2957
REACTIONS BETWEEN BROMIDE AND TRIBROMIDE IONS of OH - ions (whatever it is) is uninfluenced by adding methanol. (The values of Z1 and k for dioxane are somewhat lower than those in methanol which is due to the iorvar value of Rxr,o.) The deviation of the points at low water concent,ration can be tzseribed to a prototrope conduction due to ~ ~ e ~ h o x o>rn xrrethoxide ~u~ ions. Thc drop of the points at the q p e r 2nd of the D m i curve and the lack of this drop for the values of DOH’can be attributed probaLdy t o lhc fact that, though hydronium ions move only by the prototrope mechanism in pure water, the hydrodynamic iriotioni is successively accelerated with increasing methanol concentration, ie., D H ~ depends O also on wakr ~ o ~ ~ c ~ ~that, ~ t rifa known, ~ ~ o nshould have been sukv&racled from the DEI~O’ data at modi-
Transfer Diffusion.
V.
ate and low water concentration resulted in a lower slope. On the other hand, the good fit of the data of DOH’to the straight line seems t o suggest that the hydrodynamic mobiljt y is the samc throughout for hydroxide ions. This conclusion is supported also by the approximate identity of the intercept (DOIT= 1.2 X ern2 sec,-.l) and the value in Table 1 ( D O H ~ . = 1.0 X em2 sec,-l corresponding Go 6 = 2.57 A}. The ionic mobility of the hydronium and hydroxide ions in the mixtures of ethanol, 1-propanol, ethylene glycol, and glycerol with mater3” are very dose t o those in methanol. A similar handling of these data, however, is not possiblc, because the ?;alms of the selfdiffusion eor:%cient of water are not ~ ~ in these a solvents.
Kinetics and Mechanism of the Exchange
Reaction between Bromide and Tribromide Ions
by I,, Ruff* and V. J. Friedrich Inslih.de of Inorganic and Analytical Chemistry, L. E6tvBs Unheraity, Budapest, Hungary
(Received February 7 , 1972)
+
+
The transfer diffusion method has been applied in the study of the exchange reaction BrBr3Brgin an ionic strength of 4 M . The diffusion of tribromide ions is significantly accelerated by the presence of bromide ions due to the very fast exchange. The more than twofold increase of the diffusion coefficient within the bromide concentration range of 0-4 M yields a value of 7.6 X 109 A4’41sec-’ for the second-order rate constant which is about the half of the diffusion limit. The similarities in the kinetic data of this reaction and that between iodide and triiodide indicate the same geometry of the activated complex.
Introductian A previous successful investigation of the very fast exchange reaction of iodide with triiodide’ prompted us t o study ithe similar reaction between bromide and tribrornide. Unlike the case of the iodide-triiodide system, no nmr line broadening measurements are available in the literature. Thus the aim of this study was to obtain numerical data on the rate of the exchange process ?rather than to justify the applicability of the transfer diflusion method which has been reliably done earlier. Utilizing the advantages of the transfer diffusion method that gives information also about the distance between the reactants in the activated complex, L e . , about the ge3metry of the collision, the data obtained on the iodide-triiodide system’ proved t>he activated complex t o he a linear arrangement of the four iodine atoms invol ved, This has been supported in that
the transfer diffusion effect in iodide diffusion accelerated by the presence of triiodide ions was nine times that in triiodide diffusion enhanced by iodide ions, since the displacement of iodide ion is three times that of triiodide and the square of this value appears in the transfer diffusion term. Concerning the identical structure of the tribromide ion: it could be expected that the kinetic behavior of the bromide-tribrornide couple is similar, and the exchange rate is fast enough to measure its transfer diffusion (1) I. Ruff, V. J. Friedrich, and (1972).
IC. Csillag, b. Phys. Chem., 76,
162
(2) I. Ruff, V. J. Friedrich, K. Demeter, and E(. Csillag, ibid., 75, 3303 (1971). (3) I. Ruff and V. J. Friedrich, ibid., 76, 2954 (1972). (4) I. Ruff and M. Zimonyi, Electrochim. Acta., submitted for publication. ( 5 ) “Tables of Interatomic Distances,” The Chemical Society, London. 1958.
The Journal of Physical Chemistry, Vol. Yf3, N o . 21, 1972
~
I. RUFFANY V. J. FRIEDR~ICH
2958
centration C B ~ ,i!)~~~ the intrinsic diffusion coefficient corresponding to purely migrational movement, k the second-order rate constant of the exchange reaction, and 6 is the displacement'of the center of mass of a tribromide ion due to the exchange with a bromide ion (2.57 As is seen in Figure 1, the linear correlation of D B ~ ~ ' us. C B ~implied in eq 1 was really measured with no temperature dependence in either its slope or intercept. The deviation of the two points at the ~ o n c ~ n t r a t i o n s C B ~= 0.5 and 1.0 M a t 45" is likely due t o the shift of Br- caused by both the equilibrium Bra- ;rf. Br2 the increase in temperature and the rather low bromide excess. A11 the other points show a good fit t o the straight line. The slope yields a value of (7.6 1.7) X 1Q9AI-I sec-l lor rate constant ic provided the aetivated complex i s a linear arrangement of t h e four bromine atoms. The intercept correspoiids to Lhra = (1.25 f 0.25) X IOw5 em2 sec-I* The reliability of handling the dependence of D R ~on~ ' bromide concentration according t o ey P is supported by the constancy of viscosity within the concentration range studies (see Table 1))since such a large increase in the diffusion coefficient of tribromide ions could only result from a similar relative decrease in viscosity.
+
*
Figure 1. Dependence OS the effective diffusion coefficient of tribromide ions on bromide concentration at 2.5' (0),35' (A), and 45' (13).
Experimental Section The diff uzjion eoefscients of tribromide were measured in neutral aqueous solutions using the apparatus described elsewhere.2 Ionic strength was maintained at the constant value of 4 M by KNOs. Potassium bromide concentration was varied from 0.5, 1, and 2 M t o 4 M at 45, 35, and 25", respectively. The concentration of tribromide ions was 0 005 M in each run. Viscosity wa,s measured in an Ostwald capillary apparatus. Results and DiscusRiJion The effect of transfer diffusion arises from the acceleration of transport processes in the presence of both reactants due to fast exchange reactions! The increase in transport coefficients is the result of the displacement of the centers of mass of both reactants in the elementary act of the exchange process which is favored in the direction of the gradient in chemical potentjal; thus it adds to the common migrational motion. The quantitative relationship meeting the conditions of the present experiments is
where D B ~is~ 'the effective diffusion coefficient that can be observed in the presence of Br- ions in a con-
The Jotrnul of Physical Chemistry, Vol. 76,No. 81, 197.9
Table 1 : Viscosity of K(Br, NO,) Solutions at 35' in an Ionic Strength of 4 M IBr-I, M
rir
op
1.138 I . 119 1.088
I. 109
The diffusion-limited rate constant is (1.2 ir 0.1) X 10'0 A 4 - I which is somewhat less than twice the rate constant observed. The same ratio has been calculated for the triiodide-iodide couple. Since temperature dependence is not significant, this indicates that the efficient collision takes place only when the bromide ions collides to one of the ends of the t i bromide within an angle of about 45" on either sides of the tribromide axis. (6)
I. Ruf? and V.
J. Friedrich, J . Ph.ys. Chem., 1 5 , 3297 (1971)
