A. E. Burgess
Stow College of Engineering Glasgow, Scotland and J. 1. Lalham Kurnasi University of Science and Technology Ghana
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I
Kinetics of kst Brominations
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A potentiometric study
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I
Laboratory work on chemical kinetics in undergraduate classes is often restricted to investigations of slow rcactions (such as hydrolysis of esters and alkyl halides) in which conventional methods of analysis are used to follow the reactions. The object of this paper is to show that the kinetics of such fast reactions as the hromination of phenols in aqueous solutions are easily determined by a simple potent,iometric technique. The bromination react,ions are carried out under rate-controlled conditions which enable the stationary-state approximation to be applied. I n consequence there is ample time to take measurements using only commonplace apparatus. A single variable only requires measurement and this is an emf value which, by extrapolation, is determined a t reaction zero time. The method brings to students experience in the study of the kinetics of fast reactions. I n addition, akhough the final equations used are simple, any student who follows the dcrivation of these equations is bound to acquire considerable understanding of the principles both of potent.iomet,ry and of kinetics. This understanding will be deepened by a critical discussion of the assumptions made and the approximations used. Because of the simplicity of the experimental technique and of t,he subsequent calculations, it is possible to carry out a series of kinetic investigations in a short time. For instance, most of the data in Figure 2 can be obtained in a 3-hr period, if stock solutions of the reagents are available, and all the apparahs is a t hand. Although monobromination of phenols in aqueous solutions is the series of reactions dealt with in this paper, thereis wide scope for the development of student projects with other rapid bromination reactions. For example, the reaction of bromine with anilines or olefins in aqueous solutions can be followed by this method. That the monobromination of phenol is a fast reaction can be demonstrated by mixing equal volumes of 0.01 M aqueous phenol solution and saturated bromine water, whereupon a precipit,ate of 2,4,6tribromophenol appears to form instantaneously. I t is clear that under these conditions the rate of monobromination must be extremely fast. However, if bromine is not added externally, but is slowly generated by homogeneous chemical reaction within the Thix work was carried out while both authors were on the staff of t,he Harris College, Preston, England.
370 / Journal of Chemical Educotion
phenol solution, then the rate of organic hromination is governed by the rate a t which bromine is generated. This rate-controlling process is obtained by making use of the kinetic characteristics of the hromatebromide reaction. Stationary-Stale Brominalion Using the Bromale-Bromide Reaction
Bromate and bromide ions react in strong acid solutions to form bromine in accordance with the stoicbiometry given by BrOs- 5 B r + 6H 3Br, + 3Hs0 (1) The kinetic rate law for this reaction is well established (1) as -d[BrOa-]/dl = '/rd[Br9]/dl = kr[BrOl-I [Brrl [HtI (2) where the value of the fourth-order rate constant ka lies between 1 and 9 l3 mole-3 sec-I a t 25'C (3) (this range of values is obtained because the reaction has a large negative salt effect, that is, k4 varies inversely as the ionic strength of the solution). Depending on the initial concentrations of the reactants, the half-life of the bromate-bromide reaction can have any value within the range of a fraction of a second to many years. Consequently, initial concentrations may be chosen so that bromine is generated a t a rate convenient for ordinary measurements. I n the presence of a reactivc organic compound RH, the bromine generated by the bromate-bromide reaction is consumed by the hromination of the organic compound RH + Br2 + RBr + Hi + Br(3) This is a situation to which the stationary-state hypothesis may he applied. According to the hypothesis a stationary-stat,e is rapidly established in which bromine is present in low and steady concentration. The approximation can then be made that the rate of bromine production by the bromate-bromide reaction equals the rate of bromine removal by the bromination of the organic compound. An essential feature of the proposed method is that the bromate and bromide ions and acid arc present in much higher initial concentrations than the substance being brominated (under the experimental conditions described, only 1.33% of the bromate ions have reacted a t the end of monobromination). It is therefore an accurate approximation t.o assume that t,he rat,e of the bromate-bromide reaction, given by eqn. (2), is constant throughout the mo~iobrominat~ionof RH.
+
+
-
Denoting this constant rate of bromine production by S (mole 1-' sec-') and applying the stationary-state approximation, it follows that S equals the rate of the monobromination process. Hence, for molecular bromination reaction which conform to second-order kinetics (first-order with 'respect to both R H and bromine), the rate law is S = k2[RHl[Br~l (4) where kz is the second-order rate constant for monobromination of RH. I t is important to distinguish between the terms "rate" and "rate constant." The rate of the bromination process, under stationary-state conditions, is S, irrespective of the particular reactivity of the organic compound brominated. However, the value of the rate constant lc2 reflects the reactivity of the organic compound. Equation (4) shows that for selected S and concentration of RH, it is the stationary-state concentration of bromine which is inversely dependent upon the reactivity of RH. The stationary-state concentration of bromine can be determined by measuring the redox potential of a bright platinum electrode immersed in the aqueous reaction solution. Provided activity coefficients are ignored, this redox potential is given by 2.303RT [Brd E = EO + ---- log 2F
[Br-1'
where the constant EQat 2;i°C is 1.057 V (3) and, by introducing appropriate values of the gas constant R, 2.303RT the absolute temperature T, and the faraday F, -2F Evaluation of the Bromination Rate Constants
The reactivities of various compounds with respect to molecular bromination can be compared by means of the relative values of the rate constants. These relative values are readily obtained from emf measurements as indicated by the following treatment. Suppose two organic compounds are monobrominated in separate solutions a and b, but otherwise under identical cxperimental conditions. If emf measurements against time are taken during each stationarystate bromination reaction using the same electrode system (bright platinum and saturated calomel), then the plot of the values, extrapolated to reaction zero time, give the initial emf values E. and E,. From eqn. (5)
Values of the Rote Constants for the Monobromination of Various Phenols in Aqueous Solution a t 25'C
-
RH rn-eresol o-cresol pcresol phenol o-bromophenol o-chlorophenol pbromophenol p-chlorophenol anisole m-nitrophenol o-bromoanisole No RH present
Initial emf (mV) -
Rate constant values -----.
613 627 668 660
677 6RT, 723, 72.5 746 780 798 938
The emf measurements were made using platinum gauze and saturated calomel electrodes. In all eases the initial concentrations of the reagents were: [KBrOal = 0.01 A l , IKBri = 0.02 A,! IH.SO,I = 0.015 At', lRHl = 4 X i0-4 M or aero.
nation rate constants to be found from initial emf values without the need to establish t.he reactjon rate S. Relative values of bromination rate constants using eqn. (8) are shown in thc table (the bromination rate constant for phenol is set at 1.00). To obtain values for the bromination rate constants k2, which are not merely relative, it is necessary to measure the reaction rate S in addition to the stationary-state concentrations of bromine. In principle, S can be found by substituting initial concentrations into the. concentration terms of eqn. (2). However, it is better to determine S experimentally, because the hydrogen ion concentration is uncertain owing to the incomplete dissociation of the sulfuric acid used. Furthermore, the value of t,he fourth-order rate constant k4 of the bromate-bromide reaction is greatly dependent on the ionic strength of the solution. As S is the constant reaction rate throughout monobromination, it is easily determined by measuring the time taken to complete the monobromination reaction. A compound suited to this purpose is allyl alcohol, since the stoichiometry of the reaction it undergoes with t'he generated bromine is one to one, and redox potentiometric measurements show a sharp rise in emf a t the end of bromine addition. With allyl alcohol a t an initial concentration of 4 X mole I-', under the selected conditions the sharp rise in emf occurs at 280 see (Fig. 1). Thus the reac-
Providing each monobromination reaction is firstorder with respect to R H and to bromine, eqn. (4) holds and S = k.[RH][Br.], = ka[RHI[Brrla (7) where lc, and kb are the second-order rate constants for the monobromination of the two compounds. As the init,ial concentration of R H is common to both solutions, combination of eqn. (7) with eqn. (6) gives
Equation (8) enables the relative values of the bromi-
Figure 1.
Change in redox potential during bmminotion of ollyl olcohol.
Volume 46, Number 6, June 1969
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371
tion rate for any reactive compound brominated under the same conditions is S = 4 X 10P/280 = 1.43 X 10W6mole I-' seer'
It is interesting to note that substitution into eqn. (2) of this reaction rate, together with the initial concentrations [BrOar] = 0.01 ill, [Br-] = 0.02 M and [H+] = 0.03 M (from [HpSOa]= 0.015 ill) puts a value of 2.7 13 mole-3 sec-' upon the bromate-bromide rate constant kd. This is within the range of values, a t 25"C, quoted by Bray and Liebhafsky (I?), though somewhat inaccurate because of the incomplete dissociation of sulfuric acid mentioned above. The stationary-state concentration of bromine can be obtained from emf measurements a t any time during the monobromination of an organic compound. However, there are several advantages in choosing t o determine the bromine concentration a t reaction zero time. Here the concentration of organic compound is accurately lmown. Also the effects of any dibromination or polybromination reactions are minimized. Since the selected bromide ion concentration of 0.02 M remains effectively constant throughout the monobromination reaction, then by eqn. (5), the redox potential, a t 25"C, of a bright platinum indicator electrode is E = 1.087
+ 0.0296 log [Brd + 0 . 0 3 2 X 1.609
controlled water bath (25.0 i O.l°C), and a t bath temperature the contents of the tubes are rapidly mixed together by transfer twice repeated. A stopclack is started a t the first mixing. At this point the initial concentrations are: potassium bromxte 0.010 M, potassium bromide 0.020 M, sulfuric acid 0.015 M, and RH,0.0004 Af. The thoroughly mixed ~.enct,ionsolution is poured into 8. 1.50-ml beaker, previously clamped into the water bath. The beaker is closed by a stopper holding platinum and saturated calomel electrodes and also a motor-driven glass stirrer. With a. little practice i t is quite easy to obtain the first emf reading on the stirred solution within 50 sec of the time of mixing. Subsequent emf readings are taken a t 10-sec i n t e n d s , until ten readings have been obtained. The emf measurements, taken by the authors, were made with a Pye " I ) y n x q 9 ' pH Meter, which gave values t,o the nearest millivolt. Tho indicator electrode was a platinum gauze of the type used in quantitative electrodeposit,io~', and this was cleaned before each experiment in an ethanol flame.
Discussion
The results of a series of bromination reactions obtained by this stationary-state method are shown in Figure 2. This gives t,he emf versus time plot for each reaction, and shows the linear extrapolation back to zero time. Values for the monobromination rate constants obtained from these (and other) reactions are given in the table. Values relative t o the rate constant for monobromination of phenol (which is taken as unity) are also given in this table. These results show
I.e., E = 1.188
+ 0.0296 log[BrzI
(9 1
With a saturated calomel as reference electrode, the ~ o t e n t i a lof the reference electrode including the salt bridge is 0.245 V (4,and so the cell emf is E,,,,
=
0.943
+ 0.0296 log[Bril
= 0.943
+ 0.0296 log[Br~l.
m-OH>II>p-Br>m-NO1
(10)
Extrapolation of emf versus time measurements back to reaction zero time gives the initial emf, which is related t,o the initial bromine corlceritration by E,
(a) there is a. wide range in reactivity of t h e phenols studied (the monobromination rate constant values being spread over about five powers of ten). (b) the efiect, of t h e substituent on the ease of substitution, namely is that expected for electruphilic attack.
For the last three substituents, values of rate con-
(11)
Provided the initial concentration of organic compound [RH], is consistently selected a t 4 X mole 1-1, then with the reaction rate S = 1.43 X lo-" mole I-' sec-', eqn. (4) becomes k2 = 3.58 X 10-3/[Br~l,
(12)
Combining the logarithmic form of eqn. (12) with eqn. (11) gives log kl
=
20.41 - B,/O.O296
(13)
Values of the bromination rate constants determined from eqn. (13) are shown in the table. An example is phenol, for which the initial (extrapolated) emf a t 25'C is 0.GGQ V. Substitution of this value for I
