J. Phys. Chem. 1988, 92, 7074-7079
7074
states (and those of the 6D even less). For instance, the dehydrogenation reaction is spin forbidden from the 6S ground state and presumably involves spin-orbit mixing. For this reason, it is very inefficient. The quartet states react more efficientlybecause the dehydrogenation reaction now conserves spin and is thermodynamically favorable. The overall reactivity of Cr+ is described by the potential energy surfaces shown in Figure 5. The same simple molecular orbital arguments used successfully in explaining the reactions of atomic transition metals with H2' are used to generate this picture and appear to remain valid. The spin-forbidden surface crossings which are crucial to our interpretation of these experimental results have also been inferred in other transition-metal-ion reactions with methane3s4 and have been postulated for Cr+.I3 In this regard,
the detailed conclusions of this work are very similar to those of other recent and ongoing studies of M+ with CH4.2-4*6 Where Cr+ differs from these systems is in the estimated position of the surface crossing, about 1.8 eV above the ground-state reactants for Cr+, compared with .),10,
1u1.
(18) Liebhafsky, H.A. J . Am. Chem. SOC.1934, 56, 1500. (19) Wagman, D. D.; Evans, W. H.; Parker, V.;Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. The NBS Tables of Chemical
Thermodynamic Properties. Selected Values for Inorganic and C I and C, Organic Substances in SI Units; American Chemical Society and the American Institute of Physics for the NBS: Washington, DC, 1982. (20) Liebhafsky, H. A. J . Am. Chem. SOC.1939,61, 3513.
The Equilibrium 5HOBr
Q
2Br2 + Br03- + 2 H 2 0 + H+
The Journal of Physical Chemistry, Vol. 92, No. 25, 1988 7077
OC. The value 50.9 kJ/mol is near to the value AHR1' = -53.9 kJ/mol calculated from tabulatedlg AHfodata listed in Table 11. The apparent value of KRI determined here in 1 M H2S04is 6 times larger than the corresponding Liebhafsky value. At least & 8.04 a factor of 2 of this difference results from nonideality effects involving H+. A tabulated2' value of the acidity function Ho 7 7.76 indicates that the activity of H+ in 1 M (10%) H2SO4 is close to Y v twice [H']. We are unable to quantitatively account for possible 5 7.48 effects (vide infra) of H20Br+, but they may exist and affect the I j apparent value of KRI. The value KRI = 7 X lo7 M-2 reported 7.20 0.322 0.333 0.344 by Noszticzius et a1.22in 1 M H2S04is substantially (21 times smaller) at variance with the value reported here, and we are 100 * ( Temperoture/K )-' unable to account for this discrepancy. Figure 6. Arrhenius plot of In ( k ~vs~1 /) T for T = 20, 27, 3 1, and 35 The kinetics of reaction R1 have been investigated by Eigen OC. and Kustinz3at 20 OC and in initially neutral solutions of ionic strength 0.1 M. They reported values of kR1= 1.6 X lolo M-2 and K ~ s t i n The . ~ ~mechanistic scheme used for Br2 hydrolysis s-l and k-R1 = 110 s-l. These values were adopted by FF3 and by Eigen and Kustin is as follows. have been used in essentially all simulation work3,24*25 related to (11) the BZ reaction. However, Citri and Epstein26 have recently pointed out that in 1 M H2SO4 these rate constants yield rates (IV) exceeding the limit of diffusion control. Recalculation of the Eigen and K ~ s t i data n ~ ~in 1 M H2SO4 leads to kR1= 3.4 X lo9 M-2 s-l. Setting kR1 = 23.4 s-l retains the Eigen and Kustinf3 value of KR1 = 1.45 X lo8 MF2,which is about 10 times smaller than our data suggest. This procedure has been followed in later work by Citri and E p ~ t e i n . ~ ~ Br2 + HO- + H' We suggest revision of kR1and kR1 to values consistent with (I) the value of KRI inferred here, which suggests that equilibrium R1 lies considerably further on the Br2 side in 1 M H2SO4 than Both sets of workers concluded that the most likely route for Br2 in a nearly neutral solution. Because the Citri and E p ~ t e i n ~ ~ - ~ hydrolysis ' at pH 2 3 is 0 I11 IV. At pH -0 the route 0 value of kR1is very near the diffusion-control limit, we retain kR1 I I11 IV is even less likely. However, at pH -0 the = 3 X lo9 M-2 S-I and cause KR1 = 1.5 X lo9 M-2 by setting k - ~ ' presence of substantial protonated HOBr (H20Br+) may cause = 2 s-I, It is worth noting that a value KRI = 3.5 X lo9 M-2, which the route 0 I1 IV to become important. The apparent value is in good agreement with the value determined here, can be of KR1 may be affected if a substantial fraction of the HOBr is extracted from the Betts and MacKenzieI4data in 1.66 M HC104 present as H20Br+. at 25 OC on the basis of the methods employed here assuming A direct measurement of k-R1 in 1 M H2SO4is desirable. kR3has about the same value in 1.66 M HClO4 as it does in 1 Unfortunately, so little Br2 hydrolyzes at pH -0 that the methods M H2SO4. Furthermore, the rate of the reaction of Br2 and Br0< used by Lifshitz and P e r l m ~ t t e r - H a y r n a nand ~ ~ by Eigen and observed experimentally here is 10 times slower than the rate Kustinz3are not applicable in a strongly acid medium. It is possible calculated on the basis of the Eigen and K ~ s t i value n ~ ~ of K R I to shift equilibrium R1 to the left by addition of a bromide-ionand kR3 = 2.5 M-3 s-l. Thus the difference cannot be ascribed consuming species such as Ag+ or Hg2+,but it is not clear in such to unknown parallel reaction routes. The values of KRI and kR3 a case that direct reaction of Br2 with the metal ion can be inferred here also quantitatively rationalize data of Lamberz and excluded.29 ForsterlingZ8on the reaction of Br03- with Br2 carried out in 1 Assuming that the temperature dependence of reaction R1 is M H2SO4 under conditions where significant reaction is observed due only to the viscosity of the solvent, which correspond^^^ to in 10 min rather than the several days required in our experiments. an apparent activation energy of =15 kJ/mol, and that all of the The value of kRI inferred here in 1 M H2SO4 is nearly 50 times temperature dependence resulting from AHRl' is in reaction -R1 smaller than the Eigen-Kustin value in nearly neutral solution. we obtain the following expressions for kR1 and kR1. This difference may be diminished to the extent that kR1exceeds (M-2 s-')exp[(-15 kJ/mol)/RT] kR1 = the value 3 X lo9 M-' s-l calculated by Citri and E p ~ t e i n . ~ We .~' emphasize that our data lead only to a value of KRI and that the kR1 = 10'2.6(s-l) exp[(-68.9 kJ/mol)/RT] derived value of kR1 is dependent on the value of kR1assumed. In most work involving reaction R1 as a component in a complex The solid line in Figure 2 is a simulation using these values of mechanism the overall process is slow enough that reaction R1 kR1and kRI and the FF3 rate constants listed in Table I. The is always at equilibrium even with the lower values of kR1and agreement between experiment and simulation is adequate. As k-RI suggested here, and KRI is the important quantity. expected, simulations are very dependent on the values of KRI and The mechanism of reaction R1 is complex and has been studied kR3. The low value of kR1 suggested here is still large enough at pH 2 3 by Lifshitz and P e r l m ~ t t e r - H a y m a nand ~ ~ by Eigen that reaction R1 may be assumed always to be very close to equilibrium in the experiments reported here and in the BZ reaction. The tabulatedIg value of AGfo(HOBr) is apparently30 (21) Hammett, L. P. Physical Organic Chemistry, 2nd ed.; McGraw-Hill: derived from the Liebhafsky20 value of K R ~ . New York, 1970; Table 9.2, p 271. (22) Noszticzius, Z.; Gdspdr, V.; Forsterling, H.-D. J . Am. Chem. SOC. There has been some d i f f i c ~ l t y ~in~ simulating ,~' the minimal 1985, 107, 2314. bromate oscillator32 using other than the original FKN rate (23) Eigen, M.; Kustin, K. J . Am. Chem. SOC.1962, 84, 1355. constant values, which are clearly i n ~ o r r e c t . ~Control of the (24) Field, R. J.; Boyd, P. M. J . Phys. Chem. 1985, 89, 3707. minimal bromate oscillations is through reaction R1, and we (25) Bar-Eli, K.; Ronkin, J. J . Phys. Chem. 1984.88, 2844. (26) Citri, 0.;Epstein, I. R. J. Am. Chem. 1986, 108, 357. suggest that this discrepancy likely results from use of the Eigen
-- -
--
(27) Citri, 0.;Epstein, I. R. J . Phys. Chem. 1988, 92, 1865. (28) Lamberz, H.-J.; Forsterling,H.-D. FachbereichPhysikalische Chemie, Philipps Universitlt, Marburg, 3550 Marburg/Lahn, Federal Republic of Germany, unpublished experiments. (29) Lifshitz, A.; Perlmutter-Hayman. B. Bull. Res. Counc. Isr., Sect. A 1959,8A, 166. (30) Latimer, W. M. Oxidation Potentials, 2nd ed.;Prentice-Hall: New York, 1952; pp 6C-61.
- -
(31). Bar-Eli, K., School of Chemistry,Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, 69978 Israel, private communication. (32) Orbdn, M.; De Kepper, P.; Epstein, I. R. J . Am. Chem. SOC.1982, 104, 2657. (33) Moore, J. W.; Pearson, R. G. Kinetics and Mechanism; Wiley-Interscience: New York, 1981; p 267.
Kshirsagar and Field
7078 The Journal of Physical Chemistry, Vol. 92, No. 25, 1988
-
*
\
200
I
19.0j
K
Y v
y
7
I
/
18.04
0.322
0.327
0.332
0.337
0.342
100 * ( Ternpsroture/K )-'
Figure 7. Arrhenius plot of In (kR3/&) vs l/Tfor T = 20,27,31, and 35 OC.
and KustinZ3value of KR1. Better results should be obtained if the values of kRIand k-R1inferred here are used instead.
Temperature Dependence of Reaction 1 HOBr Decomposition. Figure 6 shows an Arrhenius plot of second-order rate constants for the decomposition of HOBr at 20, 27, 31, and 35 "c. According to eq 7 and k-R2 = A-R2 exp(-E*-w/RT), the slope and intercept of the least-squares line yield the expression below for k-R2. k-RZ = 10is~73*~02s1 (M-I s-l) exp[(-58.4 f 2.7 kJ/mol)/RT] Br0< + Br2 Reaction. Figure 7 shows an Arrhenius plot of the reciprocal first-order (see eq 9) rate constants (divided by 10[BrO
