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Equilibrium studies on complexation in water and solvent extraction of zinc(II) and cadmium(II) with benzo-18-crown-6
Talanta 51 (2000) 637 – 644 www.elsevier.com/locate/talanta
Equilibrium studies on complexation in water and solvent extraction of zinc(II) and cadmium(II) with benzo-18-crown-6 Shoichi Katsuta *, Fumiaki Tsuchiya, Yasuyuki Takeda Department of Chemistry, Faculty of Science, Chiba Uni6ersity, Yayoi-cho, Inage-ku, Chiba 263 -8522, Japan Received 19 July 1999; received in revised form 15 October 1999; accepted 15 October 1999
Abstract The formation constants (KML) in water of 1:1 complexes of benzo-18-crown-6 (B18C6) and 18-crown-6 (18C6) with Zn2 + and Cd2 + , the sizes of which are much smaller than the ligand cavities, were determined at 25°C by conductometry. Compared with Cd2 + , the crown ethers form more stable complexes with Zn2 + although the size of Zn2 + is less suited for the cavities. B18C6 forms a more stable complex with each metal ion than 18C6. Moreover, the extraction equilibria of these metal ions (M2 + ) with B18C6 (L) for the benzene/water system in the presence of picric acid (HA) were investigated at 25°C. The association between L and HA in benzene was examined for evaluating the intrinsic extraction equilibria of M2 + with B18C6. The extracted species were found to be MLA2 and ML2A2, and the overall extraction constants (Kex,1 and Kex,2, respectively) were obtained. The values of Kex,1 for these metal ions are almost the same, but the Kex,2 is larger for Zn2 + than for Cd2 + . The extraction selectivity was interpreted quantitatively by the constituent equilibrium constants, i.e. KML, the ion-pair extraction constant of ML2 + with A−, and the adduct formation constant of MLA2 with L in benzene. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Complexation; Solvent extraction; Zinc(II); Cadmium(II); Crown ether
1. Introduction The selectivities of macrocyclic compounds toward cations for complexation in a homogeneous system and for solvent extraction have been the subjects of intense research by many workers [1]. * Corresponding author. Fax: +81-43-290-2781. E-mail address: [email protected] (S. Katsuta)
It is generally believed that a crown ether effectively complexes and extracts a cation of suitable size to the ligand cavity. However, there has not been enough experimental data explaining the selectivity toward the cations that misfit into the cavity. Both Zn2 + and Cd2 + are much smaller than the cavity of 18-crown-6 (18C6); the ionic radii of Zn2 + and Cd2 + for coordination number 6 are 0.74 and 0.95 A, , respectively [2]. The cavity radius of 18C6 estimated from the CPK model is
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1.38 A, [3]. A few papers have dealt with the extraction of Zn2 + [4 – 6] and Cd2 + [6] with 18C6 derivatives such as dicyclohexano-18-crown-6 and dibenzo-18-crown-6, and some analytical utilities have been reported; however, the extraction equilibria have not been elucidated. In addition, no reliable formation constants in water have been reported for the crown ether complexes with Zn2 + and Cd2 + . The purpose of this paper is to evaluate quantitatively the selectivities of 18C6 and its derivative toward the size-misfitted small cations through equilibrium studies of complexation in water and solvent extraction. Conductometry is one of the most reliable methods for obtaining the formation constants of metal ion– macrocycle complexes [7]. However, this method has not been applied to the determination of complexation constants in water of the metal ions that are subject to hydrolysis. In this study, the conductometric determination of the 1:1 complex formation constants in water of Zn2 + and Cd2 + with benzo-18-crown-6 (B18C6) and 18C6 was done in the presence of nitric acid. Moreover, the overall extraction equilibrium constants of these metal picrates with B18C6 in benzene were determined. The association between B18C6 and picric acid in the benzene phase was examined for exact evaluation of the extraction equilibria. The extraction selectivity was discussed by analyzing the overall extraction equilibria into the constituent equilibria.
2. Experimental
2.1. Materials B18C6 (Tokyo Chemical Industry, 99%) and 18C6 (Acros Organics, 99%) were recrystallized from hexane and acetonitrile, respectively, and dried in vacuo. High purity Zn(NO3)2 · 6H2O and Cd(NO3)2 · 4H2O (Wako Pure Chemical Industries, 99.9%) were used without further purification. Benzene, nitric acid, and picric acid were analytical grade reagents. The concentration of picric acid in the stock solution was determined by acid–base titration. Benzene was washed three times with purified water. Water was distilled and
further purified with a Milli-Q Labo system (Millipore); the conductivity was less than 8× 10 − 7 S cm − 1. Other reagents were of analytical grade and used without further purification.
2.2. Conductometry The conductivity was measured with a Fuso conductivity apparatus, Model 362B, at 259 0.02°C. Cells with cell constants of 0.1963 and 0.2120 cm − 1 were used. In the cell, 200 cm3 of an aqueous solution of (1.5–3.0)× 10 − 3 M (1 M=1 mol dm − 3) metal(II) nitrate, which was acidified with nitric acid to pH 3.4–3.8, was introduced. The atmosphere was replaced by nitrogen gas. After the cell was thermally equilibrated in a water bath, the resistance of the solution was measured. A 5-cm3 portion of an aqueous solution of (1.0–2.0)×10 − 1 M crown ether was added to the cell, and after stirring for 5 min, the resistance was measured. This operation was repeated until 70 cm3 of the crown ether solution was added.
2.3. Extraction of metal ions Ten milliliters of a benzene solution of 7.0× 10 − 3 –1.0×10 − 1 M B18C6 and an equal volume of an aqueous solution containing 6.2× 10 − 3 – 2.5× 10 − 2 M picric acid and 3.3×10 − 2 M metal(II) nitrate (ionic strength, 0.11–0.12) were placed in a stoppered glass tube. The tube was shaken in a thermostated water bath at 259 0.2°C for 2 h and centrifuged. It was initially confirmed that the shaking time was sufficient to attain equilibrium. The pH of the aqueous phase at equilibrium, 2.11–2.54, was measured with a glass electrode. The metal in the benzene phase was quantitatively back-extracted into 0.10 M nitric acid aqueous solution, and the metal concentration was determined with an atomic absorption spectrophotometer (Hitachi SAS-725). The metal concentration of the aqueous phase was obtained by subtracting that of the benzene phase from the total concentration, and the distribution ratio of the metal was calculated. Scarcely any metal was extracted into benzene when B18C6 or picric acid was not present.
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2.4. Distribution of picric acid in the presence of B18C6 Ten milliliters of a benzene solution of 2.5× 10 − 2 –1.0×10 − 1 M B18C6 and an equal volume of an aqueous solution containing 6.2×10 − 5 M picric acid and 4.5×10 − 3 M nitric acid were shaken for 2 h at 2590.2°C and centrifuged. The pH of the aqueous phase at equilibrium was always 2.41, at which more than 99% of picric acid in the aqueous phase dissociates into the ions [8]. The picrate concentration of the aqueous phase was determined by UV spectrophotometry (lmax =356 nm, o = 1.45 × 104 cm − 1 M − 1). The concentration of the picric acid extracted was obtained by subtracting the picrate concentration of the aqueous phase from the total concentration, and the distribution ratio of the picric acid was calculated.
= (1− a)/a[L]
3.1. Complexation equilibria in water When the crown ether (L) forms only a 1:1 complex with the bivalent metal ion (M2 + ), the complex formation constant (KML) can be expressed by the fraction of the free metal ion (a): KML =[ML2 + ]/[M2 + ][L]
(1)
The apparent conductivity (kapp) of the metal nitrate (MX2) solution in the presence of L and nitric acid (HX) is given by kapp = kMX2 + kMLX2 + kHX
(2)
where kMX2, kMLX2, and kHX denote the conductivities of the metal salt, the metal crown ether salt, and the acid, respectively. The molar conductivities, LMX2, LMLX2, and LHX, are written as LMX2 = kMX2/[M2 + ] = kMX2/a[M]t = kMX2/a[M]t
(3)
LMLX2 = kMLX2/[ML2 + ] = kMLX2/(1− a)[M]t
(4)
LHX = kHX/[H ] +
= kHX/[H]t 3. Results and discussion
639
(5)
where [M]t and [H]t are the total concentrations of the metal salt and the acid, respectively. The apparent molar conductivity of the metal salt, defined as Lapp = kapp/[M]t, is expressed as Lapp = aLMX2 + (1− a)LMLX2 + ([H]t/[M]t)LHX = aL%MX2 + (1− a)L%MLX2
(6)
where L%MX2 = LMX2 + ([H]t/[M]t)LHX and L%MLX2 = LMLX2 + ([H]t/[M]t)LHX. The L%MX2 value equals Lapp at the start point of the conductometric titration. The concentration ratio, [H]t/[M]t, is constant throughout the titration. Combining Eqs. (1) and (6) leads to KML =
L%MX2 − Lapp (Lapp − L%MLX2)[L]
(7)
where [L]= [L]t − (L%MX2 − Lapp)[M]t/(L%MX2 − L%MLX2)
Fig. 1. Plots of Lapp versus [L]t/[M]t for Zn(NO3)2 – and Cd(NO3)2 – B18C6 systems in aqueous nitric acid solutions. , [Zn(NO3)2]init = 2.1× 10 − 3 M, pH 3.41; , [Cd(NO3)2]init = 3.0 × 10 − 3 M, pH 3.41.
(8)
It is assumed that ion-pair formation, protonation of the crown ether, and viscosity changes are negligible. The plots of Lapp versus [L]t/[M]t for the B18C6–Zn(NO3)2 and –Cd(NO3)2 systems are shown in Fig. 1. The Lapp decreases with an
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Fig. 2. Formation constants of metal(II) complexes with 18C6 and B18C6 in water as a function of ionic radius. The open symbols denote 18C6, and filled symbols B18C6. The constants for the alkaline earth metals and Hg2 + are cited from the literatures [10–12].
increase in [L]t. The results show that the crown ether forms a complex with the metal ion and that the complex is less mobile than the corresponding free metal ion. The KML was obtained by the following procedure. The [L] of Eq. (8) was calculated using the L%MLX2 value estimated from the Lapp at the highest [L]t. The values of KML and L%MLX2 were evaluated from the slope and the intercept of the (L%MX2 −Lapp)[L] − 1 versus Lapp plot according to Eq. (7). The actual KML and L%MLX2 values were obtained by an iterative procedure. The final plot of (L%MX2 −Lapp)[L] − 1 versus Lapp always gave a good linear relationship with a correlation coefficient more than 0.97, indicating that the above assumptions were valid. The control experiments without the metal salts showed that the protonation of the crown ethers was negligible. The formation constant of each complex was determined from the average value of 3–5 measurements; the log KML of Zn(18C6)2 + , Zn(B18C6)2 + , and Cd(B18C6)2 + are 0.539 0.15, 0.6090.07, and 0.1190.02, respectively; that of Cd(18C6)2 + was previously reported to be −0.0590.03 [9]. In Fig. 2, the log KML values of bivalent zinc group and alkaline earth metals with 18C6 and
B18C6 are shown as a function of the ionic radius [2]. The values for the alkaline earth metals and Hg2 + are cited from the literature [10–12]. Among the alkaline earth metals, the complex formation constant is the largest for Ba2 + that is best fitted into the ligand cavities. The ionic sizes of the zinc group metals are all smaller than the ligand cavities; they decrease in the order Hg2 + \ Cd2 + \ Zn2 + . 18C6 forms a more stable complex with Hg2 + than with Zn2 + and Cd2 + , as is to be expected from the size-fit concept. However, for 18C6 or B18C6, the complex of Zn2 + is unexpectedly more stable than the corresponding Cd2 + complex. The complexation selectivity of these crown ethers toward Zn2 + and Cd2 + does not obey the size-fit concept, but is in accord with the selectivity of oxygen-donating chelate ligands such as oxalic acid and lactic acid that generally form more stable complexes with the smaller cation [13]. For Sr2 + and Ba2 + , the formation constant of the 18C6 complex is larger than that of the corresponding B18C6 complex. On the other hand, for the smaller Zn2 + and Cd2, the constant of the 18C6 complex is almost equal to or slightly smaller than that of the B18C6 complex. A similar trend is observed for the alkali metal ion complexes: 18C6 forms more stable complexes with K+ and Rb+ than B18C6 does, whereas the reverse holds for the smaller Na+ [12]. The differences in complexing ability in water between the crown ethers can be discussed based on the following thermodynamic cycle:
DG oc,w = DG oc,g + DG oh(MLm + )− DG oh(Mm + ) − DG oh(L) (9) where subscripts (g) and (w) denote the species in the gas and water phases, respectively; DG oc,g and DG oc,w are the Gibbs free energies of complexation in the gas and water phases, respectively; DG oh is
S. Katsuta et al. / Talanta 51 (2000) 637–644
the Gibbs free energy of hydration. From Eq. (9), the difference in DG oc,w between the crown ethers, DDG oc,w =DG oc,w(B18C6) −DG oc,w(18C6), can be expressed as DDG oc,w =DDG oc,g +DDG oh(MLm + ) − DDG oh(L) (10) where DDG oc,g =DG oc,g(B18C6) − DG oc,g(18C6), m+ o DDG h(ML ) = DG oh(MB18C6m + ) − DG oh(M18C6m + ), and DDG oh(L) =DG oh(B18C6) − DG oh(18C6). For K+, Rb+, Sr2 + , and Ba2 + the size of which is close to the cavity, the crown ether probably adopts the D3d conformation and its six oxygen atoms coordinate to the metal ion [14,15]. It is well known that the benzo group exerts an electron withdrawing effect on the ether oxygens. As a result, for a given metal ion, the B18C6 complex is less stable than the 18C6 complex in the gas phase (i.e. DDG oc,g \0). The values of DDG oh(MLm + ) and DDG oh(L) are also regarded as positive because of the hydrophobicity of the benzo group. On account of the higher basicity of an aliphatic ether oxygen than an aromatic ether oxygen, hydrogen bonding of the ether oxygens with water is stronger for 18C6 than for B18C6. In the complex, the interactions with water of the ether oxygens and the metal ion are greatly decreased by ionic bonding of the ether oxygens to the metal ion. Therefore, DDG oh(L) is expected to be larger than DDG oh(MLm + ) (i.e. DDG oh(MLm + ) − DDG oh(L)B0). Such an expectation is supported by the data of transfer activity coefficients of the solutes between water and nonaqueous solvents [12]. According to Eq. (10), the positive value of DDG oc,w means that DDG oc,g \ DDG oh(MLm + ) − DDG oh(L) ; thus the lower complexing ability of B18C6, compared with 18C6, for the size-fitted metal ions in water is ascribed to the lower stability of the B18C6 complex in the gas phase. For Na+, Zn2 + , and Cd2 + that are much smaller than the cavity, the crown ether needs to be distorted from its stable planner conformation to hold the metal ion; the conformational change is less drastic for the benzo-substituted ethers because of the rigidity imposed by the benzo group [14]. Therefore, it is expected that the metal
641
ion in the B18C6 complex is less effectively shielded from the surrounding solvents by the ether oxygen atoms than in the 18C6 complexes, resulting in stronger interaction with water of the metal ion in the B18C6 complex. Since the hydrogen bond interaction between water and the uncomplexed ligand is greater for 18C6 than for B18C6, DDG oh(MLm + ) should be much smaller than DDG oh(L) (i.e. DDG oh(MLm + )− DDG oh(L) 0). According to Eq. (10), the negative value of DDG oc,w indicates that DDG oc,g B DDG oh(MLm + ) − DDG oh(L) . It can therefore be presumed that the main reasons for the higher complexing ability of B18C6 than 18C6 for the size-misfitted small metal ions in water are the less effective shielding of the metal ion in the B18C6 complex and the weaker hydrogen bonding of the uncomplexed B18C6 with water.
3.2. Extraction equilibria between benzene and water When the metal ion complex (MLi A2) into picric acid (HA), the librium constant (Kex,i ) Kex,i =
is extracted as a neutral benzene with B18C6 and overall extraction equican be defined as
[MLi A2]o[H+]2 [M2 + ][L]io[HA]2o
(11)
where the subscript ‘o’ and the lack of subscript denote the species in the organic and aqueous phases, respectively. When M2 + and ML2 + are the dominant species in the aqueous phase, the distribution ratio of the metal (DM) is expressed as n
% [MLi A2]o DM =
i=1
[M2 + ]+ [ML2 + ] n
% Kex,i [L]io =
i=1 1 1+ KMLK − d,L [L]o
K 2HAK 2d,HA[A−]2
(12)
where KHA, Kd,HA, and Kd,L are the protonation constant of a picrate ion in the aqueous phase (KHA = [HA]/[H+][A−]), the distribution constant of picric acid (Kd,HA = [HA]o/[HA]), and the distribution constant of B18C6 (Kd,L = [L]o/[L]), re-
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spectively; the values at 25°C are available, i.e. KHA =1.95 [8], KHAKd,HA =247 [16], and Kd,L = 8.76 [17]. Eq. (12) can be transformed into n
% Kex,i [L]io DM i=1 = K 2HAK 2d,HA 1 [A−]2 1+ KMLK − [L] d,L o
(13)
[HA]o + [L·HA]o =D oHA(1+Kass,o[L]o) [HA]+ [A−] (15) o HA
denotes the distribution ratio of picric where D acid in the absence of B18C6, and Kass,o is the association constant defined as [L·HA]o/ [L]o[HA]o. Eq. (15) is transformed into DHA/D oHA − 1= Kass,o[L]o
The overall extraction constant can be determined from the dependence of DM/[A−]2 on [L]o. The following equation is also derived from Eq. (12): 1 1+KMLK − d,L [L]o DM =K 2HAK 2d,HA[A−]2 n i % Kex,i [L]o
DHA =
(14)
i=1
The log–log plot of the left side of Eq. (14) versus [A−] should give a straight line with a slope of two. In the calculation of [L]o and [A−], the association between B18C6 and picric acid in the organic phase was considered. When B18C6 forms a 1:1 association complex with picric acid in the organic phase, the distribution ratio of picric acid (DHA) can be expressed as follows:
(16)
The plot of log(DHA/D oHA − 1) versus log [L]o at fixed pH is shown in Fig. 3. The initial concentration of B18C6 was made to be in large excess over that of picric acid so that [L]o could be calculated using only the distribution constant of the crown 1 ether, i.e. [L]o = [L]t/(1+ K − d,L ). The plot shows a straight line with a slope of 1.0090.02, indicating that B18C6 forms a 1:1 complex with picric acid in the benzene phase. According to Eq. (16), Kass,o = 8.229 0.30 was obtained. The mass balance equations in the extraction system can be written as follows: n
[M]t − % [MLi A2]o = [M2 + ]+ [ML2 + ]
(17)
i=1 n
[L]t − % i[MLi A2]o = [L]+[L]o + [L·HA]o i=1
+ [ML2 + ]
(18)
n
[A]t − 2 % [MLi A2]o i=1 −
= [A ]+ [HA]+ [HA]o + [L·HA]o
(19)
where [A]t is the total concentration of picric acid. In the present experiments, S[MLi A2]o, Si[MLi A2]o, and 2S[MLi A2]o were negligibly small compared with [M]t, [L]t, and [A]t, respectively. In this case, [M2 + ], [L], and [HA]o can be expressed as [L]o = [L]t/(a +b[M2 + ]+ Kass,o[HA]o)
(20)
[M2 + ]= [M]t/(1+ b[L]o)
(21)
[HA]o = [A]t/(1+ Kass,o[L]o + c) −1 d,L
log(DHA/D oHA − 1)
Fig. 3. Plots of versus log [L]o for extraction of picric acid in the presence of B18C6 at constant pH. The solid line is obtained by the calculation based on Eq. (16).
(22) −1 d,L
where a= 1+ K , b=KMLK , and c= + −1 1 K− . The combination of d,HA + (KHAKd,HA[H ]) Eqs. (20)–(22) leads to the following cubic equation for [L]o:
S. Katsuta et al. / Talanta 51 (2000) 637–644
Fig. 4. Plots of log(DM/[A−]2) versus log [L]o for extraction of Zn2 + and Cd2 + as picrates with B18C6. The solid lines are obtained by the calculation based on Eq. (13).
Table 1 The overall extraction constants, the ion-pair extraction constants, and the adduct formation constants at 25°C for the extraction of Zn2+ and Cd2+ picrates with B18C6 into benzene M2+
log Kex,1
log Kex,2
log Kex,ipa
Zn2+ −3.2090.03 −1.3690.02 1.92 Cd2+ −3.179 0.04 −1.629 0.04 2.44 a b
log Kad,ob 1.84 1.55
Calculated from Eq. (24). Calculated from Eq. (25).
abKass,o[L]3o + [a{b(1 +c) +Kass,o} +bKass,o([M]t +[A]t −[L]t)][L]2o + [(1+ c)(a +b[M]t) +Kass,o[HA]t − {b(1+c)+ Kass,o}[L]t][L]o −(1 +c)[L]t =0 (23) This equation was solved by Newton’s method to obtain [L]o. The [A−] value was calculated from the equation [A−]= [HA]o/KHAKd,HA[H+], where [HA]o was obtained from Eq. (22). The log(DM/ [A−]2) versus log[L]o plots are shown in Fig. 4. The slope of each plot increases from 1.4 to 2.0 (Zn2 + ) or 1.2 to 1.9 (Cd2 + ) with an increase of
643
[L]o. The values of the slope indicate that the extracted species are MLA2 and ML2A2, because 1 the term KMLK − d,L [L]o in Eq. (13) was much smaller than 1 (0.04 at the most). The Kex,1 and Kex,2 were determined by a nonlinear least-squares method based on Eq. (13), and the logarithmic values are listed in Table 1. The solid lines in Fig. 4 are obtained from Eq. (13) by use of the extraction constants and agree well with the experimental data. 1 The slopes of the log{DM(1+KMLK − d,L [L]o)/ − 2 (Kex,1[L]o + Kex,2[L]o)} versus log [A ] plots were 2.019 0.04 and 2.06 9 0.06 for Zn2 + and Cd2 + , respectively; they are identical with the theoretical value from Eq. (14). If the association between B18C6 and picric acid in the organic phase is neglected, the slope deviates from two (ca 1.7). These results mean that the consideration of the B18C6–picric acid association is essential for the equilibrium analysis in the present extraction systems. The formation of ML2A2 in the organic phase supports the preceding conclusion that the too small metal ion in the ML2 + complex is not effectively screened by the ether oxygen atoms of B18C6. In water, the formation of the ML22 + complex could not be detected. The very low stability of ML22 + in water can be accounted for by the remarkable interactions with water of the metal ion in ML2 + and the ether oxygens of uncomplexed L. In spite of the higher stability of ZnL2 + than CdL2 + in water, the Kex,1 values for Zn2 + and Cd2 + are almost the same. On the other hand, the Kex,2 value is larger for Zn2 + . The extraction selectivities can be explained by the constituent equilibria: the overall extraction constants are expressed as −2 1 Kex,1 = KMLKex,ipK − d,L (KHAKd,HA)
(24)
Kex,2 = Kex,1Kad,o
(25)
where Kex,ip and Kad,o are the ion-pair extraction constant of the complex cation with the picrate anion (Kex,ip = [MLA2]o/[ML2 + ][A−]2) and the adduct formation constant in the organic phase (Kad,o = [ML2A2]o/[MLA2]o[L]o), respectively. The values of Kex,ip and Kad,o were calculated accord-
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ing to Eqs. (24) and (25), respectively, and the logarithmic values are listed in Table 1. The log Kex,ip value is smaller for Zn2 + than for Cd2 + . The decrease in log Kex,ip from Cd2 + to Zn2 + just cancels the increase in log KML, which is responsible for the comparable log Kex,1 values of these metal ions. The log Kad,o value is larger for Zn2 + than for Cd2 + , and the difference in log Kad,o between the two metals is reflected by the difference in log Kex,2. The larger Kad,o value of ZnLA2 than CdLA2 suggests that, even in the MLA2 form, Zn2 + has a higher ability as an acceptor than Cd2 + . The Kex,ip is further expressed as a product of two elementary equilibrium constants, i.e. the ion-pair formation constant in water (KMLA2 = [MLA2]/[ML2 + ][A−]2) and the distribution constant of the ion-pair (Kd,MLA2 =[MLA2]o /[MLA2]). At this stage, these underlying constants are unknown. However, from the higher ability of ZnLA2 to accept an additional ligand, it is suggested that ZnLA2 be more strongly hydrated in water than CdLA2, and that the distribution constant of ZnLA2 is smaller; thus the stronger hydration of ZnLA2 is responsible for the smaller Kex,ip value.
Acknowledgements This research was partly supported by a Grant-in-Aid for Scientific Research No. 11740407 from the Ministry of Education, Science and Culture.
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References [1] Y.A. Zolotov (Ed.), Macrocyclic Compounds in Analytical Chemistry, Wiley-Interscience, New York, 1997. [2] R.D. Shannon, Acta Cryst. A32 (1976) 751. [3] J.D. Lamb, R.M. Izatt, J.J. Christensen, Stability constants of cation-macrocycle complexes, in: R.M. Izatt, J.J. Christensen (Eds.), Progress in Macrocyclic Chemistry, vol. 2, Wiley-Interscience, New York, 1981. [4] S. Dernini, A. Scrugli, S. Palmas, A.M. Polcaro, J. Chem. Eng. Data 41 (1996) 1388. [5] K. Nishizawa, T. Satoyama, T. Miki, T. Yamamoto, M. Nomura, Sep. Sci. Technol. 31 (1996) 2381. [6] M. Billah, T. Honjo, Fresenius J. Anal. Chem. 357 (1997) 61. [7] Y. Takeda, Conductometric behavior of cation-macrocycle complexes in solutions, in: Y. Inoue, G.W. Gokel (Eds.), Cation Binding by Macrocycles, Marcel Dekker, New York, 1991. [8] G. Kortu¨n, W. Vogel, K. Andrussov (Eds.), Dissociation Constants of Organic Acids in Aqueous Solution, Butterworth, London, 1961. [9] Y. Takeda, Y. Mochizuki, M. Tanaka, Y. Kudo, S. Katsuta, M. Ouchi, J. Incl. Phenom. 33 (1999) 217. [10] H. Høiland, J.A. Ringseth, T.S. Brun, J. Solution Chem. 8 (1979) 779. [11] R.M. Izatt, R.E. Terry, B.L. Haymore, L.D. Hansen, N.K. Dalley, A.G. Avondet, J.J. Christensen, J. Am. Chem. Soc. 98 (1976) 7620. [12] Y. Takeda, R. Kohno, Y. Kudo, N. Fukada, Bull. Chem. Soc. Jpn. 62 (1989) 999. [13] L.G. Sillen, A.E. Martell, Stability Constants of Metal–Ion Complexes, The Chemical Society, London, 1971. [14] J.D. Dunitz, M. Dobler, P. Seiler, R.P. Phizackerley, Acta Cryst. B30 (1974) 2733. [15] E.D. Glendening, D. Feller, J. Am. Chem. Soc. 118 (1996) 6052. [16] Y. Takeda, H. Kato, Bull. Chem. Soc. Jpn. 52 (1979) 1027. [17] Y. Takeda, H. Sato, S. Sato, J. Solution Chem. 21 (1992) 1069.
Equilibrium studies on complexation in water and solvent extraction of zinc(II) and cadmium(II) with benzo-18-crown-6 Shoichi Katsuta *, Fumiaki Tsuchiya, Yasuyuki Takeda Department of Chemistry, Faculty of Science, Chiba Uni6ersity, Yayoi-cho, Inage-ku, Chiba 263 -8522, Japan Received 19 July 1999; received in revised form 15 October 1999; accepted 15 October 1999
Abstract The formation constants (KML) in water of 1:1 complexes of benzo-18-crown-6 (B18C6) and 18-crown-6 (18C6) with Zn2 + and Cd2 + , the sizes of which are much smaller than the ligand cavities, were determined at 25°C by conductometry. Compared with Cd2 + , the crown ethers form more stable complexes with Zn2 + although the size of Zn2 + is less suited for the cavities. B18C6 forms a more stable complex with each metal ion than 18C6. Moreover, the extraction equilibria of these metal ions (M2 + ) with B18C6 (L) for the benzene/water system in the presence of picric acid (HA) were investigated at 25°C. The association between L and HA in benzene was examined for evaluating the intrinsic extraction equilibria of M2 + with B18C6. The extracted species were found to be MLA2 and ML2A2, and the overall extraction constants (Kex,1 and Kex,2, respectively) were obtained. The values of Kex,1 for these metal ions are almost the same, but the Kex,2 is larger for Zn2 + than for Cd2 + . The extraction selectivity was interpreted quantitatively by the constituent equilibrium constants, i.e. KML, the ion-pair extraction constant of ML2 + with A−, and the adduct formation constant of MLA2 with L in benzene. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Complexation; Solvent extraction; Zinc(II); Cadmium(II); Crown ether
1. Introduction The selectivities of macrocyclic compounds toward cations for complexation in a homogeneous system and for solvent extraction have been the subjects of intense research by many workers [1]. * Corresponding author. Fax: +81-43-290-2781. E-mail address: [email protected] (S. Katsuta)
It is generally believed that a crown ether effectively complexes and extracts a cation of suitable size to the ligand cavity. However, there has not been enough experimental data explaining the selectivity toward the cations that misfit into the cavity. Both Zn2 + and Cd2 + are much smaller than the cavity of 18-crown-6 (18C6); the ionic radii of Zn2 + and Cd2 + for coordination number 6 are 0.74 and 0.95 A, , respectively [2]. The cavity radius of 18C6 estimated from the CPK model is
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1.38 A, [3]. A few papers have dealt with the extraction of Zn2 + [4 – 6] and Cd2 + [6] with 18C6 derivatives such as dicyclohexano-18-crown-6 and dibenzo-18-crown-6, and some analytical utilities have been reported; however, the extraction equilibria have not been elucidated. In addition, no reliable formation constants in water have been reported for the crown ether complexes with Zn2 + and Cd2 + . The purpose of this paper is to evaluate quantitatively the selectivities of 18C6 and its derivative toward the size-misfitted small cations through equilibrium studies of complexation in water and solvent extraction. Conductometry is one of the most reliable methods for obtaining the formation constants of metal ion– macrocycle complexes [7]. However, this method has not been applied to the determination of complexation constants in water of the metal ions that are subject to hydrolysis. In this study, the conductometric determination of the 1:1 complex formation constants in water of Zn2 + and Cd2 + with benzo-18-crown-6 (B18C6) and 18C6 was done in the presence of nitric acid. Moreover, the overall extraction equilibrium constants of these metal picrates with B18C6 in benzene were determined. The association between B18C6 and picric acid in the benzene phase was examined for exact evaluation of the extraction equilibria. The extraction selectivity was discussed by analyzing the overall extraction equilibria into the constituent equilibria.
2. Experimental
2.1. Materials B18C6 (Tokyo Chemical Industry, 99%) and 18C6 (Acros Organics, 99%) were recrystallized from hexane and acetonitrile, respectively, and dried in vacuo. High purity Zn(NO3)2 · 6H2O and Cd(NO3)2 · 4H2O (Wako Pure Chemical Industries, 99.9%) were used without further purification. Benzene, nitric acid, and picric acid were analytical grade reagents. The concentration of picric acid in the stock solution was determined by acid–base titration. Benzene was washed three times with purified water. Water was distilled and
further purified with a Milli-Q Labo system (Millipore); the conductivity was less than 8× 10 − 7 S cm − 1. Other reagents were of analytical grade and used without further purification.
2.2. Conductometry The conductivity was measured with a Fuso conductivity apparatus, Model 362B, at 259 0.02°C. Cells with cell constants of 0.1963 and 0.2120 cm − 1 were used. In the cell, 200 cm3 of an aqueous solution of (1.5–3.0)× 10 − 3 M (1 M=1 mol dm − 3) metal(II) nitrate, which was acidified with nitric acid to pH 3.4–3.8, was introduced. The atmosphere was replaced by nitrogen gas. After the cell was thermally equilibrated in a water bath, the resistance of the solution was measured. A 5-cm3 portion of an aqueous solution of (1.0–2.0)×10 − 1 M crown ether was added to the cell, and after stirring for 5 min, the resistance was measured. This operation was repeated until 70 cm3 of the crown ether solution was added.
2.3. Extraction of metal ions Ten milliliters of a benzene solution of 7.0× 10 − 3 –1.0×10 − 1 M B18C6 and an equal volume of an aqueous solution containing 6.2× 10 − 3 – 2.5× 10 − 2 M picric acid and 3.3×10 − 2 M metal(II) nitrate (ionic strength, 0.11–0.12) were placed in a stoppered glass tube. The tube was shaken in a thermostated water bath at 259 0.2°C for 2 h and centrifuged. It was initially confirmed that the shaking time was sufficient to attain equilibrium. The pH of the aqueous phase at equilibrium, 2.11–2.54, was measured with a glass electrode. The metal in the benzene phase was quantitatively back-extracted into 0.10 M nitric acid aqueous solution, and the metal concentration was determined with an atomic absorption spectrophotometer (Hitachi SAS-725). The metal concentration of the aqueous phase was obtained by subtracting that of the benzene phase from the total concentration, and the distribution ratio of the metal was calculated. Scarcely any metal was extracted into benzene when B18C6 or picric acid was not present.
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2.4. Distribution of picric acid in the presence of B18C6 Ten milliliters of a benzene solution of 2.5× 10 − 2 –1.0×10 − 1 M B18C6 and an equal volume of an aqueous solution containing 6.2×10 − 5 M picric acid and 4.5×10 − 3 M nitric acid were shaken for 2 h at 2590.2°C and centrifuged. The pH of the aqueous phase at equilibrium was always 2.41, at which more than 99% of picric acid in the aqueous phase dissociates into the ions [8]. The picrate concentration of the aqueous phase was determined by UV spectrophotometry (lmax =356 nm, o = 1.45 × 104 cm − 1 M − 1). The concentration of the picric acid extracted was obtained by subtracting the picrate concentration of the aqueous phase from the total concentration, and the distribution ratio of the picric acid was calculated.
= (1− a)/a[L]
3.1. Complexation equilibria in water When the crown ether (L) forms only a 1:1 complex with the bivalent metal ion (M2 + ), the complex formation constant (KML) can be expressed by the fraction of the free metal ion (a): KML =[ML2 + ]/[M2 + ][L]
(1)
The apparent conductivity (kapp) of the metal nitrate (MX2) solution in the presence of L and nitric acid (HX) is given by kapp = kMX2 + kMLX2 + kHX
(2)
where kMX2, kMLX2, and kHX denote the conductivities of the metal salt, the metal crown ether salt, and the acid, respectively. The molar conductivities, LMX2, LMLX2, and LHX, are written as LMX2 = kMX2/[M2 + ] = kMX2/a[M]t = kMX2/a[M]t
(3)
LMLX2 = kMLX2/[ML2 + ] = kMLX2/(1− a)[M]t
(4)
LHX = kHX/[H ] +
= kHX/[H]t 3. Results and discussion
639
(5)
where [M]t and [H]t are the total concentrations of the metal salt and the acid, respectively. The apparent molar conductivity of the metal salt, defined as Lapp = kapp/[M]t, is expressed as Lapp = aLMX2 + (1− a)LMLX2 + ([H]t/[M]t)LHX = aL%MX2 + (1− a)L%MLX2
(6)
where L%MX2 = LMX2 + ([H]t/[M]t)LHX and L%MLX2 = LMLX2 + ([H]t/[M]t)LHX. The L%MX2 value equals Lapp at the start point of the conductometric titration. The concentration ratio, [H]t/[M]t, is constant throughout the titration. Combining Eqs. (1) and (6) leads to KML =
L%MX2 − Lapp (Lapp − L%MLX2)[L]
(7)
where [L]= [L]t − (L%MX2 − Lapp)[M]t/(L%MX2 − L%MLX2)
Fig. 1. Plots of Lapp versus [L]t/[M]t for Zn(NO3)2 – and Cd(NO3)2 – B18C6 systems in aqueous nitric acid solutions. , [Zn(NO3)2]init = 2.1× 10 − 3 M, pH 3.41; , [Cd(NO3)2]init = 3.0 × 10 − 3 M, pH 3.41.
(8)
It is assumed that ion-pair formation, protonation of the crown ether, and viscosity changes are negligible. The plots of Lapp versus [L]t/[M]t for the B18C6–Zn(NO3)2 and –Cd(NO3)2 systems are shown in Fig. 1. The Lapp decreases with an
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Fig. 2. Formation constants of metal(II) complexes with 18C6 and B18C6 in water as a function of ionic radius. The open symbols denote 18C6, and filled symbols B18C6. The constants for the alkaline earth metals and Hg2 + are cited from the literatures [10–12].
increase in [L]t. The results show that the crown ether forms a complex with the metal ion and that the complex is less mobile than the corresponding free metal ion. The KML was obtained by the following procedure. The [L] of Eq. (8) was calculated using the L%MLX2 value estimated from the Lapp at the highest [L]t. The values of KML and L%MLX2 were evaluated from the slope and the intercept of the (L%MX2 −Lapp)[L] − 1 versus Lapp plot according to Eq. (7). The actual KML and L%MLX2 values were obtained by an iterative procedure. The final plot of (L%MX2 −Lapp)[L] − 1 versus Lapp always gave a good linear relationship with a correlation coefficient more than 0.97, indicating that the above assumptions were valid. The control experiments without the metal salts showed that the protonation of the crown ethers was negligible. The formation constant of each complex was determined from the average value of 3–5 measurements; the log KML of Zn(18C6)2 + , Zn(B18C6)2 + , and Cd(B18C6)2 + are 0.539 0.15, 0.6090.07, and 0.1190.02, respectively; that of Cd(18C6)2 + was previously reported to be −0.0590.03 [9]. In Fig. 2, the log KML values of bivalent zinc group and alkaline earth metals with 18C6 and
B18C6 are shown as a function of the ionic radius [2]. The values for the alkaline earth metals and Hg2 + are cited from the literature [10–12]. Among the alkaline earth metals, the complex formation constant is the largest for Ba2 + that is best fitted into the ligand cavities. The ionic sizes of the zinc group metals are all smaller than the ligand cavities; they decrease in the order Hg2 + \ Cd2 + \ Zn2 + . 18C6 forms a more stable complex with Hg2 + than with Zn2 + and Cd2 + , as is to be expected from the size-fit concept. However, for 18C6 or B18C6, the complex of Zn2 + is unexpectedly more stable than the corresponding Cd2 + complex. The complexation selectivity of these crown ethers toward Zn2 + and Cd2 + does not obey the size-fit concept, but is in accord with the selectivity of oxygen-donating chelate ligands such as oxalic acid and lactic acid that generally form more stable complexes with the smaller cation [13]. For Sr2 + and Ba2 + , the formation constant of the 18C6 complex is larger than that of the corresponding B18C6 complex. On the other hand, for the smaller Zn2 + and Cd2, the constant of the 18C6 complex is almost equal to or slightly smaller than that of the B18C6 complex. A similar trend is observed for the alkali metal ion complexes: 18C6 forms more stable complexes with K+ and Rb+ than B18C6 does, whereas the reverse holds for the smaller Na+ [12]. The differences in complexing ability in water between the crown ethers can be discussed based on the following thermodynamic cycle:
DG oc,w = DG oc,g + DG oh(MLm + )− DG oh(Mm + ) − DG oh(L) (9) where subscripts (g) and (w) denote the species in the gas and water phases, respectively; DG oc,g and DG oc,w are the Gibbs free energies of complexation in the gas and water phases, respectively; DG oh is
S. Katsuta et al. / Talanta 51 (2000) 637–644
the Gibbs free energy of hydration. From Eq. (9), the difference in DG oc,w between the crown ethers, DDG oc,w =DG oc,w(B18C6) −DG oc,w(18C6), can be expressed as DDG oc,w =DDG oc,g +DDG oh(MLm + ) − DDG oh(L) (10) where DDG oc,g =DG oc,g(B18C6) − DG oc,g(18C6), m+ o DDG h(ML ) = DG oh(MB18C6m + ) − DG oh(M18C6m + ), and DDG oh(L) =DG oh(B18C6) − DG oh(18C6). For K+, Rb+, Sr2 + , and Ba2 + the size of which is close to the cavity, the crown ether probably adopts the D3d conformation and its six oxygen atoms coordinate to the metal ion [14,15]. It is well known that the benzo group exerts an electron withdrawing effect on the ether oxygens. As a result, for a given metal ion, the B18C6 complex is less stable than the 18C6 complex in the gas phase (i.e. DDG oc,g \0). The values of DDG oh(MLm + ) and DDG oh(L) are also regarded as positive because of the hydrophobicity of the benzo group. On account of the higher basicity of an aliphatic ether oxygen than an aromatic ether oxygen, hydrogen bonding of the ether oxygens with water is stronger for 18C6 than for B18C6. In the complex, the interactions with water of the ether oxygens and the metal ion are greatly decreased by ionic bonding of the ether oxygens to the metal ion. Therefore, DDG oh(L) is expected to be larger than DDG oh(MLm + ) (i.e. DDG oh(MLm + ) − DDG oh(L)B0). Such an expectation is supported by the data of transfer activity coefficients of the solutes between water and nonaqueous solvents [12]. According to Eq. (10), the positive value of DDG oc,w means that DDG oc,g \ DDG oh(MLm + ) − DDG oh(L) ; thus the lower complexing ability of B18C6, compared with 18C6, for the size-fitted metal ions in water is ascribed to the lower stability of the B18C6 complex in the gas phase. For Na+, Zn2 + , and Cd2 + that are much smaller than the cavity, the crown ether needs to be distorted from its stable planner conformation to hold the metal ion; the conformational change is less drastic for the benzo-substituted ethers because of the rigidity imposed by the benzo group [14]. Therefore, it is expected that the metal
641
ion in the B18C6 complex is less effectively shielded from the surrounding solvents by the ether oxygen atoms than in the 18C6 complexes, resulting in stronger interaction with water of the metal ion in the B18C6 complex. Since the hydrogen bond interaction between water and the uncomplexed ligand is greater for 18C6 than for B18C6, DDG oh(MLm + ) should be much smaller than DDG oh(L) (i.e. DDG oh(MLm + )− DDG oh(L) 0). According to Eq. (10), the negative value of DDG oc,w indicates that DDG oc,g B DDG oh(MLm + ) − DDG oh(L) . It can therefore be presumed that the main reasons for the higher complexing ability of B18C6 than 18C6 for the size-misfitted small metal ions in water are the less effective shielding of the metal ion in the B18C6 complex and the weaker hydrogen bonding of the uncomplexed B18C6 with water.
3.2. Extraction equilibria between benzene and water When the metal ion complex (MLi A2) into picric acid (HA), the librium constant (Kex,i ) Kex,i =
is extracted as a neutral benzene with B18C6 and overall extraction equican be defined as
[MLi A2]o[H+]2 [M2 + ][L]io[HA]2o
(11)
where the subscript ‘o’ and the lack of subscript denote the species in the organic and aqueous phases, respectively. When M2 + and ML2 + are the dominant species in the aqueous phase, the distribution ratio of the metal (DM) is expressed as n
% [MLi A2]o DM =
i=1
[M2 + ]+ [ML2 + ] n
% Kex,i [L]io =
i=1 1 1+ KMLK − d,L [L]o
K 2HAK 2d,HA[A−]2
(12)
where KHA, Kd,HA, and Kd,L are the protonation constant of a picrate ion in the aqueous phase (KHA = [HA]/[H+][A−]), the distribution constant of picric acid (Kd,HA = [HA]o/[HA]), and the distribution constant of B18C6 (Kd,L = [L]o/[L]), re-
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642
spectively; the values at 25°C are available, i.e. KHA =1.95 [8], KHAKd,HA =247 [16], and Kd,L = 8.76 [17]. Eq. (12) can be transformed into n
% Kex,i [L]io DM i=1 = K 2HAK 2d,HA 1 [A−]2 1+ KMLK − [L] d,L o
(13)
[HA]o + [L·HA]o =D oHA(1+Kass,o[L]o) [HA]+ [A−] (15) o HA
denotes the distribution ratio of picric where D acid in the absence of B18C6, and Kass,o is the association constant defined as [L·HA]o/ [L]o[HA]o. Eq. (15) is transformed into DHA/D oHA − 1= Kass,o[L]o
The overall extraction constant can be determined from the dependence of DM/[A−]2 on [L]o. The following equation is also derived from Eq. (12): 1 1+KMLK − d,L [L]o DM =K 2HAK 2d,HA[A−]2 n i % Kex,i [L]o
DHA =
(14)
i=1
The log–log plot of the left side of Eq. (14) versus [A−] should give a straight line with a slope of two. In the calculation of [L]o and [A−], the association between B18C6 and picric acid in the organic phase was considered. When B18C6 forms a 1:1 association complex with picric acid in the organic phase, the distribution ratio of picric acid (DHA) can be expressed as follows:
(16)
The plot of log(DHA/D oHA − 1) versus log [L]o at fixed pH is shown in Fig. 3. The initial concentration of B18C6 was made to be in large excess over that of picric acid so that [L]o could be calculated using only the distribution constant of the crown 1 ether, i.e. [L]o = [L]t/(1+ K − d,L ). The plot shows a straight line with a slope of 1.0090.02, indicating that B18C6 forms a 1:1 complex with picric acid in the benzene phase. According to Eq. (16), Kass,o = 8.229 0.30 was obtained. The mass balance equations in the extraction system can be written as follows: n
[M]t − % [MLi A2]o = [M2 + ]+ [ML2 + ]
(17)
i=1 n
[L]t − % i[MLi A2]o = [L]+[L]o + [L·HA]o i=1
+ [ML2 + ]
(18)
n
[A]t − 2 % [MLi A2]o i=1 −
= [A ]+ [HA]+ [HA]o + [L·HA]o
(19)
where [A]t is the total concentration of picric acid. In the present experiments, S[MLi A2]o, Si[MLi A2]o, and 2S[MLi A2]o were negligibly small compared with [M]t, [L]t, and [A]t, respectively. In this case, [M2 + ], [L], and [HA]o can be expressed as [L]o = [L]t/(a +b[M2 + ]+ Kass,o[HA]o)
(20)
[M2 + ]= [M]t/(1+ b[L]o)
(21)
[HA]o = [A]t/(1+ Kass,o[L]o + c) −1 d,L
log(DHA/D oHA − 1)
Fig. 3. Plots of versus log [L]o for extraction of picric acid in the presence of B18C6 at constant pH. The solid line is obtained by the calculation based on Eq. (16).
(22) −1 d,L
where a= 1+ K , b=KMLK , and c= + −1 1 K− . The combination of d,HA + (KHAKd,HA[H ]) Eqs. (20)–(22) leads to the following cubic equation for [L]o:
S. Katsuta et al. / Talanta 51 (2000) 637–644
Fig. 4. Plots of log(DM/[A−]2) versus log [L]o for extraction of Zn2 + and Cd2 + as picrates with B18C6. The solid lines are obtained by the calculation based on Eq. (13).
Table 1 The overall extraction constants, the ion-pair extraction constants, and the adduct formation constants at 25°C for the extraction of Zn2+ and Cd2+ picrates with B18C6 into benzene M2+
log Kex,1
log Kex,2
log Kex,ipa
Zn2+ −3.2090.03 −1.3690.02 1.92 Cd2+ −3.179 0.04 −1.629 0.04 2.44 a b
log Kad,ob 1.84 1.55
Calculated from Eq. (24). Calculated from Eq. (25).
abKass,o[L]3o + [a{b(1 +c) +Kass,o} +bKass,o([M]t +[A]t −[L]t)][L]2o + [(1+ c)(a +b[M]t) +Kass,o[HA]t − {b(1+c)+ Kass,o}[L]t][L]o −(1 +c)[L]t =0 (23) This equation was solved by Newton’s method to obtain [L]o. The [A−] value was calculated from the equation [A−]= [HA]o/KHAKd,HA[H+], where [HA]o was obtained from Eq. (22). The log(DM/ [A−]2) versus log[L]o plots are shown in Fig. 4. The slope of each plot increases from 1.4 to 2.0 (Zn2 + ) or 1.2 to 1.9 (Cd2 + ) with an increase of
643
[L]o. The values of the slope indicate that the extracted species are MLA2 and ML2A2, because 1 the term KMLK − d,L [L]o in Eq. (13) was much smaller than 1 (0.04 at the most). The Kex,1 and Kex,2 were determined by a nonlinear least-squares method based on Eq. (13), and the logarithmic values are listed in Table 1. The solid lines in Fig. 4 are obtained from Eq. (13) by use of the extraction constants and agree well with the experimental data. 1 The slopes of the log{DM(1+KMLK − d,L [L]o)/ − 2 (Kex,1[L]o + Kex,2[L]o)} versus log [A ] plots were 2.019 0.04 and 2.06 9 0.06 for Zn2 + and Cd2 + , respectively; they are identical with the theoretical value from Eq. (14). If the association between B18C6 and picric acid in the organic phase is neglected, the slope deviates from two (ca 1.7). These results mean that the consideration of the B18C6–picric acid association is essential for the equilibrium analysis in the present extraction systems. The formation of ML2A2 in the organic phase supports the preceding conclusion that the too small metal ion in the ML2 + complex is not effectively screened by the ether oxygen atoms of B18C6. In water, the formation of the ML22 + complex could not be detected. The very low stability of ML22 + in water can be accounted for by the remarkable interactions with water of the metal ion in ML2 + and the ether oxygens of uncomplexed L. In spite of the higher stability of ZnL2 + than CdL2 + in water, the Kex,1 values for Zn2 + and Cd2 + are almost the same. On the other hand, the Kex,2 value is larger for Zn2 + . The extraction selectivities can be explained by the constituent equilibria: the overall extraction constants are expressed as −2 1 Kex,1 = KMLKex,ipK − d,L (KHAKd,HA)
(24)
Kex,2 = Kex,1Kad,o
(25)
where Kex,ip and Kad,o are the ion-pair extraction constant of the complex cation with the picrate anion (Kex,ip = [MLA2]o/[ML2 + ][A−]2) and the adduct formation constant in the organic phase (Kad,o = [ML2A2]o/[MLA2]o[L]o), respectively. The values of Kex,ip and Kad,o were calculated accord-
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ing to Eqs. (24) and (25), respectively, and the logarithmic values are listed in Table 1. The log Kex,ip value is smaller for Zn2 + than for Cd2 + . The decrease in log Kex,ip from Cd2 + to Zn2 + just cancels the increase in log KML, which is responsible for the comparable log Kex,1 values of these metal ions. The log Kad,o value is larger for Zn2 + than for Cd2 + , and the difference in log Kad,o between the two metals is reflected by the difference in log Kex,2. The larger Kad,o value of ZnLA2 than CdLA2 suggests that, even in the MLA2 form, Zn2 + has a higher ability as an acceptor than Cd2 + . The Kex,ip is further expressed as a product of two elementary equilibrium constants, i.e. the ion-pair formation constant in water (KMLA2 = [MLA2]/[ML2 + ][A−]2) and the distribution constant of the ion-pair (Kd,MLA2 =[MLA2]o /[MLA2]). At this stage, these underlying constants are unknown. However, from the higher ability of ZnLA2 to accept an additional ligand, it is suggested that ZnLA2 be more strongly hydrated in water than CdLA2, and that the distribution constant of ZnLA2 is smaller; thus the stronger hydration of ZnLA2 is responsible for the smaller Kex,ip value.
Acknowledgements This research was partly supported by a Grant-in-Aid for Scientific Research No. 11740407 from the Ministry of Education, Science and Culture.
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