1] [2] [3] [6] [13] . From the thermodynamic relation of Equation (8), we can derive the following equation:

log K D , CdL = ( V MLA2 / V L ) log K D , L + C + log β 2 − log ( β 2 , org K D , A 2 ) = ( V MLA2 / V L ) log K D , L + C ′ (12)

with C ′ = C + log ( β 2 / β 2 , org K D , A 2 ) . Hence, one can see that the C’ term includes the β₂/β_2,org term corresponding to the ion-ion interactions in addition to the solute-solvent interactions term C. The plot of logK_D,CdL vs. logK_D,L for the CdI₂-18C6 extraction systems is shown in Figure 6. Its regression line was logK_D,CdL = (0.5₆ ± 0.1₅)logK_D,L + (2.4₇ ± 0.1₇) at R = 0.774, where the data of the NB and CF systems were added in the estimation, because of the plot for the ionic species. This slope was somewhat smaller than that (»0.8) of the RST plot. If this difference reflects a difference in V_j between j = CdLI₂ and CdL²⁺, then the ratio between the slopes can directly express that between V_j. So, the ratio of slope(CdLI₂)/slope(CdL²⁺) (=1.3) is equivalent to V_CdLI2/V_CdL at a fixed V_L. Therefore, the V_CdL value was estimated to be 120 ± 64 cm³∙mol^-1 from the V_CdLI2 one (=160). This value was smallest in the V_j with j = CdLCl₂, CdLBr₂, CdLI₂, and CdLPic₂. This is in good agreement with the image that the size of CdL²⁺ is smaller than those of CdLA₂.

The same trend as above can be seen in a plot of logK_D,CdLI vs. logK_D,L (see Table 3 for their data): the V_CdLI value was 155 ± 46 cm³∙mol^-1 at L = 18C6. Similarly, V_CdLBr/cm³∙mol^-1 was estimated to be 225 ± 55 from the slope (=1.0₅ ± 0.1₁ [1] ) of the logK_D,CdLBr vs. logK_D,L plot reported previously. These values satisfy the following relations: V_CdLI2 ≥ V_CdLI ≥ V_CdL and V_CdLBr2 ≥ V_CdLBr ≥ V_CdL.

From the V_j data, we can evaluate apparent sizes of Cd(18C6)A₂ or Cd18C6²⁺. Assuming V j = 4π R j 3 / 3 , namely that shapes of the ion pairs and complex ion are close to spheres, we can easily calculate apparent radii (R_j) from the V_j. Their

R_j values were 5.4 Å for j = CdLCl₂, 4.6 for CdLBr₂, 4.0 for CdLI₂, 4.1 for CdLPic₂, and 3.6 for CdL²⁺ at L = 18C6. As similar to the results of V_CdL (see the Section 2.8), the R_CdL value was smallest of the R_j ones.

The R_Cd18C6 value (=3.6 Å) was larger than the following data of bond lengths [21] ; the DFT study of [Cd(18C6)(OH₂)₂]²⁺, in which 18C6 acts as a tridentate ligand, has reported that the Cd-O and Cd-OH₂ bond lengths were 2.40 Å and 2.34, respectively. This fact suggested that the R_Cd18C6 value expresses the hydration structure around Cd18C6²⁺. Regarding this, it is demonstrated from the Karl-Fischer titration that Ca18C6²⁺ is present in the NB phase as Ca18C6²⁺∙4.7H₂O [22] , where the ion size (=0.95 Å) of the six coordinated Cd²⁺ is close to that (=1.00) of the Ca²⁺ [23] . Besides, the suggestion is supported by the facts that Cd-A bond lengths (d_Cd-A, see below for its values) in CdLA₂ crystals [24] [25] with L = 18C6 are in the order d_Cd-Cl < d_Cd-Br < d_Cd-I, while the R_j values are in that j = CdLCl₂ > CdLBr₂ > CdLI₂. Additionally, it was shown that d_Cd-Pic is apparently close to d_Cd-I.

Also, the bond lengths d_Cd-Cl and d_Cd-O in a Cd(18C6)Cl₂ crystal have been reported to be 2.364 Å and 2.752, respectively [24] . The same trend is also observed in Cd(18C6)Br₂ and Cd(18C6)I₂ crystals [25] : d_Cd-Br = 2.506 Å and d_Cd-O = 2.752 for CdLBr₂ and d_Cd-I = 2.692 and d_Cd-O = 2.768 for CdLI₂. Interestingly, the three d_Cd-O values have been almost constant among the crystals. These results suggested that CdLCl₂, CdLBr₂, and CdLI₂ with L = 18C6 are close to solvent-separated or -shared ion pairs, such as CdL(OH₂)_xA₂, in phases. If this suggestion is correct, then both the R_j and V_j values can strongly reflect the structural properties of the complexes “in the water phase”. On the basis of the above results, the V_j values obtained in the section 2.8 and those reported before seem to be self-consistent.

Commercial CdI₂ {guaranteed pure reagent (GR): >99.0%, Kanto Chemical, Japan} and Cd(NO₃)₂×4H₂O (GR: >98.0%, Kanto Chemical) were used: their purities were determined by the chelatometric titration with di-Na(I) salt of EDTA [1] [6] . Here, this nitrate was employed for the preparation of calibration curves in the AAS measurement. The crown ether, 18C6 (GR: 98.0%), was purchased from Tokyo Chemical Industry (Japan) and its solutions were prepared by weighed amounts. The ten commercial diluents were of GR grades: NB (>99.5%), oDCBz (>99.0%), DCE (>99.5%), DCM (>99.5%), BBz (>98.0%), CF (>99.0%), Bz (> 99.5%) and mX (>98.0%) were purchased from Kanto Chemical and CBz (>99%) and TE (>99.5%) done from Wako Pure Chemical Industries, Japan [1] [2] [3] [4] [6] . These diluents were washed three times with pure water and stored in the state saturated with water [1] [2] [4] [6] . Other chemicals were of GR grades. A tap water was distilled once and then deionized by passing through Autopure System (Yamato/Millipore, type WT 101 UV).

Basic operations and equipment were the same as those described before [1] - [6] . That is, the operations were constructed of original Cd(II) extraction, its back one, and Cd(II) analyses with the AAS measurements at 228.8 nm. The calibration curves of Cd(NO₃)₂ in the aqueous 0.1 mol∙dm⁻³ HNO₃ solutions were employed for the AAS determination of Cd(II). Here, differences in the calibration curve between pure water and the aqueous HNO₃ solution were experimentally negligible. So, the back extraction was operated with pure water instead of 0.1 mol∙dm⁻³ HNO₃ [1] - [6] as the back extraction phase, because the Cd(II) amounts in the latter acidic solutions analyzed by the AAS deviated largely.

In the extraction experiments, the [CdI₂]_t values were in the range of 0.0029 - 0.0081 mol∙dm⁻³ and total concentrations of 18C6 in the water phases were in the ranges of (0.5₆ - 2.1) ´ 10⁻⁵ mol∙dm⁻³ for the NB system, (0.1₁ - 5.5) ´ 10⁻⁴ for DCE, (0.2₅ - 2.5) ´ 10⁻⁵ for oDCBz, (0.01₃ - 1.1) ´ 10⁻⁴ and (0.2₅ - 4.1) ´ 10⁻⁵ for DCM, (0.2₅ - 4.1) ´ 10⁻⁵ for CBz, (0.8₂ - 2.5) ´ 10⁻⁵ for BBz, (0.2₅ - 2.5) ´ 10⁻⁵ for CF and Bz, (0.2₅ - 7.4) ´ 10⁻⁵ for TE, and (1.4 - 7.4) ´ 10⁻⁵ for mX. The water phases containing these CdI₂ and 18C6 were mixed with equal volumes of the diluents or org phases.

The following extraction model [4] was employed for the analysis of the present extraction system with L = 18C6: 1) Cd²⁺ + L ⇌ CdL²⁺ [12] and 2) Cd²⁺ + I⁻ ⇌ CdI⁺ [19] in the water phase; 3) I − ⇌ I org − , 4) CdLI + ⇌ CdLI org + , 5) CdL 2 + ⇌ CdL org 2 + , and 6) L ⇌ L_org [13] [14] between the water and org phases; 7) CdL org 2 + + I org − ⇌ CdLI org + and 8) CdLI org + + I org − ⇌ CdLI 2 , org in the org phase. Except for the processes 3)-5), 7), and 8), the equilibrium constants of the above processes at 298 K were available from the references [12] [13] [14] [19] .

Data analyses of the extraction equilibria based on this model were essentially the same as those reported before [1] [2] [4] . The parameter K ex mix has been defined as

K ex mix = [ Cd ( II ) ] org / P = ( [ CdLI 2 ] org + [ CdLI + ] org + [ CdL 2 + ] org + [ CdI + ] org + [ CdI 2 ] org + ⋯ ) / P (13)

Assuming that

[ CdLI 2 ] org + [ CdLI + ] org ≫ [ CdL 2 + ] org + [ CdI + ] org + [ CdI 2 ] org + ⋯

this equation can be rearranged into

K ex mix ≈ K ex + K D , I / ( [ Cd 2 + ] [ L ] org [ I − ] ) (2a)

in the case of [CdLI⁺]_org » [I⁻]_org which was approximately derived from the charge balance equation for the org phase [1] - [6] . At least, the conditions of [ CdLI 2 ] org + [ CdLI + ] org + [ CdL 2 + ] org ≫ [ CdI + ] org + [ CdI 2 ] org + ⋯ were checked by blank experiments of the CdI₂ extraction without L = 18C6. On the other hand, in the case of [CdLI⁺]_org/P » K_ex±/[I⁻]_org, we can immediately obtain

K ex mix ≈ K ex + ( [ CdLI + ] org [ I − ] org / P 2 ) 1 / 2 = K ex + ( K ex ± / P ) 1 / 2 (2b)

The parameter K ex mix was calculated from the experimental [Cd(II)]_org, [Cd²⁺], [18C6]_org, and [I⁻], where the latter three concentrations were determined with a successive approximation procedure, using the equilibrium constants of the processes 1), 2), and 6) [2] [4] . When a negative value for K_ex had been obtained from the analysis with Equation (2b), its analysis was performed again by fixing the K_ex value to that determined by the analysis with Equation (2a) [1] - [6] (see the footnotes c & e in Table 1).