Kinetics and Mechanism of Bromate-Bromide Reaction Catalyzed by Acetate

Article abstract of DOI:10.1021/ic0350786

The initial rate of the bromate-bromide reaction, BrO₃ ^- + 5Br^- + 6H⁺ → 3Br₂ + 3H ₂O, has been measured at constant ionic strength, l = 3.0 mol L ^-1, and at several initial concentrations of acetate, bromate, bromide, and perchloric acid. The reaction was followed at the Br ₂/Br₃^- isosbestic point (λ = 446 nm) by the stopped-flow technique. A very complex behavior was found such that the results could be fitted only by a six term rate law, v = k₁[BrO ₃^-][Br^-][H⁺]² + k ₂[BrO₃^-][Br^-]²[H ⁺]² + k₃[BrO₃^-][H ⁺]²[acetate]² + k₄[BrO ₃^-][Br^-]²[H⁺] ²[acetate] + k₅[BrO₃^-][Br ^-][H⁺]³[acetate]² + k ₆[BrO₃^-][Br^-][H⁺] ²[acetate], where k1 = 4.12 L³ mol^-3 s ^-1, k₂ = 0.810 L⁴ mol^-4 s ^-1, k₃ = 2.80 × 10³ L⁴ mol^-1 s^-1, k₄ = 278 L⁵ mol ^-5 s^-1, k₅ = 5.45 × 10⁷ L ⁶ mol^-6 s^-1, and k₆ = 850 L ⁴ Mol^-4 s^-1. A mechanism, based on elementary steps, is proposed to explain each term of the rate law. This mechanism considers that when acetate binds to bromate it facilitates its second protonation.

Full text of DOI:10.1021/ic0350786

Inorg. Chem. 2004, 43, 1395−1402
Kinetics and Mechanism of Bromate−Bromide Reaction Catalyzed by
Acetate
,‡
Carlos Eduardo S. Coˆrtes† and Roberto B. Faria*
Departamento de Qu´ımica Geral e Inorgaˆnica, Instituto de Qu´ımica, UniVersidade Federal
Fluminense, Morro do Valonguinho s/n, 24210-150 Nitero´i, RJ, Brazil, and Departamento de
Qu´ımica Inorgaˆnica, Instituto de Qu´ımica, UniVersidade Federal do Rio de Janeiro, C.P. 68563,
21945-970 Rio de Janeiro, RJ, Brazil
Received September 11, 2003
The initial rate of the bromate−bromide reaction, BrO - + 5Br- + 6H f 3Br2 + 3H O, has been measured at
+
3
2
constant ionic strength, I ) 3.0 mol L-1, and at several initial concentrations of acetate, bromate, bromide, and
perchloric acid. The reaction was followed at the Br2/Br3- isosbestic point (λ ) 446 nm) by the stopped-flow
technique. A very complex behavior was found such that the results could be fitted only by a six term rate law, ν
) k1[BrO -][Br-][H ] + k2[BrO -][Br-]2[H ] + k3[BrO -][H ] [acetate]2 + k4[BrO -][Br-]2[H ] [acetate] +
+ 2
+ 2
+ 2
+ 2
3
3
3
3
k5[BrO -][Br-][H ] [acetate]2 + k6[BrO -][Br-][H ] [acetate], where k1 ) 4.12 L3 mol-3 s-1, k2 ) 0.810 L4 mol-4
+ 3
+ 2
3
3
s-1, k3 ) 2.80 × 103 L4 mol-4 s-1, k4 ) 278 L5 mol-5 s-1, k5 ) 5.45 × 107 L6 mol-6 s-1, and k6 ) 850 L4 mol-4
s-1. A mechanism, based on elementary steps, is proposed to explain each term of the rate law. This mechanism
considers that when acetate binds to bromate it facilitates its second protonation.
BrO3- + 5Br- + 6H+ f 3Br2 + 3H2O
BrO3- + Br- + 2H+ f HBrO2 + HOBr
(1)
(2)
Introduction
Aqueous bromine chemistry received a new impetus with
the discovery of chemical oscillators.1-6 Oscillating reactions
that employ bromate, such as the Belousov-Zhabotinsky
reaction and other reactions derived from this, require a deep
comprehension of an intricate set of reactions involving
several bromine oxyacids, oxyanions, and oxides.7-10 The
starting reaction for all proposed mechanisms is the bro-
mate-bromide, reaction 1. In the FKN mechanism7 and other
mechanisms based on it, this reaction is proposed to proceed
via formation of bromous and hypobromous acids as shown
in reaction 2.
In the first study of reaction 1, Judson and Walker11 found
that it follows the fourth-order rate law, eq 3. This rate law
-d[BrO3 ]/dt ) k[BrO3 ][Br-][H+]2
(3)
-
-
has been confirmed by several authors.12-22 In addition, the
possibility for a fifth-order rate law at high bromide concen-
tration arising from a second-order term in bromide was
pointed out by Skrabal15 and by Bray and Liebhafsky.16
A
* Author to whom correspondence should be addressed. Tel: 55 21
2562-7148. Fax: 55 21 2562-7559. E-mail: faria@iq.ufrj.br.
† Universidade Federal Fluminense.
higher order for bromide ion was also found by Ra´bai et
‡ Universidade Federal do Rio de Janeiro.
(11) Judson, W.; Walker, J. W. J. Chem. Soc. 1898, 73, 410-422.
(12) Skrabal, A.; Weberitsch, S. R. Monatsh. Chem. 1915, 36, 211-235.
(13) Bray, W. C.; Davis, P. R. J. Am. Chem. Soc. 1930, 52, 1427-1435.
(14) Young; H. A.; Bray, W. C. J. Am. Chem. Soc. 1932, 54, 4284-4296.
(15) Skrabal, A. Z. Elektrochem.1934, 40, 232-246.
(16) Bray, W. C.; Liebhafsky, H. A. J. Am. Chem. Soc. 1935, 57, 51-56.
(17) Sclar, M.; Riesch, L. C. J. Am. Chem. Soc. 1936, 58, 667-670.
(18) Clarke, J. R. J. Chem. Educ. 1970, 47, 775-778.
(19) Wron´ska, M.; Cyfert, M. Rocz. Chem. 1972, 46, 347-352.
(20) Dom´ınguez, A.; Iglesias, E. Langmuir 1998, 14, 2677-2683.
(21) Burgos, F. S.; Graciani, M. del M.; Mun˜oz, E.; Moya, M. L.; Capita´n,
M. J.; Gala´n, M.; Hubbard, C. D. J. Solution Chem. 1988, 17, 653-
659.
(1) Belousov, B. P. Sb. Ref. Radiat. Med. 1959, 145.
(2) Zhabotinsky, A. M. Dokl. Akad. Nauk. SSSR 1964, 157, 392-395.
(3) Zhabotinsky, A. M. Biofizika 1964, 9, 306-310.
(4) Winfree, A. T. J. Chem. Educ. 1984, 61, 661-663.
(5) Zhabotinsky, A. M. Chaos 1991, 1, 379-386.
(6) Epstein, I. R.; Showalter, K. J. Phys. Chem. 1996, 100, 13132-13147.
(7) Field, R. J.; Ko¨ro¨s, E.; Noyes, R. M. J. Am. Chem. Soc. 1972, 94,
8649-8664.
(8) Noyes, R. M. J. Am. Chem. Soc. 1980, 102, 4644-4649.
(9) Gyo¨rgyi L.; Tura´nyi, T.; Field, R. J. J. Phys. Chem. 1990, 94, 7162-
7170.
(10) Faria, R. B.; Lengyel, I.; Epstein, I. R.; Kustin, K. J. Phys. Chem.
1993, 97, 1164-1171.
(22) Coˆrtes, C. E. S.; Faria, R. B. J. Braz. Chem. Soc. 2001, 12, 775-779.
10.1021/ic0350786 CCC: $27.50 © 2004 American Chemical Society
Published on Web 01/24/2004
Inorganic Chemistry, Vol. 43, No. 4, 2004 1395

Coˆrtes and Faria
al.,23 who were the first to use visible spectroscopy to follow
this reaction at the Br2/Br3- isosbestic point. They measured
the initial rate for a wide range of bromide concentration
(0.1 < [Br-] < 2.0 mol L-1) at low concentrations of H+
and bromate. To explain the observed behavior, especially
at high [Br-], they proposed a rate law with three terms, as
indicated by eq 4.
The initial rate of reaction, ν0, was determined by fitting a second
degree polynomial, at2 + bt + c, to the curve of total bromine
concentration versus time. The coefficient b is the initial rate. All
experimental kinetic data presented here are averages of a minimum
of five determinations.
At each total acetic acid-acetate buffer concentration, the free
concentrations of H+ and acetate ions were calculated on the basis
of the acetic acid dissociation. The value of this constant, Ka, which
is equal to 1.778 × 10-5 (pKa ) 4.750) at zero ionic strength
(25 °C), was corrected to 1.124 × 10-5 (pKa ) 4.949) for I ) 3.0
-d[BrO3 ]/dt ) k′[BrO3 ][Br-][H+]2 +
-
-
mol L-1 28
.
k′′[BrO3 ][Br-]2[H+] + k′′′[BrO3 ][Br-]2[H+]2 (4)
-
-
Experiments using the highest acetate buffer concentration
together with the highest bromate concentration employed in this
work did not show any significative modification in the UV-vis
spectra, up to 10 min. This ensures that if some reaction between
bromate and the acetate buffer occurs, it is outside the time scale
used in our bromate-bromide reaction, which was studied by the
measurement of the initial velocity using the stopped-flow technique
in a time scale maximum of 100 s.
Data treatment and curve fitting for kinetic data were carried
out by using LOTUS 1-2-3.29 The Solver facility of this program,
found in other spreadsheets,30 was employed to obtain some of the
rate constants.
In addition to these kinetic studies, only a few systems
containing oxyhalogen compounds have been proved to be
catalyzed by acetate ion. For oxyanions with halogen(V),
only the reactions bromate-iodide24 and iodate-iodide25
have been observed to be catalyzed by acetate and follow
the rate laws eqs 5 and 6, respectively, where B- can be
-
-
-
CH3CO2 , ClCH2CH2CO2 , or ClCH2CO2 .
-d[BrO3 ]/dt ) k0[BrO3 ][I-][H+]2 +
-
-
-
kb[BrO3 ][I-][H+]2[B-] (5)
Results
-
-
-d[IO3 ]/dt ) k0[IO3 ][I-]2[H+]2 +
The Supporting Information presents all the initial rate
values determined for reaction 1 at 25 °C and I ) 3.0 mol
L-1. This encompasses 44 sets of results, each one showing
the effect of the variation of the concentration of only one
species on the rate constant. Some experiments were carried
out using an excess of bromide (see Supplemental Material
1, Supporting Information) and others using an excess of
bromate (see Supplemental Material 2, Supporting Informa-
tion). In Tables 1 and 2 we present a re´sume´ of each set of
results included in the Supporting Information.
kb[IO3 ][I-]2[H+]2[B-]/(1 + k′[I-]) (6)
-
More recently, the disproportionation of HOI has been shown
to be catalyzed and suppressed by the acetic acid-acetate
buffer.26
In this paper we present evidence for acetate catalysis on
reaction 1 and we fit the experimental initial rate values to
a six term rate law, showing that this catalytic effect is much
more complex than it has been previously supposed.
Bromate Order. From the experiments to determine the
effect of the variation of bromate concentration, in the
presence of acetate and with an excess of bromide (first entry
in Table 1), we obtained a very good linear plot of log ν0 ×
Experimental Section
Analytical grade chemicals NaBrO3 and sodium acetate
(VETEC), acetic acid, HClO4, and NaClO4 (Merck), and NaBr
(Grupo Qu´ımica) were used without further purification. Water was
obtained by a Milli-Q Plus purification system and had 18 MΩ
resistivity.
Kinetics experiments were carried out by the stopped-flow tech-
nique performed by the use of the Hi-Tech dual mixing microvol-
ume stopped-flow SF-61DX2. Temperature was maintained at 25.0
( 0.1 °C by a circulating bath, and the ionic strength, I, was
adjusted to 3.0 mol L-1 with NaClO4 considering the concentrations
of all ionic species present in the solution.
The reaction was followed at the isosbestic point of the mixture
Br2 and Br3- (λ ) 446 nm, ꢀ ) 111 L mol-1 cm-1). The wavelength
and the extinction coefficient for this isosbestic point were obtained
by fitting a second degree polynomial to the experimental absor-
bance data for Br2 and Br3- determined by Raphael27 in 2 mol L-1
perchloric acid solution.
-
log [BrO3 ]0 (R2 ) 0.9999) with a slope equal to 1.000. This
clearly points to a first-order term in bromate. Additionally
it shows that the first-order term in bromate is not affected
by the acetate concentration. When an excess of bromate is
used either in the absence (first entry in Table 2) or in the
presence of acetate (second entry in Table 2), the results still
point to a first-order in bromate.
Bromide Order in the Absence of Acetate. The second
entry in Table 1 is concerned with the variation of the initial
rate with the variation in the bromide concentration in the
absence of acetate. On the basis of eq 7, the plot of
-
2
ν0/[BrO3 ]0[H+]0 [Br-]0 × [Br-]0 (see Figure 1) is linear (R2
) 0.993) and indicates the rate law shown in eq 8, where k1
(23) Ra´bai, Gy.; Bazsa, Gy.; Beck, M. T. Int. J. Chem. Kinet. 1981, 13,
1277-1288.
(28) De Robertis, A.; De Stefano, C.; Rigano, C.; Sammartano, S. J.
Solution Chem. 1990, 19, 569-587.
(24) Barton, A. F. M.; Wright, G. A. J. Chem. Soc. A 1968, 1747-1753.
(25) Barton, A. F. M.; Wright, G. A. J. Chem. Soc. A 1968, 2096-2103.
(26) Urbansky, E. T.; Cooper, B. T.; Margerum, D. W. Inorg. Chem. 1997,
36, 1338-1344.
(29) Lotus 1-2-3, version 5; Lotus Development Co.: Cambridge, MA,
1995.
(30) (a) Walsh, S.; Diamond, D. Talanta 1995, 42, 561-572. (b) Machuca-
Herrera, J. O. J. Chem. Educ. 1997, 74, 448-449. (c) Harris, D. C. J.
Chem. Educ. 1998, 75, 119-121. (d) de Levie, R. J. Chem. Educ.
1999, 76, 1594-1598. (e) Denton, P. J. Chem. Educ. 2000, 77, 1524-
1525. Nikitas, P. J. Chem. Educ. 2001, 78, 1070-1075.
(27) Raphael, L. In Chem. Appl. Bromine its Compounds, Price, D., Iddon,
B., Wakefield, B. J., Eds.; Elsevier: Amsterdam, 1986 [Publ. 1988];
Chapter 13, pp 369-384.
1396 Inorganic Chemistry, Vol. 43, No. 4, 2004

Bromate-Bromide Reaction Catalyzed by Acetate
Table 1. Re´sume´ of the Initial Rate Values for Reaction 1 Using an Excess of Bromide at I ) 3.0 mol L-1 and T ) 25.0 °C
effect of
[BrO3-]0/M
[Br-]0/M
[H+]0/10-3
M
[acetate]0/10-3
29.3
M
plot
slope (R2)
-
-
BrO3
0.100-0.250
0.0200
0.0200
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
2.50
0.372
118
log ν0 × log [BrO3
]
1.000 ( 0.005 (0.9999)
see text (0.993)
Br-
0.100-2.50
0.100-2.50
2.00-2.30
2.00-2.30
2.00-2.50
2.00-2.50
2.00-2.40
2.00-2.50
2.00-2.50
2.00-2.30
2.00-2.30
2.00-2.30
0.500
2.00
2.10
2.20
2.30
2.50
2.50
2.50
2.50
eq 7
Br-
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
0.373
102
1.75
2.34
2.93
14.9
23.5
29.3
44.1
58.5
73.1
102
1.75-102
2.34-102
1.75-102
1.75-102
1.75-102
1.75-102
27.0
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
0.80; 1.36a
Br-
2.0 ( 0.3 (0.96)
1.98 ( 0.10 (0.994)
1.95 ( 0.04 (0.999)
2.00 ( 0.02 (0.999)
2.01 ( 0.07 (0.997)
1.79 ( 0.01 (0.9998)
1.67 ( 0.01 (0.9999)
1.62 ( 0.01 (0.9998)
1.57 ( 0.04 (0.999)
1.553 ( 0.005 (0.99998)
0.61; 1.79b
Br-
Br-
Br-
Br-
Br-
Br-
Br-
Br-
Br-
acetate
acetate
acetate
acetate
acetate
acetate
H+
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [H+]
0.63; 1.67b
0.55; 1.66b
0.59; 1.64b
0.54; 1.63b
0.56; 1.61b
0.175-0.405
0.103-0.182
0.724-0.131
0.560-0.103
2.16 ( 0.02 (0.9998)
2.04 ( 0.04 (0.999)
2.03 ( 0.06 (0.998)
1.98 ( 0.05 (0.999)
H+
44.2
60.1
74.8
log ν0 × log [H+]
H+
log ν0 × log [H+]
H+
2.50
log ν0 × log [H+]
a Slope for the four lowest bromide concentration data points; slope for the four highest bromide concentration data points. b Slope for the four lowest
acetate concentration data points; slope for the four highest acetate concentration data points.
Table 2. Re´sume´ of the Initial Rate Values for Reaction 1 Using an Excess of Bromate at I ) 3.0 mol L-1 and T ) 25.0 °C
effect of
[BrO3-]0/M
[Br-]0/10-2
M
[H+]0/10-2
107
0.0373
107
M
[acetate]0/10-3
M
plot
slope (R2)
-
-
-
BrO3-
0.00100-0.00500
0.800-1.00
0.0100
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.200
70.0
log ν0 × log [BrO3
log ν0 × log [BrO3
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
log ν0 × log [Br-]
]
]
0.98 ( 0.01 (0.9993)
1.12 ( 0.02 (0.9995)
0.97 ( 0.02 (0.9992)
0.91 ( 0.008 (0.9998)
0.86 ( 0.02 (0.999)
0.62 ( 0.04 (0.993)
0.54 ( 0.01 (0.998)
0.50 ( 0.02 (0.998)
0.48 ( 0.009 (0.9990)
0.44 ( 0.005 (0.9996)
0.43 ( 0.02 (0.996)
0.43 ( 0.007 (0.9993)
1.16; 1.86a
BrO3
Br-
87.7
0.100-0.500
3.00-9.00
1.00-9.00
3.00-9.00
1.00-9.00
3.00-9.00
1.00-9.00
1.00-9.00
3.00-9.00
1.00-9.00
1.00
3.00
5.00
7.00
9.00
10.0
0.100
10.0
10.0
Br-
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
0.0373
10.0-50.0
2.34
2.92
14.6
23.4
29.2
43.9
58.5
73.1
Br-
Br-
Br-
Br-
Br-
Br-
Br-
Br-
87.7
acetate
acetate
acetate
acetate
acetate
acetate
H+
2.34-87.7
2.34-87.7
2.34-87.7
2.34-87.7
2.34-87.7
2.34-87.7
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [acetate]
log ν0 × log [H+]
0.98; 1.84a
0.89; 1.77a
0.84; 1.81a
0.81; 1.78a
0.67; 1.89a
0.100
1.00
1.00
1.99 ( 0.05 (0.998)
2.26 ( 0.03 (0.9997)
2.12 ( 0.08 (0.996)
H+
0.0175-0.0304
0.00560-0.0139
27.1
74.9
log ν0 × log [H+]
H+
log ν0 × log [H+]
a Slope for the four lowest acetate concentration data points; slope for the four highest acetate concentration data points.
) 4.12 ( 0.05 L3 mol-3 s-1 and k2 ) 0.810 ( 0.02 L4 mol-4
differently from what we have found at much lower bromide
concentration.22 It should be noticed that λ and ꢀ used by
Ra´bai et al.23 are significantly different from our values. As
expected, at low bromide concentrations, the last term in eq
8 is not important, as can be seen from the bromide order
close to 1 (see entry 3 in Table 2). A comparison of the k1
values is presented in Table 3.
s-1. This rate law had been anticipated by Bray and
ν
) k1 + k2[Br-]
(7)
[BrO3 ][H+]2[Br-]
-
ν ) k1[BrO3 ][Br-][H+]2 + k2[BrO3 ][Br-]2[H+]2 (8)
-
-
Bromide Order in the Presence of Acetate. Entries 3 to
13 in Table 1 show that the bromide order changes in the
presence of acetate. Data from experiments using a wide
range of bromide concentrations produced a nonlinear graph
of log ν0 × log [Br-]0. As indicated by entry 3 in Table 1,
the data for low bromide concentrations indicate a bromide
order of 0.80 and the data for high bromide concentration
indicate a bromide order of 1.36. This suggests that, in the
Liebhafsky16 and shows some agreement with the rate law
proposed by Ra´bai et al.,23 eq 4, where k′ ) 4.37 L3 mol-3
s-1, k′′ ) 1.4 × 10-2 L3 mol-3 s-1, and k′′′ ) 0.56 L4 mol-4
s-1 at the same I ) 3 mol L-1. As can be seen, there is no
necessity to include a first-order term in H+ as included in
eq 4 by Ra´bai et al.23 (These authors considered this term to
be the more important at low H+ and high bromide
concentrations.) Otherwise, the last term in eq 8 is imperative,
Inorganic Chemistry, Vol. 43, No. 4, 2004 1397

Coˆrtes and Faria
Figure 1. Linear fit of eq 7 to the 15 experimental data corresponding to
the second entry of Table 1.
Table 3. Selected k1 Values at High Ionic Strength (T ) 25.0 °C)
I/M
k1/M-3 s-1
main electrolytes
NaClO4
buffer NaH2PO4/H3PO4
buffer NaH2PO4/H3PO4
HBr, NaClO4
ref
3.0
3.0
3.0
3.0
3.0
3.5
38.7
21
23
23
20
4.37
Figure 2. Bromide order as a function of the acetate concentration: (9)
data obtained using bromide in excess (see Table 1); (b) data obtained
using bromate in excess (see Table 2).
17.9a
4.29
4.12
4.07 ( 0.40
HClO4, NaClO4
HClO4, NaClO4
this work
22
range from 1.16 ([Br-]0 ) 0.01 mol L-1) to 0.67 ([Br-]0 )
0.1 mol L-1). Using data from the four highest acetate
concentrations, the slopes were close to 1.8 for all bromide
concentrations.
a Recalculated in ref 22.
presence of acetate, the bromide order depends on its con-
centration, as it was also noticed in the absence of acetate
(see eq 8).
2
A plot of ν0 × [acetate]0 gave a very good rectilinear
graph (see entries 14 to 19 in Table 1 and Figure 3; see
entries 13 to 18 in Table 2 and Figure 4). Despite this, it
was not possible to obtain a unique value for a rate constant
based on a simple rate law such as eq 9, where a and b are
integers ranging from 1 to 3. The best result was obtained
using a ) 1 and b ) 3, which give values for k in the range
of 8.3 × 107 L6 mol-6 s-1 to 5.6 × 108 L6 mol-6 s-1.
Data from entries 4 to 13 in Table 1 present evidence that
acetate, as well bromide, is implicated in the modification
of the bromide order. At low acetate concentrations, the
bromide order is close to 2 (entries 4 to 8 in Table 1), but as
the acetate concentration is increased, this order decreases
to values as low as 1.5 (entries 9 to 13 in Table 1). Otherwise,
in the presence of an excess of bromate (see entries 3 to 12
in Table 2), the bromide order decreases from 1 to 0.4, as
the acetate concentration is increased, showing that at low
bromide concentrations even small acetate concentration
affect the bromide order (see Figure 2).
Acetate Order. The results in entries 14 to 19 in Table 1
show that acetate order changes significantly with concentra-
tion. Plotting log ν0 × log [acetate]0 does not give a straight
line, independent of which bromide concentration is em-
ployed. Linear fits using only the four lowest acetate
concentration data points gave slopes close to 0.6 for all
bromide concentrations (see Table 1). Using only the four
highest acetate concentration data points, a linear fit gave
slopes from 1.79 ([Br-]0 ) 0.500 mol L-1) to 1.61 ([Br-]0
) 2.50 mol L-1). A similar finding was obtained with the
data obtained using bromate in excess, as can be seen in
Table 2 (entries 13 to 18). In this case, the slopes calculated
using only data from the four lowest acetate concentrations
ν ) k[BrO3 ][Br-]a[H+]b[acetate]2
(9)
-
H+ Order. The last four entries in Table 1 show that the
H+ order is close to 2 for experiments using an excess of
bromide in the presence of acetate. At the lowest acetate
concentration employed we found an order slightly greater
than 2. When bromate is used in excess, the H+ order is still
close to 2, and again, the values show a tendency to be
slightly higher than this, as can be seen in the last two entries
of Table 2.
Overall Rate Law. As also proposed by Barton and
Wright, from a study of the catalysis in bromate-iodide24
and iodate-iodide25 reactions, the results above suggest a
rate law containing terms additional to those in eq 8. These
additional terms should contain acetate, bromide, and H+ in
varying orders (as well as the first-order bromate) in such a
way as to fit all experimental results. Due to the complexity
1398 Inorganic Chemistry, Vol. 43, No. 4, 2004

Bromate-Bromide Reaction Catalyzed by Acetate
Figure 4. Acetate second-order evidence at several bromide concentrations
in bromate excess at 25 ( 0.1 °C: [BrO3-]0 ) 1.00 mol L-1, [H+]0 ) 3.73
× 10-4 mol L-1, 2.34 × 10-3 < [acetate]0 < 8.77 × 10-2 mol L-1; (b)
0.0500 mol L-1, ([) [Br-]0 ) 0.0700 mol L-1, (+) [Br-]0 ) 0.0900 mol
L-1, (×) [Br-]0 ) 0.100 mol L-1, I ) 3.0 mol L-1 (entries 13 to 18 in
Table 2); (a) full set of data; (b) [acetate] e 1.00 mol L-1. Straight lines
are the linear fit to each data set.
Figure 3. Acetate second-order evidence at several bromide concentrations
in bromide excess at 25 ( 0.1 °C: [BrO3-]0 ) 2.50 × 10-1 mol L-1, [H+]0
) 3.73 × 10-4 mol L-1, 1.75 × 10-3 < [acetate]0 < 0.102 mol L-1; (×)
[Br-]0 ) 0.500 mol L-1, (b) [Br-]0 ) 2.00 mol L-1; (2) [Br-]0 ) 2.10
mol L-1, (1) [Br-]0 ) 2.20 mol L-1, ([) [Br-]0 ) 2.30 mol L-1, (+)
[Br-]0 ) 2.50 mol L-1, I ) 3.0 mol L-1 (entries 14 to 19 in Table 1); (a)
full set of data; (b) [acetate] e1.00 mol L-1. Straight lines are the linear fit
to each data set.
[Br-]0 ) 0.0100 mol L-1; (2) [Br-]0 ) 0.0300 mol L-1, (1) [Br-]0
)
combinations in orders for bromide, acetate, and H+. The
starting point was eq 8, and for all attempts we did not
change the values of the rate constants k1 and k2 determined
by fitting eq 7 to the experimental data. After many attempts
(see Supplemental Material 3, Supporting Information), a
good fit was found using eq 10, where k1 ) 4.12 L3 mol-3
s-1, k2 ) 0.810 L4 mol-4 s-1, k3 ) 2.80 × 103 L4 mol-4 s-1,
k4 ) 278 L5 mol-5 s-1, k5 ) 5.45 × 107 L6 mol-6 s-1, and
k6 ) 850 L4 mol-4 s-1. A comparison of the calculated initial
rate obtained by the use of eq 10 and the experimental values
is presented in the Supporting Information (Supplemental
Material 1 and 2).
of the experimental results, it was not possible to determine
these additional rate constant values using a conventional
kinetic data treatment, and so we used the SOLVER add-in
facility of the Lotus 1-2-3 spreadsheet.
As a demonstration of the SOLVER capability, it was
employed to estimate the rate constant values for k1 and k2.
In doing this, only initial rate values for the experiments
without acetate were fed to SOLVER, and the results
obtained for k1 and k2 were 3.96 L3 mol-3 s-1 and 0.87 L4
mol-4 s-1, respectively. These values showed a good
agreement with the values determinated by eq 8, revealing
the capability of the SOLVER in the rate constant estimation.
To find out the global rate law we have considered the
inclusion of several terms containing almost all possible
Many other terms should be included to improve the
agreement between calculated and experimental data points.
Inorganic Chemistry, Vol. 43, No. 4, 2004 1399

Coˆrtes and Faria
ν ) k1[BrO3 ][Br-][H+]2 + k2[BrO3 ][Br-]2[H+]2 +
-
-
are second-order terms in acetate ion (rate constants k3 and
k5 in eq 10). At lower acetate concentrations, these second-
order terms are negligible, as shown in Figure 3b. The fit of
eq 10 to the experimental data indicates that acetate can
present a first-order behavior (term containing k4 in eq 10).
Figure 4a shows that, in an excess of bromate, for all acetate
concentrations used, the acetate presents a second-order
behavior with rate constants k3 and k5 in eq 10. In addition,
the k5 term in eq 10 is identical to eq 9 and the value obtained
for k5 in eq 10 has the same order of magnitude as the k
value found fitting eq 9.
Second-order in H+ was also verified in most experiments.
However, orders slightly higher than 2 were found using an
excess of bromate (Table 2, last two entries), indicating the
possibility of a third-order for this ion, and the inclusion of
k5 term in the rate law (eq 10). This term also appeared when
eq 9 was fitted to the results obtained on changing the acetate
concentration.
Mechanism for the Terms without Acetate. In the rate
law given by eq 10, each term corresponds to a different
pathway and rate determining step. In trying to build a
mechanism for each term, we considered several possibilities
before we arrived at the set of elementary steps presented
below.
For the first and second terms of eq 10, which describe
the reaction in the absence of acetate, let us start with the
following steps, based on the proposition made by Ra´bai
et al.23
-
k3[BrO3 ][H+]2[acetate]2 +
k4[BrO3 ][Br-]2[H+]2[acetate] +
-
k5[BrO3 ][Br-][H+]3[acetate]2 +
-
-
k6[BrO3 ][Br-][H+]2[acetate] (10)
This rate law is a result of trying to keep a limited number
of terms. The rate constants obtained for the terms including
acetate (last four terms) have values that are a compromise
for a best fit to both data sets (excess of bromide and excess
of bromate). If any of these rate constants are changed in
order to improve the agreement with one data set, the
agreement with the other is reduced. For the data sets
obtained with an excess of bromide and an excess of bromate
the average errors are 8.5% and 12.3%, respectively.
Discussion
Based on Barton and Wright’s results24 for the bromate-
iodide reaction catalyzed by acetate, eq 5, this complex rate
law, eq 10, was unexpected, indicating that the catalytic
behaviors of acetate in the bromate-iodide and bromate-
bromide reactions are very different. A rate law presenting
a similar complexity, with five terms, was obtained by
Sigalla31 for the bromate reactions in a medium containing
bromide and chloride. Thus, it is reasonable to suppose that
the complexity of the rate law obtained by us is a special
feature of the aqueous solution chemistry of bromine.
K1
BrO3- + H+ {
\} HBrO3
(11)
The first two terms in eq 10 have been demonstrated by
the results obtained in the absence of acetate, and the values
for k1 and k2 were determined (see Figure 1) from eq 8. The
terms involving the participation of acetate and the rate
constants k3, k4, k5, and k6, which were estimated by
SOLVER, find support in the experimental observations.
First-order bromate was confirmed for all the experimental
conditions used (see Table 1 entry 1 and Table 2 entries 1
and 2).
HBrO3 + H+ {K2
\
} H2BrO3
(12)
(13)
+
H2BrO3+ + Br- 9k′8 products
K3
H2BrO3+ + Br- {
\} H2Br2O3
(14)
(15)
H2Br2O3 + Br- 9k′′′8 products
Figure 2 (9) shows that, in the presence of acetate and
with an excess of bromide, the order of bromide remains
approximately 2 for concentrations of acetate lower than 23.4
× 10-3 mol L-1. At concentration values higher than this,
the bromide order decreases to a value between 1 and 2
(approximately 1.5), indicating the possibility of the existence
of first- and second-order terms for bromide, and thus the
terms containing k4, k5, and k6 in eq 10. When an excess of
bromate was used (Figure 2 (b)), it was observed that, when
the acetate concentration increases, the bromide order
decreases quickly, tending to a value between 1 and 0
(approximately 0.4), indicating the presence of both first-
and zero-order terms in bromide and hence the incorporation
of a term without bromide, as can be seen in the term
containing k3 in the rate law (see eq 10).
One point worth mentioning is the fact that the reactants
in both reactions 13 and 14 are the same but in one case
(reaction 13) they react to form product in a slow step and
in the other case (reaction 14) they react to form an inter-
mediate species. In addition, on the basis of the very low
+
stability of bromate in strong acid solutions,32,33 the H2BrO3
species should not be considered as a stable intermediate.
+
As HBrO3 is a very strong acid,33 so the H2BrO3 species
should not be formed at the acid concentrations used to study
the bromate-bromide reaction.
Instead, we propose that bromide should be bound to the
bromine atom of the bromate assisting the entrance of the
H+ (avoiding the formation of the bromic acid, HBrO3, or
+
H2BrO3 ). In this way, the mechanism goes through other
intermediates until H2Br2O3 is formed which suffers a
Figure 3a shows that, with an excess of bromide, and for
acetate concentrations higher than 23.4 × 10-3 mol L-1, there
(32) Fonteyne, R. Natuurwet. Tijdschr. (Ghent) 1939, 21, 141-144.
(33) Alves, W. A.; Te´llez S., C. A.; Sala, O.; Santos, P. S.; Faria, R. B. J.
Raman Spectrosc. 2001, 32, 1032-1036.
(31) Sigalla, J. J. Chim. Phys. 1958, 55, 758-767.
1400 Inorganic Chemistry, Vol. 43, No. 4, 2004

Bromate-Bromide Reaction Catalyzed by Acetate
rearrangement to the products, as can be seen in the reactions
16 to 21 written using Lewis structures.34
decomposes to HOBr and HBrO2. Although Lewis structures
are not the best way to describe accurately electronic
structures, we tried to show with these that the negative
charge is hidden inside the bromate ion, making difficult
the H+ attack. In species A, the two negative charges should
avoid each other, and because of this we have drawn them
in the oxygens. The B species can be represented with the
negative charge on the isolated oxygens (which can be
represented by two resonant structures) or with the negative
charge on the central bromine (which we call BN). In the
sequence of steps which represent the mechanism for the
second term in eq 10 (reactions 16, 17, 22, and 23), we
decided to use BN to emphasize the idea that each bromide,
which is added to bromate, contributes to expose the negative
charges on the oxygens which thereby attract H+.
This mechanism should be contrasted with the mechanism
proposed by Agreda B. et al.35 for the Dushman reaction
which goes through H2IO3 and H2I2O3 species. Iodic acid
The way we have written reaction 23 is only one of the
possibilities. Similarly, reactions 18 and 19 can be replaced
by a single reaction in which species B reacts with H+ and
produces HOBr and HOBrO directly, avoiding the interme-
diate C. In the same way, another possibility for reaction 23
+
is not as strong as bromic acid, and thus the supposition for
+
the formation of the H2IO3 species is reasonable in the
Dushman reaction. Otherwise, the Dushman reaction presents
only a second-order behavior for the iodide, which suggests
that the mechanism for the bromate-bromide reaction should
not be the same which is in agreement with our proposal.
The HOBr formed in reaction 19 will react rapidly with
bromide,36 forming bromine by the very well-known reac-
tion 20.
-
is the formation of intermediate H2Br3O3 , which would
decompose to the same products as in reaction 23. There is
no way of distinguishing kinetically these possibilities. Again,
our mechanism for the k2 term in eq 10 (reactions 16, 17,
22, and 23), which considers that bromide attack precedes
H+ attack, is in opposition to that proposed by Agreda et
al.35 for the Dushman reaction, under the second-order halide
conditions.
HOBr + Br- + H+ f Br2 + H2O
(20)
Our proposal for the k1 and k2 terms of eq 10 disagree
with the mechanism proposed by Ra´bai et al.23 too. These
authors consider that H+ attack to bromate, forming HBrO3
and H2BrO3+ intermediates, precedes bromide attack. How-
ever, their mechanism considers the formation of the same
C species which rearranges to products, accounting for their
k′ term in eq 4 (this accounting the same as the k1 in eq 10).
A similar C species is present in the Agreda et al.35
mechanism too, with iodine atoms in the place of bromine
atoms, but however here it does not rearrange to products.
In addition, our mechanism does not consider the participa-
tion of the intermediate BrBrO2, which can be considered
as a particular case of a general species XYO2, proposed by
many authors37 in the mechanisms for reactions involving
oxyacids or oxyanions of Cl, Br, and I. It does not mean
The HBrO2, formed in reaction 19, will also react rapidly
with bromide,10 forming HOBr (reaction 21).
HBrO2 + Br- + H+ f 2HOBr
(21)
We propose that bromide attack on bromate is the first
step because bromate should be a very weak base and should
not attract the H+ efficiently. Only the A species, which has
a double negative charge, should be able to easily attract
two H+ to form the C species, which must be unstable and
(34) Straub, D. K. J. Chem. Educ. 1995, 72, 889-891.
(35) Agreda B., J. A.; Field, R. J.; Lyons, N. J. J. Phys. Chem. A 2000,
104, 5269-5274.
(36) Eigen, M.; Kustin, K. J. Am. Chem. Soc. 1962, 84, 1355-1361.
Inorganic Chemistry, Vol. 43, No. 4, 2004 1401

Coˆrtes and Faria
that these species should not exist but only that in our
mechanism the BrBrO2 does not play an important role.
Another point we must consider is the possibility that
bromate, after two protonations, loses water and forms the
has been proposed previously26 in a mechanism for acetate
catalysis in the hypoiodous acid disproportionation reaction.
Again, it is not possible to ensure that the nonmetal
complex decomposition is the rate determining step or if it
is the last H+ attack that determines the rate of the reaction.
However, from reactions 24 to 26, it appears that bromate
may form several different nonmetal complexes with dif-
ferent numbers of bromide, acetate, and OH groups. Our
kinetic analysis allowed us to suggest only some of the more
important of them.
+
BrO2 species as has been considered by other authors.19,31
However, this possibility has been ruled out by the results38,39
on the rate of exchange of isotopic oxygen between the oxy-
-
anions XO3 (X ) Cl, Br) and water as these rates are
significantly lower than the reactions of these oxy-anions
with X- (X ) Cl, Br, I).
Mechanism for Acetate Catalysis. Our proposal for the
elementary steps, that accounts for the terms of eq 10
involving the acetate catalysis, follows Barton and Wright24,25
ideas. In the formulation of the mechanism for each one of
the last four terms in eq 10, we have considered that the
global reaction, reaction 1, occurs at much lower [H+] when
in the presence of acetate. This suggests that acetate binds
to bromate and, in the same fashion as the bromide, it makes
easier the protonation of the bromate. After the binding of
the bromide, the coordination anion or nonmetal complex
rearranges to form the products in the rate determining step.
For the terms containing k4, k5, and k6 in eq 10 we propose
the following.
For the k3 term in eq 10 we must consider a different route
because it is a term independent of the bromide concentra-
tion. One of the possibilities, which we consider the most
probable, is the formation of the peroxyacetic acid. It means
that the rearrangement of the nonmetal complex will bind
the OH group with the acetate group in the same way it binds
to the bromide to form HOBr in reactions 24 to 26. The
peroxyacetic acid should then react with bromide in a fast
reaction to form HOBr as shown by reactions 27 and 28.
BrO3- + 2AcO- + 2H+ a
[Br(AcO)2(OH)2O]- f BrO- + 2AcOOH (27)
AcOOH + Br- f AcO- + HOBr
(28)
BrO3- + 2Br- + AcO- + 2H+ a
[Br(Br)2(AcO)(OH)2O]2- f 2HOBr + AcO- + BrO- (24)
Until now we do not have any evidence for the formation
of the peroxyacetate in this reaction. However, from our
kinetic analysis we noticed that the k3 term is very important
for the data obtained with low bromide concentration, but
can it be discarded for the data with an excess of this ion.
Comparison of our mechanism (reactions 16 to 28) with
the schemes proposed by Barton and Wright24,25 to explain
the acetate catalysis on the bromate-iodide and iodate-
iodide reactions shows that our proposal is a step further
since we state that protonation of bromate is not the first
step in the presence or absence of acetate.
BrO3- + Br- + 2AcO- + 3H+ a
[Br(Br)(AcO)2(OH)3]- f HOBr + 2AcO- + HBrO2 + H+
(25)
BrO3- + Br- + AcO- + 2H+ a
[Br(Br)(AcO)(OH)2O]- f HOBr + AcO- + HBrO2 (26)
The formation of intermediates with two acetate bonded
to a halogen atom species is not new. One such intermediate
Acknowledgment. This work was sponsored by Conselho
Nacional de Desenvolvimento Cient´ıfico e Tecnolo´gico-
CNPq, Fundac¸a˜o de Amparo a` Pesquisa do Estado do Rio
de Janeiro-FAPERJ, Fundac¸a˜o Jose´ Bonifa´cio-FUJB, and
Finaciadora de Estudos e Projetos-FINEP.
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H.; Dodgen, H. J. Am. Chem. Soc. 1949, 71, 3330-3336. (c) Edwards,
J. O. Chem. ReV. 1952, 50, 455-482. (d) de Meeus, J.; Sigalla, J. J.
Chim. Phys.-Chim. Biol. 1966, 63, 453-459. (e) Emmenegger, F.;
Gordon, G. Inorg. Chem. 1967, 6, 633-635. (f) Grant, J. L.; De
Kepper, P.; Epstein, I. R.; Kustin, K.; Orba´n, M. Inorg. Chem. 1982,
21, 2192-2196. (g) Valdes-Aguilera, O.; Boyd, D. W.; Epstein, I.
R.; Kustin, K. J. Phys. Chem. 1986, 90, 6696-6702. (h) Ra´bai, G.;
Beck, M. T. Inorg. Chem. 1987, 26, 1195-1199. (i) Peintler, G.;
Nagypa´l, I.; Epstein, I. R. J. Phys. Chem. 1990, 94, 2954-2958. (j)
Fa´bia´n, I.; Gordon, G. Inorg. Chem. 1992, 31, 2144-2150. (k) Ra´bai,
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S.; Margerum, D. W. Inorg. Chem. 1998, 37, 4321-4327. (m)
Nicoson, J. S.; Margerum, D. W. Inorg. Chem. 2002, 41, 342-347.
Supporting Information Available: Tables containing addi-
tional rate data. This material is available free of charge via the
Internet at http://pubs.acs.org.
IC0350786
(38) Hoering, T. C.; Butler, R. C.; McDonald, H. O. J. Am. Chem. Soc.
1956, 78, 4829-4829.
(39) Hoering, T. C.; Ishimori, F. T.; McDonald, H. O. J. Am. Chem. Soc.
1958, 80, 3876-3879.
1402 Inorganic Chemistry, Vol. 43, No. 4, 2004