Anal. Cbem. 1980, 52, 1039-1044 V. H. Kulkarni and Mary L. Good, Anal. Chem., 50, 973 (1978). V . N. Tikhonov, Zh.Anal. Khim., 32(7), 1435 (1977). A. T. Pilipenko and M. M. Tananaiko, Talanta, 21, 501 (1974). C. c a m a r a Rica, A. Sanz-Medel, and J. A. Perez-Bustamente, An. Quim., 74, 930 (1978). (9) A. Sanz-Medel, Rev. Acad. Cienc. Zaragoza, Serle 11, Tomo, 28(2), 161 (1973). (10) J. A. Perez-Bustamente, Doctoral Thesis, Universidad Complutense, Madrid, 1967. (5) (6) (7) (8)
1039
(11) F. W. E. Strelow and C. H. S.W. Weinert, Anal. Chem., 47, 2292 [ 1975). (12) V. Svoboda and V. Chromv, Talanra, 12, 431 (1965). (13) M. L. Nichols and B. H. Kindt, Anal. Cbem., 22, 785 (1950). (14) I. P. Alimarin, S. B. Sawin, and L. A. Okhanova, Tabnta, 15, 601 (1968).
for review October
1 7 3
Accepted March
l19
1980.
Transfer Activity Coefficients in Various Solvents of Several Univalent Cations Complexed with Dibenzo- 18-crown-6 I. M. Kolthoff" and M. K. Chantooni, Jr. Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455
Transfer activity coefficients, logMeyS(LM'), are reported at 25 'C, Me denoting methanol and S denoting the solvents: water, acetonitrile (AN), propylene carbonate (PC), DMF, and DMSO, respectively. LM' represents the complex of M' with dibenzo-18-crown-6 (L), M' being sodium, potassium, rubidium, cesium, silver, or thalllum(1) ion. With all these cations, LM' was found to be on a much higher free energy level in water than in the above organic solvents. In the latter, the following empirical relation holds at 25 'C for Na', K', Rb', and Ag': log MeyS(LMf) = 1.03 log MeyS(L) 0.37 log MeyS(M'), S denoting AN, PC, DMF, and DMSO, respectively. An interpretation of the results has been presented. The formation constants K'(LM+) in water are very small. It is postulated that L Is hydrogen bonded to water but that the solvation of LM' is hydrophobic. In water and the above organic solvents, the selectivity of K+ over Na' as expressed by K'(LK')/K'(LNa') is very small: in Me, it is 4; in water and DMSO, 3; In AN, PC, and DMF, of the order of unity, L being dibenzo18crown-6. On the other hand, the selectivity with 18-crown-6 as ligand is 100 in Me and 10 to 16 in the other solvents.
+
Several hundred papers have been written on macrocyclic molecules since Pedersen (I) published his pioneering work, in which he described the preparation and complexing properties with cations in solution and in crystalline solids of macrocyclic ethers, called crown ethers by him. Soon after his publication, Frensdorff ( 2 )reported the stability constants of alkali ions with a few crown ethers in water and with several crown ethers in methanol. Extensive reviews have been published on crown ethers and cryptands (3-5). Analytically, the crown ethers promise to be particularly important after Frensdorff (6) reported extraction constants of picrates of alkali ions complexed with a crown ether. No information is found in the literature on transfer activity coefficients, S1ySz(LM+),of complexed alkali and other univalent ions between two solvents SIand S2. A positive value of log S1yS2(LM') denotes that LM+ is more strongly solvated in SIthan in Sz.In the present paper we present such data between methanol (SI in the above expression), and the solvents; water, acetonitrile, propylene carbonate, dimethylsulfoxide, and N,N-dimethylformamide, respectively (represented as S a in the above expression). Values of transfer activity coefficients (or the related free energy data) provide the relation between the solvation of the complexed cation, 0003-2700/80/0352-1039$01 .OO/O
LM+, and the solvation of the crown ether, L, and the cation M+. In addition to alkali ions, we have included in the present study silver and thallium ions. Dibenzo-18-crown-6, denoted by (DB-18), hiis been used as the crown ether, L. The solubility of this crown ether in the above solvents is small enough to permit the determination of "'yS(L) between methanol (Me) and the other solvents from the ratio of solubilities. From the complexation constant Kf(LM+),
M+ + L
-
LM+,
Kf[LM+]= [LM+]/[L][M+]
(1)
in methanol and the other solvents, and from the known transfer activity coefficients of M+, MeyS(M+), the values of MeyS(LM+)are readily obtained from the relation [log K'(LM+)],, - [log Kf(LM')], = MeASlog Kf(LM') = log MeyS(LM+) - log ,'yrS(L) -
log ""yS(M+) ( 2 ) Activity coefficients, 3 , of LM+ and M+ are considered to be equal. We have also determined values of Kf(LM+) (at 25 "C) with unsubstituted 18-crown-6 in the various solvents and discussed the selectivity of K+/Na+ with the two crown ethers. Several values of Kf(LM+)which we have determined are to be found in the literature, and a comparison has been made between those and our values. Complexation constants of a variety of univalent cations complexed with crown ethers have been determined by various authors by different methods: (a) with cation selective electrodes which yield a(M') ( 2 , 7 ) ;( b ) by precise conductometry ( 8 , 9 ) ;(c) by NMR spectroscopy, e.g., Cs+( I O ) , T1+ (11); (d) spectrophotometrically (12); (e) by thermometric titration (13-15); and (f) polarographically (16-18). In aqueous media in which Kf(LM+)values are too small to yield sufficiently accurate values by using an ion-selective electrode for the determination of the activity of M+, a(M+), we have made use of the increase of the solubility of DB-18 upon complexation. T h e concentration of L was determined in the ultraviolet ( I ) . Our method is a slight variation of a procedure described by Shchori et al. (19). In methanol (the solubility of DB-18 is also very small), we determined the solubilities of sodium, potassium, and rubidium iodates and of thallous bromide in the absence and presence of DB-18, all solutions being saturated to the latter. From the total solubilities of L and from the concentrations of the anions, Kf(LM+)was calculated, making use of the solubilities of the salts and their solubility products. In dipolar aprotic solvents, C 1980 American Chemical Society
1040
ANALYTICAL CHEMISTRY, VOL. 52, NO. 7, JUNE 1980
conditioned and calibrated ion-selective electrodes were used (Frensdorff (2)) for measurements of a ( M + ) in the absence a n d presence of crown ether.
EXPERIMENTAL Chemicals. Methanol was Fisher "Spectroquality" grade distilled once over magnesium turnings. Acetonitrile and dimethylsulfoxide were Aldrich Co., Milwaukee, Wis., products, distilled twice over calcium hydride at atmospheric pressure and in vacuo, respectively. Acetonitrile was further distilled over phosphorous pentoxide. Propylene carbonate was from Burdick and Jackson Laboratories, Muskegon, Mich., while 2,2-dichloroethane was Matheson, Coleman and Bell Co., Norwood, Ohio, spectroquality grade, both used without further purification. The water content of the solvents ranged from 0.003 to 0.01 % , Sodium and potassium iodates were Fisher certified grade and Mallinckrodt Co., St. Louis, Mo., products, respectively. Rubidium iodate was prepared by neutralizing the hydroxide with Merck Co., Rahway, N.J., iodic acid. The hydroxide was prepared in aqueous solution by passing rubidium bromide (Ventron Corp., Danvers, Mass.) through a column of Dowex 1X-8resin in the hydroxide form. The iodates were recrystallized three times from water and dried a t 70 "C at atmospheric pressure. Sodium, potassium, rubidium, cesium, and thallium(T) picrates were prepared by neutralizing the hydroxides in aqueous solution with J. T. Baker Chemical Co.. Phillipsburg, N.J., picric acid and recrystallizing from water. Sodium and potassium nitrates were Baker Co. products, recrystallized from water. Silver and thallium(1) nitrates were Mallinckrodt and Fisher Co. reagent grade products, used without further purification. Silver perchlorate was from Ventron Corp., recrystallized from benzene and dried in vacuo at 50 "C. Thatlium(1) bromide (ZO), tetraethylammonium (21), and alkali metal (20) perchlorates were the same as used previously. Aldrich Co. dibenzo-18-crown-6was recrystallized 4 times from acetone, mp 163 "C, lit, 164 "C (221,while Parish Co., Provo. L'tah, purified 18-crown-6was used as received. Both crown ethers were dried a t atmospheric pressure a t 50 "C:. Solubility Determinations i n Water and Methanol a t 25 " C . DB-18. Approximately 0.5 mmol of DR-18 was added to a s m d volume (0.5-2 mL) of the silver or thallium(1) nitrate solution in water or methanol. The suspension was stirred, and the resulting solution poured off. Ten to 25 mIAof methanolic or 100 mL of the aqueous salt solutions were added. In a different experiment, a few drops of methanol were added to 0.5 mmol of DB-18 and 0.5 mmol of alkali iodate or thallium(1) bromide. The liquid was poured off and 10 mL of methanol was introduced. All solutions were stirred a t 25 "C with a magnetic stirrer for 2 days and filtered through a fine porosity glass frit in a nitrogen atmosphere. Stirring for 2 additional days did not affect the solubility. In order to estimate the concentration of DB-18 in the saturated solutions, it was necessary to remove the nitrate or iodate salts, as the anions interfere in the spectrophotometric determination of DB-18 in the UV. Typically, 1 mL of the saturated solution of MX and DR-18 in methanol was taken to dryness and the residue transferred to a 60-mI, separatory funnel with 10 mL of water and 10 mI, of 1,2-dichloroethane. The lower organic phase was drained and the extraction repeated twice with 5-mL fresh portions of dichloroethane. A further extraction with still another 5-mL portion of dichloroethane resulted in a negligible absorbance a t 275 nm in this phase, indicating quantitative transfer of the crown ether into dichloroethane. The combined extracts were made up to 250 mL and the absorbance was measured at 275 nm in a 1-cm cell in a McPhersori spectrophotometer. The molar absorptivity of DB-18 in water free dichloroethane a t 275 nm is 5.4, X lo3 and it is ~ 5 . 6X ~lo3 in dichloroethane saturated with water. Beer's law was followed to a t least 1.3 X 10 M DB-18. Under the above experimental conditions, only DB- 18 was extracted with no salt. Iodates and Bromide. For estimation of alkali iodates or thallium(1) bromide in the presence of DB-18, a similar extraction procedure was employed. The lower dichloroethane layer was drained into another separatory funnel, washed with 10 mL of water and the procedure reported twice. The combined aqueous extracts containing the iodate were titrated iodometrically. The
end point was detected by the disappearance of the brown iodine tinge when shaken with a little dichloroethane. T o show that a negligible amount of sodium was extracted as complexed LNaI03, M into the organic phase, the residue from 2 mL of 3.6 X NaI03 plus 5.25 X M DB-18 in methanol was taken up in 5 mL of water and 5 mL of dichloroethane. The organic phase was separated and shaken with 5 mL of aqueous 0.01 M KI after acidification. The dichloroethane layer was colorless. The total thallium(1) bromide concentration in methanol saturated solutions, both in absence and in presence of DB-18, was determined by taking an aliquot to dryness, adding water, removing DB-18 by extraction with dichloroethane and titrating the aqueous phase photometrically with silver nitrate. Potentiometry a t 25 "C. A Markson Co., Del Mar, Calif., Catalog No. 1002 K+ and a Markson Co., Catalog No. 1001 Na+ ion-selective electrode were conditioned for 3-4 days in a 0.01 M solution of the perchlorate or picrate salt in the same solvent in which pa(M+)measurements were made. The K+ electrode was also used for Rb+, Cs', and T1+ after conditioning. When not in use, the electrodes were stored in these solutions. With methanol, conditioning in a series of water-methanol mixtures of increasing methanol content was required to prevent possible cracking of the electrodes (2). Calibration of the electrodes was performed in 1 X 10.' to 7 x M solutions of sodium, potassium, or thallium(1) perchlorates in DMSO and methanol. They were also calibrated in 0.5 x to 2 x M solutions of the above perchlorates in acetonitrile, and in 1.6 X lo4 to 4 x M sodium, potassium and thallium(1) picrates in propylene carbonate. W'ith the exception of thallium(1) picrate in propylene carbonate, the salts are completely dissociated at the above concentrations. Stable potentials (to within f l mV) were usually obtained in 5 min with exception in propylene carbonate, which required 1&20 min. Electrode response to a(M+)was practically Nernstian (59.1 f 0.5 mV/pa(M+))for all ions in acetonitrile, dimethylsulfoxide, and propylene carbonate, except K+in DMSO (63.8 mV) and T1+ in PC (54.0 mV). A silver wire (3-mm diameter) served as indicator electrode for pa(Ag+)determinations. To show that DB-18 does not interfere with pa(Ag+) measurements in methanol, pa(Ag+)was found in a solution containing excess silver nitrate over DB-18. Under our experimental conditions c(AgN0,) = [Ag+] + [ AgNO,] + [ LAg'], L.4gN03 being completely dissociated. Using a value of Kd(AgN03)= 1.3 X lo-* ( 2 3 ) ,pa(Ag+)was calculated for a solution 6.00 X 10 M AgNO,, 1.72 X lo-, M in L was 2.56 as compared to the observed value of 2.60. All potentiometric studies were carried out in the three-compartment half cell described previously ( 2 4 ) . The three compartments were separated by fine glass frits. The middle and a side compartment were filled with 0.010 M tetraethylammonium perchlorate solution in the same solvent in which pa(Ag+) or pa(M+) measurements were made. The 0.010 M AgN03/Ag reference electrodes in MeOH, DMSO, AN, and 0.010 M AgC104/Ag electrode in PC, which dipped into the other side compartment, were constructed as done previously ( 2 4 ) . With cation specific electrodes, a Corning Model 10 pH-meter with expanded millivolt scale was used and with the silver wire electrode, a Dana 3800A digital multimeter was used. Conductonetry. As before (13,an Industrial Inc., Cedar Grove, N.J., Model RC 16B1 conductance bridge was used with Jones type cells having cell constants of 0.273 and 0.685.
RESULTS C o m p l e x a t i o n of Univalent C a t i o n s with Crown Ethers. All results were obtained at 25 "C. For t h e sake of brevity, all results of measurements necessary for obtaining values of Kf(LM+)are omitted, h u t are available from t h e authors upon request. Solubility Measurements. DB-18 solubilities found in this investigation in the various solvents a t 25 "C and several reported by Pedersen (25) at 26 "C are as follows: in water, 2.0 X 1 0 ~ 51.28 , X 1 0 ~M 5 (Shchori e t al. (19)) a t 25 "C; in 1X M (25); in acetonitrile, 6.34 X methanol, 1.38X lo-*,'7.9 X M (25);in N,N-dimethylformamide, 5.6 X lo-' M (25); dimethylsulfoxide, 4.8 X M ( 2 5 ) ;in propylene carbonate, 1& X 1 O P M.
ANALYTICAL CHEMISTRY, VOL. 52, NO. 7 , JUNE 1980 ____
(31.5) (see conductometric section). Considering uncertainties in c(MA), a(M+), and c(L), agreement between values of ([LTl+] [LTlNO,]{ obtained from the total thallium(1) nitrate concentration (Equation 4) and from the total concentration of L (Equation 5 ) is satisfactory.
Table I. K f ( L K + )from Solubility of DB-18 ( L ) in Aqueous Potassium Nitrate Solution cKN03M ,
c ( L ) spectro, M
0 0.0209 0.0521 0.0870
2.00 x lo-3.34 x 10-5 6.50 x 10-5 8.40 x 10-5
~
f
+
L(K + )
3.2 X 10' 4.3 x 1 0 ' av.
c(MA) = [M+] + [LM+]+ [LMAI
3.7 x l o 1 3.7 x 1 0 '
+ [MA]
Similar agreement also has been found in silver nitrate-L systems and in MIO,-L systems in methanol. This indicates absence of formation of 2:l complexes, Le., L 2 M t and L2MA. It is evident from Table I1 that association of LM+ with A- is very slight, as deduced from a comparison of the average value of {[LM+]+ [LMA]] obtained from Equations 4 and 5 with that of [LM+] found conductometrically (vide infra). When MA is slightly soluble in methanol, as is the case with alkali metal iodates and thallium(1) bromide, the solutions have been saturated both with respect to MIO, (or TlBr) and the crown. T h e activity of uncomplexed M + was calculated simply from the total ionic concentration [IO,-] (found conductometrically) and from the solubility product of MI03. Since [LM'] = [IO,-] - [M+], [LM+] is known. from which Kf(LM+)is estimated using Equation 1. Finally, the quantity {[LM+]+ [LMIO,]) as calculated from the total iodate (Equation 4) was compared with that from the total L (Equation 5 ) . As an example, data in a solution saturated to both potassium iodate and DB-18 are presented in Table 111. Solubility products in methanol are as follows: sodium, 1.5 x lo-:; potassium, 5.0 X rubidium iodates, 2.7 X and thallium(1) bromide, 6.1 x As a further illustration of the estimation of the complexation constant, Kf(LM+),from the enhancement in solubility of MA by L , Liotta and Dabdoub (26) found the solubility
a constant value of Kf(LM+)was obtained over the concentration range indicated. T h e average value is in excellent agreement with that of Shchori (19). In similar fashion, the 1:l complexation constants of silver and thallium(1) with DB-18 were found in methanol. As both M N 0 3 and L M N 0 3 are slightly associated in methanol (vide infra), systems saturated with L and containing MNO, are quite involved. In addition to the total solubility of L, c(L), the conductivity of these solutions yielded [NO,-], while values of a(M+)were derived from the potential of the T1+ cationic-specific or silver electrode. As an example, data for the thallium(1) nitrate-L systems are presented in Table 11. The ionic mobility of LTl+ has been taken equal to that of LK'
Table 11. Kf(LT1') from Solubility of DB-18 ( L ) in MeOH in Presence of TINO, at 25 "C c(L), M conductivity, - ' cm-I .4(LTINO,) E , cation electrode,a mV paw') Y
iT1*1 '[LT~;1 ITlNO, l b [LTl'j i - [LTlNO,] j , from c(TlNO,), Equation 4 {[LTI'] + [LTlNO,] }, from c(L), Equation 5 ~ f L (T ~) +
a
vs. 0.010 M AgNO,/Ag.
3.12 x 10-3 M 4.25 x 10-3 2.26 x lo-' 80.1 443 3.76 0.81 2.14 x 10.'
2.60 x 0.36 x 2.6 x
io-,
2.88 x 1 0 - 3
6.12 x 10-3 M
1.02 x
7.08 x 10-3 4.26 x 1 0 - 4 75.3 - 424 3.44 0.76 4.81 x 5.19 x 10-3 1.45 X 10.' 5.5 x 10-3
1.13 X lo-' 6.68 X 70.3 -415 3.28 0.70 7.50 x 8.75 x 3.1 x 1 0 - 4 9.1 x 10-3
5.71 x 10-3
9.g4 x
0.89 x i o 4 0.79 x 104 av. Kf(LTl'), 8.4 x l o 3
Calculated from the expression [TINO,]
=
M
1 0 - 3
0.85 x l o 4
(a(T1')[NO;]y/Kd(TINO,)).
Table 111. K f ( L K + )from Solubility of Potassium Iodate in Methanol in Absence and Presence of DB-18 ( L ) at 2 5 " C in absence of L 2.61 x
2.70 x
in satd solution of L a
0 /I KIO, ( )
or"ii (LKIO, )
IK'1. M
(LK'], from conductance Y2
[KIO,I, M [LKIO,I, M {[LK'] + [LKIO,]}, from c ( K I 0 3 ) ,Equation 4 {[LK'] + [LKIO,] :t, from c(L), Equation 5
K~(LK+) a
Ref. 32.
(4)
(5)
T h e estimation of K f ( L M f ) in water from the effect of sodium, potassium, silver, and thallirim(1) nitrates (0.02 to 0.1 M) on the solubility of DB-18 is illustrated in Table I for potassium nitrate. T h e activity coefficient of L was taken as unity, while y(M+)was assumed equal to y(LM+),and the salt regarded as completely dissociated, as had been done by Shchori (19) in similar experiments. Using Equation 3
c(TlN0,)
1041
2.30 x 10-5,2.73 x 10-5 a 95.6 (-2(KI03)) 2.40 x 1 0 - 4 0 0.88
- 2 x 10-5 0 0 0
4.66 X 6.51 x 10-3 2.46 X 68.9 ( A ( L K I O ~ ) ) 2.3 x 10-6 3.57 x 10-3 0.62 -2 x 10-5 1.1 x 10-3 4.6 x 10-3 5.13 x 10-3 1 . 1 2 x 105
1042
ANALYTICAL CHEMISTRY, VOL. 52, NO. 7, JUNE 1980
Table IV. Potentiometric Determination of K f ( L K + )(25 " C )in Acetonitrile ( L = DB-18). E = -0.009-59.1 p a ( K + ) c(KC10,), M
c(L), M
0.998 x 0.942 x 0.899 x 10-3 0.853 X (j.786 x 10-3 0.679 X
1.43 x 10-3 2.50 x 10-3 3.66 X 5.36 x 10-3 8.06 X
paK 3.03 4.59 5.11 5.35 5.58 5.91
+
0
[K'I 0.998 x 10-3 2.83 x 10-5 8.44 x 1 0 - 6 4.85 x 2.g1 x 1 0 - 6 1.32 x
[LK'I
[LI
~
0 5.13 x 1.61 X 2.81 x 10-3 4.58 X 7.38 x
0
y.13 x i o 8.91 X I O - " 8.48 x 1 0 . ~ 7.83 x 6.78 x lo''
f
LK ( +)
6.3 X 10' 6.56 X l o 4 6.2 x 104 6.1 x 10' 6.9 x 104 av. 6.4 x lo4
Table V. Complexation Constants (log Kf(LM') of Crown Ethers with Monovalent Cations in Various Solvents water
methanol
18-cr-6
DB-18
Na' K+
0 . 8 0 , ~( 0 . 3 ) a 2 .O 3 ,e 2.0 6'
i.i6,f l.lb 1.67,f 1.6h
Rb'
1 . 5 ~ ~ 1 . 0 , e 0.sa 1.50,~ 1.6a 2.27e
1.0gf 0.83f
Cs Ag'
+
T1+
( 1.4),f 1.5
1.5, 1 . 5 b
18-cr-6 4 . 3 ~ 4.36' ,~ 6.1a 6.0gn 4 . 6 ~ ~ 4.57d 5.2Gd
acetonitrile DB-18
18-cr-6
DB-18
4.36,a 4.5,'n 4.4' 5 . 0 0 , ~5.0 4.60 ,g 4.6 9c 4.23' 3.55a
4.55d 5.70~
4.85,d 5.00: 5 . 0 h 4.81,~ 4.70," 4.gh 3.70" 3.50," 3.59,d ( 1 . 5 ) '
4.04h'd
3.92,b,d 3.80'
4.9og
4.00"
propylene carbonate 18-cr-6 DB-18 Na K' Rb' cs
+
5. 25d 6.32d
Ag
4.2,' 4 . 5 ~ ~ 7.10~
T1*
7.13d
+
5.20~ 5.13d 3.91~ 3.31~
N,N-dimethylformamide 18-cr-6 DB-18
18-cr-6
dimethylsulfoxide DB-18
1.43d 3.21~ (2.0)'
(2.1)
(3.0)'
(1.5);
(1.3)
5 . 8 ~ ~
5.0gd
Ref. 2, cation selective electrode studies. This work, solubility of dibenzo-18-crown-6in presence of MNO,. ' This work, solubility of MIO, or TlBr, solutions also saturated with dibenzo-18-crown-6. This work, cation selective or Ag wire electrode. e Ref. 13, calorimetric titration. Ref. 19, solubility of DB-18 spectrophotometrically in presence of MC1, MNO,. Ref. 17, polarographic study. Ref. 9, conductometric study. Ref. 10, '"Cs NMR study. j Ref. 43, conductometric study. Calculated from the value of log Kf(LL1') - log K f ( L C s + )(Srivanavit et al. ( I I ) ) and that of Kf(LCs+)from Popov et al. ( 1 0 ) . Ref. 44, calorimetric method. Ref. 45, calorimetric method. ' Ref. 46, calorimetric method. a
'
'
of potassium chloride in acetonitrile in the presence of 0.15 M 18-crown-6 to be 0.055 M. In this saturated solution, potassium is present as LK+ and LKCl, [K'] being negligibly small. Assuming Kd(LKC1) = Kd(Et4NC1),the latter being (27), [LK+] = 3.9 X and [LKCl] = 1.6 x 3x T h e partially extended Debye-Huckel relation with a = 4 A was used to calculate the activity coefficient. Using Equation 5, [L] = 0.095 M. Introducing the above values of [LK+],y 2 , [L], a n d the previously determined value of the solubility product of KCl in acetonitrile, 1.0 X (28),into the relation Kf(LK+)= [LK+]2y2/[L]Ksp(KC1), Kf(LK+)is found to be 5.8 X lo5, in the excellent agreement with the value of 5.0 X lo5 found potentiometrically in the present study (vide infra). Potentiometric Measurements. Cationic ion selective electrodes have proved to be valuable for estimation of 1:l complexation constants of M+ with macrocyclic polyethers in nonaqueous media (2) when Kf(LM+)2 10'. In some instances where 2:l complexation (L2M+)occurs, the stepwise formation constant p(LM+) can be estimated (2). In the present investigation, solutions were typically 0-0.015 M in DB-18 or 18-crown-6. In methanol a n d dimethylsulfoxide. t h e alkali metal perchlorate or thallium(1) nitrate concenM, while in acetonitrile and trations ranged from 1-3 X propylene carbonate 0.3-1.0 X M alkali metal, thallium(1) perchlorate, or picrate solutions were used. As an example, M potassium perpotentiometric data of 0.68-1.0 X M DB-18 are chlorate in acetonitrile containing 0-8.1 X presented in Table IV. All complexed and uncomplexed salts were considered completely dissociated under the experimental conditions, with the exception of uncomplexed thallium(1) nitrate in methanol and picrate in propylene carbonate.
Incomplete dissociation of these salts was taken into account in the calculation of Kf(LM+)using values of Kd(MA)in Table VI. Values of Kf(LM+)of the various monovalent cations in water, methanol, acetonitrile, N,N-dimethylformamide, dimethylsulfoxide, and propylene carbonate are collected in Table V, 18-crown-6 and DB-18 being the ligands. In general, agreement in K f ( L M + ) found from several independent methods mentioned in the introduction is good. With both crown ethers, cesium. and to a lesser extent, rubidium and thallium(1) in acetonitrile and propylene carbonate yield systematically increasing values of Kf(LM+)with ligand concentration, calculated on the basis of 1:l complexation. Such behavior was ascribed by Frensdorff ( 2 ) to 2:1 complexation, Le., LzM+formation. An iterative procedure employing Equations 4a and 5a was used, again considering all salts as completely dissociated.
c(MA)
=
[M+] + [LM+] + [L,M+] + [LMA4]+ [L,MA] + [MA] (4a)
c(L) = [L] + [ L M + ] + 2[L,M+]
+ [ L M A ] + P[L,MA] (5a)
Preliminary estimates of Kf(L2M+)= [ L 2 M f ]/ [L]'[M+] were made, Kf(LM+)was calculated, and the value of Kf(L2M+) adopted which yielded the minimum in standard deviation in Kf(LM+). Values of log Kf(L2M+)for the various 2 : l complexes are L2Cs+,5.2,; L2Rb+,6.1; L2Tl+= 7.78 (L = DB-18); L,T1+ 9.2 (L = 18-crown-6), all in PC, while in AN log Kf( L ~ C S +=) 6.5 (L = DB-18). Ionic Mobilities and Dissociation Constants of Salts. The following ionic mobilities have been reported in propylene
ANALYTICAL CHEMISTRY, VOL. 52, NO. 7, JUNE 1980
obtain reliable values of Kf(LM+). For this reason, values of Kf(LM+)reported by Matsuura et al. (33)in DMF and DMSO are omitted from Table V. Moreover, in these solvents &(M+) ho(LM+),as the uncomplexed cation is strongly solvated.
Table VI. Dissociation Constants of Simple and Complexed Salts. L = DB-18 K~(MA) in methanol
MA
NaIO, KIO, RbIO, AgNO, TlBr
1.9 X
2.5 x 1 0 - 3
c 1.3X lo-* c
Kd(LMA)a 7.3 X 6X c -4X
-
Kf(LMA)b
DISCUSSION
lo3 io4 io3
6.8 X 4.7 x -3x
Transfer Activity Coefficients. T h e major objective of
c
in propylene carbonate 1.1x 2.2 x
AgClO, TlPi
lov2 lo-*
c c
a Kd(LMA) = a(LM+)a(A-)/[LMA]. Kf(LMA) = [LMA]/[L][MA]. Salt practical? completely dissociated under experimental conditions. Ref. 23.
carbonate: C1-, 20.20 ( 2 4 ) ;C104-, 18.78 (29);Ag+, 21.2; and
T1+,17.6. T h e latter two are found in this study from -io of AgN03 and TlPi, while &,(Pi-) = 10.6 was evaluated from that in acetonitrile using the Walden rule. In methanol, the ionic mobilities are: Na+ 45.2, (30);K+, 52.4 (30);Rb+, 55.9 (31); Tl', 50.9 (this work); IO;, 49 (32);C1-, 52.3 (31);Br-, 56.5 (30). Ionic mobilities in methanol of the DB-18 complex ions were estimated as follows: Evans et al. (9) report A(LKC1) = 76.6 M in L , in a solution 1.00 x M in KC1 and 0.59 X M in NaCl while ,i(LNaCl) = 79.7 in a solution 1.35 X M in L. From these data &(LK+) = 32.9 and and 1.02 X XO(LNa+)= 34.6. In the present study, it is assumed that ho(LK+)= Xo(LRb+)= Xo(LAg+)= Xo(LT1+). In solutions of thallium(1) bromide in M saturated with DB-18, appreciable amounts of uncomplexed TlBr are present, hence the "overall" electrolyte mobility, -ioverall = 1O3~/c(T1),is given by
Aoverall= A,,(LTlBr)
+
[Tl+](-i,,(TlBr) - &(LTlBr)} [T1+]
(6)
+ [LTl+]
A series of successive approximations beginning with a rough estimate of Kf(LTl+) was employed in the evaluation of using Equation 6. Conductometrically determined dissociation constants of the alkali iodates, silver and thallium(1) perchlorates, nitrates or picrates in methanol or propylene carbonate are listed in Table VI. T h e uncertainty in these constants is about 10%. In solvents in which Kf(LM+) is small, t h e conductance method must be very precise in order t o
the present study is the determination of the transfer activity coefficients, MeyS(LM+)(molar scale) of M+ complexed with DB-18 between methanol (Me) on the one hand, a n d water, acetonitrile (AN), propylene carbonate (PC), dimethylsulfoxide (DMSO) a n d N,N-dimethylformamide (DMF) on the other. These values are found using Equation 2. From the solubility of DB-18 (L) in the various solvents (see Results) log MeyS(L)was obtained. T h e values are -1.65, -1.06, -1.60, and -1.54, S being water, AN, P C , DMF, a n d DMSO, respectively. Values of log MeyS(M+)and log MeyS(LM+)presented in Table VI1 are based on the Parker (34) assumption that SlyS2(Ph4As+)= SlyS2(BPh4-),which is a slight modification of the well-known Grunwald (35)assumption. For log MeyS(M') the most reliable values in the literature (20, 36,37) are taken. Values of log MeyPC(Mt)in Table VI1 are based on recent work which will be presented elsewhere. Most unexpected is the result that log MeyW(LM+) of the univalent ions studied is positive and quite large, while the corresponding log MeyS(M+)values between methanol and the dipolar aprotic solvents are negative. Evidently, LM' is on a considerably higher free energy level in water t h a n in methanol, even though the opposite is true of the uncomplexed ions, M', which are stronger solvated in water t h a n in methanol, mainly as a result of the Born effect. When two benzo groups are attached to 18-crown-6, the resulting ligand becomes very hydrophobic. I t appears reasonable to attribute the very slight hydration of uncomplexed DB-18 to hydrogen bonding of the ether oxygens with water. In the complex LM+, such hydrogen bonding is greatly suppressed as a result of the coordination of the ether oxygens to M'. Consequently, only a slight hydrophobic solvation of L occurs in LM+. This interpretation is supported by results reported by Iwachido et al. (38). From the increase by DB-18 of the solubility of water in nitrobenzene saturated with water (at 25 "C), they conclude that 1 mol of L reacts with 0.7 mol of water. On the other hand, the increase of water concentration was found equal to only 0.1 mol per mol of LK'. I t would appear that the hydrophobicity of L in aqueous LM+ has increased to such an extent that little hydration can occur
Table VII. Transfer Activity Coefficients at 25 " C of LM' and M' ( L = D B - 1 8 ) between Methanol and S
3.7 5 3.55
Na K' Rb'
+
Cs
-1.3 -1.3ea -1.9 -1.84' -1.8 -1.92' -2.5 -1.9 - -3.6a
+
T1+ Ag +
3.6
-0.3 -0.52a -1.35 -1.15' -1.22 -1.27' -1.48 -1.13 -0.24 - 0 . 1 3 ~
-3.1
-
-2.79' -2.94a -2.9ga
-2.9
-2.9
-2.9c
-
--3.1d
-
-3.24'
-
-3.03a --3.03' -2.'3ga -
-4.25a
" e y Plo qM+)
Mi Na
+
K'
Rb Cs T1+ Ag +
+
+
-1.4
0.9
1043
-1.7 -1.7
-0.4
1.54 -0.16
-0.6
-0.48
-1.6 -0.6 -1.2
-0.8
-0.66
0.9 -5.1
2.6
1.05
-3.1 -3.5 -3.6 -3.3 -2.7 -4.3
-3.9 -3.9 -3.7 -3.9 -4.3 -7.2
a Calculated from the relation log "'yS(LM') = 1.03 log MeyS(L)+ 0.37 log MeyS(M+), Equation. 7. From value of K'(LNa+) in DMF reported by Shchori, Grodzinski, Luz, and Schporer, Ref. 43, used to calculate log MeyDMF(LNa+). and Values of K'(LCs') in DMF and DMSO reported by Mei and Popov, Ref. 10, used to calculate MeyDMF(LCs+) MeYDMSO(LCs+).
1044
ANALYTICAL CHEMISTRY, VOL. 52, NO. 7, JUNE 1980
MeAslog Kf(LM2+) = ( a
selectivity 18-cr-6 DB-18
solvent water methanol acetonitrile propylene carbonate DMSO
16 100 15 10 60
( b - l){lOg MeyS(M1+) - log Meys(M2+)} (9) Equation 9 describes the selectivity for K+/Na+ in Table VI11 going from methanol to acetonitrile or propylene carbonate taking b = 0.37 for both crown ethers.
3
on t h e part of the surface of M+ (in LM+) exposed to the solvent, t h e water molecules being in a plane perpendicular to t h a t of t h e crown. In the organic solvents it is found in this study that Kf(LM+) varies to a considerable extent with MeyS(M+).The free energy of transfer of the 1:l complex of DB-18 with the various monovalent cations between methanol and the aprotic solvents, AN, PC, DMF, and DMSO can be regarded as a linear function of the contribution of the free energies of transfer of L a n d of M + in LM' viz.
+
-
M log [ K fe ( L M , + )l / Ks f ( L M 2 + ) ]=
4 3 1 1
log MeyS(LM+) = a log Meys(L) b log MeyS(M+)
+
1) log MerS(L) ( b - 1) log MeyS(M2f) T h e solvent dependence on the selectivity is then
Table VIII. Selectivity Kf(LK+)/(LNa') with 18-cr-6 and DB-18
(7)
T h e coefficients a and b in Equation 7 were evaluated by a linear regression method using the transfer activity coefficients of LNa+, LK', LRb', and LAg+ in Table VII. Presently, sufficient d a t a on Meys(LTlf)and MeyS(LCs+)are lacking for such a treatment. Values of a, b, and the correlation coefficient are 1.03, 0.37, a n d 0.978, respectively. Since a is practically unity, one may conclude that the free energy contribution of L to t h e solvation of LM+ is practically that of the uncomplexed crown. I t would appear that the conformation of L in LM' is the same in methanol as in the dipolar aprotic solvents, even though log Meys(L) is of the order of -1.5. Equation 7 does not hold for water. Quite generally, in all solvents the free energy of solvation of the fraction of surface of M+ in LM+ exposed to the solvent must be considerably smaller t h a n that of the same surface area of uncomplexed M'. This is a result of the binding of M' to the six oxygens of the crown ether; hence the interaction of M + with t h e solvent is greatly decreased. Consequently, b < 1 in Equation 7 for DB-18. A value of b = 0 in Equation 7 should be the situation when the central metal atom in LM' is completely screened from the solvent as in the cryptand complexes (39-44). Selectivity of K+/Na' w i t h DB-18 and 18-Crown-6. With a given crown ether, the selectivity, Kf(LM,+)/Kf(LM2+), varies with the solvent, a t least in part due to changes in log Me,s(M+). With the considerably less flexible DB-18 the selectivity varies much less with the solvent t h a n with the more flexible 18-crown-6 (Table VIII). With the exception of water as solvent, the selectivity of K + / N a f is more than 10 times greater with 18-crown-6 t h a n with DB-18. Crys' has an adjusted tallographically (42)it has been found that K diameter in (18-crown-6.K') of 2.74-2.86 A, while the corresponding value for (DB-18-Na') is 2.52-2.75 A. These values refer to the crystalline state. Both K+ and Na+ are coordinated to six oxygens in both crowns. From the selectivity of K+/Na+ presented in Table VIII, it would appear that the conformation of L in LM+ is more affected by the solvent when L is 18crown-6 t h a n when it is DB-18. T h e solvent dependence of the selectivity of a given crown for two different cations can easily be formulated from Equation 8, derived by substituting Equation 7 into Equation 2:
MeAs log Kf(LM1+)= ( a - 1) log MerS(L)+ ( b - 1) log Me*/s(M,+) ( 8 ) Likewise
LITERATURE CITED (1) Pedersen, C. T. J . Am. Chem. SOC.1967, 89,7017. (2) Frensdorff, H. K. J . Am. Chem. SOC. 1971, 93,600. (3) Christensen, J.; Hill, J. 0.; Izatt, R. M. Science 1971, 774,459. (4) Christensen, J.; Eatough, D. J.; Izatt, R . M. Chem. Rev. 1974, 74, 251. (5) For a more recent review, see Koithoff, I.M. Anal. Chem. 1979,5 1 , 1R. (6) Frensdorff, H. K. J . Am. Chem. SOC. 1971, 93,4684. (7) Izutsu, K.; Nakamura, T.; Murayama. T.; Fujinaga, T. Bull. SOC. Chem. Jpn. 1978, 51. 2905. (8) Shchori, E.; Grodzinski, J. I s r . J . Chem. 1971, 93,600. (9) Evans, D. F.; Wellington, S. L.; Nadis, J. A.; Cussler, E. L. J . Solution Chem. 1972, I, 499. (IO) Mei, E.; Popov, A.; Dye, J. J . fhys. Chem. 1977, 87, 1677. (11) Srivanavit, C.; Zink, J. 1.; Dechter, J. J. J . Am. Chem. SOC. 1977,99, 5876. (12) Chock, P. f r o c . Natl. Acad. Sci. USA 1972, 69, 1939. (13) Izatt. R. M.; Terry. R. E.; Haymore, B. L.; Hansen, L. D.; Daliey, N. K.: Avondet, A. G.; Christensen, J. J. J . Am. Chem. SOC. 1976,98,7620. (14) Izatt. R. M.; Terry, R. E.; Nelson, D. P.; Chan, Y.; Eatough, D. J.;
Bradshaw, J. S.; Hansen. L. D.; Christensen, J. J. J . Am. Chem. SOC.
1976, 98,7626. (15) Izatt, R. M.; Lamb, I . D.: Asay, R . E.; Maas. G. E.; Bradshaw, J. S.; Christensen, J. J. J . Am. Chem. SOC.1977, 99,6134. (16) Agostiano, A.; Caselli, M.; Della Monica, M. J . Electroanal. Chem. 1976, 74,95. (17) Hofmanova. A.; Koryta, J.; Brezina, M.; Mittal, M. Inorg. Chim. Acta 1978,28, 73. (18) Peter, F.; Gross, M.; Pospisil, L.; Kuta, J. J . Nectroanal. Chem. 1978, 90,239, 251,and references cited therein. (19) Shchori. E.; Nae, N.; Grodzinski, J. J . Chem. Soc., Dahon Trans, 1975, 2381. (20) Kolthoff. I . M.; Chantooni, M . K., Jr. J . fhys. Chem. 1972, 7 6 , 2024. (21) Kolthoff, I. M.; Chantooni, M. K., Jr. J . fhys. Chem. 1966, 70,856. (22) Pedersen, C. J.; Frensdorff, ti. K. Angew. Chem., Int. Ed. Engl. 1972, 1 7 , 16. (23) Busby, R. E.; Griffiths, V. J . Chem. SOC.1963,902. (24) Kolthoff, I. M.; Chantooni, M. K., Jr. J . Am. Chem. SOC. lg65, 8 7 , 4428. (25) Pedersen, C. J. J . Am. Chem. SOC.1970, 92,386. (26) Liotta and Dabdoub, unpublished resuits cited by Liotta C. in "Synthetic Multidentate Macrocyclic Compounds", Izatt R., Christensen, J., Eds.; Academic Press: New York, 1978;p 115. (27) Davies, C. "Ion Association"; Butterworths: Washington, D.C. 1962;p
96. (28) Kolthoff, I . M.; Chantooni, M . K., Jr. J . Am. Chem. Sac. 1969, 97, 462 1. (29) Mukherjee, L.; Boden, D.; Lindauer, R. J . fhys. Chem. 1970, 74,1942. (30) Prue, J.; Sherrington, P. J. Trans. Faraday SOC.1951, 1795. (31) Spiro, M. I n "Physical Chemistry of Organic Solvent Systems"; Covington, A.; Dickinson. T., Eds.: Plenum: New York, 1973;p 673. (32) Koithoff, I . M.; Chantooni, M. K., Jr. J . fhys. Chem. 1973, 77,523. (33) Matsuura, N.; Umenoto, K.; Takeda. Y.; Sasaki. H. Bull. Chem. SOC. Jpn. 1976, 49, 1246. (34) Alexander, R.; Parker, A. J. J . Am. Chem. SOC., 1967, 89, 5549. (35) Grunwald, E.; Baughman, G.; Kohnstam, C. J . Am. Chem. SOC.1960, 82,5801. (36) Cox, 0.;Hedwig, G.; Parker, A. J.; Watts, D. Aust. J . Chem. 1974,27, 477. (37) Popovych, 0.I n "Treatise on Analytical Chemistry", Part I,Vol. 1, 2nd Ed.; Kolthoff, I . M., Eiving, P. J., Eds.; Wiley-Interscience: New York, 1978;p 757. (38) Iwachido, T.; Kimura, M.; Toei. K. Chem. Len. Jpn. 1976, 1101. (39) Gutknecht, J.; Schneider, H.; Stroka, J. J , Inorg. Chem. 1978, 17, 3326. (40) Bessiere, J.; Lqaille, M. F. Anal. Len. 1979, 72, 753. (41) Lejaille, M.; Livertoux, M.; Guidon, C.; Bessiere, J. Bull. SOC.Chlm. France 1976,373. (42) Dailey, M. K. I n "Synthetic Mukidentate Macrocyclic Compounds"; Iz~tt. R., Christensen, J., Eds.; Academic Press: New York, 1978; p 207. (43) Shchori, E.; Grodzinski, J.; Luz, 2.; Schporer, M. J . Am. Chem. SOC. 1971, 93,7133. (44) Nelson, P. P. Ph.D. Thesis, Brigham Young University, Provo, LJtah. 1971. (45) Fruh. P. U.; Simon, W. I n "Protides of the Biological Fluids", 20th Colloquium, Peeters, Ed.; Pergamon Press: New York 1978. (46) Lamb, J. Ph.D. Thesis, Brigham Young University, Provo, Utah, 1978.
RECEIVED for review December 17, 1979. Accepted March 10, 1980. We thank the National Science Foundation fro Grant CH75-22642 in support of this work.
