THE RATE OF BROMATE FORMATION I N AQUEOUS SOLUTIONS CONTAINING HYPOBROMOUS ACID AND ITS ANION HERMAN A. LIEBHAFSKY
AND
BENJAMIN MAKOWER
Department of Chemistry, University of California, Berkeley, California Received January Si, 1933
I n connection with other kinetic investigations, we have found it convenient to prepare aqueous solutions containing hypobromous acid by adding bromine to a phosphate buffer solution containing silver ion;’ as hydrogen ion and bromide ion are rapidly removed, the hydrolysis equilibrium of bromine is shifted, Brz
+ H20
HBrO
+ H+ + Br-
(1)
and the concentration of hypobromous acid is increased. Although the rate laws given by Skrabal and Weberitsch (1) for the reaction2 5HBrO = BrOl-
+ H+ + 2Br2 + 2Hz0
(2)
indicate that3 (HBrO) in our solutions should decrease to half its value in, say, seconds, we found that approximately twenty-four hours elapsed before so much decomposition occurred. Duplication of part of the work of Skrabal and Weberitsch has convinced us that their results are entirely reliable, and that the source of this surprising conflict must consequently 1 After several unsuccessful attempts to prepare aqueous solutions containing only hypobromous acid by the distillation methods recommended in the older literature led us to conclude that this could not be accomplished, we discovered that Pollak and Doktor (Z. anorg. allgem. Chem. 196, 89 (1931)) had already reached this conclusion as a result of similar experiments. 2 The stoichiometric equation for the formation of bromate ion will assume different forms under different experimental conditions. BrO-, Br3-, or Brz may appear as reactant instead of HBrO, and what substances, in addition to BrOa-, appear as resultants is also subject t o change. Decomposition of bromine compounds to yield oxygen is negligible under all experimental conditions with which we have here to deal. 3 As in other communications, the following conventions will be observed: ( means “concentration of” in moles per liter; the units for all specific rates are moles, liters, minutes; when no temperature is specified, 25°C. (or nearly 25°C.) is meant; + will be restricted to steps which may be rate-determining. Rate laws will usually be referred to by letter only; the proper letter used as subscript will indicate to which law a specific rate constant belongs. 1037
1038
HERMAN A. LIEBHAFSKY AND BENJAMIN MAKOWER
be sought in their interpretation of these data. We have concluded that much of the conflict has resulted from several errors, which we shall point out, and that our preliminary rate measurements, some twenty in number, indicate how the mechanism of reaction 2 may be directly investigated. We have no intention a t present of undertaking a further investigation ourselves. In table 1are summarized the rate laws that should govern the stability of hypobromous acid in all solutions not strongly alkaline. We shall now consider evidence to show that C (or C’) is more plausible than B (or B’), that A is not experimentally established, and that the kinetic data upon which table 1 is based can be interpreted in terms of the rate-determining step 2HBrO
+ BrO-
--t
BrOs-
+ 2H+ + 2Br-
(3 1
given by Kretzschmar (2). (The intimate mechanism of this rate-determining step will be discussed later.) To secure data that may aid in deciding the relative plausibility of B’ and C’ (or, of B and C) we have measured the stability of hypobromous acid in phosphate buffer solutions a t the low (Br-) insured by the presence of Ag+. These experiments, given in table 2, together with all others in which the rate of disappearance of hypobromous acid was measured, were carried out as follows. The reaction mixture, contained in a glass-stoppered flask and shielded from direct sunlight, was placed in a thermostat at 25°C. At convenient intervals samples were withdrawn, run into a n iodide solution containing H2P04-, and titrated with 0.004 N thiosulfate. Calculations and blank tests concurred in showing that the bromate present was not reduced rapidly enough under the conditions employed to cause any error in the titration. The experimental results in table 2 agree in order of magnitude with the rates calculated from C’-but not a t all with those from B’. Further, the actual rate a t which hypobromous acid disappears under the above conditions is (virtually) independent of (Br-), in agreement with C’ but not with B’. Our experimental evidence, joined to that of Skrabal and Weberitsch (X, Versuche 11 to 14 inclusive), has convinced us that of the two rate laws C’ is far the more plausible. We must admit, however, that the proof is not complete; for, as will appear later, extension of the results in table 2 has not permitted the deduction of a definite rate law. Skrabal and Weberitsch were led to adopt B because this differential equation, when properly combined with that for the reduction of bromate by bromide ion in acid solution, gave the equilibrium constant for reaction 2 (X, pp. 249-52); we are not certain that this agreement between a quotient of specific rates and an equilibrium constant warranted changing
TABLE 1 S u m m a r y of rate laws for reaction. I The’ae laws are intended to govern -dZ(Brg)/dt except in strongly alkaline solutions; z(Br2) = (Brz) (Brs-) (HBrO)
+
+
RATE
LAW
SPECIFIC RATE AT 26’C.
CONCENTRATION TERMS
REFERENCE
COMMENT
-
A
6. 5(104)
(OH-) (Br3-)2 (Br-)3
X,* p. 244 et seq.
Adopted for their “rapid reaction” by S. and W.
B
8.3(1022)t
(OH-)4 (Brs-)a (Br-)?
X, p. 246 et seq.
Adopted for their “slow reaction’’ by S. and W.
B‘
2 , 7 (lo0)t$
(HBrO)3 (OH-)
Alternative form$ of B
m-1 C
As for B
2.4(10z3)t
Given directly by the experimental evidence. Not adopted by S. and W. because they considered B more plausible. ’
C‘
7.9(10g)t$
(HBr0)3 (OH-)
C”
Definite value cannot be given
(HBr0)z (BrO-)
Alternative form1 of c Kretzschmar (2)
Alternative form$ of c
* See reference 1.
t We have calculated these specific rates from Versuch 14 (X, p. 248),
employing for this purpose the correct concentrations: namely, (Br3-) = 0.059 and (Br-) = 0.34. In their calculations, Skrabal and Weberitsch assumed (mistakenly) (Br3-) = z(Br2) = 0.07, and obtained kg = 3.8(1022); the difference between this and 8.3(1OZ2), which corresponds t o the correct concentrations, serves to emphasize how sensitive are specific rates involving high orders to relatively small concentration changes. Verauche 11,12, and 13, for which Skrabal and Weberitsch did not evaluate kg, give for k ~ ( 1 0 - ~ respectively, ~), 1.9, 3.9, and 2.3; these, together with the value 2.4(10aa), given above, show what concordance may be reasonably expected from such measurements. $ B and B’ are alternative forms of one rate law, C and C’ of another, for the equilibrium HBrO 2Br- E BraOH(4) is always maintained; the value of its equilibrium constant, the cube of which is involved in each transformation, is (X, p. 245; see reference 1)
+
+
(OH-) = 3.2(10-6) at 25°C. (HBrO) (Br-)2 $ The identity of C’ and C” is made obvious by writing (BrO-) = l/Kasd.(HBrO) (OH-) the uncertainty in the value of R h y d . precludes giving an exact value for Kc-,. 1039
1040
HERMAN A . LIEBHAFSKY AND BENJAMIN MAKOWER
the experimentally derived halide term4 in C to that in B. We wish to emphasize that the specific rate of reaction 3 need stand in no simple relation to the equilibrium constant of reaction 2. The experimental evidence in X (see reference 1) upon which A is based involves Versuche 5 , 6 , and 7 (Versuche 8 , 9 , and 10 deal with the influence of electrolytes) ; of these, Versuch 6 is used in the calculation of the specific rate. I n this calculation (X, p. 244) there is implicit the assumption that the rate due to C’ (or to B’) is negligible. At t = 15, -d2(Brz)dt in Versuch 6 was 1.4(10-4) moles per minute per liter; from C‘ we calculate a corresponding rate, in these units, of 114(10-4); and from B’, of 39(10-4); TABLE 2 Rate of disappearance of hypobromous acid i n potassium phosphate buffer solutions at (HBrO) = 5(10-4) RATES I N MOLES PER LITER PER MINUTE EXPERIMDNT
8 19 15 17 6 7 5
(OH-)10**
0.67 1.15 4.8 19.6 47 47 52
1 1.2 2.6 5.2 4.3 13 X lo6 7 x 105
2.2 x 3.3 x 6.2 X 12.7 X 37 x 12 x 2.5 x
108 108 lo8 lo8 108 102 104
1
C’
1
0.66 1.1 4.7 19 46 46 51
I
x
lo8
Measured
2.2 19 46 71 21 13 17
* (OH-) was calculated from the data given by Cohn (J. Am. Chem. SOC.49, 173 (1927)); we need not distinguish between (OH-) and its activity. In experiments 5, 6, 7, and 8, total phosphate was 0.05 M ; in the others, 0.2 d f . t Values of (Br-) are approximate; except in experiments 5 and 7, silver bromide and (usually) silver phosphate were present as solids; in these cases, (Br-) was calculated from (Agf) (Br-) = 5.3(10-13) and (when necessary) from (Ag+)a(PO,---) = 1.6(10-18), these calculations may be verified by use of the data in table 3. The magnitudes of these rates leave no doubt that C’, which we have adopted as more plausible than B’, must be considered in the interpretation of these data; indeed, they suggest that all the observed rate in Versuch 6 may be due to reaction 3, for which C’ is one form of the rate law. And this suggestion becomes more plausible when we observe the constancy of IC3 in Versuch 6, a constancy also found in Versuche 5 and 7. (We do not believe that ICz is, in any of these experiments, sufficiently constant to permit the valid derivation of a rate law.) Even if we adopt k3, and thus the term, we have yet to show that the rate obeys not the (OH-) and l/(Br-)3 terms in A, but the (OH-)4 and l/(Br-)6 terms in C. We observe next that the orders given in A for these concentrations were We have duplicated Versuche 11 and 14 (X, p. 247) and found l/(Br-)E.l for the halide term; Skrabal and Weberitsch obtained l/(Br-)s.s.
I
1041
BROMATE FORMATION
not correctly calculated, and for this reason: They were obtained from the effects on k2 of changing (OH-)-Versuche 5 and 6- and Br--Versuche 5 and 7. But kz involves Z(Br2) = (HBrO)
+ (Br,) + (Br3-)
Manifestly, altering either (OH-) or (Rr-) will alter the distribution of 2(Brz) among these three terms (cf. reaction 4);if a t least two of these are of appreciable magnitude, this change in distribution will be reflected in the rate; in comparing values of kz from two experiments designed to determine the order with respect to some reagent, this change must be TABLE 3 Recalculation of Versuch 6* (OH-) = 2.1(10-9 M ; (Br-) = 1.0 ill 1
0
15 30 75
(HBrO)103
(Brz)lO3
0.50 0.39 0.33 0.24
8.15 6.32 5.35 3.90
5.30 4.11 3.47 2.49
kmt S. and
W.
1.36 1.10 0.90
Corrected
3.93 3.18 2.60
S. and W. Correct.ed
112 112 116
549 549 568
* X, p. 241. cf. also X, p. 244.
t The units for all specific rates are moles, minutes, liters.
(To express the specific rates in X in these units, the k~ given there must be multiplied by 2(lO3), and the k3 by 4(106)). The “S. and W.” rate constants are defined by
dz(Brz) - kzZ(Br2)2 = ksZ(Br2)3 dt The “corrected” rate constants are defined by - dZ(Br2) = k2(Br3-)2 = ks(Br3-)3 dt
at constant (OH-) and (Br-),
considered, or an erroneous result will be obtained. We have allowed for this change in calculating the orders given in table 4, in which a comparison of the seventh and eighth columns will reveal the importance of considering the distribution of Z(B,rz). (See also the last four columns in table 3.) The terms and 1/(Br-)5.9 are in yatisfactory agreement with those to be expected from C. Taken by themselves, the results in table 4 are as good evidence for C as can be adduced from any other experimental work in X ; for the kc values in table 4 agree as well among themselves as do those from the phosphate buffer solutions (cf. table 1, footnote?). The average of the latter, 2.4 (1OZa), is some seventyfold greater than 3.5
1042
HERMAN A. LIEBHAFSKY AND BENJAMIN MAKOWER
(loz1), the mean of the values in table 4;we hesitate to ascribe all this difference to equilibrium salt effects, although these will be unusually large in the reaction system with which we are dealing. (If the ratedetermining step, reaction 3, is correct, the l/(Br-)6 term, to give one example, will be due entirely to equilibria preceding this step; such a state of affairs makes for large salt effects.) Nevertheless, we have concluded that there is evidence in X for only one rate law, C, for which the rateTABLE 4 Carbonate-bicarbonate bu$er solution experiments used to establish rate law A* VERSUCE
Br-
(Br2)lOa
(Brs-)lOa
(HBr0)103
1 . 0 0.58 1 . 0 0.33 0.51 0.31
S. and W.
___--
---____
5 6 7
(OH-)lO5
9.41 5.35 2.53
3.01 3.47 3.16
1.04 2.08 1.04
16 113 188
Cor-
rected
42.3 552 2520
- = [2$]";
Variation of k3 with (OH-): From Nos. 5 and 6: :23 oc
3.8 3.0 3.8
x
1
= 3.7.
1.24 0.97 1.24
Rate
(0H)a.'
-
Variation of k 3 with (Br-): From Nos. 5 and 7 : 2520 - [E1]"; 2/ = 5.9. Rate 42.3 1 -iC (Br-)5.g * X, p. 241. t Cf. footnotet, table 3. In our definition of z(Br,), (BrO-) has been omitted. In justification of this procedure we mention that it is simplest, and that (BrO-) cannot be calculated until the dissociation constant of HBrO is known. We observe that considering (BrO-) tends to increase both k c and the orders obtained for (OH-) and l/(Br-): thus, assuming K = (H+) (Bra-) = 10-9, gives (OH-)6.3 and l/(Br-)'.I, HBrO while assuming K = 10-10 scarcely changes the results in table 4. Since the assumption of the larger value leads to no simple kinetic conclusions, we have preferred omitting (BrO-) from consideration, a procedure tantamount to assuming for K a value of 10-10, or less. If our kinetic interpretation of the data in table 4 is correct, further experiments of the same sort over a range of OH-concentrations may provide a way of obtaining the dissociation constant of HBrO from kinetic data.
determining step is reaction 3; the numerical value of the corresponding specific rate is uncertain. Kretzschmar (2) in 1904 completed the first extensive kinetic investigation of reaction 2. He presents kinetic evidence (reference 2, pp. 794-8) for reaction 3 as a rate-determining step; this interpretation he considers plausible because reaction 3 is analogous to the rate-determining step found by Foerster and Jorre (3) for the formation of chlorate ion through the decomposition of hypochlorous acid. Kretzschmar made rate measurements on solutions of hypobromous acid, prepared by distillation, to which
BROMATE FORMATION
1043
had been added a known amount of potassium hydroxide; he assumed that one mole of added base yielded one mole of hypobromite ion. His measurements give for C a specific rate of approximately 3(1019),5which is to be compared with the values 2.4(1OZ3) (phosphate buffer) and 3.5(1021) (carbonate-bicarbonate buffer) obtained from the measurements of Skrabal and Weberitsch. I n explaining why Kretzschmar obtained such low values for kc, two things, in addition to salt effects, must be considered: first, our experience indicates that his hypobromous acid solutions probably contained (H+) a t an appreciable, though unknown, concentration; and second, when base is added to an hypobromous acid solution the amount of BrO- formed depends upon the dissociation constant of this acid, which is not definitely known. Our review of the rate laws in table 1 is now complete and leads to this conclusion: Over a wide range of experimental conditions, the law that governs the rate of reaction 2 is formally identical with C”, as found by Kretzschmar (2)) and assumes more complex forms (e.g., C) as the composition of the reaction mixture changes. We observe that one form (C ”) of this law is analogous to that found by Foerster and Jorre (3) for hypochlorous acid solutions, while another (C) corresponds to one found by Skrabal (4) for the formation of iodate ion. It appears, therefore, that the law -dZ(Xz)/dt = k(HX0)2(XO-)
(5)
is of general importance in the formation of the halate ion, X03-, through the decomposition of these lower-valent halogen compounds. This law obviously suggests 2HX0
+ XO- -+ XOa- + 2X- + 2H+
(6)
as a rate-determining step; when we come to consider, however, what the intimate mechanism of reaction 6 might be, we are faced with several possibilities, of which none can be definitely eliminated. That reaction 6 is trimolecular-i.e., that it involves only triple collisions-seems very improbable; and this justifies the assumption that an equilibrium is involved. The compound X302-,which has been postulated by Skrabal (4) and favored by Bray ( 5 ) , may be assumed; but the mechanism
+
XaOz- + H20 (or H2X303-) + HzO + XOa- + 2X- + 2H+
Equilibrium: 2HX0 XORate-determining: X302-
(6a) (6b)
6 Kreteschmar’s data give ICCJJ = 100 a t 25°C. (cf. reference 2, p. 798); to convert them to our units, his specific rates must be multiplied by 400. If 10-10 is assumed to be the dissociation constant of hypobromous acid (this corresponds to a hydrolysis then kct = 100/10-4, or lo6; and kc = lo6/ [3.2(10-s)13, or constant for BrO- of 3 (lozg).
1044
HERMAN A. LIEBHAFSKY A N D BENJAMIN MAKOWER
does not exhaust the possibilities. No matter what mechanism is chosen, however, the simplest procedure, and therefore most logical so long as no conflict with experiment is involved, will be t.0 consider it valid for all the halogens. Kretzschmar (reference 2, pp. 790-3) also measured the rate of decomposition of hypobromite solutions, which proved to be surprisingly stable. H e attempted no kinetic evaluation of these results, but he considered the mechanism 3Br0-
---f
BrOB-
+ 2Br-
(7)
not improbable. I n most of his experiment,s the concentration changes are not appreciable enough to permit the certain deduction of a mechanism; for Uebersicht 3, however, we have found that the rate law is6 d(BrO-) dt
--=
0.056 (BrO-12 a t 80°C.
(8)
corresponding to the rate-determining step
Assuming that this rate law is valid also in the experiments a t lower temperatures, we have calculated that the rate of reaction 9 a t any temperature is given by
Within the experimental error, which is rather large,’ the Arrhenius constant of reaction 9 is identical with the collision number. ( l O I 3 moles per liter per minute is the collision number for a bimolecular gas reaction at unit concentration of the reactants.) The stability of these hypobromite solutions might be utilized in the preparation of hypobromous acid. Equation 8 is formally identical with the rate law found by Foerster and Dolch (6) to govern the stability of hypochlorite solutions, and this circumstance is additional evidence for our interpretation of Kretzschmar’s The specific rate was calculated for (OH-)= 1.89; in such basic solutions, (HBrO) is probably negligible, for the rate is (virtually) independent of (OH-). Since the change in (Br-) that took place during the experiment was not reflected in the rate, we conclude that (Br-) does not belong in the rate law. 7 We estimate the error in the heats of activation in equations 10 and 12 to be f2000 calories; there is, of course, a corresponding uncertainty in the values of the Arrhenius constants.
BROMATE FORMATION
1045
results. From the data given by Foerster and Dolch for 25, 50, and 90°C., we have calculated that the rate of the reactions 2c10-
ClOz-
-+
+ c1-
(11)
a t any temperature is given by
Although the experimental error is rather large, there is no doubt that the analogous reactions 9 and 11 have almost identical Arrhenius constants and heats of activation. We shall close with a brief discussion of our rate measurements. Although the rate was followed until nearly all the HBrO had disappeared in some twenty reaction mixtures like those of table 2, no definite order could be established either for (HBrO) or for (OH-); the one most nearly obeyed with respect to (HBrO) is the second; with respect to (OH-), the order is not higher than the first. Under some conditions the second order constant with respect to (HBrO) decreased as the run progressed, often it increased, and sometimes it remained unchanged. I n all probability we are dealing here with a mixture of reactions, and a change of temperature or of (OH-) might do much to simplify matters. At any rate, the fact that the rates we measured are independent of (Br-) leaves little doubt that the rate a t which HBrO decomposes into bromate is being measured directly, i.e., that no equilibria are maintained in front of the rate-determining steps. I n addition to reaction 3, a second step of the type HBrO
+ HBrOz
--t
Br0,-
+ 2H+ + Br-
(13)
may be involved. SUMMARY
1. I n agreement with the results of Pollak and Doktor (7), it has been found impossible to prepare, by distillation, aqueous solutions containing only hypobromous acid. 2. At low (Br-), solutions of HBrO are far more stable than one law given by Skrabal and Weberitsch (1) for the rate of the reaction 5HBrO = Bi-0,-
+ 2Br2 + H f + 2H?O
(2 1
At low (OH-) the rates measured by Foerster and Dolch were independent of (OH-) and, within limits, of (Cl-), which nearly doubled in magnitude as some of their experiments progressed (cf. Uebersicht 1, reference 6,p. 140). We see no reason for doubting the plausibility of the above mechanism (in this connection cf. reference 6, p. 144).
1046
HERMAN A. LIEBHAFSKY AND BENJAMIN MAKOWER
allows; a reexamination of their kinetic evidence has led to the conclusion that, except in strongly alkaline solution, the rate of reaction 2 should be governed by -dZ(Br2)/dt = Iccrr(HBr0)a (BrO-)
.
(At 25"C., widely different values, ranging from approximately lo2 to nearly lo6,have been obtained for k p under different experimental conditions.) I n this, its simplest form, the rate law is identical with that found by Kreteschmar (2) ; further, it appears not irreconcilable with the stability we have observed in our hypobromous acid solutions. 3. Since this rate law is analogous to those found for the formation of c103-and IO3-under certain experimental conditions, it has been concluded that the rate-determining step 2HX0
+ XO- + XOa- + 2X- + 2H+
(6)
is of general importance in the formation of halate ions through the decomposition of the halogens (or substances in equilibrium with them). 4. The intimate mechanism of the rate-determining step, reaction 6, cannot be definitely settled; an intermediate compound, like X302-, in and equilibrium with HXO and XO- (and, consequently, with X3-, Xz, X-) may be involved, for reaction 6 is probably not the result of triple collisions alone. 5. From the measurements of Kretzschmar (2) in strongly alkaline solution, we have deduced the rate law -d(BrO-)/dt
= 0.056(BrO-)a at 80°C.
(8)
corresponding to the rate-determining step 2Br0-
+ Br02-
+ Br-
(9)
which is analogous to that found by Foerster and Dolch (6) in C10- solutions, Reaction 9 and its C10- analogue have nearly identical heats of activation and Arrhenius constants. 6 . Our rate measurements, as well as those of Pollak and Doktor (7), on reaction 2, indicate a need for further work, which we have no intention at present of undertaking. REFERENCES
(1) SKRABAL AND WEBERITSCH: Monatsh. 36, 237 (1915). This paper is the tenth of a series and will be designated by X. Papers I11 and IV also deal with reaction 2. (2) KRETZSCHMAR: Z. Elektrochem. 10, 789 (1904). (3) FOERSTER AND JORRE: J. prakt. Chem. 69, 53 (1899). (4) SKRABAL: Monatsh. 32,815 (1921). (5) BRAY:J. Am. Chem. SOC.62,3580 (1930). (6) FOERBTER AND DOLCH: Z. Elektrochem. 23, 137 (1917). (7) POLLAK AND DOKTOR: Z. anorg. allgem. Chem. 196, 89 (1931).
