7939
J. Phys. Chem. 1993,97, 7939-7941
Kinetics and Mechanism of the Brz-HCN Reaction Ivan Valent and Lubica AdamECkovB' Department of Physical Chemistry, Comenius University, 842 I5 Bratislava, Slovak Republic Received: January 27, 1993; In Final Form: April 13, 1993
The reaction between bromine and cyanide in aqueous acid solution (HC104) has been studied a t 25 "C using a conventional spectrophotometric method. Under conditions of an excess of CN-, H+, and B r ions the experimental kinetic law has the form -d[Br3-]/dt = (a b [ B r ] + c[H+])[HCN][Br3-]/(1 + d[Brl)[H+l, where a = 7.5 f 1 s-l, b = 45 f 10 M-l s-I, c = 48 f 4 M-l s-l, and d = 12 f 4 M-l. The results are consistent with a mechanism involving steps Br2 CNBrCN B r with rate constant kl = (6.7 f 0.9) X lo9 M-I s-l, Br3- CNBrCN 2 B r with k l = (2.4 f 0.6) X 109 M-l s-l, and Br2 H C N BrCN B r H+with k3 = 48 f 4 M-l s-l. A nonlinear regression method was successfully used in analysis of the experimental data.
+
-
+
+
Introduction It has been found14that the BrO3-SCN- reaction may exhibit "exotic behavior". An interesting clock behavior can be observed under closed-batch conditions,lJ irregular oscillationsunder openbatch conditions,3 and various phenomena, including simple periodic, complex, and chaotic oscillations, under CSTR cond i t i o n ~ However, .~ the BrO3-SCN- system is extremely sensitive to perturbation,2J and therefore it is not clear if the complex behavior observed can be related directly to intrinsic nonlinear chemical kinetics of the Br03-SCN- reaction or if it is rather caused by unavoidable fluctuations in the experimental system. To answer this question, it is necessary to know the detailed mechanism of the bromate-thiocyanate reaction. Since the reaction of bromine with cyanide is one of the crucial subprocesses involved in the entire Br03--SCN- system, we focused on the kinetics and mechanism of this reaction. It is known that the reaction proceeds accordingto the stoichiometry5 Br2
+ HCN
-
BrCN
+ Br- + H+
(R1)
The equilibrium lies overwhelmingly to the right with a AGO H -70 kJ mol-' (ref 2), so that the reaction may be treated as irreversible. Some previous experiments1V2and stopped-flow measurements6 have revealed that the Br2-HCN reaction is relatively rapid; nevertheless, under certain conditions,the kinetics of this reaction can be studied by a conventional spectrophotometric method.
Experimental Section The following analytical grade chemicals were used without further purification: liquid Br2 (Fluka AG), NaCN, NaBr (Lachema), 70% HC104 (Jenapharm), LiC104.HzO (BDH Chemicals), Stock solutions were prepared from water redistilled with an addition of KMn04. The solution of LiC104 was filtered before use. The concentrationof HC104 solution was determined by titration with a standardizedNaOH solution. Theapproximate concentration of the bromine stock solution was estimated by measuring the absorbance at 400 nm (e = 172 M-* cm-l). The reaction kinetics were followed by monitoring changes in absorbance of Br3-(aq) on a SPECORD UV-vis double-beam spectrophotometer, operating at 270 nm. This wavelength corresponds to the absorption maximum of Br3- ions (e = 30 600 M-1 cm-1) which may be considered to be the only absorbing species, as a sufficient excess of bromide was always added into the reaction mixture,and hence the absorbanceofthe free bromine was negligible. The other reacting species (CN-, H+) were also held in at least 25-fold excess over the total concentration of
+ +
-
+
-
+
+
bromine in order to achieve pseudo-first-order kinetics. Ionic strength was maintained constant at 1.OM by addition of LiClO4. The reaction was started by the final rapid addition of NaCN into the photometric cell of 5 cm optical path. The total volume of the reaction solution was always 10 mL. The cell compartment of the spectrophotometerwas kept at 25 f 0.1 OC by circulating water from a MLW thermostat. Solutions were brought to the same temperature before mixing. First-order rate constants k,, were determined from kinetic plots by a nonlinear regression method. Kinetic parameters of the reaction were evaluated from k,, dependences using both linear and nonlinear least-squares analysis. RWult.9
The measured absorbance traces corresponding to decay of Br3- ions during course of the reaction were always of an exponential type, thus one may assume pseudo-first-order kinetics with respect to the concentration of Br3- ions, according to the equation
-d [Br;] /dt = k,,[Br;] (1) where k , is the experimentalrate constant. The value of k, was determinedby a nonlinear regression analysis:' The experimental absorbance-time dependence was fitted by the exponential functiony = s t r U ; the parameters sand t , and the parameter u, which corresponds to the rate constant k,,, were optimized according to the least-squares method. A typical example is shown in Figure 1. This way we were able to obtain results of higher accuracy than by the conventional linear regression method. The relative error of k , evaluation was less than 3%. In order to find out a complete experimental kinetic law, the dependences of k , upon the concentrations of bromide, cyanide, and hydrogen ions were investigated in series of kinetic experiments in which one of these concentrations was varied while the other two were held constant. Both bromide and hydrogen ions show an inhibitory effect on the reaction, whereas increase of the HCN concentration brings about acceleration of the reaction progress. The results are documented in Figures 2-4. The dependence of k , on the concentration of bromide ions is of a hyperbolic type and fits the equation
+
The parameters p , q, and r were evaluated analogously as in the previous case of the exponentialfunction. The dependence of k , on the HCN concentration is linear, slightly shifted from the
0022-3654/93/2097-7939$04.00/00 1993 American Chemical Society
7940 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993
Valent and Adam6ikovA
V."
0
200 TIME is)
100
300
0
400
2
1
3
ldx [HCNI
Figure 1. Absorbance at 270 nm vs time during the reaction of Brz/Br3and HCN/CN- at 25 OC. Initial concentrations: [Br21t = 1.8 X M,[HCN] = 5.0 X 10-4M, [Br] = 0.10 M, [HCIO4] = 0.48 M;ionic strength 1.0 M (LiC104); optical path 5 cm. The circles represent the experimental values, the solid curve is an exponentialfit according to the function y = 0.119 + 1.43 exp(4.0136~).
4
(MI
Figure 3. Dependence of k, on the HCN concentration (total cyanide concentration). [Br21t = 9.6 X 1od M, [Br] = 0.30 M, and [HClOJ = 0.67 M.
,
I
5
0
10
15
20
25
l/[H*] (M-')
0' 0
I
0.1
1
0.2
0.3
I
a4
QS
I Q6
[&-I (MI Figure 2. Dependenceof theexperimentalrateconstant kaon the bromide concentration. [HCN] = 1.0 X 10-3 M, [HClO4] = 0.47 M;initial concentration of [Br21twas varied in the range 3.7 X 1ksto 9.3 X 1od M in order to maintain an approximately constant level of the initial absorbancevalue. The experimentalvalues of k, (0)can be fitted with thefunctiony = (0.0657 + 0.0964~)/(1+11.9~) within theexperimental error. origin probably on account of a small escape of volatile HCN from the solution to the free space in the reaction cell. The dependence of k,, on the concentration of hydrogen ions is linear in the coordinates k,, against l/[H+] with a positive intersection with t h e y axis. The results suggest the following form of the experimental rate equation (a + b[Br-] + c[H+])[HCNl [Br;] d[Br;] --= (3) dt (1 + d[Br-])[H+] with a self-consistent set of values for a, b, c, and d at 25 OC and ionic strength 1.0 M: a = 7.5 f 1 s-l, b = 45 f 10 M-l s-1, c = 48 f 4 M-1 s-l, and d = 12 f 4 M-*. Discussion
The experimentally obtained rate equation (3) is in accordance with the proposed mechanism
Figure 4. Inverse acid dependence of the experimentalrate constant keX. [Br21t = 1.8 X M,[HCN] = 5.0 X 10-4 M, and [Br] = 0.10 M.
Br,
+ Br- F? Br,-
Br,
+ CN-
Br,-
+ CN-
Br,
+ HCN
ki
-
(R2)
BrCN
+ Br-
(R4)
BrCN
+ 2Br-
(R5)
+ Br- + H+
(R6)
kr
ki
BrCN
The protolytic reaction (R3) isvery fast, in the thermodynamically favorable reverse direction essentially diffusion-controlled, as expected for normal acids.* The rate constants for both forward and reverse directions of reaction R 2 are also high enough9 to assure sustained equilibrium for reaction R 2 in the system under study. The relatively slow steps (R4)-(R6) are rate-determining. Hypobromous acid HOBr which is also at equilibrium with bromine via hydrolysis
Br,
+ H,O e HOBr + Br- + H+
(R7)
is not involved in the mechanism, since the concentration of HOBr is at least 5 orders of magnitude smaller than the concentration
The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 1941
Kinetics and Mechanism of the Br2-HCN Reaction
TABLE I: Rate Constants for the XrHCN and the X2-XReactions at 25 OC constants (X = Br),
M-1 s-1
reaction
1.5 x 109' X.7 + X- -C X3- (R2) 6.7 x 109 X2 CN- XCN X- (R4) 2.4 x 109 X3- CN- XCN + 2X- (R5) X2 HCN XCN X- H+(R6) 48
+ + +
-+
+
+
constantb (X = I), M-I s-I
+ + +
5.6 x 1 0 9 4 6.2 x 109 1.0 x 109 65
Ionic strength 1 .O M unless otherwise noted. Ionic strength 0.2 M unless otherwise .noted. Ionic strength not specified. Turner et al. reported the value 6.2 X lo9 M-l S-I (ionic strength 0.02 M), ref 12. a
of bromine under the conditions of our experiments (excess of bromide and hydrogen ions). A theoretical kinetic law can be derived from the proposed mechanism by the following way. One may suppose that the rapid reactions (R2) and (R3) are always at equilibrium [Br;]/[Br,][Br-]
=K
[H'] [CN-] / [HCN]
(4) (5)
KA
The reaction rate is given as -d[Br,],/dt = k, [Br,] [CN-]
+ k2[Br;]
[CN-]
+
k,[Br,I WCNI ( 6 ) where [Br21t denotes the total concentration of Br2/Br3-
Taking into account eq 4, the concentrations [Br21t and [Brz] in 6 can be expressed via [Br3-]. Hence
k,K[CN-] [Br-]
+ k,[HCN])
(8)
and with respect to eq 5 we finally have
(klKA
+ k2KAK[Br-]+ k3[H+])[HCN][Br;l (1
+ K[Br-])[H+]
(9)
The kinetic law derived is in agreement with the experimental kinetic equation. Comparison of eq 3 and 9 gives a = klKA, b = L~KAK,c = k3, and d = K. The parameter d corresponds to the equilibrium constant of reaction R2 and the experimentally obtained value for d is in accord with the known value K = 17 M-1 (ref 9 ) , considering that the parameter d can be estimated from the nonlinear fit only with a relatively high error. Using the values K = 17 M-l and KA = 1.12 X IW M (ionic strength 1.OM),l0the rate constantsfor reactions R k R 6 can be calculated as kl = (6.7 f 0.9) X lo9 M-I s-I, k2 = (2.4 f 0.6) X lo9 M-I s-1, and k, = 48 f 4 M-I s-l. While the value of the rate constant k3 is in good agreement with the results obtained by Epstein et a1.6 (k3 = 52 f 5 M-l s-l; 25 OC; ionic strength 1.5 M), our value of kl is twice as high as the value6 kl = (3 f 0.7) X 109 M-* s-l. This discrepancy could be attributed in part to the difference in the equilibrium constant KA which depends on ionic strength. The proposed mechanism (R2)-(R6) is the same as the mechanism of the I r H C N reaction.11 The rate constants for the X r H C N systems complemented with those for X r X reactions9are summarized in Table I. The rate constants of the step (R4) are almost equal for bromine and iodine and comparable with the rate constant of the I r I - reaction, suggestingthat these reactions are diffusion-controlled. Diffusion-control limits cal-
culated according to the Smoluchowski equation" are 9.2 X IO9, 1.25 X 1010, and 1.5 X 1010 M-1 s-I for the Br2-CN-, I A N - , and I2-I-, reactions, respectively; however, it is known14 that the Smoluchowski equation may slightly overestimate the real diffusion-controllimit. Interestingly, the Brz-Br reaction is not diffusion-controlled. Ruasse et al.9 elucidated this fact by a mechanism based on the partial halide ions desolvation as a ratedeterminingfactor. The Br2-Br reaction is slower since bromide interacts with water more strongly than iodide. This mechanism could be valid for the pseudohalide cyanide ions as well; unfortunately, the rate constant of the X2-CN- reaction is unexpectedly high as the Gibbs energy of hydration of cyanide is comparable to that of bromide.15 We propose an alternative hypothesis based on an assumption that the reactions X2-X- and X2-CN- are activation-controlled. They might be treated as a nucleophilic attack of the dihalogen molecule by halide (pseudohalide) ions. The similarity of the Br2-CN- and the I2-CN- (and also the &I-) reactions suggests the nucleophilicity of the attacking species to be a possible rate-determining factor. The rate constants for the BrrBr, 1 2 4 , and Br2-CN- (or I2-CN-) reactions reflect the nucleophilicity values16for B r , I-, and CN(3.89,5.04, and 5.1, respectively). Eigen and Kustin" estimated the rate constant for the reaction HOX XHOX2- (X = Br, I) as 5 X 109 M-1 s-l. This value is very close to the values in Table I, supporting the idea that the rate constant for the envisaged type of reactionsdepends on the nature of the attacking anion rather than the nature of the electrophile. It is noticeable that an excellent linear correlation between logarithm of the rate constant and the anion nucleophilicity has been found for the CN-).l* HOCl-X reactions (X = C1-, B r , I-, Reaction R5 is very similar, but somewhat slower than R4. This can be explained simply by repulsion of the accordingly charged reacting ions. The differencebetween the rate constants of the Br3--CN- and the 13--CN- reactions is likely due to the different ionic strength used in the experiments. Both (R4) and (R5) probably proceed via Br2CN- complex, and formation of the product BrCN occurs at a following very rapid stage. But, in fact, we have no experimental data to resolve this sequence of the overall process. The slowest reaction (R6) is obviously an electrophilic substitution. Iodine is expected to be more reactive than bromine, as the 1-1 bond is weaker and of higher polarizability. The rate constants for the step R6 are consistent with this supposition.
+
-
References and Notes (1) Valent, I.; AdamElkovil, L. Collect. Czech. Chem. Commun. 1991, 56, 1565. (2) Zhang, X.-Y.; Field, R. J. J . Phys. Chem. 1992,96, 1224. (3) Valent, I. Thais, Comenius University, Bratislava, 1990. (4) Simoyi, R. H. J. Phys. Chem. 1987,91,1557. (5) Kolthoff, I. M.; Belcher, R.; Stenger, V. A,; Matsuyama, G. Volumetric Analysis; New York, 1957; Volume 3. (6) Epstein, I. R.; Kustin, K.; Simoyi, R. H. J . Phys. Chem. 1992,96, 6326. (7) Neogrildy, P.; Krill, D. Unpublished work. (8) Eigen, M. Angew. Chem., In?. Ed. Engl. 1964,3, 1. (9) Ruasse, M.-F.;Aubard, J.; Galland, B.; Adenier, A. J . Phys. Chem. 1986,90,4382. (10) Kotrlfr,S.;Slcha, L. Handbookof Chemical Equilibria in Analytical Chemistry; Honvood: Chichester, U.K., 1985; p 90. (11) Smith, R. H. Aust. J. Chem. 1970,23,431. (12) Turner, D. H.; Flynn, G. W.; Sutin, N.; Beitz, J. V. J. Am. Chem. SOC.1972.94. 1554. (13) Smoluchowski,M. Y. Z.Phys. 1916,17,583;Z.Phys. Chem.(Leipzig) 1917,92, 129. (14) Dubois, J. E.; El-Alaoui, M.; Toullec, J. J . Am. Chem. Soc. 1981, 103, 5393. (15) Marcus, Y. J. Chem. Soc., Faraday Tram. 1 1987,83, 339; 1986, 82,233. (16) Hine, J. Physical Organic Chemistry; McGraw-Hill: New York, 1962; p 161. 1171 Einen. M.: Kustin. K. J. Am. Chem. Soc. 1962.84, 1355.
