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Solvent effects on extraction of alkali metal picrates with 15-crown-5 into various organic solvents. Elucidation of fundamental equilibria which govern extraction-efficiency and -selectivity
Talanta 47 (1998) 67 – 75
Solvent effects on extraction of alkali metal picrates with 15-crown-5 into various organic solvents. Elucidation of fundamental equilibria which govern extraction-efficiency and -selectivity Yasuyuki Takeda *, Shigeharu Hatai, Hiroshi Hayakawa, Yasumasa Ono, Tsuyoshi Yahata, Kiyokazu Endo¯, Shoichi Katsuta Department of Chemistry, Faculty of Science, Chiba Uni6ersity, Yayoi-cho¯, Inage-ku, Chiba 263 -8522, Japan Received 12 August 1997; accepted 26 January 1998
Abstract Extractions of alkali metal (Na–Cs) picrates (MA) with 15-crown-5 (15C5) into various diluents of low dielectric constant were conducted at 25°C. Using the extraction data, the ion-pair formation constants (KMLA) in water of 15C5–MA 1:1:1 complexes were determined by an equation derived from the regular solution theory (log KMLA = 4.43 9 0.27 for Na, 3.27 90.42 for K, 3.58 90.35 for Rb, and 2.78 90.41 for Cs). The actual overall extraction equilibrium constants were obtained by considering the concentrations of the 1:1:1 15C5 complexes and the ion-pair formation between uncomplexed alkali metal and picrate ions in the aqueous phase. The distribution constants of the 15C5 complexes were calculated and their partition behavior is explained by the regular solution theory. Molar volumes and solubility parameters of 15C5 itself and the complexes were determined. Extraction-efficiency and -selectivity of 15C5 for alkali metal picrates were completely elucidated from the standpoint of equilibrium. © 1998 Elsevier Science B.V. All rights reserved.
1. Introduction It was reported that, for the benzene system, the extraction-selectivity order of 15-crown-5 (15C5) for alkali metal picrates is not determined by the stability order in water, but perfectly by the extractability order of 15C5 – alkali metal ion complexes with picrate ions [1]. For further study * Corresponding author. E-mail: [email protected]
on molecular grounds of the extraction efficiency and selectivity of 15C5 for alkali metal picrates, thermodynamic parameters for the overall extraction reaction and the distribution of 15C5 were measured for benzene [2] and chloroform [3] systems. The distribution behavior of 15C5, the ionpair extraction of 15C5–alkali metal picrate complexes, and the overall extraction process were discussed in detail from the thermodynamic point of view [2,3]. The ion-pair extraction consists of the two fundamental chemical processes,
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Y. Takeda et al. / Talanta 47 (1998) 67–75
namely the ion-pair formation in water and the distribution of the 15C5 – alkali metal picrate complex. It is next to impossible to determine the two basic equilibrium constants because of the low stability of the 15C5 – alkali metal ion complexes in water. The ion-pair formation constants in water give a clue to develop the field of liquid– liquid partition study of electroneutral crown ether–metal salt complexes. In order to determine the ion-pair formation constant of a crown ether– metal salt 1:1:1 complex in water, an equation was derived from the regular solution theory [4] and its predictions were verified experimentally by solvent extraction using benzo-18-crown-6, potassium picrate, and various diluents of low dielectric constant [5]. Then the ion-pair formation constant in water of a 15C5 – sodium picrate 1:1:1 complex was determined and the distribution behavior of the 15C5 complex was quantitatively explained by the regular solution theory [6]. In this study, for the final elucidation of fundamental equilibria which govern the highest extraction selectivity of 15C5 for Na + among alkali metal ions and of distribution behavior of 15C5– alkali metal picrate 1:1:1 complexes, the partition constants of 15C5, the actual overall extraction equilibrium constants and the ion-pair formation constants in water of the 15C5 complexes were determined at 25°C by a more completed method considering the ion-pair formation between the uncomplexed alkali metal ion and the picrate ion in the aqueous phase.
2. Experimental
2.1. Materials 15-Crown-5 (Nisso) was purified by distillation under vacuum. All the organic solvents were analytical grade. 1,2-Dichloroethane was purified by distillation, but the other solvents were used as received. They were washed three times with deionized water prior to use. Picric acid and alkali metal hydroxides were analytical grade. The abbreviations of the diluents are given in the footnotes of Table 1.
2.2. Extraction of alkali metal (K, Rb, Cs) picrates with 15C5 The experimental procedures were almost the same as those described in the previous paper [6]. Extractions were conducted at 259 0.2°C. Concentrations of 15C5, alkali metal hydroxides, and picric acid were 1.2×10 − 5 –1.9×10 − 1 M, 8.4× 10 − 3 –2.0×10 − 2 M and (1.8–7.2)×10 − 3 M, respectively. In order to keep the ionic strength in the aqueous phase as constant as possible, the sum of the initial total electrolyte concentrations was held between 1.0 × 10 − 2 and 2.8 ×10 − 2 M throughout the extraction experiments. Extractions were carried out at pH 11–12.
3. Theory and results When an aqueous phase of an alkali metal picrate (MA) and an organic phase of a crown ether (L) attain equilibrium, the equilibrium constants are defined as Kex = [MLA]o/[M + ][L]o[A − ] ,
(1)
Table 1 Solvent parameters at 25°C No.
Solventa
db
Vc
ET
1 2 3 4 5 6 7 8 9 10 11
DCM 1,2-DCE CBu BZ TE mX CB BB o-DCB CF Water
9.7 9.8 8.4 9.16 8.93 8.80 9.5 9.87 10.0 9.3 17.55g
63.9 79.4 104 89.4 106.9 123.5 102.1 105 112.8 80.7 18.1
41.1 41.9 — 34.5 33.9 — 37.5 37.5 — 39.1 —
d
or e 8.93 10.36 7.39f 2.275 2.379 2.4 5.62 5.40 9.93 4.81f —
a DCM, dichloromethane; 1,2-DCE, 1,2-dichloroethane; CBu, chlorobutane; BZ, benzene; TE, toluene; mX, m-xylene; CB, chlorobenzene; BB, bromobenzene; o-DCB, o-dichlorobenzene; CF, chloroform. b Solubility parameter (cal1/2 cm−3/2) Refs. [4,8]. c Molar volume (cm3 mol−1). Ref. [9] (density). d Transition energy (kcal mol−1). Ref. [10]. e Ref. [11]. f 20°C. g Ref. [12].
Y. Takeda et al. / Talanta 47 (1998) 67–75
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Table 2 Extraction equilibrium constants for 1:1:1 15C5–alkali metal picrate complexes at 25°C No.
1 2 3 4 5 6 7 8 9 10
log Kex a
Solvent
DCM 1,2-DCE CBu BZc TE mX CB BB o-DCB CFd
log Kex,ip
Nab
K
Rb
Cs
Na
K
Rb
Cs
4.99 9 0.02 4.829 0.03 5.09 9 0.01 5.0590.01 5.149 0.01 5.189 0.03 5.639 0.01 5.42 9 0.01 5.45 90.01 4.0990.01
4.099 0.03 4.339 0.01 3.469 0.03 2.9690.03 2.999 0.04 2.8990.02 3.849 0.03 3.499 0.01 4.369 0.04 3.699 0.01
4.22 90.02 4.61 9 0.02 3.60 90.03 3.42 9 0.02 3.38 90.05 3.33 90.04 3.89 90.03 3.67 9 0.02 4.48 9 0.04 3.65 90.01
3.67 90.01 4.05 9 0.02 2.66 90.02 2.43 90.03 2.72 9 0.03 2.29 9 0.07 3.34 9 0.01 3.08 90.03 3.72 90.03 3.18 9 0.01
4.94 4.13 3.20 3.55 3.29 3.11 4.18 4.27 4.26 4.31
3.99 3.60 1.52 1.41 1.10 0.78 2.35 2.30 3.12 3.87
4.24 4.01 1.78 1.99 1.61 1.34 2.52 2.60 3.37 3.95
3.51 3.26 0.66 0.83 0.77 0.12 1.79 1.83 2.42 3.30
a
Each value is the average of 10–30 measurements. The uncertainties are the standard deviations. Recalculated from the data in Ref. [6]. c Recalculated from the data in Ref. [1]. d Recalculated from the data in Ref. [3]. b
KD,L =[L]o/[L] ,
(2)
KML =[ML + ]/[M + ][L] ,
(3)
+
−
KMLA =[MLA]/[ML ][A ] ,
(4)
KD,MLA = [MLA]o/[MLA] ,
(5)
+
−
KMA =[MA]/[M ][A ] ,
(6)
where the subscript ‘o’ and the lack of a subscript designate the organic and aqueous phase, respectively. The dissociation of MLA into ML + and A − in the organic phases was neglected because of the low dielectric constants (or) of the diluents used in this study. The overall extraction equilibrium constant (Kex) can be written as 1 Kex = K − D,LKMLKMLAKD,MLA ,
(7) +
−
where KMLAKD,MLA =[MLA]o/[ML ][A ]= Kex,ip. The distribution ratio (D) of the metal is expressed by D =[MLA]o/([M + ]+ [MA] +[ML + ]+ [MLA]) . (8) In the case that [M + ] [MA]+ [ML + ]+[MLA], Eq. (8) is transformed into D=Kex[L]o[A − ] .
(9) +
−
From the mass balances, [M ], [L]o, and [A ] are given by
[M + ]= ([M]t − [MLA]o) /{1+ a[L]o + (KMA + b[L]o)[A − ]} , −
(10)
+
[L]o = ([L]t − [MLA]o)/{c + (a+ b[A ])[M ]} , (11) [A − ]= ([HA]t − [MLA]o) /{1+(KMA + b[L]o)[M + ]} ,
(12)
1 −1 where a= K − D,LKML, b= K D,LKMLKMLA, c=1+ −1 K D,L, and the subscript ‘t’ represents the total concentration. As a first approximation, it is assumed that 1a[L]o + (KMA + b[L]o)[A − ] (Eq. (10)), c +a[M + ] b[M + ][A − ] (Eq. (11)), and 1+ KMA[M + ] b[L]o[M + ] (Eq. (12)). The [L]o and [A − ] values of Eq. (9) were calculated on this assumption. Plots of log(D/[A − ]) versus log[L]o always give a straight line with a slope of 1 in every case. This shows that 15C5 forms a 1:1 complex with the metal ion and the validity of the above assumptions is justified. The first approximate Kex value for each system was determined on these assumptions. The partition constant (KD,L) of the crown ether is estimated by Eq. (13) derived from the regular solution theory [4]:
RT ln KD,L/(dw − do)= VL(dw − 2dL)+ VLd %o, (13)
Y. Takeda et al. / Talanta 47 (1998) 67–75
70
where do%= do +RT(1/Vo −1/Vw)/(dw − do); dw, do, and dL refer to the solubility parameters of water, the organic solvent, and the crown ether, respectively; VL, Vo, and Vw are the molar volumes of the crown ether, the organic solvent, and water, respectively. The partition constant (KD,MLA) of an MLA ion-pair complex is estimated by RT ln KD,MLA/(dw −do) = VMLA(dw −2dMLA) +VMLAdo%,
(14)
where VMLA and dMLA designate the molar volume and solubility parameter of MLA, respectively. Combination of Eqs. (13) and (14) leads to log KD,MLA = {VMLA(dw +do% −2dMLA) / VL(dw +do% −2dL)}log KD,L. (15) Eq. (16) is obtained by adding log KMLA to both sides of Eq. (15).
Fig. 1. Plot of actual log Kex,ip values vs. log KD,L for the 15C5 – sodium picrate system. The solvent numbers correspond to those in Table 1.
Fig. 2. Plot as in Fig. 1, for the 15C5 – potassium picrate system.
Fig. 3. Plot as in Fig. 1, for the 15C5 – rubidium picrate system.
Y. Takeda et al. / Talanta 47 (1998) 67–75
71
log Kex,ip = (VMLA/VL)log KD,L + log KMLA.
(17)
Plots of the first approximate log Kex,ip values versus log KD,L values show a good linear relationship for the respective alkali metals except for CF. The first approximate values of log KMLA were determined from the intercepts of the log Kex,ip versus log KD,L plots. The second approximate [A − ] value was calculated from Eq. (12) by the first approximate values of [M + ], [L]o, and KMLA. The actual [M + ], [L]o, [A − ], KMLA, and Kex values were calculated from Eqs. (1), (7), (10)–(12) and (17) by a successive-approximation method. The log Kex and log KMLA values are compiled in Tables 2 and 4, respectively. The plots of the actual log Kex,ip values versus log KD,L values also show a good linear relationship for the respective alkali metals except for CF (Figs. 1–4). The correlation coefficients for the Na, K, Rb, and Cs systems are 0.916, 0.937, 0.951 and 0.939, respectively. Fig. 4. Plot as in Fig. 1, for the 15C5–caesium picrate system.
4. Discussion
log Kex,ip = {VMLA(dw +do% −2dMLA) / VL(dw +do% −2dL)}log KD,L +log KMLA.
(16)
When the d values of L and MLA are nearly equal, Eq. (16) leads to
The log KD,MLA values for 15C5 calculated from the log Kex,ip and log KMLA values are summarized in Table 3. The RT ln KD,MLA/(dw −do) versus do% plots for the Na(15C5)A complex in Fig. 5 show a linear relationship; those for the potassium, rubidium, and caesium picrate com-
Table 3 Distribution constants for 15C5 and 1:1:1 15C5–alkali metal picrate complexes at 25°C No.
1 2 3 4 5 6 7 8 9 10 a
Ref. [6].
Solvent
DCM 1,2-DCE CBu BZ TE mX CB BB o-DCB CF
log KD,L a
0.64 0.02 −1.20 −0.81 −1.15 −1.37 −0.75 −0.45 −0.50 0.92
log KD,MLA Na
K
Rb
Cs
0.51 −0.30 −1.23 −0.88 −1.14 −1.32 −0.25 −0.16 −0.17 −0.12
0.72 0.33 −1.75 −1.86 −2.17 −2.49 −0.92 −0.97 −0.15 0.60
0.66 0.43 −1.80 −1.59 −1.97 −2.24 −1.06 −0.98 −0.21 0.37
0.73 0.48 −2.12 −1.95 −2.01 −2.66 −0.99 −0.95 −0.36 0.52
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Y. Takeda et al. / Talanta 47 (1998) 67–75
Fig. 5. RT ln KD,MLA/(dw − do) vs. do% for 15C5–sodium picrate complex. The solvent numbers correspond to those in Table 1.
Fig. 7. Plot as in Fig. 5, for 15C5 – rubidium picrate complex.
Fig. 6. Plot as in Fig. 5, for 15C5–potassium picrate complex.
Fig. 8. Plot as in Fig. 5, for 15C5 – caesium picrate complex.
Y. Takeda et al. / Talanta 47 (1998) 67–75
73
Table 4 Fundamental equilibrium constants, molar volumes, and solubility parameters at 25°C L= 15C5
log KMLA log KMA a log KML b
V d
M Na
K
Rb
Cs
4.4390.27 1.38 0.70
3.2790.42 1.64 0.74
3.58 9 0.35 1.94 0.62
2.78 90.41 2.07 0.8
L
MLA
1899 34c 12.0 90.1c
2109 34 12.09 0.1
374 976 12.0 9 0.1
353 9 66 12.0 9 0.1
386 9 82 12.0 90.1
a
Ref. [7]. Ref. [13]. c Ref. [6]. b
plexes with 15C5 in Figs. 6 – 8 also show a linear relationship except for CF. The abnormal behavior of CF is not observed for the Na complex (Fig. 5), but for the K, Rb, and Cs complexes (Figs. 6–8). Except for CF, the correlation coeffi-
cients (r) for Na, K, Rb, and Cs complexes are 0.921, 0.880, 0.895, and 0.887, respectively. The Na(15C5)A complex where the Na + ion fits most nicely into the 15C5 cavity obeys the regular solution theory best of all the 15C5 complexes.
Fig. 9. Plots of log KD,MLA values of 15C5 vs. crystal ionic radii rc of alkali metals for various diluents.
Fig. 10. Log KD,MLA vs. ET plots for 15C5 – alkali metal picrate complexes. The solvent numbers correspond to those in Table 1.
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Y. Takeda et al. / Talanta 47 (1998) 67–75
Fig. 11. Plots of log KML, log KMLA, log KD,MLA, and log Kex vs. rc of alkali metals.
The same tendency is found for the 18-crown-6 (18C6) 1:1:1 complex with potassium picrate among the 18C6 complexes with alkali metal (Li– Cs) picrates 1. This reflects the weaker interaction of the size-fitted MLA complex with some organic solvents (including CF) and/or the smaller variation with the diluent of the number of water molecules attached to the size-fitted MLA complex, compared with the size-misfitted MLA complexes. For K, Rb, and Cs, the M(15C5)A complex does not obey the regular solution theory so closely as the corresponding M(18C6)A complex. This is due to the lower shielding of the central alkali metal ion by 15C5 compared with 18C6. The V and d values for the M(15C5)A complex were determined from the slope and the intercept, respectively, except for CF. They are listed in Table 4. The d values of 15C5 and the M(15C5)A complexes are equal. This shows the validity of Eq. (17). As is to be expected, the V15C5 value is smaller than any other VM(15C5)A one. The VM(15C5)A val-
ues of K + , Rb + , and Cs + which are larger in size than the 15C5 cavity are unexpectedly much greater than the VNa(15C5)A value. The magnitude of VMLA value is closely related to that of KMLA value. The greater the KMLA value is, the smaller the VMLA value is. The log KM(15C5)A value is greater than the corresponding log KMA value. Stronger hydration of an alkali metal ion causes a smaller log KMA value [7]. Generally, the order of the log KM(15C5)A value is the reverse of that of the log KMA value. This indicates that the more nicely the alkali metal ion fits into the 15C5 cavity, the more water molecules bound to the cation are liberated. For K, Rb, and Cs, the log KMLA value of 15C5 is lower than that of 18C6, but the reverse is true for Na.1 The log KMLA value of 15C5 for Na is nearly equal to that of 18C6 for Cs and smaller than those of 18C6 for K and Rb.1 It follows from this that in water the picrate ion is not directly in contact with the alkali metal ion in the 15C5 cavity owing to water molecules. Of all the alkali metals, the log KD,MLA value of Na is the smallest for DCM, 1,2-DCE, and CF, but the largest for the other diluents (Table 3 and Fig. 9). For alkali metals M1 and M2 whose dMLA values are equal, Eq. (18) is derived from Eq. (14). RT ln(KD,M1LA/KD,M2LA) =(VM1LA − VM2LA) {(dw + do − 2dMLA)(dw − do) 1 −1 +RT(V − o − V w )} ,
(18)
where dMLA = dM1LA = dM2LA. The dMLA values of Na, K, Rb, and Cs are identical. The VMLA value is smaller for Na than for K, Rb, and Cs. Except for DCM, 1,2-DCE, and CF, the value of (dw + 1 −1 do − 2dMLA)(dw − do)+ RT(V − o − V w ) of Eq. (18) is always negative. This is the reason why the log KD,MLA value of Na is the largest. For DCM and 1,2-DCE, the do values are close to the dMLA 1 r =0.935, 0.919, 0.949, 0.920, and 0.943 for Li, Na, K, Rb, and Cs, respectively. Log KMLA values of 18C6 are 3.29 (Na), 4.76 (K), 4.62 (Rb), and 4.49 (Cs). These values are reported in Anal. Sci. 14 (1998) 215. 2 RT ln(KD,M1LA/KD,M2LA)=(VM1LA−VM2LA){−(do−dMLA)2 1 −1 +(dw−dMLA)2 +RT(V − o −V w )}.
Y. Takeda et al. / Talanta 47 (1998) 67–75
ones and the Vo values are small, resulting in the positive value of (dw +do −2dMLA)(dw − do)+ 1 −1 RT(V − of Eq. (18).2 Thus, the o −V w ) log KD,MLA value of Na is the smallest. Except for DCM and o-DCB, the difference in the log KD,MLA values between Na and the other alkali metal is fairly greater than that between the two alkali metals other than Na. This is attributable to the much smaller VMLA value of Na compared with the other alkali metals, except for CF, because the dMLA values of Na, K, Rb, and Cs are the same (Eq. (18)). The do value of DCM is close to the d values of 15C5 and the MLA complexes, whereas that of mX is not. The Vo value of DCM is the smallest among all the diluents, whereas that of mX is the largest. This is responsible for the fact that the log KD values of 15C5 and the MLA complexes are the highest for DCM and the lowest for mX, except for CF. The plots of log KD,MLA versus ET for the diluents in Fig. 10 show a linear relationship. Great positive deviations of CF are observed for the size-misfitted K, Rb, and Cs complexes, but not for the size-fitted Na complex. The magnitude of the Kex value is governed largely by that of the KMLA value. The Kex value varies with the organic solvent. The organic solvent whose do and Vo values are close to the d values of 15C5 and M(15C5)A and small, respectively, shows a high Kex value (Eq. (7)),2 because the dL and dMLA values are equal. Fig. 11 shows plots of log Kex and log KD,MLA for representative diluents, log KMLA, and log KML against crystal ionic radii of alkali metals. The extraction-selectivity order of 15C5 is Na\ Rb \K \Cs, except for CF. The same order is observed for the KMLA values and the KD,MLA values for BZ and mX. Favorable contributions of the KD,MLA values to the Na extraction selectivity of 15C5 are observed for CBu, BZ, TE, mX, CB, and BB, whereas
.
75
unfavorable contributions and hardly any contribution are found for 1,2-DCE and CF and for DCM and o-DCB, respectively (Table 3 and Fig. 9). This is responsible for the fact that the extraction selectivity of 15C5 for Na over for the other alkali metals is fairly higher for CBu, BZ, TE, mX, CB, and BB than for DCM, 1,2-DCE, oDCB, and CF (Table 2). Only for BZ and mX, the KD,MLA values make contributions to the extraction selectivity of 15C5 for the alkali metals. Scarcely any contribution to the extraction selectivity is found for the KML values. The extraction selectivity order of 15C5 for the alkali metals is determined completely by the order of ion-pair formation constants of the M(15C5)A complexes in water (Fig. 11).
References [1] Y. Takeda, H. Goto, Bull. Chem. Soc. Jpn. 52 (1979) 1920. [2] Y. Takeda, T. Namisaki, S. Fujiwara, Bull. Chem. Soc. Jpn. 57 (1984) 1055. [3] Y. Takeda, N. Ikeo, N. Sakata, Talanta 38 (1991) 1325. [4] J. H. Hildebrand, R. T. Scott, The Solubility of Nonelectrolytes, 3rd edn., Dover, New York, 1964. [5] Y. Takeda, H. Sato, S. Sato, J. Solution Chem. 21 (1992) 1069. [6] Y. Takeda, C. Takagi, Bull. Chem. Soc. Jpn. 67 (1994) 56. [7] T. Iwachido, Bull. Chem. Soc. Jpn. 45 (1972) 432. [8] A.F.M. Barton, Chem. Rev. 75 (1975) 731. [9] D.R. Lide, Handbook of Chemistry and Physics, 75th edn., CRC Press, Boca Raton, FL, 1994 – 1995. [10] C. Reichard, K. Dimroth, Forschr. Chem. Fortsch. 11 (1968) 1. [11] J.A. Riddick, W.B. Bunger, Organic Solvents, 3rd ed., Wiley, New York, 1970. [12] T. Wakahayashi, S. Oki, T. Omori, N. Suzuki, J. Inorg. Nucl. Chem. 26 (1964) 2255. [13] 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.
.
Solvent effects on extraction of alkali metal picrates with 15-crown-5 into various organic solvents. Elucidation of fundamental equilibria which govern extraction-efficiency and -selectivity Yasuyuki Takeda *, Shigeharu Hatai, Hiroshi Hayakawa, Yasumasa Ono, Tsuyoshi Yahata, Kiyokazu Endo¯, Shoichi Katsuta Department of Chemistry, Faculty of Science, Chiba Uni6ersity, Yayoi-cho¯, Inage-ku, Chiba 263 -8522, Japan Received 12 August 1997; accepted 26 January 1998
Abstract Extractions of alkali metal (Na–Cs) picrates (MA) with 15-crown-5 (15C5) into various diluents of low dielectric constant were conducted at 25°C. Using the extraction data, the ion-pair formation constants (KMLA) in water of 15C5–MA 1:1:1 complexes were determined by an equation derived from the regular solution theory (log KMLA = 4.43 9 0.27 for Na, 3.27 90.42 for K, 3.58 90.35 for Rb, and 2.78 90.41 for Cs). The actual overall extraction equilibrium constants were obtained by considering the concentrations of the 1:1:1 15C5 complexes and the ion-pair formation between uncomplexed alkali metal and picrate ions in the aqueous phase. The distribution constants of the 15C5 complexes were calculated and their partition behavior is explained by the regular solution theory. Molar volumes and solubility parameters of 15C5 itself and the complexes were determined. Extraction-efficiency and -selectivity of 15C5 for alkali metal picrates were completely elucidated from the standpoint of equilibrium. © 1998 Elsevier Science B.V. All rights reserved.
1. Introduction It was reported that, for the benzene system, the extraction-selectivity order of 15-crown-5 (15C5) for alkali metal picrates is not determined by the stability order in water, but perfectly by the extractability order of 15C5 – alkali metal ion complexes with picrate ions [1]. For further study * Corresponding author. E-mail: [email protected]
on molecular grounds of the extraction efficiency and selectivity of 15C5 for alkali metal picrates, thermodynamic parameters for the overall extraction reaction and the distribution of 15C5 were measured for benzene [2] and chloroform [3] systems. The distribution behavior of 15C5, the ionpair extraction of 15C5–alkali metal picrate complexes, and the overall extraction process were discussed in detail from the thermodynamic point of view [2,3]. The ion-pair extraction consists of the two fundamental chemical processes,
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Y. Takeda et al. / Talanta 47 (1998) 67–75
namely the ion-pair formation in water and the distribution of the 15C5 – alkali metal picrate complex. It is next to impossible to determine the two basic equilibrium constants because of the low stability of the 15C5 – alkali metal ion complexes in water. The ion-pair formation constants in water give a clue to develop the field of liquid– liquid partition study of electroneutral crown ether–metal salt complexes. In order to determine the ion-pair formation constant of a crown ether– metal salt 1:1:1 complex in water, an equation was derived from the regular solution theory [4] and its predictions were verified experimentally by solvent extraction using benzo-18-crown-6, potassium picrate, and various diluents of low dielectric constant [5]. Then the ion-pair formation constant in water of a 15C5 – sodium picrate 1:1:1 complex was determined and the distribution behavior of the 15C5 complex was quantitatively explained by the regular solution theory [6]. In this study, for the final elucidation of fundamental equilibria which govern the highest extraction selectivity of 15C5 for Na + among alkali metal ions and of distribution behavior of 15C5– alkali metal picrate 1:1:1 complexes, the partition constants of 15C5, the actual overall extraction equilibrium constants and the ion-pair formation constants in water of the 15C5 complexes were determined at 25°C by a more completed method considering the ion-pair formation between the uncomplexed alkali metal ion and the picrate ion in the aqueous phase.
2. Experimental
2.1. Materials 15-Crown-5 (Nisso) was purified by distillation under vacuum. All the organic solvents were analytical grade. 1,2-Dichloroethane was purified by distillation, but the other solvents were used as received. They were washed three times with deionized water prior to use. Picric acid and alkali metal hydroxides were analytical grade. The abbreviations of the diluents are given in the footnotes of Table 1.
2.2. Extraction of alkali metal (K, Rb, Cs) picrates with 15C5 The experimental procedures were almost the same as those described in the previous paper [6]. Extractions were conducted at 259 0.2°C. Concentrations of 15C5, alkali metal hydroxides, and picric acid were 1.2×10 − 5 –1.9×10 − 1 M, 8.4× 10 − 3 –2.0×10 − 2 M and (1.8–7.2)×10 − 3 M, respectively. In order to keep the ionic strength in the aqueous phase as constant as possible, the sum of the initial total electrolyte concentrations was held between 1.0 × 10 − 2 and 2.8 ×10 − 2 M throughout the extraction experiments. Extractions were carried out at pH 11–12.
3. Theory and results When an aqueous phase of an alkali metal picrate (MA) and an organic phase of a crown ether (L) attain equilibrium, the equilibrium constants are defined as Kex = [MLA]o/[M + ][L]o[A − ] ,
(1)
Table 1 Solvent parameters at 25°C No.
Solventa
db
Vc
ET
1 2 3 4 5 6 7 8 9 10 11
DCM 1,2-DCE CBu BZ TE mX CB BB o-DCB CF Water
9.7 9.8 8.4 9.16 8.93 8.80 9.5 9.87 10.0 9.3 17.55g
63.9 79.4 104 89.4 106.9 123.5 102.1 105 112.8 80.7 18.1
41.1 41.9 — 34.5 33.9 — 37.5 37.5 — 39.1 —
d
or e 8.93 10.36 7.39f 2.275 2.379 2.4 5.62 5.40 9.93 4.81f —
a DCM, dichloromethane; 1,2-DCE, 1,2-dichloroethane; CBu, chlorobutane; BZ, benzene; TE, toluene; mX, m-xylene; CB, chlorobenzene; BB, bromobenzene; o-DCB, o-dichlorobenzene; CF, chloroform. b Solubility parameter (cal1/2 cm−3/2) Refs. [4,8]. c Molar volume (cm3 mol−1). Ref. [9] (density). d Transition energy (kcal mol−1). Ref. [10]. e Ref. [11]. f 20°C. g Ref. [12].
Y. Takeda et al. / Talanta 47 (1998) 67–75
69
Table 2 Extraction equilibrium constants for 1:1:1 15C5–alkali metal picrate complexes at 25°C No.
1 2 3 4 5 6 7 8 9 10
log Kex a
Solvent
DCM 1,2-DCE CBu BZc TE mX CB BB o-DCB CFd
log Kex,ip
Nab
K
Rb
Cs
Na
K
Rb
Cs
4.99 9 0.02 4.829 0.03 5.09 9 0.01 5.0590.01 5.149 0.01 5.189 0.03 5.639 0.01 5.42 9 0.01 5.45 90.01 4.0990.01
4.099 0.03 4.339 0.01 3.469 0.03 2.9690.03 2.999 0.04 2.8990.02 3.849 0.03 3.499 0.01 4.369 0.04 3.699 0.01
4.22 90.02 4.61 9 0.02 3.60 90.03 3.42 9 0.02 3.38 90.05 3.33 90.04 3.89 90.03 3.67 9 0.02 4.48 9 0.04 3.65 90.01
3.67 90.01 4.05 9 0.02 2.66 90.02 2.43 90.03 2.72 9 0.03 2.29 9 0.07 3.34 9 0.01 3.08 90.03 3.72 90.03 3.18 9 0.01
4.94 4.13 3.20 3.55 3.29 3.11 4.18 4.27 4.26 4.31
3.99 3.60 1.52 1.41 1.10 0.78 2.35 2.30 3.12 3.87
4.24 4.01 1.78 1.99 1.61 1.34 2.52 2.60 3.37 3.95
3.51 3.26 0.66 0.83 0.77 0.12 1.79 1.83 2.42 3.30
a
Each value is the average of 10–30 measurements. The uncertainties are the standard deviations. Recalculated from the data in Ref. [6]. c Recalculated from the data in Ref. [1]. d Recalculated from the data in Ref. [3]. b
KD,L =[L]o/[L] ,
(2)
KML =[ML + ]/[M + ][L] ,
(3)
+
−
KMLA =[MLA]/[ML ][A ] ,
(4)
KD,MLA = [MLA]o/[MLA] ,
(5)
+
−
KMA =[MA]/[M ][A ] ,
(6)
where the subscript ‘o’ and the lack of a subscript designate the organic and aqueous phase, respectively. The dissociation of MLA into ML + and A − in the organic phases was neglected because of the low dielectric constants (or) of the diluents used in this study. The overall extraction equilibrium constant (Kex) can be written as 1 Kex = K − D,LKMLKMLAKD,MLA ,
(7) +
−
where KMLAKD,MLA =[MLA]o/[ML ][A ]= Kex,ip. The distribution ratio (D) of the metal is expressed by D =[MLA]o/([M + ]+ [MA] +[ML + ]+ [MLA]) . (8) In the case that [M + ] [MA]+ [ML + ]+[MLA], Eq. (8) is transformed into D=Kex[L]o[A − ] .
(9) +
−
From the mass balances, [M ], [L]o, and [A ] are given by
[M + ]= ([M]t − [MLA]o) /{1+ a[L]o + (KMA + b[L]o)[A − ]} , −
(10)
+
[L]o = ([L]t − [MLA]o)/{c + (a+ b[A ])[M ]} , (11) [A − ]= ([HA]t − [MLA]o) /{1+(KMA + b[L]o)[M + ]} ,
(12)
1 −1 where a= K − D,LKML, b= K D,LKMLKMLA, c=1+ −1 K D,L, and the subscript ‘t’ represents the total concentration. As a first approximation, it is assumed that 1a[L]o + (KMA + b[L]o)[A − ] (Eq. (10)), c +a[M + ] b[M + ][A − ] (Eq. (11)), and 1+ KMA[M + ] b[L]o[M + ] (Eq. (12)). The [L]o and [A − ] values of Eq. (9) were calculated on this assumption. Plots of log(D/[A − ]) versus log[L]o always give a straight line with a slope of 1 in every case. This shows that 15C5 forms a 1:1 complex with the metal ion and the validity of the above assumptions is justified. The first approximate Kex value for each system was determined on these assumptions. The partition constant (KD,L) of the crown ether is estimated by Eq. (13) derived from the regular solution theory [4]:
RT ln KD,L/(dw − do)= VL(dw − 2dL)+ VLd %o, (13)
Y. Takeda et al. / Talanta 47 (1998) 67–75
70
where do%= do +RT(1/Vo −1/Vw)/(dw − do); dw, do, and dL refer to the solubility parameters of water, the organic solvent, and the crown ether, respectively; VL, Vo, and Vw are the molar volumes of the crown ether, the organic solvent, and water, respectively. The partition constant (KD,MLA) of an MLA ion-pair complex is estimated by RT ln KD,MLA/(dw −do) = VMLA(dw −2dMLA) +VMLAdo%,
(14)
where VMLA and dMLA designate the molar volume and solubility parameter of MLA, respectively. Combination of Eqs. (13) and (14) leads to log KD,MLA = {VMLA(dw +do% −2dMLA) / VL(dw +do% −2dL)}log KD,L. (15) Eq. (16) is obtained by adding log KMLA to both sides of Eq. (15).
Fig. 1. Plot of actual log Kex,ip values vs. log KD,L for the 15C5 – sodium picrate system. The solvent numbers correspond to those in Table 1.
Fig. 2. Plot as in Fig. 1, for the 15C5 – potassium picrate system.
Fig. 3. Plot as in Fig. 1, for the 15C5 – rubidium picrate system.
Y. Takeda et al. / Talanta 47 (1998) 67–75
71
log Kex,ip = (VMLA/VL)log KD,L + log KMLA.
(17)
Plots of the first approximate log Kex,ip values versus log KD,L values show a good linear relationship for the respective alkali metals except for CF. The first approximate values of log KMLA were determined from the intercepts of the log Kex,ip versus log KD,L plots. The second approximate [A − ] value was calculated from Eq. (12) by the first approximate values of [M + ], [L]o, and KMLA. The actual [M + ], [L]o, [A − ], KMLA, and Kex values were calculated from Eqs. (1), (7), (10)–(12) and (17) by a successive-approximation method. The log Kex and log KMLA values are compiled in Tables 2 and 4, respectively. The plots of the actual log Kex,ip values versus log KD,L values also show a good linear relationship for the respective alkali metals except for CF (Figs. 1–4). The correlation coefficients for the Na, K, Rb, and Cs systems are 0.916, 0.937, 0.951 and 0.939, respectively. Fig. 4. Plot as in Fig. 1, for the 15C5–caesium picrate system.
4. Discussion
log Kex,ip = {VMLA(dw +do% −2dMLA) / VL(dw +do% −2dL)}log KD,L +log KMLA.
(16)
When the d values of L and MLA are nearly equal, Eq. (16) leads to
The log KD,MLA values for 15C5 calculated from the log Kex,ip and log KMLA values are summarized in Table 3. The RT ln KD,MLA/(dw −do) versus do% plots for the Na(15C5)A complex in Fig. 5 show a linear relationship; those for the potassium, rubidium, and caesium picrate com-
Table 3 Distribution constants for 15C5 and 1:1:1 15C5–alkali metal picrate complexes at 25°C No.
1 2 3 4 5 6 7 8 9 10 a
Ref. [6].
Solvent
DCM 1,2-DCE CBu BZ TE mX CB BB o-DCB CF
log KD,L a
0.64 0.02 −1.20 −0.81 −1.15 −1.37 −0.75 −0.45 −0.50 0.92
log KD,MLA Na
K
Rb
Cs
0.51 −0.30 −1.23 −0.88 −1.14 −1.32 −0.25 −0.16 −0.17 −0.12
0.72 0.33 −1.75 −1.86 −2.17 −2.49 −0.92 −0.97 −0.15 0.60
0.66 0.43 −1.80 −1.59 −1.97 −2.24 −1.06 −0.98 −0.21 0.37
0.73 0.48 −2.12 −1.95 −2.01 −2.66 −0.99 −0.95 −0.36 0.52
72
Y. Takeda et al. / Talanta 47 (1998) 67–75
Fig. 5. RT ln KD,MLA/(dw − do) vs. do% for 15C5–sodium picrate complex. The solvent numbers correspond to those in Table 1.
Fig. 7. Plot as in Fig. 5, for 15C5 – rubidium picrate complex.
Fig. 6. Plot as in Fig. 5, for 15C5–potassium picrate complex.
Fig. 8. Plot as in Fig. 5, for 15C5 – caesium picrate complex.
Y. Takeda et al. / Talanta 47 (1998) 67–75
73
Table 4 Fundamental equilibrium constants, molar volumes, and solubility parameters at 25°C L= 15C5
log KMLA log KMA a log KML b
V d
M Na
K
Rb
Cs
4.4390.27 1.38 0.70
3.2790.42 1.64 0.74
3.58 9 0.35 1.94 0.62
2.78 90.41 2.07 0.8
L
MLA
1899 34c 12.0 90.1c
2109 34 12.09 0.1
374 976 12.0 9 0.1
353 9 66 12.0 9 0.1
386 9 82 12.0 90.1
a
Ref. [7]. Ref. [13]. c Ref. [6]. b
plexes with 15C5 in Figs. 6 – 8 also show a linear relationship except for CF. The abnormal behavior of CF is not observed for the Na complex (Fig. 5), but for the K, Rb, and Cs complexes (Figs. 6–8). Except for CF, the correlation coeffi-
cients (r) for Na, K, Rb, and Cs complexes are 0.921, 0.880, 0.895, and 0.887, respectively. The Na(15C5)A complex where the Na + ion fits most nicely into the 15C5 cavity obeys the regular solution theory best of all the 15C5 complexes.
Fig. 9. Plots of log KD,MLA values of 15C5 vs. crystal ionic radii rc of alkali metals for various diluents.
Fig. 10. Log KD,MLA vs. ET plots for 15C5 – alkali metal picrate complexes. The solvent numbers correspond to those in Table 1.
74
Y. Takeda et al. / Talanta 47 (1998) 67–75
Fig. 11. Plots of log KML, log KMLA, log KD,MLA, and log Kex vs. rc of alkali metals.
The same tendency is found for the 18-crown-6 (18C6) 1:1:1 complex with potassium picrate among the 18C6 complexes with alkali metal (Li– Cs) picrates 1. This reflects the weaker interaction of the size-fitted MLA complex with some organic solvents (including CF) and/or the smaller variation with the diluent of the number of water molecules attached to the size-fitted MLA complex, compared with the size-misfitted MLA complexes. For K, Rb, and Cs, the M(15C5)A complex does not obey the regular solution theory so closely as the corresponding M(18C6)A complex. This is due to the lower shielding of the central alkali metal ion by 15C5 compared with 18C6. The V and d values for the M(15C5)A complex were determined from the slope and the intercept, respectively, except for CF. They are listed in Table 4. The d values of 15C5 and the M(15C5)A complexes are equal. This shows the validity of Eq. (17). As is to be expected, the V15C5 value is smaller than any other VM(15C5)A one. The VM(15C5)A val-
ues of K + , Rb + , and Cs + which are larger in size than the 15C5 cavity are unexpectedly much greater than the VNa(15C5)A value. The magnitude of VMLA value is closely related to that of KMLA value. The greater the KMLA value is, the smaller the VMLA value is. The log KM(15C5)A value is greater than the corresponding log KMA value. Stronger hydration of an alkali metal ion causes a smaller log KMA value [7]. Generally, the order of the log KM(15C5)A value is the reverse of that of the log KMA value. This indicates that the more nicely the alkali metal ion fits into the 15C5 cavity, the more water molecules bound to the cation are liberated. For K, Rb, and Cs, the log KMLA value of 15C5 is lower than that of 18C6, but the reverse is true for Na.1 The log KMLA value of 15C5 for Na is nearly equal to that of 18C6 for Cs and smaller than those of 18C6 for K and Rb.1 It follows from this that in water the picrate ion is not directly in contact with the alkali metal ion in the 15C5 cavity owing to water molecules. Of all the alkali metals, the log KD,MLA value of Na is the smallest for DCM, 1,2-DCE, and CF, but the largest for the other diluents (Table 3 and Fig. 9). For alkali metals M1 and M2 whose dMLA values are equal, Eq. (18) is derived from Eq. (14). RT ln(KD,M1LA/KD,M2LA) =(VM1LA − VM2LA) {(dw + do − 2dMLA)(dw − do) 1 −1 +RT(V − o − V w )} ,
(18)
where dMLA = dM1LA = dM2LA. The dMLA values of Na, K, Rb, and Cs are identical. The VMLA value is smaller for Na than for K, Rb, and Cs. Except for DCM, 1,2-DCE, and CF, the value of (dw + 1 −1 do − 2dMLA)(dw − do)+ RT(V − o − V w ) of Eq. (18) is always negative. This is the reason why the log KD,MLA value of Na is the largest. For DCM and 1,2-DCE, the do values are close to the dMLA 1 r =0.935, 0.919, 0.949, 0.920, and 0.943 for Li, Na, K, Rb, and Cs, respectively. Log KMLA values of 18C6 are 3.29 (Na), 4.76 (K), 4.62 (Rb), and 4.49 (Cs). These values are reported in Anal. Sci. 14 (1998) 215. 2 RT ln(KD,M1LA/KD,M2LA)=(VM1LA−VM2LA){−(do−dMLA)2 1 −1 +(dw−dMLA)2 +RT(V − o −V w )}.
Y. Takeda et al. / Talanta 47 (1998) 67–75
ones and the Vo values are small, resulting in the positive value of (dw +do −2dMLA)(dw − do)+ 1 −1 RT(V − of Eq. (18).2 Thus, the o −V w ) log KD,MLA value of Na is the smallest. Except for DCM and o-DCB, the difference in the log KD,MLA values between Na and the other alkali metal is fairly greater than that between the two alkali metals other than Na. This is attributable to the much smaller VMLA value of Na compared with the other alkali metals, except for CF, because the dMLA values of Na, K, Rb, and Cs are the same (Eq. (18)). The do value of DCM is close to the d values of 15C5 and the MLA complexes, whereas that of mX is not. The Vo value of DCM is the smallest among all the diluents, whereas that of mX is the largest. This is responsible for the fact that the log KD values of 15C5 and the MLA complexes are the highest for DCM and the lowest for mX, except for CF. The plots of log KD,MLA versus ET for the diluents in Fig. 10 show a linear relationship. Great positive deviations of CF are observed for the size-misfitted K, Rb, and Cs complexes, but not for the size-fitted Na complex. The magnitude of the Kex value is governed largely by that of the KMLA value. The Kex value varies with the organic solvent. The organic solvent whose do and Vo values are close to the d values of 15C5 and M(15C5)A and small, respectively, shows a high Kex value (Eq. (7)),2 because the dL and dMLA values are equal. Fig. 11 shows plots of log Kex and log KD,MLA for representative diluents, log KMLA, and log KML against crystal ionic radii of alkali metals. The extraction-selectivity order of 15C5 is Na\ Rb \K \Cs, except for CF. The same order is observed for the KMLA values and the KD,MLA values for BZ and mX. Favorable contributions of the KD,MLA values to the Na extraction selectivity of 15C5 are observed for CBu, BZ, TE, mX, CB, and BB, whereas
.
75
unfavorable contributions and hardly any contribution are found for 1,2-DCE and CF and for DCM and o-DCB, respectively (Table 3 and Fig. 9). This is responsible for the fact that the extraction selectivity of 15C5 for Na over for the other alkali metals is fairly higher for CBu, BZ, TE, mX, CB, and BB than for DCM, 1,2-DCE, oDCB, and CF (Table 2). Only for BZ and mX, the KD,MLA values make contributions to the extraction selectivity of 15C5 for the alkali metals. Scarcely any contribution to the extraction selectivity is found for the KML values. The extraction selectivity order of 15C5 for the alkali metals is determined completely by the order of ion-pair formation constants of the M(15C5)A complexes in water (Fig. 11).
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.