# Pb(II) Extraction with Benzo-18-Crown-6 Ether into Benzene under the Co-Presence of Cd(II) Nitrate in Water

^{*}

## Abstract

**:**

^{−}] and 0, 0.58, 15, 48, or 97 mmol·dm

^{−3}Cd(NO

_{3})

_{2}by benzo-18-crown-6 ether (B18C6; L as its symbol) into benzene (Bz) was studied. Three kinds of extraction constants, K

_{ex}, K

_{ex±}, and K

_{Pb/PbL}(or K

_{ex2±}), were determined at 298 K: these constants were defined as [PbLPic

_{2}]

_{Bz}/P, [PbLPic

^{+}]

_{Bz}[Pic

^{−}]

_{Bz}/P, and [PbL

^{2+}]

_{Bz}/[Pb

^{2+}][L]

_{Bz}(or [PbL

^{2+}]

_{Bz}([Pic

^{−}]

_{Bz})

^{2}/P), respectively. The symbol P shows [Pb

^{2+}][L]

_{Bz}[Pic

^{−}]

^{2}and the subscript “Bz” denotes the Bz phase, Bz saturated with water. Simultaneously, conditional distribution constants, K

_{D,Pic}(=[Pic

^{−}]

_{Bz}/[Pic

^{−}]), of Pic

^{−}with distribution equilibrium-potential differences (dep) were determined. Then, based on the above four constants and others, the component equilibrium constants of K

_{1,Bz}(=[PbLPic

^{+}]

_{Bz}/[PbL

^{2+}]

_{Bz}[Pic

^{−}]

_{Bz}), K

_{2,Bz}(=[PbLPic

_{2}]

_{Bz}/[PbLPic

^{+}]

_{Bz}[Pic

^{−}]

_{Bz}), and K

_{D,PbL}(=[PbL

^{2+}]

_{Bz}/[PbL

^{2+}]) were obtained. Using these constants, the Pb(II) extraction with B18C6 under the co-presence of Cd(II) in the water phase was characterized. In such a characterization, I and I

_{Bz}dependences on the constants were mainly discussed, where their symbols denote the ionic strength of the water phase and that of the Bz one, respectively.

## 1. Introduction

_{ex}and K

_{ex±}, have been employed for evaluating their extraction-abilities and -selectivities [1,2,3,4,5,6]. Here, the constants K

_{ex}and K

_{ex±}have been generally defined as [MLA

_{z}]

_{org}/P and [MLA

_{z}

_{−1}

^{+}]

_{org}[A

^{−}]

_{org}/P, respectively, with P = [M

^{z}

^{+}][L]

_{org}[A

^{−}]

^{z}at z = 1 and 2 [1,7,8,9]. The symbols M

^{z}

^{+}, A

^{−}, and the subscript “org” denote a metal ion with the formal charge of z+, a univalent pairing anion, and an organic phase, respectively. For evaluating the ability and selectivity of L for its extraction, many studies have been present [1,2,3,4,5,6,7,8,9], but those for clarifying ionic strength (I) dependences of the equilibrium constants seemed to be few [10,11]. Recently, one of the authors reported the I and I

_{DCE}(with HNO

_{3}as an I conditioner) dependences of the K

_{ex}and K

_{ex±}values in the silver picrate (AgPic) extraction with benzo-18-crown-6 ether (B18C6) into 1,2-dichloroethane (DCE), where I

_{DCE}refers to the I value for the DCE phase [12]. At the same time, conditional distribution constants (K

_{D,A}= [A

^{−}]

_{org}/[A

^{−}]) of the picrate ion Pic

^{−}(=A

^{−}) into the DCE (=org) phases have been determined [12] and thereby distribution equilibrium potential-differences (dep; Δφ

_{eq}as a symbol in an equation) have been evaluated [7,8,12].

^{II}Pic

_{2}extraction one, we determined at 298 K the K

_{ex}, K

_{ex±}, and K

_{D,Pic}values for PbPic

_{2}extraction with B18C6 into benzene (Bz) under a co-presence of Cd(NO

_{3})

_{2}in a water phase. Then, I and I

_{Bz}dependences of these equilibrium constants were mainly examined [12]. Similar examinations were performed for other overall or component equilibrium-constants, such as K

_{Pb/PbL}, K

_{ex,ip}, and K

_{1,Bz}(see Equations (6)–(8) for their definitions), derived from the above equilibrium constants. This study is expected to be useful for comparisons between the K

_{ex}and K

_{ex±}values, because magnitudes of their comparable values depend on I [10,11] or I

_{Bz}in general. Consequently, such data relevant to I and I

_{Bz}can make more precise comparisons between the values possible.

^{z}

^{+}separation with solvent extraction [13] and membrane transport experiments has been studied [14,15]. However, these quantitative considerations based on any equilibrium constants have not been reported. This situation reveals the importance of these fundamental studies [10,11,12] and this work as well, which can make a prediction for their separation more precise.

^{−}at the water/Bz interfaces were evaluated from the determined K

_{D,Pic}values [16]. Moreover, the relationship between log K

_{ex±}and dep was quantitatively discussed [7,16].

_{ex,Pb}/K

_{ex,Cd}) value of 9.73 for the Pb(II) and Cd(II) extraction with 18C6 [9]. However, against our plan, such an extraction behavior was not observed here.

## 2. Results and Discussion

#### 2.1. Determination of Composition of Extracted Species with Pb(II) at Some [Cd]_{t}/[Pb]_{t} Values

_{ex}or K

_{ex±}definition [1,8,19,21]: K

_{ex}= [MLA

_{2}]

_{org}/P and K

_{ex±}= [MLA

^{+}]

_{org}[A

^{−}]

_{org}/P with P = [M

^{2+}][L]

_{org}[A

^{−}]

^{2}at z = 2. Taking common logarithms of both sides of these definitions and then rearranging them, we can easily obtain

_{0}/[A

^{−}]

^{2}) = log K

_{ex}+ log [L]

_{org}

_{+}/[A

^{−}]) = log K

_{ex+}+ log [L]

_{org}

_{0}= [MLA

_{2}

^{0}]

_{org}/[M

^{2+}], D

_{+}= [MLA

^{+}]

_{org}/[M

^{2+}] (see the Section 2.9), and K

_{ex+}(=K

_{ex±}/K

_{D,A}) = [MLA

^{+}]

_{org}/[M

^{2+}][L]

_{org}[A

^{−}] [1,8,19]. From applying the approximate that D

_{0}and D

_{+}nearly equal D for Equations (1) and (2), respectively, the following equations were derived:

^{−}]

^{2}) ≈ log K

_{ex}+ log [L]

_{org}

^{−}]) ≈ log K

_{ex+}+ log [L]

_{org}

_{(species analyzed by AAS measurement)}/([Pb(II)]

_{t}− [Pb(II)]

_{(species analyzed by AAS measurement)})

_{org}. In addition, [Pb(II)]

_{t}refers to a total concentration of Pb(NO

_{3})

_{2}employed. Therefore, in terms of a plot of log (D/[A

^{−}]

^{2}) versus log [L]

_{Bz}come from Equation (1a) or that of log (D/[A

^{−}]) from Equation (2a), we can determine the Pb(II):L compositions in the extraction systems from their slopes [9]. Figure 1 shows such plots based on Equation (1a).

^{−3}of Cd(II) (or [Cd]

_{t}/[Pb]

_{t}= 0), 1.0 for that with 0.58 of Cd(II) (or 1.06), 0.97 for that with 14 of Cd(II) (or 26.6), 0.98 for that with 48 of Cd(II) (or 88.4), and 1.0 for that with 97 of Cd(II) (or 178). From these results, we can see easily that the compositions of Pb(II):B18C6 are 1:1 for all the systems. In the present study, there was no need of employing Equation (2a). The compositions of Pb(II):Pic(−I) were speculated to be 1:2 from similarity to the systems [3] reported before for M(II) extraction with 18C6 into Bz and from a charge balance in the Bz phases [1,8,19,21]: approximately [PbLPic

^{+}]

_{Bz}≈ [Pic

^{−}]

_{Bz}from more-precisely 2[Pb

^{2+}]

_{Bz}+ 2[PbL

^{2+}]

_{Bz}+ [PbLPic

^{+}]

_{Bz}+ [PbPic

^{+}]

_{Bz}≈ [Pic

^{−}]

_{Bz}+ [NO

_{3}

^{−}]

_{Bz}, because it was expected that [PbLPic

^{+}]

_{Bz}>> 2[Pb

^{2+}]

_{Bz}+ 2[PbL

^{2+}]

_{Bz}+ [PbPic

^{+}]

_{Bz}and [Pic

^{−}]

_{Bz}>> [NO

_{3}

^{−}]

_{Bz}[9,21].

#### 2.2. Determination of K_{ex}, K_{ex±}, and K_{D,Pic}

_{ex}

^{mix}) has been proposed:

_{ex}

^{mix}= log {([MLA

_{2}]

_{org}+ [MLA

^{+}]

_{org}+ [ML

^{2+}]

_{org}+ …)/P}

≈ log {K

_{ex}+ (K

_{D,A}/[M

^{2+}][L]

_{org}[A

^{−}])}

_{D,A}≈ [MLA

^{+}]

_{org}/[A

^{−}]. Using this equation, we can immediately obtain the K

_{ex}and K

_{D,A}values from a plot of log K

_{ex}

^{mix}versus −log ([M

^{2+}][L]

_{org}[A

^{−}]). In addition, Equation (3) can be rewritten as:

_{ex±}value (with the K

_{ex}one; see Table 1) can be obtained from a plot of log K

_{ex}

^{mix}versus −log P

^{1/2}. Figure 2 and Figure 3 show examples of such plots.

_{D,Pic}, K

_{ex±}, and K

_{ex}values were determined at 298 K. Table 1 lists these extraction constants, K

_{ex}and K

_{ex±}, and the conditional distribution constants, K

_{D,Pic}, with averaged ionic strength-values (I) for the water phase in the five [Cd]

_{t}/[Pb]

_{t}conditions. The K

_{ex}values determined with Equation (4) were equal or close to those with Equation (3). This fact raises the credibility of the values themselves and also shows the effects of Equations (3) and (4) on evaluation. The K

_{ex}and K

_{ex±}values at [Cd]

_{t}/[Pb]

_{t}= 0 were smaller than those (10

^{11.712}mol

^{−3}·dm

^{9}and 10

^{4.1}mol

^{−2}·dm

^{6}[9]) reported before at I = 0.0059 mol·dm

^{−3}for the PbPic

_{2}extraction with 18C6 into Bz.

#### 2.3. Dep Determination from K_{D,Pic}

_{D,Pic}values listed in Table 1, using the following equation and a standardized distribution constant (K

_{D,Pic}

^{S}), we can easily obtain the dep (or Δφ

_{eq}) values for the five [Cd]

_{t}/[Pb]

_{t}conditions at 298 K:

_{eq}= −0.05916(log K

_{D,Pic}− log K

_{D,Pic}

^{S}) = Δφ

_{Pic}

^{0}′ − 0.05916log K

_{D,Pic}

_{D,Pic}

^{S}value is defined as the K

_{D,Pic}one at Δφ

_{eq}= 0 V, equals antilog (Δφ

_{Pic}

^{0}′/0.05916) (=exp (Δφ

_{Pic}

^{0}′/0.02569) [23]), and, as its common logarithmic value, −8.208 or −7.4473 is available from references [24,25]. In addition, the minus sign of −0.05916 (=−2.303RT/F ) and the symbol Δφ

_{Pic}

^{0}′ denote the formal charge of Pic

^{−}and the standard formal potential for the Pic

^{−}transfer across the water/Bz interface, respectively. We mainly employed the former value for the evaluation described below. Table 1 lists the dep/V values evaluated from log K

_{D,Pic}

^{S}= −8.208 [24].

#### 2.4. Determination of K_{Pb/PbL}, K_{ex,ip}, K_{1,Bz}, K_{2,Bz}, and K_{D,PbL}

_{Pb/PbL}= log ([PbL

^{2+}]

_{Bz}/[Pb

^{2+}][L]

_{Bz}) ≈ log (D/[L]

_{Bz}),

_{ex,ip}= log ([PbLPic

_{2}]

_{Bz}/[PbL

^{2+}][Pic

^{−}]

^{2}) = log (K

_{ex}K

_{D,L}/K

_{PbL}),

_{1.Bz}= log ([PbLPic

^{+}]

_{Bz}/[PbL

^{2+}]

_{Bz}[Pic

^{−}]

_{Bz}) ≈ log {K

_{ex±}/K

_{Pb/PbL}(K

_{D,Pic})

^{2}}

_{ex±}/K

_{ex2±}),

_{2,Bz}= log ([PbLPic

_{2}]

_{Bz}/[PbLPic

^{+}]

_{Bz}[Pic

^{−}]

_{Bz}) = log (K

_{ex}/K

_{ex±}),

_{D,PbL}= log ([PbL

^{2+}]

_{Bz}/[PbL

^{2+}]) ≈ log (K

_{Pb/PbL}K

_{D,L}/K

_{PbL}).

_{Pb/PbL}values, they were obtained as the averages of D/[B18C6]

_{Bz}at every [Cd]

_{t}/[Pb]

_{t}value [27]. For the above evaluation at 298 K, 0.943 [2] and 3.19 [29] were used as the logarithmic values of K

_{D,B18C6}(=[B18C6]

_{Bz}/[B18C6]) and K

_{PbB18C6}(=[PbB18C6

^{2+}]/[Pb

^{2+}][B18C6]), respectively. These five logarithmic K-values are summarized in Table 2, together with the ionic strength-values (I

_{Bz}) for the Bz phase.

#### 2.5. Correlation between log K_{ex±} and Dep

^{+}extraction with Pic

^{−}.

_{ex±}= 2log K

_{D,Pic}+ log K

_{Pb/PbL}+ log K

_{1,Bz}

= 2log K

_{D,Pic}

^{S}− 2(F/2.303RT)Δφ

_{eq}+ log K

_{Pb/PbL}·K

_{1,Bz}

_{Pb/PbL}·K

_{1,Bz}term was in the range of 8.7 to 9.1 (see the data in Table 2) and log K

_{D,Pic}

^{S}(=−8.208 [24] or −7.4473 [25]) equals log K

_{D,Pic}at Δφ

_{eq}= 0 V. Hence, we obtained to be −7.7 to −7.3 for the former K

_{D,Pic}

^{S}value or the −6.2 to −5.8 for the latter one as the term of 2log K

_{D,Pic}

^{S}+ log K

_{Pb/PbL}⋅K

_{1,Bz}(see Table 1 and Table 2). In addition, 2F/2.303RT becomes 33.80 V

^{−1}at T = 298.15 K. Rearranging Equation (11), we can immediately derive

_{ex±}≈ (−7.7 to −7.3) − 33.80Δφ

_{Equation}

_{ex±}= (−5.

_{3}± 1.

_{4}) − (27.

_{3}± 4.

_{2})Δφ

_{eq}at |R| = 0.967, where the symbol R denotes a correlation coefficient. This regression line is close to Equation (11a) which was estimated from the experimental K values. This fact indicates the presence of dep, as similar to the results reported previously [7,8,12,16,21,22].

#### 2.6. I Dependences of log K_{ex} and log K_{ex,ip}

_{ex}is K

_{ex}

^{0}= [PbLPic

_{2}]

_{Bz}/a

_{Pb}[L]

_{Bz}(a

_{Pic})

^{2}, where a

_{Pb}and a

_{Pic}refer to activities of Pb

^{2+}and Pic

^{−}in the water phase, respectively, and it was assumed that [PbLPic

_{2}]

_{Bz}is equal to the activity in the Bz phase, because PbL

^{2+}(Pic

^{−})

_{2}is charge-less. The same is true of [B18C6]

_{Bz}too. Taking the common logarithms of both sides of the K

_{ex}

^{0}definition, we can obtain

_{ex}

^{0}= log K

_{ex}− log {y

_{Pb}(y

_{Pic})

^{2}}

_{Pb}= a

_{Pb}/[Pb

^{2+}] and y

_{Pic}= a

_{Pic}/[Pic

^{−}]. Introducing the extended Debye–Hückel (DH) equation [30,31] in Equation (12) and arranging it, the following equation was obtained:

^{−3}[30] as you know, we approximately employed it for the condition of I = 0.29 (see Table 1). Figure 5 shows curve-fittings of the plots for Equation (12a).

_{ex}= (9.91 ± 0.03) − 6 × (0.5114)$\sqrt{I}$/(1 + (3.4

_{0}± 0.4

_{6})$\sqrt{I}$) at R = 0.980, where the coefficient A was fixed to 0.5114 mol

^{−1/2}·dm

^{3/2}[30] and the ${\xe5}_{\pm}$ value in water was evaluated to be 10 Å (=3.4

_{0}/0.3291) at 298 K.

_{ex,ip}values were analyzed. Their constants were expressed as

_{ex,ip}

^{0}= [PbLPic

_{2}]

_{Bz}/a

_{PbL}(a

_{Pic})

^{2}= K

_{ex,ip}/y

_{PbL}(y

_{Pic})

^{2}

_{ex,ip}= (7.66 ± 0.03) − 6 × (0.5114)$\sqrt{I}$/(1 + (3.4

_{1}± 0.5

_{1})$\sqrt{I}$) at R = 0.975 and then the a

_{±}value was evaluated to be 10 Å. The accordance between Pb

^{2+}–Pic

^{−}distance and PbB18C6

^{2+}–Pic

^{−}one suggests that the former interaction between the Pb

^{2+}and Pic

^{−}ions in water saturated with Bz is equivalent with the latter one between PbB18C6

^{2+}and Pic

^{−}.

_{5}Å) of the ion-size parameters [32] between Pb

^{2+}(4.5 Å) and Pic

^{−}(7 Å) for water. This K

_{ex,ip}

^{0}value was well in accord with that (=10

^{7.66}mol

^{−1}·dm

^{3}) calculated from the thermodynamic cycle of K

_{ex,ip}

^{0}≈ K

_{ex}

^{0}K

_{D,L}/K

_{PbL}(=10

^{9.91}× 10

^{0.943}/10

^{3.19}).

_{ex}values are most precise ones of the some extraction constants determined here (see their errors in Table 1), the fair dependences of log K

_{ex}on I indicate a simple role of Cd(NO

_{3})

_{2}only as the ionic strength conditioner in the present extraction systems. In other words, the authors were not be able to clearly find out positive or negative effects of Cd(NO

_{3})

_{2}on the present Pb(II) extraction with B18C6 into Bz.

#### 2.7. I_{Bz} Dependences of log K_{1,Bz} and log K_{2,Bz}

_{Bz}and the DH limiting law [30], both log K

_{1,Bz}

^{0}and log K

_{2,Bz}

^{0}can be expressed as

_{PbLPic,Bz}≈ y

_{Pic,Bz}and

_{1,Bz}= (5.9

_{8}± 0.4

_{9}) − 4 × (63 ± 89)$\sqrt{{I}_{\mathrm{Bz}}}$ at R = 0.449 except for the point of [Cd]

_{t}/[Pb]

_{t}= 178 and log K

_{2,Bz}= (6.8

_{1}± 0.6

_{8}) − 2 × (282 ± 195)$\sqrt{{I}_{\mathrm{Bz}}}$ at R = 0.641. These lines intersected with each other at I

_{Bz}

^{1/2}= 2.

_{7}× 10

^{−3}mol

^{1/2}·dm

^{−3/2}, yielding log K

_{1,Bz}= log K

_{2,Bz}= 5.3

_{1}. This fact indicates that, in the lower I

_{Bz}range less than 7.

_{1}× 10

^{−6}mol·dm

^{−3}, the K

_{2,Bz}values are larger than the K

_{1,Bz}ones. The latter values may be estimated to actually be the smaller values because of the approximation [33] for the K

_{1,Bz}determination (see Equation (8)). Unlike the case of the CdPic

_{2}–B18C6 extraction system [33], unfortunately, we do not have the procedure which corrects such deviations for the present extraction systems, because of a lack of adequate data used for the correction.

_{1}and b

_{2}denote empirical curve-fitting parameters [30,31] which were simply predicted in this study from the plot shapes (see Figure 6). The regression analyses of the plots at 298 K gave log K

_{1,Bz}= (6.1

_{6}± 0.8

_{0}) − 4 × (179 ± 247)$\sqrt{{I}_{\mathrm{Bz}}}$ + (2.

_{3}± 2.

_{7}) × 10

^{5}I

_{Bz}at R = 0.569 and log K

_{2,Bz}= (8.8

_{0}± 0.9

_{8}) − 2 × (1625 ± 603)$\sqrt{{I}_{\mathrm{Bz}}}$ + (7.

_{6}± 3.

_{3}) × 10

^{5}I

_{Bz}at 0.914 (see Figure 7). Modifying these equations like the Davies one [30,31], their 2nd and 3rd terms became −4 × (179 ± 247)($\sqrt{{I}_{\mathrm{Bz}}}$ − (3.

_{2}± 5.

_{9}) × 10

^{2}I

_{Bz}) and −2 × (1625 ± 603)($\sqrt{{I}_{\mathrm{Bz}}}$ − (2.

_{3}± 1.

_{3}) × 10

^{2}I

_{Bz}), respectively. These b

_{1}/4A

_{Bz}and b

_{2}/2A

_{Bz}values of about 320 and 230 mol

^{−1/2}·dm

^{3/2}for the Bz phases are much larger than 0.3 [31] for the aqueous solution at 298 K. Equation (14b) intersects Equation (15b) around I

_{Bz}

^{1/2}= 3.

_{3}× 10

^{−3}mol

^{1/2}·dm

^{−3/2}, yielding log K

_{1,Bz}= log K

_{2,Bz}= 6.3

_{0}, and then their two lines equal with each other within the experimental errors (see the plots in Figure 7).

_{Bz}

^{1/2}/mol

^{1/2}·dm

^{−3/2}= 0.002

_{7}to 0.003

_{3}, while their corresponding log K

_{1,Bz}(=log K

_{2,Bz}) value changed from 5.3 to 6.3.

_{Bz}range less than 1.

_{1}× 10

^{−5}mol·dm

^{−3}, the K

_{2,Bz}values are larger than the K

_{1,Bz}ones. From the results of the calculation based on Equations (14a,b) and (15a,b), the relation of K

_{1,Bz}< K

_{2,Bz}holds in the range less than (0.7

_{1}− 1.

_{1}) × 10

^{−5}mol·dm

^{−3}(see above). According to the paper [8], such a fact suggests a structural change around Pb(II) in the reaction of Pb(B18C6)Pic

^{+}

_{Bz}+ Pic

^{−}

_{Bz}⇌ Pb(B18C6)Pic

_{2,Bz}, such as Cd(18C6)Pic

_{2,Bz}of the Cd(II) extraction systems [33]. Trends similar to K

_{1,Bz}< K

_{2,Bz}are observed in the reactions of Cd18C6

^{2+}with Pic

^{−}, Cl

^{−}, and Br

^{−}in the Bz phases for fixed I

_{Bz}values [1,8]. The higher I

_{Bz}range may lead to the formation of ion-pair complexes with other coordination structures around Pb(II), although their structures are not clear.

_{1,Bz}and K

_{2,Bz}between the experimental and estimated values, the |dif.| values estimated from Equations (14b) and (15b) were essentially smaller than those done from Equations (14a) and (15a). Especially, the former equations seem to be superior to the latter ones in the I

_{Bz}range, namely the present experimental [Cd]

_{t}/[Pb]

_{t}range, of 4 × 10

^{−7}to 8 × 10

^{−6}mol·dm

^{−3}in the cases of the prediction of K

_{2,Bz}. Unfortunately, chemical and physical meanings of b

_{1}and b

_{2}are not clear still now.

#### 2.8. I_{Bz} Dependences of log K_{ex±}^{0}′, log K_{D,Pic}^{0}′, and log K_{Pb/PbL}^{0}

_{ex±}

^{0}is equal to (y

_{±,Bz})

^{2}K

_{ex±}

^{0}′, with y

_{±,Bz}= (y

_{PbLPic,Bz}·y

_{Pic,Bz})

^{1/2}and K

_{ex±}

^{0}′ = [PbLPic

^{+}]

_{Bz}[Pic

^{−}]

_{Bz}/(a

_{Pb}[L]

_{Bz}(a

_{Pic})

^{2}). Taking the common logarithms of the both sides in this equation and rearranging it with the DH limiting law, we can easily obtain

_{ex±}

^{0}′ versus I

_{Bz}

^{1/2}based on Equation (16). The regression analysis of this plot gave the equation of log K

_{ex±}

^{0}′ = (3.1

_{1}± 0.6

_{9}) + 2 × (315 ± 196)$\sqrt{{I}_{\mathrm{Bz}}}$ at R = 0.680. From this K

_{ex,±}

^{0}value and the K

_{ex}

^{0}one, we calculated log K

_{2,Bz}

^{0}to be 6.8

_{0}± 0.6

_{9}, being in good agreement with that (=6.8) evaluated from Equation (15a).

_{D,Pic}

^{0}′ versus I

_{Bz}

^{1/2}was performed in Figure 9, where K

_{D,Pic}

^{0}′ is defined as [Pic

^{−}]

_{Bz}/a

_{Pic}. This plot is based on the equation

_{D,Pic}

^{0}′ = (−3.0

_{0}± 0.3

_{6}) + (258 ± 210)$\sqrt{{I}_{\mathrm{Bz}}}$ at R = 0.578.

_{Bz}). This value, 245 mol

^{−1/2}·dm

^{3/2}, is comparable to the b

_{1}/4A

_{Bz}(=~320) and b

_{2}/2A

_{Bz}(=~230) values estimated above.

_{Pb/PbL}

^{0}′ (=log ([PbL

^{2+}]

_{Bz}/a

_{Pb}[L]

_{Bz})) values were analyzed. This constant was related with the log K

_{Pb/PbL}

^{0}(=log (a

_{PbL,Bz}/a

_{Pb}[L]

_{Bz})) value by the following equation:

_{Pb/PbL}

^{0}′ values were plotted against the I

_{Bz}

^{1/2}ones. The regression line based on Equation (18) was log K

_{Pb/PbL}

^{0}′ = (3.546 ± 0.001) + 4 × (2.1

_{6}± 0.1

_{6})$\sqrt{{I}_{\mathrm{Bz}}}$ at R = 0.997, except for the two points of I

_{Bz}= 4.

_{4}× 10

^{−7}and 1.

_{7}× 10

^{−6}mol·dm

^{−3}(see Table 2). These two log K

_{Pb/PbL}

^{0}′ values excluded from the regression analysis are included in the regression line within experimental errors. However, the A

_{Bz}value is much smaller than the others. In addition, the analysis was tried by using an equation similar to Equations (14b) and (15b). However, its regression line showed the result of A

_{Bz}< 0.

_{D,Pic}

^{0}, the log K

_{Pb/PbL}

^{0}can be changed into log K

_{ex2±}

^{0}(=log (a

_{PbL,Bz}(a

_{Pic,Bz})

^{2}/a

_{Pb}[L]

_{Bz}(a

_{Pic,Bz})

^{2})) = log K

_{Pb/PbL}

^{0}+ 2log K

_{D,Pic}

^{0}. Thus, the log K

_{ex2±}

^{0}value was estimated to be −2.4

_{5}± 0.3

_{7}from Equation (17) (the linear type) or −4.9

_{6}± 0.1

_{3}from Equation (17a) (the f (p) = a + bp + cp

^{2}type). Using log K

_{ex±}

^{0}= 3.1

_{1}obtained from Equation (16) and log K

_{1,Bz}

^{0}= 5.9

_{8}from Equation (14a) (the linear type), the log K

_{ex2±}

^{0}value was calculated to be −2.8

_{7}± 0.8

_{5}. On the other hand, the log K

_{ex2±}

^{0}value became −3.

_{1}± 1.

_{1}in the calculation with log K

_{1,Bz}

^{0}= 6.1

_{6}from Equation (14b) (the f (p) = a + bp + cp

^{2}type). Except for −4.9 from Equation (17a), the values calculated from the three equations agreed with each other within their calculation errors. According to the thermodynamic cycle, the relation of K

_{ex±}= K

_{Pb/PbL}K

_{1,Bz}(K

_{D,Pic})

^{2}holds. From this relation, we obtained log K

_{ex±}

^{0}= 3.5

_{4}± 0.7

_{2}(=log K

_{Pb/PbL}

^{0}+ log K

_{1,Bz}

^{0}+ 2log K

_{D,Pic}

^{0}). This value is in agreement with that (=3.1) calculated from Equation (16) within the calculation error of ±0.7. In addition, the same calculation was performed with the values obtained from the polynomial Equations (14b) and (17a). Its value was 1.2

_{0}± 0.8

_{3}, being much smaller than 3.1. These results suggest that the linear-type equation is the more reliable than the polynomial-type one, from the thermodynamic points of view.

_{Bz}/mol

^{−1/2}·dm

^{3/2}values based on Equations (14a), (15a), (16), and (17), except for the value obtained from Equation (18), their average value was estimated to be 230. Consequently, this A

_{Bz}value for Bz saturated with water was about 2-times larger than that (=103.3 mol

^{−1/2}·dm

^{3/2}) calculated for pure Bz with ε

_{r}= 2.275 [2] at 298.15 K. To agree with this conclusion, however, a reasonable reason will be required for the omission of the result of Equation (18).

#### 2.9. A Try for Estimation of Detailed Separation Factor

^{−}and L.

_{ex,Pb}/K

_{ex,Cd}) = log (D

_{0,Pb}/D

_{0,Cd}),

_{ex±,Pb}/K

_{ex±,Cd}) = log (D

_{+,Pb}/D

_{+,Cd}),

_{Pb/PbL}/K

_{Cd/CdL}) = log (D

_{2+,Pb}/D

_{2+,Cd})

_{0,Pb}= [PbLPic

_{2}]

_{Bz}/[Pb

^{2+}] = K

_{ex}[L]

_{Bz}[Pic

^{−}]

^{2},

_{+,Pb}= [PbLPic

^{+}]

_{Bz}/[Pb

^{2+}] = K

_{ex±}[L]

_{Bz}[Pic

^{−}]/K

_{D,Pic},

_{2+,Pb}= [PbL

^{2+}]

_{Bz}/[Pb

^{2+}] = K

_{Pb/PbL}[L]

_{Bz}.

_{0,Pb}, D

_{+,Pb}, and D

_{2+,Pb}show the values of M = Pb at z = 0, 1, and 2, respectively. The same is true of the definitions for the Cd(II) (=M(II)) extraction system with B18C6.

_{0,Pb}/D

_{0,Cd}) = log ([PbLPic

_{2}]

_{Bz}/[CdLPic

_{2}]

_{Bz}) + log ([Cd

^{2+}]/[Pb

^{2+}])

^{2+}]/[Pb

^{2+}] approximately equals [Cd

^{2+}]

_{t}/[Pb

^{2+}]

_{t}, then we can estimate the more detailed value than the separation factor. In the Pb(II) extraction with Cd(II) by B18C6 into Bz, the log (D

_{0,Pb}/D

_{0,Cd}) value was 7.09 in which the log K

_{ex}value (=9.44

_{8}) was estimated at I = 0.095 [33] from the regression line of Figure 5. From Equation (25) and [Cd

^{2+}]

_{t}/[Pb

^{2+}]

_{t}= 55.

_{5}estimated from a correlation between [Cd]

_{t}/[Pb]

_{t}and I in Table 1, the log ([PbLPic

_{2}]

_{Bz}/[CdLPic

_{2}]

_{Bz}) value became 5.35. At least this result shows that the actual separation of Pb(II) from a test solution with an 56 excess amount of Cd(II) is possible. The same can be true of an application based on the handling for D

_{+,Pb}/D

_{+,Cd}and D

_{2+,Pb}/D

_{2+,Cd}, if the K

_{ex±,Cd}and K

_{Cd/CdL}values are determined about the CdPic

_{2}extraction with B18C6 (=L) into Bz.

#### 2.10. Relative Concentrations of the Three Species Extracted into Bz

_{2}, PbLPic

^{+}, and PbL

^{2+}in the Bz phases from the D

_{0,Pb}, D

_{+,Pb}, and D

_{2+,Pb}values, respectively [8,24,30]. For example, the percentage of the relative concentration of PbLPic

_{2}can be obtained from 100D

_{0,Pb}/(D

_{0,Pb}+ D

_{+,Pb}+ D

_{2+,Pb}). In addition, the concentrations of PbLPic

^{+}and PbL

^{2+}were evaluated from similar equations. The thus-calculated values were: 46% for PbLPic

_{2}, 10% for PbLPic

^{+}, and 44% for PbL

^{2+}at I = 0.0074 mol·dm

^{−3}(or [Cd]

_{t}/[Pb]

_{t}= 0); 38%, 25%, and 37% at 0.0060 (or 1.06

_{1}), respectively; 35%, 32%, and 34% at 0.048 (or 26.6

_{3}), respectively; 24%, 53%, and 23% at 0.15 (or 88.4

_{8}), respectively; and 26%, 49%, and 25% at 0.29 (or 177.

_{5}), respectively.

_{2}and PbL

^{2+}into Bz is dominant in the lower I or [Cd]

_{t}/[Pb]

_{t}values, while that of CdLPic

^{+}is dominant in the higher I ones. That is, in the I range more than 0.15 mol·dm

^{−3}, the distribution of PbLPic

^{+}with Pic

^{−}may be dominant, compared with those of both PbLPic

_{2}

^{0}and PbL

^{2+}with 2Pic

^{−}. Now, the authors cannot clearly explain this result; namely, in the higher I range, why is the univalent cationic complex more extractable to the Bz phase than the other complexes are? Conversely, can they call this phenomenon “salting out effect”? However, these data can be useful for the discussion of membrane transport phenomena with L [34]. That is, what species mainly transfer through the membrane?

## 3. Materials and Methods

#### 3.1. Materials

_{3})

_{2}(Wako, 99.9%) and Cd(NO

_{3})

_{2}·4H

_{2}O (Kanto, Guaranteed pure reagent (GR), >98.0%) were determined by an EDTA titration with Na

_{2}EDTA·2H

_{2}O (Dojin, Kumamoto in Japan, >99.5%): their purities obtained were 98.3% for Pb(II) and 96.6–98.7% for Cd(II). A basic aqueous solution (pH > 10) of picric acid, HPic·mH

_{2}O, (Wako, GR, >99.5%: added water 15–25%) was analyzed at 355 or 356 nm by using a Hitachi UV–Visible spectrophotometer (type U-2001) (Hitachi High-Technologies Corporation, Tokyo, Japan) and then its concentration was determined with the calibration curve (ε

_{356}= 1.45 × 10

^{4}cm

^{−1}·mol

^{−1}·dm

^{3}[35]) for Pic

^{−}. Using a calibration curve (ε

_{273}= 2.50 × 10

^{3}·cm

^{−1}mol

^{−1}·dm

^{3}[6]) of B18C6 at 273 nm, a concentration of an aqueous solution with its ether (Tokyo Chemical Industry, Co. Ltd., Tokyo, Japan, >98.0% and others) was determined spectrophotometrically. The diluent Bz (Wako Pure Chemical Industries, Ltd., Osaka, Japan, or Kanto Chemical Co., Ltd., Tokyo, Japan) was washed three times with pure water and then saturated with water. Other chemicals were of the GR grades. Pure water was prepared as follows: a tap water was distilled once with a stainless-steel still and then passed through the Autopure system (Yamato/Millipore, type WT 101 UV) (Tokyo, Japan).

#### 3.2. Extraction Procedures

_{8}× 10

^{−4}mol·dm

^{−3}Pb(NO

_{3})

_{2}, 1.27

_{2}× 10

^{−3}HPic, x Cd(NO

_{3})

_{2}, 0.019

_{8}HNO

_{3}, and y B18C6 was prepared and mixed with the equal volume (10 or 12 cm

^{3}) of Bz saturated with water in a stoppered glass tube of about 30 cm

^{3}. Here, x was fixed at 0 mol·dm

^{−3}, 5.81

_{0}× 10

^{−4}, 0.0145

_{9}, 0.0484

_{7}, or 0.0972

_{6}and, at a fixed x, y was changed in the ranges of 6.5 × 10

^{−6}to 1.6 × 10

^{−4}mol·dm

^{−3}(see circle in Figure 1), 3.9 × 10

^{−6}to 1.9 × 10

^{−4}(square), 1.3 × 10

^{−5}to 4.4 × 10

^{−4}(diamond), 3.9 × 10

^{−6}to 2.6 × 10

^{−4}(full circle), or 3.7 × 10

^{−5}to 7.4 × 10

^{−4}(triangle), respectively. The glass tubes with some kinds of the L concentrations were agitated for 2 min. by hands and then mechanically shaken for 2 h in a water bath thermostated at 25 ± 0.3 °C. After it, the mixtures were centrifuged. The Bz phases were separated at 25 °C, transferred into the other tubes, and some cubic centimeters of 0.1 mol·dm

^{−3}HNO

_{3}were added to them. These mixtures in the tubes were handled with the same manner as that described above. The Pb(II) amounts of the acidic water phases, into which the Pb(II) species normally-extracted into Bz was back-extracted, were determined at 283.3 nm by the atomic absorption spectrophotometer (Hitachi, type Z-6100) (Hitachi High-Technologies Corporation, Tokyo, Japan) with an air–C

_{2}H

_{2}flame. At the same time, the amounts of Cd(II) in all the acidic phases were atomic-absorption-spectrophotometrically measured at 228.8 nm, but its element was not detected.

#### 3.3. Extraction Model Employed for the Analysis of the System

^{2+}+ L ⇌ PbL

^{2+}[29] (K

_{CdL}= 0.89 mol

^{−1}·dm

^{3}[18] was omitted; (2) Pb

^{2+}+ Pic

^{−}⇌ PbPic

^{+}[21]; (3) Cd

^{2+}+ Pic

^{−}⇌ CdPic

^{+}[1]; and (4) H

^{+}+ Pic

^{−}⇌ HPic [33] in the water phase; (5) Pic

^{−}⇌ Pic

^{−}

_{Bz}; (6) HPic ⇌ HPic

_{Bz}[36]; (7) L ⇌ L

_{Bz}[2]; and (8) PbL

^{2+}⇌ PbL

^{2+}

_{Bz}between the water and Bz phases; and (9) PbL

^{2+}

_{Bz}+ Pic

^{−}

_{Bz}⇌ PbLPic

^{+}

_{Bz}; and (10) PbLPic

^{+}

_{Bz}+ Pic

^{−}

_{Bz}⇌ PbLPic

_{2,Bz}in the Bz phase. Except for the Processes (5), (8)–(10), the equilibrium constants of the above processes at 298 K were available from References [1,2,18,21,29,36,37]. Analytic method of the extraction system based on this model was essentially the same as that reported before [1,9] (see Section 2.2).

## 4. Conclusions

_{ex}, K

_{ex±}, K

_{Pb/PbL}, K

_{ex,ip}, and K

_{D,Pic}were determined at 298 K. The same is also true of the K

_{1,Bz}

^{0}and K

_{2,Bz}

^{0}values at I

_{Bz}→ 0 for the simple Bz phases. It was demonstrated that the thermodynamic relations, K

_{ex}

^{0}≈ K

_{ex,ip}

^{0}K

_{PbL}/K

_{D,L}, K

_{2,Bz}

^{0}= K

_{ex}

^{0}/K

_{ex±}

^{0}, K

_{ex2±}

^{0}= K

_{Pb/PbL}

^{0}(K

_{D,Pic}

^{0})

^{2}, K

_{ex2±}

^{0}= K

_{ex±}

^{0}/K

_{1,Bz}

^{0}, and K

_{ex±}

^{0}= K

_{Pb/PbL}

^{0}K

_{1,Bz}

^{0}(K

_{D,Pic}

^{0})

^{2}, hold in the system. It seems that the linear equation is superior to the polynomial-type one for the I

_{Bz}dependences of the above equilibrium constants, although the R values with the former were less than those with the latter. Consequently, these results make comparisons between the K

_{ex}, K

_{ex±}, or K

_{1,Bz}values reported in different I or I

_{org}conditions possible. However, there may be a fact that this study must be applied to the more practical extraction and separation systems. Moreover, it was clarified experimentally that log K

_{ex±}is proportional to dep.

_{t}/[Pb]

_{t}≈ 60 was confirmed experimentally and theoretically. This condition exceeds [PbLPic

_{2}]

_{Bz}/[CdLPic

_{2}]

_{Bz}= 2.2 × 10

^{5}at B18C6 (=L) and satisfies a measure (=10

^{4}) of the separation factor. The K

_{ex,Pb}/K

_{ex,Cd}ratio at the fixed I condition can promise more precise evaluation of Pb(II) selectivity of L against Cd(II), compared with the ratio calculated at different I conditions. While, the co-presence of Cd(NO

_{3})

_{2}less than 180 of [Cd]

_{t}/[Pb]

_{t}has no clear effect to the experimental Pb(II) extraction with B18C6 into Bz. This Cd(II) salt in the present system acted only as the ionic strength conditioner in the water phases.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

K_{ex} | Extraction constant for MLA_{2} |

K_{ex±} | Extraction constant for MLA^{+} with A^{−} |

I | Ionic strength for the water phase |

K_{D,A} | Conditional distribution constant of A^{−} into the org phase |

K_{M/ML} | Incorporative constant of M^{2+} with L into the org phase |

K_{ex,ip} | Ion-pair extraction constant for MLA_{2} |

K_{1,org} | Ion-pair formation constant for ML^{2+} with A^{−} in the org phase |

D_{0}, D_{+}, D | Distribution ratio for MLA_{2}, that for MLA^{+}, that for mixture |

K_{ex+} | Extraction constant for MLA^{+} |

K_{ex}^{mix} | Extraction-constant parameter |

Dep, Δϕ_{eq} | Distribution equilibrium potential between the bulk water and org phases |

K_{D,Pic}^{S} | Standard distribution constant of Pic^{−} into the org phase |

Δϕ_{Pic}^{0}′ | Standard formal potential for the Pic^{−} transfer across the water/org interface |

K_{2,org} | Ion-pair formation constant for MLA^{+} with A^{−} in the org phase |

K_{D,PbL} | Conditional distribution constant of PbL^{2+} into the org phase |

K_{ex2±} | Extraction constant for ML^{2+} with 2A^{−} |

K_{D,L} | Distribution constant of L into the org phase |

K_{PbL} | Complex formation constant of Pb^{2+} with L in water |

K_{ex}^{0} | Thermodynamic extraction constant of K_{ex} |

å_{±} | Ion-size parameter, a mean value |

K_{ex,ip}^{0} | Thermodynamic ion-pair extraction constant of K_{ex,ip} |

K_{1,Bz}^{0} | Thermodynamic ion-pair formation constant for ML^{2+} with A^{−} in the Bz phase |

K_{2,Bz}^{0} | Thermodynamic ion-pair formation constant for MLA^{+} with A^{−} in the Bz phase |

K_{ex±}^{0} | Thermodynamic extraction constant of K_{ex±} |

K_{Pb/PbL}^{0} | Thermodynamic incorporative constant of Pb^{2+} with L into the org phase |

K_{ex2±}^{0} | Thermodynamic extraction constant of K_{ex2±} |

D_{2+,Pb} | Distribution ratio for PbL^{2+} |

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**Figure 1.**Plots for composition determination based on Equation (1a) under the conditions of [Cd]

_{t}/[Pb]

_{t}= 0 (open circle), 1.06 (square), 26.6 (diamond), 88.5 (full circle), and 178 (triangle).

**Figure 2.**Plot of log K

_{ex}

^{mix}versus −log ([Pb

^{2+}][L]

_{Bz}[Pic

^{−}]) with L = B18C6 at [Cd]

_{t}/[Pb]

_{t}= 88.5. The line is based on Equation (3).

**Figure 3.**Plot of log K

_{ex}

^{mix}versus −log P

^{1/2}with B18C6 at [Cd]

_{t}/[Pb]

_{t}= 88.5. The line is based on Equation (4).

**Figure 4.**Plot of log K

_{ex±}versus dep for the Pb(II) extraction with Cd(NO

_{3})

_{2}and B18C6 into Bz. The line corresponds to Equation (11a).

**Figure 5.**Plot of log K

_{ex}versus I

^{1/2}for the Pb(II) extraction with Cd(NO

_{3})

_{2}and B18C6 into Bz. The line is based on Equation (12a).

**Figure 6.**Plots of log K

_{1,Bz}(circle) and log K

_{2,Bz}(square) versus I

_{Bz}

^{1/2}for the Pb(II) extraction with Cd(NO

_{3})

_{2}and B18C6 into Bz. The regression lines were based on Equations (14a) and (15a). The full circle was omitted from the regression analysis of log K

_{1,Bz}.

**Figure 7.**Plots of log K

_{1,Bz}(circle) and log K

_{2,Bz}(square) versus I

_{Bz}

^{1/2}for the Pb(II) extraction with Cd(NO

_{3})

_{2}and B18C6 into Bz. The regression lines were based on Equations (14b) and (15b).

**Figure 8.**Plot of log K

_{ex±}

^{0}′ versus I

_{Bz}

^{1/2}based on Equation (16) for the Pb(II) extraction with Cd(NO

_{3})

_{2}and B18C6 into Bz. The symbol K

_{ex±}

^{0}′ was defined as K

_{ex±}/y

_{Pb}(y

_{Pic})

^{2}.

**Figure 9.**Plot of log K

_{D,Pic}

^{0}′ versus I

_{Bz}

^{1/2}based on Equation (17) for the Pb(II) extraction with Cd(NO

_{3})

_{2}and B18C6 into Bz. The symbol K

_{D,Pic}

^{0}′ was defined as K

_{D,Pic}/y

_{Pic}. The error bars in the figure are those of the log K

_{D,Pic}values.

**Table 1.**Basic data for the Pb(II) extraction by B18C6 from the water phase with co-presence of Cd(NO

_{3})

_{2}into Bz at 298 K.

[Cd]_{t}/[Pb]_{t} ^{1} | I^{2}/mol dm^{−3} | log K_{ex}[] ^{3} | log K_{ex±} ^{3}(log y _{Pic} ^{4}) | log K_{D,Pic}(Δφ _{eq} ^{5}/V) |
---|---|---|---|---|

0 | 0.0074 | 9.715 ± 0.006 (9.70 ± 0.01) | 2.6_{6} ± 0.2_{5}(−0.04) | −3.2_{1} ± 0.1_{4}(−0.3 _{0}) |

1.06 | 0.0060 | 9.68 ± 0.02 (9.61 ± 0.04) | 3.9_{0} ± 0.2_{3}(−0.03) | −2.4_{4} ± 0.1_{3}(−0.3 _{4}) |

26.6 | 0.048 | 9.58 ± 0.02 (9.51 ± 0.03) | 3.9_{7} ± 0.2_{5}(−0.07) | −2.3_{7} ± 0.1_{6}(−0.3 _{5}) |

88.5 | 0.15 | 9.39 ± 0.03 (9.24 ± 0.05) | 3.9_{5} ± 0.1_{9}(−0.10) | −2.6_{0} ± 0.1_{5}(−0.3 _{3}) |

178 | 0.29 | 9.31 ± 0.02 (9.21 ± 0.03) | 3.6_{8} ± 0.1_{6}(−0.12) | −2.65 ± 0.09 (−0.33) |

^{1}[Pb(NO

_{3})

_{2}]

_{t}= 5.48 × 10

^{−4}mol·dm

^{−3}.

^{2}Averaged ionic strength for the water phase.

^{3}Values determined from Equation (4).

^{4}Logarithmic activity coefficient of Pic

^{−}in water, calculated from the I value.

^{5}Dep values calculated from Equation (5).

**Table 2.**Some equilibrium constants obtained from the Pb(II) extraction experiments by L = B18C6 from the water phase with co-presence of Cd(NO

_{3})

_{2}into Bz at 298 K.

[Cd]_{t}/[Pb]_{t} | log K_{Pb/PbL}(log y _{Pb}^{ 1}) | log K_{ex,ip} | log K_{1,Bz}(I _{Bz}^{ 2}/10^{−6}) | log K_{2,Bz} | log K_{D,PbL} |
---|---|---|---|---|---|

0 | 3.42 ± 0.05 (−0.16) | 7.47 | 5.7 ± 0.3 (0.4 _{4}) | 7.1 ± 0.2 | 1.18 |

1.06 | 3.42 ± 0.08 (−0.14) | 7.143 | 5.4 ± 0.3 (2. _{6}) | 5.8 ± 0.2 | 1.17 |

26.6 | 3.2_{3} ± 0.1_{2}(−0.34) | 7.34 | 5.5 ± 0.4 (2. _{7}) | 5.6 ± 0.2 | 0.9_{8} |

88.5 | 3.1_{3} ± 0.2_{1}(−0.50) | 7.15 | 6.0 ± 0.4 (1. _{7}) | 5.4 ± 0.2 | 0.8_{8} |

178 | 2.9_{5} ± 0.2_{8}(−0.62) | 7.06 | 6.0 ± 0.3 (7. _{8}) | 5.6 ± 0.2 | 0.7_{1} |

^{1}Logarithmic activity coefficient of Pb

^{2+}in water, calculated from the averaged I value.

^{2}Averaged ionic strength for the Bz phase.

**Table 3.**Comparison between Equations (14a) and (15a) and Equations (14b) and (15b) in the re-production of the experimental K

_{1,Bz}and K

_{2,Bz}values

^{1}at 298 K.

[Cd]_{t}/[Pb]_{t} | log K_{1,Bz} | log K_{2,Bz} | ||||||
---|---|---|---|---|---|---|---|---|

Equation (14a) | |Dif.| ^{2} | Equation (14b) | |Dif.| ^{2} | Equation (15a) | |Dif.| ^{2} | Equation (15b) | |Dif.| ^{2} | |

0 | 5.8_{1} | 0.2 | 6.1_{6} | 0.2 | 6.4_{4} | 0.6 | 6.9_{8} | 0.1 |

1.06 | 5.5_{8} | 0.2 | 5.6_{1} | 0.2 | 5.9_{1} | 0.1 | 5.5_{4} | 0.2 |

26.6 | 5.5_{6} | 0.1 | 5.6_{1} | 0.1 | 5.8_{7} | 0.3 | 5.5_{0} | 0.1 |

88.5 | 5.6_{6} | 0.4 | 5.6_{2} | 0.4 | 6.0_{8} | 0.6 | 5.8_{7} | 0.4 |

178 | 5.2_{8} | 0.8 | 5.9_{6} | 0.1 | 5.2_{4} | 0.4 | 5.6_{2} | 0.0 |

^{1}See Table 2 for these values.

^{2}Absolute value for the difference between the experimental K

_{1,Bz}or K

_{2,Bz}value and their estimated one.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kudo, Y.; Nakamori, T.; Numako, C. Pb(II) Extraction with Benzo-18-Crown-6 Ether into Benzene under the Co-Presence of Cd(II) Nitrate in Water. *Inorganics* **2018**, *6*, 77.
https://doi.org/10.3390/inorganics6030077

**AMA Style**

Kudo Y, Nakamori T, Numako C. Pb(II) Extraction with Benzo-18-Crown-6 Ether into Benzene under the Co-Presence of Cd(II) Nitrate in Water. *Inorganics*. 2018; 6(3):77.
https://doi.org/10.3390/inorganics6030077

**Chicago/Turabian Style**

Kudo, Yoshihiro, Tsubasa Nakamori, and Chiya Numako. 2018. "Pb(II) Extraction with Benzo-18-Crown-6 Ether into Benzene under the Co-Presence of Cd(II) Nitrate in Water" *Inorganics* 6, no. 3: 77.
https://doi.org/10.3390/inorganics6030077