J. Phys. Chem. 1986, 90, 6281-6284 Wagner-Meerwein rearrangement, may result by means of a mechanism via intimate ion pairs as represented in eq 4. The correlations obtained in the gas-phase pyrolyeses of aliphatic primary, secondary, and tertiary chlorides support Maccoll's theory on the heterolytic nature of the transition state for alkyl halide pyrolysis in the gas phase.4
Acknowledgment. This work was supported by the Consejo
6281
Nactional de Investigaciones Ciendficas y Tecnolbgicas (CONICIT) under project No. 51.78.31-S-1072.W e are thankful to Maria L. Tasayco, Matilde Gbmez, Angelina Morales, and Magaly Santana for mass spectra and N M R determination and interpretations. Registry No. CH3CHCICN, 1617-17-0; CH,CHCI(O)OMe, 1763993-9; CH,CHClCH,C(O)OMe, 8 17-76-5.
Kinetic Study of the Complexations of Cryptand 222 with Alkaline Earth Ions by the Conductance Stopped-Flow Method Hiromi Kitano, Jitsuya Hasegawa, Satoshi Iwai, and Tsuneo Okubo* Department of Polymer Chemistry, Kyoto University, Kyoto, Japan (Received: April 8, 1986)
Two relaxation steps are observed in the complexation reaction between alkaline earth ions (Ca2+,S?+,and Ba2+)and cryptand 222 using the conductance stopped-flow (CSF) method. The faster relaxation step (relaxation time 71) shows a large amplitude of conductancechange, and the reciprocal value ( l / q ) increases linearly with the concentration of cryptand under the condition [cryptand] >> [metal ion]. The slower relaxation step (relaxation time (72)) shows a relatively small amplitude,and its reciprocal value (1/7*)first increases and then levels off with increase in the concentration of cryptand. We propose a reaction mechanism involving three steps; the faster step of the encounter reaction observed is a cleavage of the coordinated water molecules from a metal ion. The slower step is an inclusion of a metal ion into the cavity of cryptand. There exists another step prior to the faster step that is a conformational change of cryptand but is too fast to observe by the CSF method. Thermodynamic parameters of the faster and the slower steps are evaluated and these values support the proposed mechanism. Ionic radii of alkaline earth ions show a great influence on the faster and the slower steps.
Introduction The formation of stable complexes of the synthetic macrobicyclic ligand 4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo[8.8.8]hexacosane (cryptand 222) with alkali and alkaline earth ions was fmt described by Lehn and wworkers'2 and the chemical properties of the cryptand have been extensively studied by many researcher^.^" They insist in their reports that cryptand has a conformational rearrangement (endo-endo F? exo-exo) in the position of lone pairs of nitrogen atoms.'V2 Kinetic studies of complexation of cryptands with alkali ions and Ti+ using 'H NMR6 or 23Na NMR,' with Li+ using 'Li NMR,8 and with alkaline earth ions using potentiometric titration6 or the stopped-flow method in the presence of metal indicatorg have been reported. But the direct analysis by a spectrophotometric method has not been carried out owing to the lack of significant visible or ultraviolet spectral changes. The CSF method is a convenient technique for kinetic analyses of ionic reactions such as the present complexations because most ionic reactions are accompanied by a significant change in condbctance in the course of the reaction. Recently we constructed several types of CSF apparatus and applied them to various ionic reaction systems including metalmacroion complexations and macrocation-macroanion complexations (polyelectrolyte complex).'*'6 (1) Dietrich, B.; Lehn, J. M.; Sauvage, J. P.Tetrahedron Lett. 1969,34, 2885. ( 2 ) Dietrich, B.;Lehn, J. M.; Sauvage, J. P. Tetrahedron Lett. 1969,34, 2889. ( 3 ) Lehn, J. M. Struct. Bonding (Berlin) 1973, 16, 1. (4) Izatt, R. M.; Christensen, J. J. Synthetic Multidentate Macrocyclic Comwunds: Academic: New York. 1978. (j)Izatt,'R. M.; Bradshaw, J. S.; Niclsen, S. A.; Lamb, J. D.; Christensen, J. J; Sen, D. Chem. Rev. 1985,85, 271. (6) Lehn, J. M.; Simon, J.; Wagner, J. Angew. Chem. In?.Ed. Engl. 1973,
-
12. . -,57% . -.
(7) Ceraso, J. M.; Dye, J. L. J. Am. Chem. SOC.1973, 95, 4432. (8) Cohen, Y. M.; Dye, J. L.; Popor, A. I. J . Phys. Chem. 1975, 79, 1292. (9) Loyola, Y.M.; Pizer, R.; Wilkins, R. G. J. Am. Chem. Soc. 1977,99, 7185. (IO) Okubo, T.;he, N. Polym. Bull. (Berlin) 1978, I , 109. (11) Okubo,T.; Kitano, H.; Ishiwatari, T.;Ise, N. Proc. R. Soc. London, 1979, 366, 81.
Recently Cox and co-workers have measured the dissociation rates (kd)of metal cryptates in various kinds of solvents from the change in conductance caused by the addition of excess acid to the cryptate solution and evaluated the apparent second-order rates of complex formation with eq l,"-" where K is a stability constant.
kf = k&
(1)
The complexations of cryptand with metal ions were analyzed as one-step reactions hitherto. However, other complexations, such as valinomycin and crown ether with metal ions, were reported to have at least two steps. In this report we observed two relaxation steps in the complexation reaction, which suggests that this reaction has at least two more steps in addition to the rapid conformational change of the cryptand molecule.
Experimental Section Materials. Cryptand 222 was obtained from Merck and used without further purification. All other reagents were of guaranteed grade. Ca(OH)2, Ba(OH),, and Sr(OH), were dissolved in water that was deionized and distilled just prior to use. The pH of each solution was maintained higher than 11.0 in order to fully deprotonize the cryptand molecule. (12) Okubo, T. Biophys. Chem. 1980, 11,425. (13) Okubo,T.;Enokida, A. J . Chem. SOC.,Faraday Trans. 1 1983, 79, 1639. (14) Okubo, T. In Dynamic Aspects of Polyelectrolytes and Biomembranes; Osawa, F., Ed., Kodansha: Tokyo, 1982; pp 11 1-1 17. (15) Okubo,T.; Hongyo, K.;Enokida, A. J. Chem. SOC.,Faraday Trans. I 1984,80, 2087. (16) Okubo, T. Makromol. Chem. Suppl. 1985, 14, 161. (17) Cox, B. G.; Schneider, H. J. Am. Chem. SOC.1977,99, 2809. (18) Cox, B. G.; Schneider, H.; Stroka, J. J . Am. Chem. SOC.1978,100, 4746. (19) Cox, B. G.; Guminski, C.; Firman, P.;Schneider, H. J. Phys. Chem. 1983,87, 1357. (20) Cox, B. G.; van Fruong, Ng.; Schneider, H. J. Am. Chem. SOC.1984, 106, 1273. (21) Cox, B. G.; van Fruong, Ng.; Garcia-Rosas, J.; Schneider, H. J. Am. Chem. SOC.1984,88,996.
0022-3654/86/2090-628 1$01.50/0 0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 23, 1986
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Apparatus. Reaction rates were measured by the conductance stopped-flow (CSF) The platinum plates (2 mm X 10 mm) were fixed on inside opposing walls (2 mm apart) of the observation cell made of epoxy resin. The mixing ratio is 1:1. The mixer, which was made of Teflon, was of a four-jet type. The dead time of the apparatus was estimated to be 1 ms. For each individual run, about 0.2 cm3 of solution was required. A value of 1.30 cm-' was obtained for the cell constant. An ac current of 50 kHz was given to the Wien bridge. The applied voltage across the cell was kept at 2 V (root mean square). The average value of the current used was of the order of 100 PA. The time change of the deviation of the solution conductance from its equilibrium value was amplified in two steps and monitored by a memorimpe and/or digital memory and an X-Y recorder after rectification. The polarization effects caused by electrolysis were concluded to be negligible except at high concentrations of electrolyte, above 0.1 mol/L. Determination of Kinetic Parameters. We propose here the reaction scheme shown in eq 2 and 3 and obtained the theoretical k'
exo-exo -f, endo-endo ki Ca2+
+ endo-endo
(2)
k+l
S[Ca2+(endo-endo)]
k+l
k-I
k-1
faster
slower
[Ca(endo-endo)] z+ (3)
eq 4-6 under the condition 1 1>>~l/sl ~ or 1/70 = k; k
Sr2+ 5 Ca2+, which shows that there are some coordinated water molecules remaining after the faster step. Furthermore the table shows that when the ionic radius of metal ions is a better fit to that of the cavity of cryptand (Ba2+> Sr2+> Ca2+),the k2/k_, value is largerSgThese results again support that the slower step is an inclusion process of the metal ion into the cavity followed by binding of the metal ion with the reaction sites of the cavity. Thermodynamic Parameters of the Faster Step. From temperature dependencies, thermodynamic parameters are evaluated and compiled in Table 11. Entropies of activation (AS*) in the faster step are very sensitive to metal ions. This supports that the bimolecular substitution of a metal ion by a cryptand molecule is accompanied by the cleavage of the coordinated waters, which affects the faster step. The reasons are as follows. AS* should increase with the quantity of loss of coordinated waters. The strength of the hydration will increase with a decrease of ionic radius in the order Ca2+ < SrZ" < Ba2+.25On the contrary the bimolecular association of a metal ion with a cryptand tends to decrease the entropy of activation. It is understandable that the values 9 cal/(mol.deg) for Ca2+,-12 cal/(mol.deg) for Ba2+,and 2 cal/(mol.deg) for Sr2+ as AS* are determined by these two factors; one is the increase of entropy by the cleavape of coordinated waters, and the other is the decrease of entropy by the in the bimolecular association. The enthalpy of activation (AH*) faster step depends on the electrostatic energy of the binding between a metal ion and the coordinated water. These energies increase with a decrease of the ionic radius as follows:33CaZ+> SrZ+> Ba2+. The values in Table I1 support this idea. Thermodynamic Parameters of the Slower Step. The entropies of activation of three metal ions are all negative and decrease in the order Ca2+ > Sr2+ > Ba2+. These results support that the slower step represents the inclusion of a metal ion into the cavity of cryptand. Kinetic and thermodynamic parameters support our reaction scheme, which clarified why the complexation of cryptand is much slower than that of valinomycin or crown ether and depends on the ionic size of metal ions, especially alkaline earth ions. In conclusion, the complexation of alkaline earth ions with cryptand 222 consists of three steps as follows: 1. The fastest step, prior to the faster step, is the conformational change (exc-exo endo-endo) of cryptand. 2. T h e faster step is t h e substitution of the coordinated water molecules of a metal ion by cryptand in the SN2pathway. 3 . The slower step is an inclusion process of a metal ion into the cavity of cryptand.
Acknowledgment. We thank Professor Norio Ise for his advice and encouragement throughout this work. We also thank the Kurata Foundation for its financial support. Registry No. Ca2+, 14127-61-8; Sr2+,22537-39-9: Ba2+,22541-12-4; cryptand 222, 23978-09-8. (33) Gurney, R. W. Ionic Processes in Solution:Dover: New York, 1953.
