I. Rum, V. J. FRIEDRICH, AND K, CSILLAG
162
action product develop readily detectable amounts of SO*. during the course of the reaction. Mechanisms
-
based on reaction products can accommodate this radical as an intermediate in the reaction.
Transfer Diffusion. 111. Kinetics and Mechanism of the Triiodide-Iodide Exchange Reaction by I. RufP,* V. J. Friedrich, and K. Csillag Institute of Inorganic and Analytical Chemistry, L. EBtvds University, Budapest, Hungary
(Received July 6, 1971)
Publication costs borne completely by The Joumal of Physical Chemistry
The I 2 transfer in the exchange reaction of iodide with triiodide ion has been studied by the transfer diffusion method. The product of the rate constant and the square of the reactant distance in the activated complex (ICs2)has been measured. The geometry of the activated complex was supposed to be a linear arrangement of the four iodine atoms with an interatomic distance of 2.90 A which value correspondsto the available crystallographic data. The second-order rate constant calculated from the value of k P with the former assumption is about 2.3 X lo9iM-l sec-' in good agreement with the value of (2.4 rt 0.4) x lo9 determined by nmr line broadening. Taking into account the nonspherical symmetry of the triiodide ion in the collision with iodide, the observed rate constant seems to be identical with the diffusion limit.
1. Introduction I n previous p a p e r ~ , l -the ~ effect of transfer diffusion has been applied to study reaction rates near the diffusion limit. The theoretical basis of the method has been given in the first part of this seriesJ3and its applicability has been demonstrated by the kinetic investigation of the ferrocene-ferricinium electron exchange r e a ~ t i o n . ~According to this, transfer diffusion seems to give reliable information also about the geometry of the activated complex as a directly measurable parameter. No other methods with such an advantageous property have been known so far. The effect of transfer diffusion appears in the increase of the diffusion coefficient because the exchange reaction results in a displacement of the mass centers of the reactants in every successful collision; Le., they gain the path length of the distance between the mass centers of the reactants in the activated complex. An elementary step of this accelerating effect on the migration of the species is shown schematically in Figure 1 for the iodide-triiodide exchange. It is seen that iodide is displaced by the distance 6 8 , while the mass center of the triiodide ion jumps the distance AX. It can be shown that the flux of the transferring particle X (Iz in the present case) is
where the flux is defined for the moles of Izcrossing the unit area of a surface s along which the concentration is the diffusion coeffiof the reactants is constant, D I ~ cient of the triiodide ions, k is the second-order rate constant of the exchange reaction (I13-$ 13I-), the 6's are the corresponding displacement of the mass centers, while CI,, and cia., are the concentration of the iodide and triiodide ions along the surface in question, respectively. The increase in the diffusion rate is related to the second term in the brackets in eq 1. It has been shown3that this term exceeds the errors in the determination of D I ~if, the rate constant is equal to the diffusion limit or approaches this value at least up to about one or two orders of magnitude. This lower limit in the determination of the rate constant coincides with the upper limit of the isotope exchange and nmr line broadening techniques.
+
+
2. Experimental Section Materials. All chemicals were of analytical grade purchased from the Reanal Co. Apparatus. Triiodide diffusion was measured in the photographic apparatus described el~ewhere.~Iodide diffusion was determined in a modified Oeholm cylinder.' (1) I. Ruff and I. Kor&&dor, Inorg. Chem., 9, IS6 (1970). (2) I. Ruff, Electrochim. Acta, 15, 1959 (1970). (3) I. Ruff and V. J. Friedrich, J . Phys. Chem., 75,3297 (1971). (4) I. Ruff, V. J. Friedrich, K. Demeter, and K. Csillag, ibid., 75, 3303 (1971).
The Journal of Physical Chemistry, Vol. 76, No. 2, 1972
ERRATA
The figures published on pages 158-160 of this issue of The Journal of Physical Chemistry in the paper by Edward G. Janzen titled "Electron Spin Resonance Study of the SOz. - Formation in the Thermal Decomposition of Sodium Dithionite, Sodium and Potassium Metabisulfites, and Sodium Hydrogen Sulfite" are incorrect. The correct figures for Dr. Janzen's paper are printed below.
I'd/
-2.0063
. 9 -2.0059 -2.0055
I
Figure 1. Repeat esr trace obtained in heating sodium hydrogen sulfite (NaHS03)as a function of time at 200' (lower) and 227" (upper); continuous curve is a temperature record as a function of time (in minutes).
,
,
,
,
,
-2005'
t
, 10
Figure 2 . Esr signal of SOZ. - in sodium dithionite a t different temperatures.
,
20
I_i__i-.lA-
30
40 50 TIMECMIN)
60
, 70
I
80
90
Figure 4. Plot of esr signal peak height of SO%.- in sodium dithionite as a function of time at different temperatures ( " C ) .
r
I
A
Figure 5. Plot of esr signal peak height of SOa. - in sodium metabisulfite (NaOZSSO3Na)as a function of time at different temperatures. 7 6
i
5
9 9
Figure 7. Plot of esr signal peak height of SO2. - in potassium metabisulfite (KOzSS03K)as a function of time at different temperatures.
4
'1
100
* 3
m z a
m 2 1
0
Figure 6. Calibrated plot of esr signal peak height of SOz. - in sodium metabisulfite (NaOzSS03Na),-0-0- at 180", -0-0at 200°, and -x-x- at 220'; similar plot of SO,.- in sodium metabisulfite at 180" after y-radiolysis at room temperature, -A-A-, similar plot of SO2.- in sodium dithionite at 180", -0-0-as in Figure 4.
Figure 8. Plot of esr signal peak height of SOZ.- in sodium hydrogen sulfite (HOS02Na) as a function of time a t different temperatures.
163
TRIIODIDE-IODIDE EXCHANGE REACTIONS
---@
-0
dependent on the position coordinate; Le., a normal concentration distribution should be observed with a constant apparent diffusion coefficient D I ~ '
This equation involves a linear relationship between the apparent diffusion coefficient and the concentration of the nondiffusing species. The slope of this straight line gives information about the value of La2 which can be compared to that calculated from the crystallographic and nmr data. For the flux of the iodide ions, an equation similar to eq 1 can be formulated, but with exchanged subscripts. The data of the experiments in which iodide is the diffusing particle and the concentration gradient of the triiodide ions is zero can be evaluated according to the equation
Figure 1.
(4)
The ionic strength of the solution was adjusted to 5 M by KBr. The initial concentrations in the photographic measurements were 0.01 M KI3, 0.1-5 M KI, and 4.9-0 M KBr in the lower. solution, while in the upper one an additional amount of 0.01 M KBr was added instead of KL. The iodide concentration was always constant all along the tube which permitted a simplification of the correlation in eq 1. When measuring the diffusion of iodide, the lower solution contained 3.5-5.0 fM KI and 1.5-0M KIa. The composition of the upper solutions ranged between 2.5 and 5.0 M KBr and 1.5 and 0 M KIa, and the excess iodide was always twice as much as the triiodide concentration (except the case of no triiodide present), Here the concentration of the triiodide was kept constqnt all along the tube. Concentration distribution was determined either by photographic method using a Zeiss microphotometer or by iodometric titrations of the fractions obtained by slowly draining the solution from the Oeholm column. In this latter case every tenth drop was used which was supposed to correspond to a given height in the column. The concentration distribution curves were, then, evaluated by the curve-fitting method described earlier.'** 3. Results and Discussion Since one reactant was macroscopically immobile and only one reactant could diffuse, eq 1 becomes much simp1er
where a transformation has been made for linear diffusion with respect to the axis x, and 6 denotes the displacement of the mass center of the triiodide ions due to the exchange reaction 61, in eq 1. It is seen that the term in the brackets a t the right-hand side became in-
where DI' and DI are the apparent and real diffusion coefficients of the iodide ions, respectively, and the factor of 9 arises from inserting the correlation SI = 361, = 36 assuming a linear arrangement for the activated complex. This assumption is supported by the smallest possible coulombic repulsion between the two negative charges of the activated complex, though its correctness is to be proved by the experiments. As it is seen in Figure 2, the apparent diffusion coefficients of triiodide show a linear increase with increasing concentration of iodide a t all the three temperatures investigated. This increase which is about 100% in the whole concentration range appreciably exceeds the errors. The slopes of the straight lines measured by triiodide diffusion result in (2.1 f 0.4) X lo9,(2.4 f 0.1) X loe, and (2.3 0.5) X lo9 M-l sec-' for the second-order rate constant a t 15, 25, and 35O, respectively, using the crystallographic interatomic distance of 2.90 A. These values are in excellent agreement with the nmr measurements which gave (2.4 f 0.4) X lo9M-' sec-' a t 27°.5*6 The intercepts correspond to the true diffusion coefficient of the triiodide ion. This value is (8.6 f 1.0) X cm2 sec-' independently of the temperature. To test the reliability of the photographic method, the diffusion coefficient of the triiodide ions was determined also under the same conditions as in ref 7 in which a cm2 sec-' in 0.1 M MI has been value of 11.3 X
*
(5) "Tables of Interatomic Distances," The Chemical Society, London, 1960. (6) 0. E. Myers, Symposium on Exchange Reactions, Brookhaven, 1965; E. E . Genser, U. 8. Atomic Energy Commission, UCRL-9846 (1962). (7) J. D. Newson and A. C. Riddiford, J. Electrochem. Acta, 108, 695 (1961).
The Journal of Physical Chemistry, Vol. 76, No. 2, 1072
I, RUFF,V. J. FRIEDRICH, AND K. CBILLAGI
164 A
ure 2. The expected ninefold increase in the slope of this straight line has been really found which can be seen from the parallelism of the line with those of the triiodide diffusion taking into account the ninefold shortage of the scale on the ordinate. With respect to the errors, the slope is 8.3 f 0.8 times that of the triio-
T",
& P
4 5.35.-
/ L
15.-
15
r
15.C
Figure 2.
reported. This coulometric datum could be satisfactorily reproduced in the photographic equipment: (10.4 i 1.0) X cm2sec-'. To exclude the possibility that the increase in the diffusion coefficient is due to some other effect of the change in the composition of the rather concentrated electrolyte solution, the viscosity was also measured as the function of the Br-/I- ratio in 5 M total ionic strength. The results in Table I show that the small decrease in the viscosity cannot be responsible for the twofold increase in the diffusion coefficient. Table I : Viscosity of 5 M K (I, Br) Solutions at 25' [I-], M
1 2 3 4
LBr-1, M
st
OP
1.089 1.074 1.068 1,057
Iodide diffusion was studied in a much narrower concentration range than that in the former measurements, since a certain amount of iodide is required for keeping the iodine-triiodide equilibrium to be shifted towards practically complete triiodide formation and, thus, the difference in iodide concentration between the two solutions of the diffusion system rapidly decreases with increasing triiodide content. The apparent diffusion COefficients of iodide are plotted in the upper part of FigThe Journal of Physical Chemistry, Vol. 76, N o . 2, 1972
4.75 0.50 4.50 1.00 4 .OO 2.00 3.75 2.50
0.25 0.25 0.50 0.50
0.00 4.25 0.00 3.50
1.00
0.00
1.00 1.25 1.25
2.00 0.00 1.25
1,093 1.090 1.133 1,187 1.277 1.311 1.343 1.361
The temperature dependence of the rate constant determined by the transfer diffusion method is less than about 2 kcal/mol. This is in agreement with some simple theoretical calculations on the coulombic repulsion energy that can be estimated to be less than 1 kcal/mol. On the other hand, the diffusion limit can be calculated3 to be 5.5 X l o 9 M-I sec-', if spherically symmetrical reactants are considered. This value is also independent of temperature, since the diffusion coeficient of neither the iodide nor the triiodide ions depends on it within the experimental errors. Considering, however, that the collision probability is not spherically symmetrical with respect t o the shape of the triiodide ion and the activated complex, the difference between the diffusion limit and the observed rate constant can be attributed to the fact that the only efficient approach of an iodide to a triiodide is that to one of the ends of the triiodide ion within an angle of about 45" on the either side of the 18- axis. This would lower the diffusion limit by a factor of about 1/2. In this way, the reaction under discussion can be regarded as a diffusion-controlled one, since an energy of activation less
THEPHOTOCHEMISTRY OF BENZENE than 1 kcal/mol means no restriction in comparison to RT, while the spacial requirement for the collision explains the slower rate. Thus the energy of activation observed in the nmr measurements to be 4 f 1 kcal/ mols can arise from the different conditions, i.e., from the temperature dependence of the diffusion coefficient of the reactants in the more dilute solutions which results in an enhancement of the diffusion limit itself.
165 Hence, it seems that not the reaction, but the translational movement of the reactants-when approaching each other-needs some energy of activation, if any. It can be concluded from the results discussed above that transfer diffusion is suitable for gaining information about significant details in the mechanism of very fast exchange reactions and can be successfully applied in their kinetic study.
The Photochemistry of Benzene in Oxygenated Aqueous Solution in the lBzuFirst Excited Singlet State by Menahem Luria and Gabriel Stein* Department of Physical Chemistry, Hebrew University, Jerusalem, Israel
(Received March 16?1971)
Publication costs assisted by Israel Academy of Sciences
The photochemistry of benzene in water, by excitation at 2288, 2537, and 2652 8 into different vibrational levels of the first excited singlet state (IBtu), gives in the presence of 02 at neutral pH only one major stable product. The kinetics and mechanism of its formation was investigated using continuous illumination and also flash photolysis techniques. The quantum yield of the product is steady with increasing quantum energy; the fluorescence yield decreases, A mechanism is proposed which involves formation of a labile energetic isomer of the ground state singlet from a nonstationary energy-rich state of the excited singlet before the fluorescent level is reached, and in competition with intersystem crossing. This labile isomer adds 02. The primary photooxide rearranges to give the final product.
Introduction The pathways of reaction-radiative and nonradiative-of excited molecules are modified by introducing the molecule into a solvent. Even if the solvent does not participate chemically in the reactions, it provides a route to partial energy loss by the excited solute, which otherwise could occur only by a radiative pathway. Therefore in solution specific states, still energy rich, may be readily reached. Under suitable conditions, water is such a chemically inert solvent for benzene. Comparison with the absorption spectrum of benzene in the gas phase indicates that the ground and excited state the solute molecule is little perturbed in water, less so than, e.g., in cyclohexane. Chemical product formation permits one to follow interactions resulting from the excited state resulting on light absorption, before thermal equilibrium is established. We studied the photoreactions of benzene in the presence of oxygen in aqueous solution, under conditions where oxygen did not interact with the ground or primary excited state of benzene, and served only to fix
by chemical reaction an intermediate in competition with a pathway to radiationless deactivation. The photochemistry of benzene has been investigated, especially in the vapor phase, but also in the liquid phase and in solution. Little has been published on the photooxidation of benzene in these systems. The photochemistry in the vapor phase has been thoroughly studied in all regions of the uv spectrum. I n the far-uv (1165-1470 A), the photoproducts are hydrogen and various hydrocarbons from CzHz to C ~ H ~ C C HI ~n .the ~ *range ~ 1600-2000 A an isomer of benzene was obtained which is probably f u l ~ e n e ~ , ~ rather than benzvalene,6z6 as previously proposed. 1 : has also been shown that photochemistry at 1849 A (1) R. Hentz and 9.J. Rzad, J . Phys. Chem., 71, 4096 (1967).
(2) W. M. Jackson, J. L. Faris, and B. Donn, ibid., 71, 3346 (1967). (3) L. Kaplan and K. E. Wilzbach, J . Amer. Chem. Soc., 89, 1030 (1967). (4) H. R. Ward and J. S. Wishnok, ibid., 90, 5353 (1968). (6) K. Shindo and S. Lipsky, J . Chem. Phys., 45, 2292 (1966). (6) J. K. Foote, M. H. Mallon, and J. N. Pitts, Jr., J . Amer. Chem. ~YOC.,88, 3698 (1966).
The Journal of Physical Chemistry, Vol. 76, N o . 8, 1978
