105
Kinetics of the Permanganate-Bromide Reaction
(28) (29) (30) (31) (32) (33)
(34) (35)
(36) The electrochemical rate constants (cm sec-') for the Fez+(Fe3+ cou1 1 MHCi04, Hg electrode, 25O (ref 37a); 3 X pled are 7 X M H2SO4, Pt electrode (ref 34a); 5 X IO2, 1 M HZS04,Pt electrode (ref 34b). The eiectrochemical rate constant for the Ru(bpy)3*+1Ru(bpy)s3+ couple has not been reported although a value of 1 , l cm sec- has been published for the analogous iron complex in DMF at 25' (ref 37b). The latter value probably represents a lower limit (ref 37c). Based on the homogeneous exchange rates of the Fe2+IFe3+ and Ru(bpy)32+1Ru(bpy)33+couples, the electrochemical rate constant for the latter couple IS expected to be 2104 times larger than the former (ref 35). (37) (a) J. E. B. Randles and K. W. Somerton, Trans. Faraday Soc., 48, 937 (1952); (b) T. Saji, T. Yamada. and S. Aoyagui, Bull. Chem. SOC.Jpn.. 48, 1641 (1975); (c) T. Saji, T. Yamada. and S. Aoyagui, Nectroanal. Chem. lnterfacial Nectrochem., 61, 147 (1975). (38) The difference between the surface and bulk concentrations will tend to be small when the individual fluxes are very small or when the homogeneous electron transfer rates (in the presence of light) are very large.
6864 (1973); (b) J. N. Demas, E. W. Harris, C. M. Flynn, Jr., and D. Diemente, ibid.. 97, 3838 (1975). B. M. Gordon, L. L. Williams, and N. Sutin, J. Am. Chem. Soc., 83, 2061 (1961). M. H. Ford-Smith and N. Sutin, J. Am. Chem. Soc., 83, 1830 (1961). E. K . Rideal and E. C. Williams. J. Chem. Soc.. 127, 258 (1925). E. Rabinowitch. J. Chem. Phys., 8, 551 (1940). (a) R. Gomer, Electrochim. Acta, 20, 13 (1975); (b) S. W. Feidberg, personal communication. Values of 0.42. 0.61, and 0.62 have been reported for the electrochemical transfer coefficient for the reduction Fe3+ e- 6 Fez+ at a R electrode in 1 M H2SO4 (ref 34). The electrochemical transfer coefficient for the reduction of R ~ ( b p y ) 3 ~has + not been reported. There are theoretical grounds for expecting that electrochemical transfer coefficients will not, in general, differ greatly from 0.5 (ref 35). (a) H. Gerischer, 2. Elektrochem., 54, 366 (1950); (b) M. D. Wijnen and W. M. Srnit, Recueil, 79, 289 (1960). R. A. Marcus, J. Phys. Chem., 67, 853 (1963).
+
Kinetics of the Permanganate-Bromide Reaction at Low Reagent Concentrations Samuel A. Lawani Department of Chemistry, State University College, Buffalo, New York 14222 (Received August 7, 1975)
A study of the kinetics of the permanganate-bromide reaction at low reagent concentrations has been done at 251°C using a stopped-flow spectrophotometer. The monitoring was achieved by following the disappearance of permanganate, Mn04- 5Br- 8H+ Mn2+ 5/2Br2 4H20, at 520 nm and the appearance of Brs-, Brz BrBrs-, a t 267 nm. The reaction changes from first order to zero order with respect to permanganate as the reagent concentrations become lower; and the orders with respect to bromide and hydrogen ion concentrations are two and three, respectively. A mechanism which fits these findings is 2H+ + BrMn04- =t (H2Mn04Br) ( K ) ;(HzMn04Br) H+ BrHsMnO.% Brq (k). The activation parameters for the rate constant, ko, are AH* = 1.4 f 0.1 kcal/mol and A S * = -19.9 f 0.4 eu.
+
+
+
+
+
Introduction The kinetics of the reaction between permanganate and bromide ions a t high reagent (Br- and H + ) concentrations was studied by Lawani and Sutter.l Their aim was to elucidate the mechanism of this redox reaction in acid medium. I t was found that the results can be explained in terms of a set of coupled first-order reaction scheme:
+
+
A,
A-k
=z==
A4
where A1 is permanganate and the other A's are intermediates formed with Mn04- ion. However, a t very low reagent concentrations this scheme no longer holds. Since the data obtained for the high reagent concentration region were extensive and complex to analyze, no attempt was made to pursue the very low concentration region. The purpose of the study presented here is to show how the electron-transfer mechanism changes from first to zero order with respect to [MnOd-] in the latter region.
Experimental Section The procedure, instruments, and chemicals used in this study are the same as described by Lawani and Sutter. The only difference is in the treatment of raw data. Photographs of the kinetic traces were read and, with the help of
-
+
a computer program, the readings were converted to absorbances, D . Since ( D - D m )would be negative a t 267 nm where Br,j-, MnOd-, and Brz absorb but positive a t 520 nm where only Mn04- absorbs, the computer was instructed to plot absolute values of ( D - Dm) vs. time and take the slopes. Stoichiometric determinations' show that the reaction proceeds according to the equation MnO4-
,P * j
+
+ 5Br- + 8H+
-
+
Mn2+ YLBrz
+ 4H20
Results It was previously reported' that at low bromide and hydrogen ion concentrations the first-order plots are concave down at the beginning, becoming linear after a length of time. As the concentrations become lower a stage is finally reached where only the last few points at the end of the plot lie on a straight line (see Figure 1). At this point one begins to question the validity of the first-order plot. A zero-order plot for the same set of data gives a straight line with only a few points falling off a t the end as shown in Figure 2. The plots in Figures 1 and 2 are chosen because they illustrate the change from one order to another; but most of the data presented here comes from plots a t even lower concentrations where most or all of the data obey the zero-order rate law. The slopes of the zero-order plots are designated as the observed rate constants, hc,ilsd. A plot of kl,tl*d vs. [Br-]? is linear with an intercept which The Journal of Physical Chemistry, Vol. 80,No. 2, 1976
106
2.8
:
3.0
-
5.4
-
5.6
-
3.2 3.4
3.6 3.8 4.0
,.8 0
-?
Samuel A. Lawani
4.2 4.4 4.6
4.8 5.0 5.2
5.8
TABLE I: Dependence of Observed Rate Constants on Bromide Ion Concentration@
'.
0.040 6.61 0.010 0.520 0.030 3.63 0.006 0.226 0.020 1.79 0.005 0.168 a [H+] = 0.265 M: [MnO,-1, = 9.25 X lo-' M ; ionic strength, I = 0,919 M ; temperature = 25.1"C.
~
1
2
3
4
5
6
ii;; 1
8
9
1
TABLE 11: Dependence of Observed Rate Constants on Hydrogen Ion Concentrationsa [H,SO,
0
Figure 1. Concave down first-order plot: [Br-] = 4.00 X lo-* M; [H+l0 = 0.265 M; [MnO4-Io = 1.47 X M; temperature = 25.1 C; ionic strength, I = 0.919 M. -
.Ob
.
10' 0bs,d M sec-
[H+I,M
0.132 0.106 0.06 0.079 0.04 0.053 0.02 0.027 a [Br-] = 0.10 M ; [MnO,-1, = 4.63 X ture = 25.1"C; I = 0.919 M . 0.10 0.08
i (see)
07
I, M
3
4.24 2.50 1.11 0.623 0.225 M ; tempera-
gram which gave AH* = 1.4 f 0.1 kcal/mol and AS* = -19.9 f 0.4 eu.
Discussion A mechanism which fits the observed behavior of this reaction is the following K
2A t B t C = D D
\.
.0:
t
.
+A+B
k
products
where A = H+, B = Br-, and C = Mn04-. If step I1 is much slower than step I, the former may be neglected in calculat-
(sac)
Figure 2. Zero order plot for the same data in Figure 1.
In the early life of the reaction, approximately is approximately zero by the least-squares method. Table I shows the experimental data. All h&d values in this work are pseudo in [Br-] and [H+] which are in high excess compared to [MnO4-]. The hydrogen ion dependence is shown in Table 11. A plot of k,bsd against [H+l3is h e a r with an essentially zero intercept. The kobsd with all concentration terms removed is represented as ko. The value of ko, calculated from [Br-] dependence, is (2.35 f 0.02) X lo7 M-5 sec-' while a value of (3.79 f 0.09) X lo7 M - j sec-l is obtained from [H+] dependence. Each [H+] given here had to be calculated for several reasons. First, the second dissociation of sulfuric acid is not complete and secondly, K+ ions from the KBr used as the reducing agent and the &SO4 used to keep the ionic strength constant associate with Sod2- ions.2 A combination of the Davies? equation and the work of Jenkins and Monk2 was used to arrive at the [H+] values by the method of successive approximations. For this reason one cannot rely on these quantities as much as on bromide ion concentrations which were measured directly. This in turn means that the true rate constant, ko, from [Br-] dependence should be more dependable. The temperature dependence of the true rate constant (see Table IV) was used in a least-squares computer proThe Journal of Physical Chemistry, Vo/, 80, No. 2, 1976
[AI = [AI0 - 2 P I ; [BI = [BIo - [DI; [CI = [CIo - [DI (111) where the zero subscript indicates initial concentration. Since [C]o
