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 AJAC  Vol.9 No.11 , November 2018
CdI2 Extraction with 18-Crown-6 Ether into Various Diluents: Classification of Extracted Cd(II) Complex Ions Based on the HSAB Principle
Abstract: CdI2 in water was extracted with 18-crown-6 ether (L) into 10 diluents at 298 K. The following equilibrium constants were determined or evaluated: some extraction constants (Kex/mol-3·dm9 & Kex,ip/mol-2·dm6 for CdLI2, Kex±/mol-2·dm6 for CdLI+ with I-, & Kex2±/mol-1·dm3 for CdL2+ with 2I-), conditional distribution constants (KD,I for I-, KD,CdLI for CdLI+, & KD,CdL for CdL2+) between the two phases, and an ion-pair formation constant (K1,org/mol-1·dm3) for CdLI+ and that (K2,org/mol-1·dm3) for CdLI2 in the organic (org) phases. Using the K1,org and K2,org values, acidities of the complex ions, CdL2+ and CdLA+ (A- = I-, Br-, & Cl-), in the 11 diluents were classified by applying the HSAB rule. Especially, the CdLA+ ions were classified as the soft acids in 9 diluents. Also, molar volumes (Vj/cm3·mol-1) of j = CdLI2 and CdL2+ were determined with the regular-solution-theory plot of logKex,ip vs. logKD,L and its pseudo-plot of logKD,CdL, respectively. Here, KD,L denotes the distribution constant of L between the two phases. So, sizes among CdLA2 and CdL2+ were compared by using the Vj values. Additionally, some distribution equilibrium potentials (dep/V) between the water and org bulk phases were topically calculated from an equation of KD,I with KSD,I, where the symbol KSD,I shows a standard distribution constant of I- at dep = 0 V for a given diluent.

1. Introduction

It is well known that crown ethers (L) extract Cd(II) and Pb(II) salts, such as metal picrates (MPic2) [1] [2] [3] [4] [5], the former chloride [6], and bromides [1] [6], into various diluents. Similar extraction behaviors into benzene (Bz) and nitrobenzene (NB) have been reported for Ca(II), Sr(II), and Ba(II) picrates with L [7] [8] . In these studies, the distribution equilibrium potentials (dep or Δϕeq) for monovalent anions (A) between the water and diluent bulk phases and the ion-pair formation for ML2+ and MLA+ in the diluent phases saturated with water have been examined and clarified, respectively [1] - [6] [8] . For the latter [1] [2] [4] [6] [8], the reactivities of CdL2+ and CdLA+ with A = Cl, Br, and picrate ion Pic in various organic (org) phases have been quantitatively discussed at L = 18-crown-6 ether (18C6). The complex ions composed of a soft Cd2+ and hard L, Cd18C62+ and CdB18C62+, have been classified in terms of the HSAB rule [9] as the hard acids in water [10], where B18C6 refers to benzo-18C6. This classification would make the studies on reactivity of the Cd(II) complexes and properties of the diluent molecules in the extraction interesting. However, there were few comprehensive studies for the M(II) extraction systems with L and various diluents [11] .

In the present paper, by doing extraction experiments of CdI2 with 18C6 into ten diluents, we determined extraction constants, Kex and Kex±, and their related equilibrium constants, KD,I and KCd/CdL, [4] [5] at 298 K. Here, Kex, Kex±, KD,I, and KCd/CdL were defined as [CdLI2]org/P, [CdLI+]org[I]org/P with P = [Cd2+][L]org[I]2, [I]org/[I], and [CdL2+]org/[Cd2+][L]org [1] - [6], respectively. From these values and the thermodynamic relations, K1,org and K2,org values were evaluated: K 1 , org = K ex ± / ( K Cd / CdL K D , I 2 ) and K2,org = Kex/Kex± [4] [5] (see the Section 2.4). Using these evaluated K1,org and K2,org values, reaction properties of CdLA+ and CdL2+ with mainly A = I, Br, and Cl in the org or diluent phases were also classified based on the HSAB principle [9] [10] [11] . Moreover, molar volumes (V/cm3∙mol-1) of the ion-pair complex CdLI2 and complex ion CdL2+ were determined at 298 K with the plots based on the regular solution theory (RST) [1] [2] [3] [4] [6] and then their comparable sizes were estimated from these V. On the basis of these data, the HSAB acidic and structural properties of the Cd(II) complexes with 18C6 were discussed independently.

2. Results and Discussion

2.1. Composition Determination of Cd(II) Species Extracted into Various Diluents

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 Kex [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.

2.2. Determination of KD,I, Kex±, and Kex by Using the Parameter K e x m i x

For the determination of KD,I, Kex±, and Kex, 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 KD,I and Kex 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 Kex± and Kex ones from that of log K ex mix vs. −logP1/2 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 Kex 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 Kex = KCdLKex,ip/KD,L [1] - [7], the Kex,ip values were evaluated at the same time (see Table 1). Here, the symbols KCdL, Kex,ip, and KD,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

Figure 1. Plots of log K ex mix vs. −log([Cd2+][L]org[I]) based on Equation (2a) at L = 18C6. CdI2 was extracted with L into NB (square), DCE (circle), BBz (triangle), and CF (diamond).

Table 1. Logarithmic values of KD,I, Kex±, Kex, and Kex,ip for the CdI2 extraction with 18C6 into various diluents at 298 K.

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 logKex,ip = logKex − logKD,18C6- logKCd18C6 = logKex - logKD,18C6 + 0.05. See ref. [12] ; e. Not determined with Equation (2b).

Figure 2. Plots of log K ex mix vs. −logP1/2 based on Equation (2b). CdI2 was extracted with 18C6 into NB (square), DCE (circle), BBz (triangle), and CF (diamond).

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 Kex,ip and KD,L values are employed for the RST plot [1] - [6] [13] .

2.3. Estimation of Dep for Some Diluent Systems

The relation between dep or Δϕeq and KD,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 zA 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 KD,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 zI = -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.

2.4. Determination of K1,org and K2,org

Referring to the previous papers [1] - [6] [8] [17], the K1,org and K2,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 (Iorg) in the org phase. Here, the equilibrium constant KCd/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 KCd/CdL and their corresponding Iorg values.

Figure 3 shows the K1,org and K2,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 K1,org ³ K2,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] .

Figure 3. LogK1,org (triangle) and logK2,org (circle) values with ten kinds of diluents described in Table 2.

Table 2. Logarithmic values of KCd/CdL, K1,org, and K2,org for the CdI2 extraction with L = 18C6 into various diluents at 298 K.

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.

2.5. Determination of Kex2±, KD,CdLI, and KD,CdL and Their Characterization

The extraction constant Kex2± {see Equation (4)} and the two conditional distribution constants, KD,CdLI and KD,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 β2,org = K1,orgK2,org, which is an overall ion-pair formation constant for the org phase. As described in Equation (3a), KD,CdLI and KD,CdL are expressed as functions of Δϕeq 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 Δϕeq = 0 V) + (Δϕeq term)} at zCdLI = +1 and log K D , CdL = log K D , CdL S + ( 2 Δ ϕ eq / 0.0 591 6 ) at zCdL = +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 = 100.17 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 (≈yII+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 (yII+) of CdL2+ in water was evaluated from the Davies equation [20] . These calculated values, with the KD,18C6 values available from references [13] [14] were listed in Table 3. The logKex2± values were energetically (−ΔG˚/2.303RT = logK) the

Table 3. Logarithmic values of Kex2±, KD,CdLI, KD,CdL, and KD,L for the CdI2 extraction with L = 18C6 into various diluents at 298 K.

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: logKex2± < logKex± < logKex (see Table 2 for Kex & Kex±). Equations (7) and (8) are related with pseudo-RST plots described in the Section 2.8.

As shown in Figure 4, the KD,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.

2.6. For Relative Concentrations of CdLI2, CdLI+, and CdL2+ Extracted into the Diluents

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)

Figure 4. Variation of logKD,j with kinds of diluents. Here, j = I (full circle), L (full diamond), CdL2+ (square), and CdLI+ (triangle) at L = 18C6. For the DCM system, the logKD,I value of −4.2 in Table 1 was used for this plot.

and

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

at each experimental point. Here, the Kex, Kex±, KD,I, and KCd/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/Dt and f+ = 100D+/Dt with Dt = 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+/Dt) 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 K1,org/K2,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 K1,org and K2,org values in Table 2, the log (K1,org/K2,org) values were calculated to be negative (namely K1,org < K2,org) for the org = DCE and mX systems, while their values to be positive (namely K1,org > K2,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 K1,org and K2,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.

Figure 5. Variation of the relative concentrations of CdLI2 (circle), CdLI+ (triangle), and CdL2+ (square) with kinds of diluents at L = 18C6. Their concentrations are expressed by f0, f+, and f2+, respectively.

2.7. Classification of the Acidity of CdL2+ and CdLA+ in the Org Phases Based on the HSAB Rule

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 Iorg values on K1,org, K2,org, and β2,org, because the Iorg values were in the lower ranges [1] [2] [3] [6] : see Table 2 as an example.

For example, the K1,NB and β2,NB (=K1,NBK2,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 K1,oDCBz values were in the order Br < I < Cl, while the β2,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 K1,org and β2,org can reflect the soft acidity of the intermediate ion-pair complex ion, Cd(18C6)A+; namely the effect of K2,org. A similar trend was observed in the Bz systems: they were classified as the hard acid from K1,Bz (Br < I < Cl) and as the borderline acid from β2,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 K1,org were in accordance with those by β2,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 K2,org(A)/K2,org(Cl) = [CdLA2]org[CdLCl+]org[Cl]org/([CdLCl2]org[CdLA+]org[A]org) at L = 18C6 was proposed and simply expressed as K2,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 logK2,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 K2,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 K2,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 logK2,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 {logK2,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.

2.8. Comparisons of Molar Volumes among the Ion-Pair Complexes

We obtained the regression line from the RST plot [1] [2] [3] [6] [13] of logKex,ip vs. logKD,18C6 for the present Cd(II) extraction systems, except for the points of the NB and CF ones [3] [13] : logKex,ip = (0.75 ± 0.21)logKD,18C6 + (6.80 ± 0.25) at R = 0.800. Also, using V18C6 = 214 ± 47 cm3 mol-1 [13] reported by Takeda, the VCdLI2 value was calculated to be 160 ± 57 from the slope of the RST plot. Adding the data of previous papers, the Vj values became in order VCdLI2 ≤ VCdLPic2 (=171 cm3 mol-1 [2] ) ≤ VL [13] ≤ VCdLBr2 (=248 [1] ) < VCdLCl2 (=398 [6] ) at L = 18C6. At least, there is a tendency in the order of VCdLA2 among A = Cl, Br, and I.

In general, the RST plot for the M(II) extraction system is expressed as logKex,ip = (VMLA2/VL)logKD,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 β22,org term corresponding to the ion-ion interactions in addition to the solute-solvent interactions term C. The plot of logKD,CdL vs. logKD,L for the CdI2-18C6 extraction systems is shown in Figure 6. Its regression line was logKD,CdL = (0.56 ± 0.15)logKD,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 Vj between j = CdLI2 and CdL2+, then the ratio between the slopes can directly express that between Vj. So, the ratio of slope(CdLI2)/slope(CdL2+) (=1.3) is equivalent to VCdLI2/VCdL at a fixed VL. Therefore, the VCdL value was estimated to be 120 ± 64 cm3∙mol-1 from the VCdLI2 one (=160). This value was smallest in the Vj 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 logKD,CdLI vs. logKD,L (see Table 3 for their data): the VCdLI value was 155 ± 46 cm3∙mol-1 at L = 18C6. Similarly, VCdLBr/cm3∙mol-1 was estimated to be 225 ± 55 from the slope (=1.05 ± 0.11 [1] ) of the logKD,CdLBr vs. logKD,L plot reported previously. These values satisfy the following relations: VCdLI2 ≥ VCdLI ≥ VCdL and VCdLBr2 ≥ VCdLBr ≥ VCdL.

2.9. Estimation of Apparent Sizes for the Cd(II) Complexes

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

Figure 6. Pseudo-RST plot of logKD,CdL vs. logKD,L at L = 18C6.

Rj 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 VCdL (see the Section 2.8), the RCdL value was smallest of the Rj ones.

The RCd18C6 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 RCd18C6 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 (dCd-A, see below for its values) in CdLA2 crystals [24] [25] with L = 18C6 are in the order dCd-Cl < dCd-Br < dCd-I, while the Rj values are in that j = CdLCl2 > CdLBr2 > CdLI2. Additionally, it was shown that dCd-Pic is apparently close to dCd-I.

Also, the bond lengths dCd-Cl and dCd-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] : dCd-Br = 2.506 Å and dCd-O = 2.752 for CdLBr2 and dCd-I = 2.692 and dCd-O = 2.768 for CdLI2. Interestingly, the three dCd-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 Rj and Vj values can strongly reflect the structural properties of the complexes “in the water phase”. On the basis of the above results, the Vj values obtained in the section 2.8 and those reported before seem to be self-consistent.

3. Experimental

3.1. Chemicals

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).

3.2. Extraction Procedure

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.

3.3. Extraction Equilibrium Model and Its Data Handlings

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 ⇌ Lorg [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 » Kex±/[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 Kex had been obtained from the analysis with Equation (2b), its analysis was performed again by fixing the Kex value to that determined by the analysis with Equation (2a) [1] - [6] (see the footnotes c & e in Table 1).

4. Conclusions

The ion-pair formation in the 11 diluents saturated with water was classified in terms of the HSAB principle, although the hardness and softness of the simple A- in the diluents were assumed to be the same as those in water. This classification mainly showed us the two results. 1) CdL2+ and CdLA+ with L = 18C6 and A- = Cl-, Br-, and I- change from the hard acids in water to almost the soft or borderline acids in the extraction into the org phases at least. 2) The charge effects on CdLA+ and CdL2+ in the org phases are remarkable. Namely, CdLA+ softens more its acidity than CdL2+ does in the extraction. Especially, DCE, oDCBz, DCM, CBz, BBz, and CF have the higher ability to soften the HSAB acidity of the complex ions.

The presence of dep was also observed in the CdI2-18C6 extraction into NB, DCE, and DCM. The relation of f+ < f0 simply reflects that of K1,org < K2,org, about which the structural changes around Cd(II) were suggested, while the relation of f+ > f0 does that of K1,org > K2,org.

The molar volumes Vj obtained from the RST plots indicated the size-dependence on the Cd(18C6)A2 (=j) ion pairs. Additionally, the VCd18C6 value was evaluated from the pseudo-RST plots and then was the smallest of the Vj ones of all the Cd(18C6)A2 examined. At the same time, it was demonstrated that the apparent radii Rj, estimated from the Vj values, reflects inversely the bond lengths of Cd-A with A- = Cl-, Br-, and I- in the crystallographic and DFT studies. These Vj and Rj results proved validities for the analyses of the RST and pseudo-RST plots about such extraction systems and thereby indicated a possibility that the two plots give the structural information about some complexes, although it is unclear which of org or water phase is the corresponding phase.

Acknowledgements

Y. K. and Y. I. thank Mr. Quan Jin for his experimental support with the comparison between the AAS calibration curve with pure water and that with the acidic solution.

Appendix

The following Table A1 is supplementary data for the discussion in the Section 2.6. The numbers of Table A1 express the diluents in Figure 5.

In the following Table A2 are listed basic data for the HSAB classification. The data were used for consideration in the Section 2.7. The Pic with parenthesis in Table A2 was not employed for it.

Table A1. Relative concentrationsa, f0 for CdLI2, f+ for CdLI+, and f2+ for CdL2+, in the CdI2 extraction with L = 18C6 into various diluents at 298 K.

a. Definition: f0 = 100D0/Dt; f+ = 100D+/Dt; f2+ = 100D2+/Dt with Dt = D0 + D+ + D2+. All the values were mean ones; b. See the footnote a in Table 1; c. The values were employed for the plots of Figure 5.

Table A2. Orders of the K1,org, K2,org(A/Cl), and β2,org valuesa at 298 K for the HSAB classification.

a. See Refs. [1] [2] & [6] for the numerical data; b. See the footnote a in Table 1; c. Refs. [10] & [26] ; d. See the Section 2.5 for its definition; e. Ratio between the ion-pair formation constant for A- in water, defined as [CdLA2]/[CdLA+][A-], & that for Cl-; f. Overall ion-pair formation constant for water defined as [CdLA2]/[CdL2+][A-]2.

The evaluation of log{K1(average)} for the CdPic2 extraction with B18C6 into Bz was as follows. Using K 1 0 = 6.4 × 104 mol−1∙dm3 [26] at 298 K and the Davies equation [20], we calculated its value from the thermodynamic relation of

log K 1 0 { = log K 1 + log ( y CdLA / y II + y A ) } log K 1 log y II +

where the activity coefficient ratio yCdLA/yA » 1. Rearranging this equation and then introducing the Davies equation in it, the following equation can be easily obtained at 298 K:

log K 1 log K 1 0 0.511 4 × 2 2 × { I 1 / 2 / ( 1 + I 1 / 2 ) 0.3 I } (A1)

So, introducing K 1 0 and I = 0.095 mol∙dm−3 [3] in this equation without the ion-size parameter of CdL2+, we obtained immediately logK1 » 4.39. Here the I value was an average one for the Bz extraction system [3] . Similarly, the log{K1(average)} values calculated from Equation (A1) with the I data [3] at 298 K were 4.57 for the NB system with B18C6 and CdPic2, 4.60 for DCE, 4.56 for oDCBz, DCM, CF, and mX, 4.55 for CBu and dibutylether, 4.49 for CBz and TE, and 4.53 for BBz.

Cite this paper: Kudo, Y. , Ishikawa, Y. and Ichikawa, H. (2018) CdI2 Extraction with 18-Crown-6 Ether into Various Diluents: Classification of Extracted Cd(II) Complex Ions Based on the HSAB Principle. American Journal of Analytical Chemistry, 9, 560-579. doi: 10.4236/ajac.2018.911041.
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