2118
Eyring et al.
TABLE 11: Phenomenological Coefficients for Zeokarb 225 (Na+Form)/Methanol-Water System
vestigation. The authors are grateful to Professor J. Th. G. Overbeek and Professor P. Mears for constructive comments.
References and Notes fraction cm3s" of water V-' deg-' 0.00 0.20 0.40 0.60 0.80 0.95 1.00
2.43 0.41 -2.41 15.47
ohm-'
din-'
deg-'
deg-'
1.10 1.50 2.25 3.40 4.50 5.25 7.10
din-' V-' deg-l
0.00 0.20 0.40 0.60 0.80 0.95 1.00
9.12 0.94 0.93
(L22/ T)107
ohm-' deg-' 2.00 2.40 3.00 4.05 5.20 6.10 7.85
A 2 , 4491 (1964). A. S. Tombalakian, J. fhys. Chem., 72, 1752 (1966). R. P. Rastogi, K. Singh, J. Singh, and R. Kumar, Ind. J. Chem., 14A,
729-731 (1976).
-0.89 -1.03 -1.36 -0.48
-1.57 -1.81 -1.93 1.64
TABLE 111: Phenomenological Coefficients for Zeokarb 225 (Ba2+Form)/Methanol-Water System
(LZ1/ Mole T)106 fraction cm3s-' of water V-' deg-I
N. Lakshminarayanaiah and V. Subrahmanyan, J . Polym. Sci., Part
(L2111
T2)10'6
&2/
T2)10'0
ampcm4 ampcm' dyn-2 dyn-' deg-' V-' deg-'
-1.39 -1.88 -3.05
-1.45 -1.95 -1.53
cients for different cases are recorded in Tables 1-111 for the H+, Na', and Ba2+forms, respectively. It should be noted that the results could not be analyzed in all cases.
Acknowledgment. Thanks are due to University Grants Commission, New Delhi (India) for supporting the in-
R. P. Rastogi and K. M. Jha, Trans. Faraday Soc., 62, 565 (1966). D. K. Hale and D.C. McCauley, Trans. Faraday Soc.,57, 135 (1961). T. R. E. Kerssman, P. A. Stanbridge, and F. L. Tye, Trans. Faraday SOC.,59, 2129 (1963). A. S. Tombalakan, H. J. Barton, and W. F. Graydon, J. fhys. Chem.,
66, 1006 (1962). M. Block and K. S. Spiegler, J. Electrochem. Soc., 110, 577 (1963). C. W. Carr, R. McClintock, and K. Soliner, J. Electrochem. SOC., 109, 251 (1962). A. F. Hadermann, P. F. Waters, and J. W. Woo, J . fhys. Chem., 78, 65 (1974). V. Saxen, Wed. Ann., 47, 46 (1892). G. Schmid and H. Schwarz, Z. Electrochem., 56,35 (1952). G. Schmid, Z. Electrochem., 56, 181 (1952). Y. Toyoshima and H. Nozaki, J. fhys. Chem., 73, 2134 (1969). R. L. Blokhra and T. C. Singhai, J. fhys. Chem., 78, 2304 (1974). J. M. Diamond, J. fhysioi., 161, 503-527 (1962). D. H. Smyth and E. M. Wright, J. fhysioi., 172, 61-62 (1964). R. P. Rastogi, M. L. Srivastava, and S. N. Singh, J . fhys. Chem., 74, 2960 (1970). R. P. Rastogi, K. Singh, and J. Singh, J. fhys. Chem., 79, 2574 (1975). R. P. Rastogl, K. Slngh, and S. N. Singh, J . fhys. Chem., 73, 1593
(1969). R. P. Rastogi, K. Singh, and S. N. Singh, Ind. J. Chem., 6.46 (1968). R. P. Rastogi and K. M. Jha, J. fhys. Chem., 70, 1017 (1966). F. Heifferich, "Ion-Exchange", McGraw-Hill, New York, N.Y., 1962, p 101. R. E. Kesting, "Synthetic Polymeric Membranes", McGraw-Hill, New York, N.Y., 1971, pp 185-186. Reference 23. D 329. R. P. Rastogi, K . Singh, and M. L. Srivastava, J. fhys. Chem., 73,
46 (1969).
Kinetic Studies of the Complexation of Monovalent Sodium, Potassium, Rubidium, Thallium, and Silver Cations by Aqueous 15-Crown-5 Liceslo J. Rodrlguer,la Gerard W. Llesegang,lb Robert D. Whlte,lc Michael M. Farrow,lbNeil Purdie,ld and Edward M. Eyring"lb Department of Chemistry, University of Utah, Salt Lake City, Utah 841 12 (Received June 14, 1977) Publication costs assisted by the Office of Naval Research and the Air Force Office of Scientific Research
A kinetic study of the rapid conformational equilibrium of aqueous 15-crown-5 (1,4,7,10,13-pentaoxacyclopentadecane) and of its complexation of monovalent sodium, potassium, rubidium, thallium, and silver cations at 25 "C in aqueous solution has been carried out by ultrasonic absorption in the 15-205-MHz frequency range. A concentration independent absorption with a maximum at 22.9 f 0.4 MHz detected in aqueous solutions of 15-crown-5with no cations added has been attributed to a conformational rearrangement of the crown ether. The kinetics of the complexation of the polyether with sodium, potassium, rubidium, silver, and thallium(1) ions were then investigated at various polyether and metal concentrations with concentration dependent relaxations occurring between -15 and -55 MHz. These data, together with the conformationalrearrangement data, were analyzed in terms of a two step mechanism, CR1 e CR2 ( k l z , kzl) and CR2 + M+ ~ iMCR2' : (k23, k32), in which CR2denotes the conformation of the ether which participates in the complexation reaction, and MCR2+is the complex ion. From kinetic considerations, it is possible to calculate both k23 and k32 and to demonstrate that K,, is much less than unity. Introduction Macrocyclic polyethers are ever more widely used in chemistry as complexing agents of certain cations, and much work has been done on the fundamental properties of these compounds and their metal complexes.2 The The Journal of Physlcal Chemistry, Val. 81, No. 22, 1977
kinetics of the complexation process have also received some attention,3 mostly by NMR t e c h n i q ~ e s . ~ ~ - ~ Infrared,4 x-ray cry~tallographic,~ and ab initio model studies6 indicate that the macrocyclic polyethers adopt different conformations in the complexed and uncom-
2119
Complexation of Monovalent Cations by 15-Crown-5
TABLE I: Experimental Absorption as ( a / f z )in Np cm-I sz for Aqueous 15-Crown.5 at 25 "C [15-crown*5]= 1.00M [15-crown-5]= 0.801 M [ 15-crown-51= 0.714 M
40.94 35.16 32.94 31.88 30.71 30.66 29.94 29.67 29.48 29.12 28.87 28.57 28.72 28.52 28.24 28.13 28.17 28.21 27.92 28.03 26.51 26.16 27.04
15.18 25.26 35.42 45.56 55.70 65.82 75.94 86.08 96.18 106.3 116.4 126.5 136.7 146.8 156.9 167.1 177.2 187.3 197.4 207.6 217.7 227.8 238.0
15.11 25.29 35.41 45.60 55.72 65.83 75.94 86.06 96.20 106.3 116.4 126.6 136.7 146.7 156.9 167.1 177.2 187.3 197.5
36.17 32.62 30.47 29.36 28.28 27.86 27.68 27.52 26.90 26.86 26.97 27.12 26.83 26.34 25.68 25.41 25.65 25.84 26.17
15.20 25.30 35.37 45.58 55.70 65.82 75.93 86.08 96.19 106.3 116.4 126.6 136.7 146.8 156.9 167.1 177.2 187.3 197.4 207.6
33.95 30.87 29.48 28.30 27.78 27.39 27.27 26.90 26.90 26.40 26.12 25.82 26.08 26.21 26.04 26.90 24.79 25.00 25.47 23.43
plexed states. This was pointed out in Chock's pioneering temperature jump kinetic study of metal complexation by dibenzo-30-crown-10in methanol.3a Previous studies in this lab0ratory~3~ of 18-crown-6in water, by an ultrasonic absorption technique, confirmed the existence of a concentration independent relaxation (fp, = 101 MHz) in aqueous solutions of that particular pure crown ether that was attributed to a conformational equilibrium. 15-Crown-5 has a similar geometry to 18-crown-6, although ring size and hole diameter of the former are smaller. The smaller ring size will cause 15-crown-5 to be more rigid and, as has been shown,gcomplexation is less favored. These facts suggest that 15-crown-5may undergo a slower conformational change than 18-crown-6,so much so that it might interfere with and slow down cation complexation. This possibility is considered below along with a comparison between the kinetics of cation complexation by 15-crown-5 and 18-crown-6. Finally, in aqueous 18-crown-6 complexation, the enhanced stability of K+ and T1+ complexes is attributable to their slower decomplexation rates. Since aqueous 15-crown-5has no apparent cation selectivity ~ e q u e n c eit, ~is of interest to see whether the rates of decomplexation are also devoid of selectivity patterns.
TABLE 11: Relaxation Parameters from Computer Analysis for Aqueous 15-Crown-5 at 25 Ca
Experimental Section Measurements of the ultrasonic absorption were carried out at a temperature of 25.0 f 0.1 "C over the frequency range 15-205 MHz using a laser acousto-optic technique.1° The argon ion laser was operated at the 514.5-nm green line, and the acoustic transducer was a gold-plated, 5-MHz fundamental frequency, x-cut quartz crystal operated at odd harmonics over the frequency range. The acoustic beam was modulated under computer control to facilitate synchronous detection of the resulting optical signal, and adjustments in the ultrasonic transducer position, mirror position, and orientation of the sample cell plane to the Bragg angle were all computer controlled. Solutions were prepared using deionized, redistilled water. The 15-crown-5(Parish Chemical Co., Provo, Utah) was redistilled under vacuum (bp range collected 125-140 "C at 0.5 mmHg [loo-135 OC at 0.2 mmHgll]). Stock solutions were prepared by volume at 25 "C using a density
where A is the amplitude of the relaxational process, f and are the experimental and relaxational frequencies respectively, and B is the nonrelaxational background absorption. This last parameter B is meant to consist of classical solvent absorption plus contributions from very high frequency solvent-relaxational processes. A value of B equal to 21.7 X Np s2 cm-l is commonly reported from measurements made over the frequency range of this study. The experimental data fit eq 1 very well. The calculated relaxational parameters, summarized in Table 11, give evidence for the existence of a concentration independent relaxation at a frequency of 22.9 f 0.4 MHz. Background absorption values show a dependence on solution concentration which is typical of, and is to be expected from, solutions of increased viscosity over water. The single relaxational process is appropriately assigned to the rapid equilibrium interconversion between two structural forms of the polyether in solution.
1017~ [ 15-Crown-51, frr,C M I V ~ H ~c,fIPs2 1.00 0.801 0.714
23.1 22.5 23.1
16.3 14.8 11.9
101'~1018(rms)b NP cm-1 s 2
NP cm-1 s2
28.3 26.3 25.8
1.0 0.7 1.0
Root-mean-square a All symbols as defined in text. deviation. C f,,I(average) = 22.9 * 0.4 MHz.
of the pure product: 1.095 f 0.001 g/mL.12 The inorganic ions were all of analytical reagent grade. Sodium, potassium, and rubidium ions were added as chloride salts; thallium(1) and silver ions were in the form of nitrates. Results Ultrasonic absorption data, expressed as total absorption ( a / f ) Np ~ s2 cm-', for the pure 15-crown-5aqueous solutions at different concentrations are presented in Table I. Analyses of the data were made in terms of a relaxational and a nonrelaxational contribution to the total absorption in accordance with the expression
fR
The Journal of Pbysical Chemlstty, Vol. 81, No. 22, 1977
2120
Eyring et al.
+
TABLE 111: Relaxation Parameters from Computer Analysis [NaC1ln, M
[15-Crown-5In, M
0.217 0.327 0.417
0.0953 0.0905 0.0906
17.0 19.6 21.9
0.100 0.200 0.306 0.404
0.100 0,100 0.100 0.100
21.9 25.7 32.1 38.4
f, 11, M
~
Z1 0 1 7 ~
284 244 224
77.4 82.1 68.2 55.6
1018(rms) 1.6 1.5 0.9
1.4 1.1 1.0 0.9
7;' = k12 k21 (4) Reactions 2 and 3 are obviously kinetically interdependent through the commonality of CR2,but the question remains as to how intimately they are coupled. Very close coupling of two discrete steps can, within the error limits of the absorption measurements, produce what appears to be a single relaxation. We have explored the two extreme interpretations, viz. the rigorous case of full coupling, followed by the totally uncoupled case, and have compared the results below. Making no assumptions regarding the relaxation times, rate constants, absorption amplitudes, etc., the result of the secular determinant for the above reaction scheme is 7-2 - S7-l P= 0 (5)
+
0.0959 0.180 0.278 0.466
0.117 0.117 0.117 0.117
[AgNO,Io, M
[15-Crown-510, M 0.117 0.117 0.117 0.105
0.115 0.215 0.359 0.443
31.1 35.2 37.6 44.3
39.6 51.6 50.5 43.5
where S and P are the sum and product of the roots.
0.7 0.7 2.4 0.8
f r 11, M
~
24.4 31.8 43.7 55.7
Z
1 0 " ~ 1o1*(rms) 184 154 85.5 51.5
1.2 1.6 1.1 0.5
P = k12k23([CRI]+ k32P-12
0.137 0.170 0.263 0.320
0.120 0.120 0.0900 0.102
20.2 23.5 31.1 35.4
222 184 85.9 81.3
0.9 1.9 1.4 0.9
+
kia
CR, .T--f CR, k21 '7.3
(3)
k32
The concentration independent relaxation time for the conformation change in pure crown solutions is 71, which relates to the specific rate constants through the equation The Journal of Physical Chemistry, Vol. 81, No. 22, 1977
(7)
and Kzl in this context is k Z l / k l 2 .The extent of coupling is determined by the magnitudes of kzl and k , , [ M + ] . Substitution for (k12+ k2J with 71-l and for k12with 7c1/(1 Kzl) in eq 6 and 7 gives the eq 8 in k23 and k32in which
Data from ultrasonic absorption measurements on aqueous mixtures of Na+, K", Rb', Ag", and T1" salts with 15-crown-5 solutions as a function of cation concentration have been incorporated into an Appendix available as supplementary material. (See paragraph at end of text regarding supplementary material.) Analyses according to eq 1showed an excellent correspondence between the data for each solution and the theoretical equation for a single relaxation expressed as the root mean square (rms) deviation in Table 111. Table I11 also lists the relaxation parameters A and fR. In the analyses, B was left as a variable quantity. The values of B which provided the best fit were found to differ only slightly from the background value for pure water. The relaxation frequency for the 15-crown-5conformation equilibrium falls within the range of those relaxation frequencies calculated for the equilibria between the metal ions and the polyether. Coupling between the steps is possible and is considered in the interpretation. In a parallel study of 18-crown-6 with the same metal fR for the conformation equilibriumwas observed to be -101 MHz, and coupling between relaxations was not found in the interpretation. Distinguishing the two conformers of 15-crown-5by CR1 and CR2as before and arbitrarily taking CR, to be the one which preferentially complexes with the metal ions, the basic reaction scheme used for data interpretation is the two-step process
M+ t CR, e MCR;
+ 1221)
[a2] + [m])+
7-l = 2xfTis the reciprocal relaxation time calculated from the experiment. The bars indicate that concentrations of reactant species are those at equilibrium. Equation 8 can be further rearranged to contain only the rate constants as unknowns: 7-1
- 7;1 -
rM+i
k 23 (9) KT is the experimentally determined overall complexation constant
previously measured for each cation by Izatt et Results from the graphical solutions of eq 9, Figure 1, are given in Table IV. The equilibrium constant K23for the second step, eq 3, is given by k 2 3 / k 3 2and , KP1can then be evaluated after substitution into eq 10 from the equation (11) K2l = [(K23/KT) -l1 Calculated values of KZ3agree with experimental values of KT to within the error limits of the latter; therefore, Kzl cannot be calculated with acceptable precision. Considering the error margins in the KT values, it is only possible to say that Kzl 5 0.1.
Complexation of Monovalent Cations by 15-Crown-5
2121
'I 6
-20
-12
-16
-4
-8
(r-l-T r ' ){ I +KT([CR,] + [CRd))-Til[ M'] K,
0
, M-i
r + [M'] Flgure 1. Plot of the silver, thallium, and potassium ultrasonic absorption data of Table I11 in terms of eq 9. Data for sodium and rubidium have not been included for clarity.
TABLE IV: Rate Constants and Equilibrium Constant for Complexation by 15-Crown-5 in Aqueous Solution at 25 C When Coupling is Assumed Cation k,,, M - l s - l
k,,, s-'
Na' 2.6 X 10' K' 4.3 X 10' Rb' 4.4 x 10' T1+ 8.0 x 10' Ag+ 6.7X 10' a Reference 9.
5.1 X lo7 7.8 X lo7 1.4x 10'
5.0 X l o 7 8.2X lo7
log K,, (calcd)
log KTa
0.71 0.74 0.50 1.20 0.91
0.70 f 0.04 0.74* 0.04 0.6 f 0.1 1.23 f 0.04 0.94 i 0.04
TABLE V: Rate Constants and Equilibrium Constant for Complexation by 15-Crown-5 in Aqueous Solution at 25 C, No Coupling Assumed Cation Na'
K' Rb' T1' A$
k2,', M - ' s - '
2.4 X 4.3 x 4.6 X 7.1 X 6.4 X
10' 10' lo* 10' lo*
k,,, s-'
4.8 x 7.8 x 1.2 x 4.2 X 7.4 x
107 107 10' 10' 107
log K,, (calcd)
0.67 0.74 0.58 1.23 0.94
In the uncoupled case, T~ is considered to make no contribution to the observed relaxation times 7. The equation13 derived for the 18-crown-6 complexation reactions was used in the interpretati01-1,~~~ i.e. Graphical presentations of the data according to eq 12 are shown in Figure 2, and the resultant rate and equilibrium constants are given in Table V.
Discussion The backward rate constants k32 for each cation are essentially independent of the method of analysis (coupled or uncoupled), with the greatest discrepancy between the values occurring for Ag+ and T1+ ions. The discrepancy amounts to ca. 20% and would usually be considered an acceptable limit for constancy in a rate constant measured using fast reaction techniques. Likewise, kZ3and k23' are within the acceptable limits of constancy, with the possible exception of T1.' Although numerically equivalent, kB and k23/are not kinetically equivalent in terms of the assumed mechanism. In fact, k23/ = k23/(l + K 2 J . Only if KZ1is very small is it possible that k23/ = k23. Both interpretations of the data, as coupled and as uncoupled reactions, yield the same result that K2,
