4382
J . Phys. Chem. 1986, 90,4382-4388
Kinetic Study of the Fast Halogen-Trihaiide Ion Equilibria in Protic Media by the Raman-Laser Temperature-Jump Technique. A Non-Diffusion-Controlled Ion-Molecule Reaction Marie-FranGoise Ruasse,* Jean Aubard, Bernard Galland, and Alain Adenier Institut de Topologie et de Dynamique des SystBmes de I'UniuersitZ Paris VU, associZ au C.N.R.S., 1 rue Guy de la Brosse. 75005 Paris, France (Received: December 9, 1985; In Final Form: February 20, 1986) ~
Forward (k,) and reverse (k-) rate constants of the X2 + X- + X3- equilibrium in water, methanol, ethanol, and acetic acid for X = Br and in water and methanol for X = I have been measured by the Raman-laser temperature-jump technique. For X = Br chemical relaxation signals are always very fast, in the 20-75-11s range; the relaxation times are then obtained by deconvoluting the experimentally observed signals by the response function of the apparatus. Rate constants k , are found to be around lo9 M-I s-' , and k- values vary from 6 X lo5 to 5 X lo7 s-l, depending on the solvent and the halogen. When X = I the k+ values approach the diffusion-controlled limit, whereas for X = Br these values are significantly smaller than the diffusion rates evaluated by the Smoluchowski equation. The slope of the rate-equilibrium relationship, which is near zero when X = I but 0.25 for X = Br, supports this conclusion. The addition of an iodide ion to iodine is almost diffusion-controlled but that of bromide is clearly activation-controlled. This result is discussed in terms of the dynamics of halide ion solvation, which could be an important rate-determining factor, as supported by the linear relationship between the k , rates and the free energies of halide ion transfer
In the early days of temperature-jump techniques for studying rapid chemical reactions in solution, Eigen and Kustin' investigated the kinetics of halogen hydrolysis (eq 1). They were unable to describe this system completely because the kinetic parameters of the very fast X2/X3- reaction (eq 2) were too high for their X2
+ H20
XOH
+ X- + H+
(1)
apparatus. Relaxation times then accessible were only in the millisecond range, the equilibria being perturbed by ca. ~ O - M S duration Joule heating T jumps of about 10 "C in water. Data on equilibrium 2 for X = I in water at 35 OC had been obtained2 by 1271N M R spectroscopy, but the result was severely criticized' because the forward rate constant ( 5 X 1 O ' O M-' s-l) of reaction 2 was found to be higher than the reasonable estimate of the diffusion-controlled limit. Later on, Turner et al. were able3 to measure relaxation times in the nanosecond range by means of a Raman-laser temperature-jump apparatus. With this improved technique, they found a more reasonable value for the rate of the iodine-iodide reaction (eq 2) in water, but they did not obtain data in other solvents or for other halogens. In order to cover a wider range of rate data on equilibrium 2 in various solvents, we have investigated this system with our Raman-laser T-jump setup,4 which makes it possible to observe accurate relaxation signals in the nanosecond range with a 6-8 O C jump in water. This is achieved by means of pulsed spectrophotometric detection ( I ) Eigen, M.; Kustin, K. J . Am. Chem. SOC.1962, 84, 1355. (2) Myers, 0.E. J. Chem. Phys. 1958, 28, 1027. (3) Turner, D. H.; Flynn, G. W.; Sutin, N.; Beitz, J. V. J . Am. Chem. SOC. 1972, 94, 1554. (4) (a) Aubard, J.; Meyer, J. J.; Dubois, J. E. Chem. Insrrum. 1977.8, 1. (b) Meyer, J. J.; Aubard, J. Reu. Sci. Znstrum. 1977, 48, 695. (c) Since the laser heating is not homogeneous, the general solution of the chemical relaxation equation applied to the species i, the X3- anion in our study, is to be written as (sc,(r)) = (l/n)x$,6C,a(0) exp(-r/T,). where (8C,(r))represents the average value of the conceniration variation of the species i , K J O ) the amplitude factor, and a a number related to the temperature gradient in a6T with 6T
