Dee. 5 , 1932
N E W KATE
EXPRESSION FOR
IODINE-CATALYZED AROMATIC
carbinol-dye interaction will have time to occur to a significant extent and abnormal rates will be observed. Figure 11, showing k vs. (2-01-1 data for M. G.,33and for C.V. with various salt concentra,931 R
H DIIIPRJIprivate
c o m t i i i i i i i c d t i ~ n unpublished .
data
BROM~NATION
5995
tions, shows that deviations from normal behavior persist to higher alkali concentrations the greater the salt concentrations; i.e., the lower the rate constant. SEW YURK,T ’E’
[ C O N T R I B U T I O N FROM T H E I S S T I T I J T E FOR C I I E M I C A I . I C E S E A R C H . K Y O T O U N I V E R S I T Y
Kinetics of Iodine-catalyzed Aromatic Bromination.
1
I. A New Rate Expression
R Y TEIJITSURUTA, KEN-ICIII S.S.IKI A N D JUNJI J?rravs.iw.~ RECEIVED FEBRUARY 6, 1962 Previous interpretations of data on the rate of the iodine-catalyzed bromination of aromatic derivatives are not satisfactory. The experimental data of Bruner have been recalculated through the use of a new expression for the rate law, iii which it is assumed that the rate-determining step is the loss of hydrogen bromide from a 1: 1 aromatic-bromine complex. This step is proportional in rate to some power, about three ill the case of benzene, of the concentration of the BrI present. The new rate expression and mechanism account for both the iodine catalysis of the bromination and for the optimum rates observed with increasing amounts of iodine.
Detailed experimental data on the iodine-catalyzed bromination of benzene have been presented by Bruner.’ Price? suggested that Bruner’s measurements corresponded to the rate law d[C6HSBr]/dt = k [C6H6][Br2]a/2[12]’/~
(A)
He assumed such higher order of the rate expression (A) might be due to some sequence of reactions involving, e.g., IBr2(-) or I3BrS3 Suppose his mechanism were valid, but recalculation according to it leads to equation (B) instead of equation (A). d [ C B H ~Ildt B ~ = k [CsHs][Br?la/%[I?l5/z/[I,(-) ] [I(+)]
t i v e ~ j - ~ ;these are formed rapidly and equilibrium constants for their formation have been measured in some cases. The present paper presents a reinterpretation of Bruner’s results, which is based upon a simple rate law and utilizes this new information as to the molecular species present in the reacting system. Derivation of a New Rate Expression As stated above, in a solution of bromine, iodine and an aromatic compound in an inert solvent, the following equilibria exist
(B)
In equation (B), [Brz] and [I?] should be the concentrations of free bromine and iodine, respectively. On the other hand, since Price calculated the experimental results taking the total unreacted bromide as [Brz], i t is obvious that his [Brt] included not only free bromine but BrI, IaBr and other bromides which appeared in his mechanism. ;is [I?],he took the total quantity of iodine added, but on account of large equilibrium constant for BrI formation there should remain only an extremely small quantity of free iodine when iodine was mixed with excess of bromine. Further, according to equation (A) the greater the quantity of iodine used, the greater is the reaction rate; however, Bruner’s data show an optimum in it. Iodine in excess of a given amount decreases the rate of reaction. Robertson and his co-worker~,~ who used mesitylene as the reactant and carbon tetrachloride or chloroform as solvent, criticized Price’s work and established other rate expressions. I n order to account for the experimental results they assumed complicated successive and competing paths which involved the assumed existence of such complexes as Brq, IBr3, IBrs and IzBr4. Recently evidence has been presented in favor of 1: 1 complexes between several halogens and a variety of benzene deriva(1) L. Bruner. Z . p h y s i k . Chem., 41, 614 (1902). JOURNAL, 68, 1834, 2102 (1986): ( b j C. C. (2) (a) C. C. Price, THIS Price and C. E. Arntzen, ibid., 60, 2835 (1938). (3) C. C. Price, Chem. Revs.,29, 42 (1941). (4) P. W. Robertson, J. E. Allan, K.N. Haldane and hl. G. Simmers, J . C h e w SOC.,933 (1940).
Br?
+ 11
Ki 2BrI
Kz Br2 + CGHB J_ C&h*Br2
(1)
(2)
K3
IP BrI
+ C G HJ ~’ C6H6.12
(3 1
+ CsH6 If CfiH6.BrI
(4)
where K l , K?,K3 and Kq are equilibrium constants. As Robertson4 has already indicated, the order of the rate law in aromatic bromination depends upon a number of factors, such as the nature of the aromatic derivative, the concentrations of the reagents and the solvent. He attributed this variation in order mainly to the differences in capacity for 1: 1 complex formation of the aromatic ring against the halogen. lo I n the present analysis, on the other hand, a single kind of aromatic-halogen complex (1:1)is assumed in accordance with the work cited above, and any requirement for higher orders probably referred to the process of removal of hydrogen bro(5) Tr, Fairbrother, S n l w e , 160, 87 (1947): J . Chem. SOL., 1051 (1948). (6) J. Kleinberg and A. W. Davidson, Chem. R e v s , 4 2 , 601 (1948). (7) H. A. Benesi and J. H . Hildebrand, THISJOURNAL, T O , 2832, 3978 (1948); 71, 2703 (1949). (8) N. 3. Bqyliss, Xulztuc, 143, 764 (1949). (9) (it) R. M. $eefes and L. J. Andrews, THISJOURNAL, ‘13, 4677, 5170 (1950); (6) R. M. Keefer t)nd L. J. A n d r e w , i b i d . , 79, 462 (1951). (10) Robertson assumed iq his mecha,nism the 1 : l complex as an intermediate. But he considered t h a t this complex was formed through the complicated successive reactions and the variation in order af the rate law was wqiqly attributed t o these reactions.
TEIJITSURUTA, KEN-ICHISASAKI AND JUNJI FURUKAWA
5996
mide. When a reactive aromatic hydrocarbon, e.g., mesitylene, is used as a reactant, removal of hydrogen bromide from the complex takes place so readily that a catalyst would not be needed. With benzene, this is not the case; bromobenzene is formed in the dark only with the aid of catalysts. I n Bruner's experiments in which bromine is in escess compared to iodine it is reasonable to assume that BrI is the only catalyst present for removal of hydrogen bromide. Vile therefore assume the mechanism
+ mBr1 +CBHb.Br + HBr + mBrI
:I
c
kdc'"
(Ti)
and from the equilihrium relation.: of (1)-(4) it fo110ws that K . = c"(nbr K2 = dI(a4) lis = c / ( b $ )
(6) (7) (8)
K4 = f/(Cdi
(9)
The titers of total bromine X (moles per ml.) and of total iodine Y (moles per ml.) are given by 2 X = 2n + c + 2d + f (10) 2Y = 26 + c + 2e + f (11) From equations (6)-( 11) the following relations are easily obtained a =
b
--KI(X
4K12(S
=
(2.Y - y c ) / 2 n ( 2 I' - y d '28
(12) (13)
+ Y)Y +
+ 1')2y? + 4 k ' , Y l 7 ( l r r R - A-,-/*)]/
+
+
(4nB
- KIT?)
(14)
+
where a = 1 K& /3 = 1 K & and y = 1 K44. If the aromatic compound is used in sufficient excess, its concentration (4) and hence CY, /3 and y may be considered as constants. Since a , b and c have been all expressed in terms of X , Y and constants, i t would appear possible to test equation (5). But because the form of equation (14) is not proper for further calculations, i t is desired to simplify by expanding in a power series. Thus
+
+
d/K,a(X m - y a 4K1XE"(lcr3 - KIT')= K1(.T E')?{ 1 ('/3)(L/KI).fSY/(S II)? ('j8)(Ljiil)Z1G.T*J'~j(S 1 7 4 3-
+
where L
+
+
+
+
(16)
(1')
where k is a rate constant of reaction (1') and m is a constant which is determined in response to the sorts of reactant and the other experimental conditions. The way in which IBr reacts to remove hydrogen bromide cannot be detailed, but it is reasonably assumed that the less reactive compounds will demand more molecules of IBr than the more reactive ones do. In the rate study, the only experimental observation is the titration for total halogen present; its rate of decrease denotes the rate (v) of formation of bromobenzene. If a, b, . . ., f and 4 denote the concentrations (moles per ml.) of the following reactants when reaction has attained to a steady state: [Brz] = a, [I21 = b, [BrI] = c, [C6Hs. Br2] = d , [CsH6.12] = e, [ C B H ~ . B ~= I ] f, and [CP,H,] = $, the reaction rate v would be given by
c = {
If X is not equal to Y,i t follows that 0 < 4 X Y / Y)2< 1. Since aO/y2is always larger than zero and L is negative in the present case owing to a comparable magnitude of y to a or fi and a larger value of K1ll, i t follows that 1 L / K l I < 1 and hence I ( L / K , ) 4 X Y / ( X Y ) * /< 1. Therefore, if bromine is present in excess conipared to iodine, neglecting terms below the fourth of equation (15), the following approximation is possible c = 2[{XE'/(X 1')) - ( ( I d / K , ) X 2 Y 2 / ( X Y ) $ l l / r
(.Y
k
C$H$.Br2
and
VOl. 74
+
= (+$/y')
+
-
Kl.
+
I (16)
Therefore it follows that a = [{X2/(X I'll ~(L/KI)X~Y~/(X VIlla(l7) b = [ { I"/(S Y)] { ( L / K i ) X ' Y ' / ( X Y)'))/P(18) and d = K?+[[Sz/(.Y+ IT)] + { ( L / K i ) X 2 Y * / ( X+ I')']]/a
+ ++
+
+
+
(19)
Inserting equations (16) a n d (19) into equation ( 5 ) , it follows that ?I =
xuwm
where (2/~)"Kzk+/c~
31
21
=
+ ni + I ( L / K , ) X * Y Z / ( X+ 1 7 3 1
(X~/(S
and 'io =
(20 )
{.YY/(.Y
+ I,)\
- {(Td/K1)>Y2Y*/(.Y
Hence log ( v / u ) = log .I1
+ m log zu
+ 1731 (21)
Since ill and m are constants, equation (21) indicates that there should be a linear relation between log ( v / u ) and log w . Even if the exact value of L / K 1 cannot be known, it may be considered to be almost equal to -1, because K 1 is large (about 40011). Thus the authors have assumed L/K1 = - 1 in their calculations. Bruner's results on benzene have verified the linear relation demanded in equation (21) as i t is seen in Fig. 1. I n the case of benzene, from the inclination in Fig. 1, the authors found that m was equal to three. Therefore, for benzene, equation (20) is transformed into equation (20') v = Muw3
(20')
The validity of equation (20') can be ascertained in Table I. The authors have so far discussed about the validity only of equation (5). However, if Bruner's data fit equation ( 5 ) , they will also fit the following equations as well as any combination of these, because Bruner's measurements were all held in benzene without any added solvent. v = kac" zi = k'af"
(22) (23 1
and v =
k"dfm
(24)
where k's are rate constants. Therefore, i t is impossible to determine which is the most probable mechanism among these equations; so, from Bruner's data themselves, we can only indicate that equation (5) is one of the possible mechanisms. Experiments which give us infor(11) D hZ. Yost T F. Anderson and I7 Skoop, THIS J O U R N A L 66, 5r,? (1913)
NEWRATEEXPRESSION FOR IODINE-CATALYZED AROMATIC BROMINATION
Dec. 5, 1952
5997
TABLE I
x
Xa
10'. moles ml .
-
x
Ye 104,
moles ml.
x
uwa 1018,
v lo', moles ml. day
x
M =
u/uw'
x ,1'-:1 (S) (L) moles
day
1.24 55.50 1.14 28.20 1.14 11.57 1.08 6.45 1.11 3.96 1.21 2.72 1.14 3.36 1.21 1.81 1.52 1.08 1.11 0.86 0.93 0.41 1.16 13.60 1.05 4.94 1.24 2.46 1.11 2.53 1.03 1.67 1.18 1.56 0.92 0.83 1.14 1.09 1.14 0.77 0.98 .38 1.04 .53 .36 1.07 .29 1.20 1.24 .23 1.14 .16 3A .91 0.92 3B .72 1.20 3B 1.13 .48 3B 40.70 1.20 4A 1.04 16.40 4A 1.18 9.05 4A 1.19 24.00 4B 1.20 14.90 4B 1.34 4.44 4B 1.17 13.80 4C 1.52b 11.30 4C 5.25 1.01 4C 1.20 4.07 4C 4.53 1.37 4E 1.45 1.11 4E Mean [1.13 i 0.0681 a,\' arid Y wcre calcu1;ltctl from the Rruncr data. h This value was omitted from the mean.
1A 1A 1B 1B 1B 1B 1C 1C 1D 1D 1D 2A 2A 2A 2B 2B 2B 2B 2c 2C 2C 3A 3A 3A 3A
7.88 5.70 5.73 4.19 3.26 2.66 4.07 2.90 3.58 2.54 1.92 6.15 3.62 2.54 4.53 3.62 3.17 2.58 3.97 2.98 2.16 2.51 2.04 1.72 1.50 1.33 2 31 1.90 1.63 7.25 4.84 3.53 8.32 5.89 3.63 9.60 6.79 5.25 4.08 7.80 3.90
2.14 2.14 1.42 1.42 1.42 1.42 1.07 1.07 0.86 .86 .86 1.44 1.44 1.44 0.90 .90 .90 -90 .71 .T1 .7l .71 .71 .71 .71 .71 1.06 1.06 1.06 2.04 2.04 2.04 1.50 1.50 1.50 1.14 1.14 1 11 1.14 0.76 0.79
44.60 24.70 10.12 5.95 3.58 2.25 2.95 1.50 1.40 0.78 0.44 11.73 4.69 2.02 2.28 1.62 1.32 0.90 1.05 0.68 .39 .51 .34 .24 .19 .14 .99 .60 .43 33.80 15.73 7.63 20.20 12.43 3.30 11.75 7.45 5.17 3.37 3.31 1.31
ination as to the dependence of the concentration of aromatic compound upon the reaction rate, would afford a n approach to a unique mechanism. It is seen that equation (21) is in good accord with the experimental results provided the ratio of broY )is not too small. I n this paper mine to iodine (X/ evaluation of equation (21) has been limited to those experiments in which the ratio X:Y was at least 3. When the titer of bromine falls to be equivalent to that of iodine, ;.e., X = Y,equation (14) can be simp1,ified without any approximation ; and hence, for benzene, the following expression can be immediately derived from equations (5), (7), (12) and (14) where
v = MUWaX4
(2.5)
5.7
-
-
-
5.9 4.0 4.1 z.2 3.3 log w. Fig. 1.-log v/u vs. log w . 3C, 3D and 3E, where Y / X is too large, and 4D, which involves some questionable data, have been neglected.
and
5.8
w = d Z A ( 2 G / Y ) +dKl
The rate of reaction a t X = U, is hard to estimate from Bruner's data, owing to the extremely small value of the tangent a t X = Y except for a few examples, but it is not necessarily difficult to estimate the range in which the value lies. At Bruner's experiment 3 0 and 3E, however, velocity v can be obtained with a tolerable accuracy. The mean value of MUWa in 3 0 and 3E was about (1.74 X 1O'O) (ml./moles)3 (l/day). In Table I1 it is seen that any VO, calculated by inserting (1.74 X 10'0) (ml./rnole~)~(l/day) for M U W 3 of equation (25), lies in the range of experimental values, which has been estimated graphically, with a few exceptions. Thus equation (25) also has been verified. TABLE 11" Experimental number of Bruner's
X' X 1 0 ' 4 (moles/ml.)'
20. 70 4.12 1.30 1c 2A 4.25 0.25 3A 3B 1.27 3c 4.00 3D 20.40 64.00 3E 16.00 4A ,. Experiments, which had of X = Y or involve some neglected in this table. 1A 1B
Vobad. x los, moles/(ml. day)
vu x lo', moles/ml. day
36.0 52.1-27.2 7.2 49.5- 7.0 2.3 7.2- 1 . 9 8.7- 3.6 7.4 1.2- 0 . 2 0.4 5.0- 1.8 2.2 15.9- 5 . 5 7.0 37.8 35.5 111.2 103.5 27.8 58.3-10.0 not been held in the vicinity questionable data, have been
Moreover, if equations (20') and (25) both hold
599h
1 ' E I J I 'r'SURUT.4, ( . i r c ~ - 3 / . i r 1= (1.74 i.i;j)(i(i
2)
(ret
hcllc€ 1 11.
= iiO13
(27J
If IC1 (the equilibrium constant of reaction (1)) iii benzene was assumed to be the saine as in carbon tctrachloride, v'i?? should be equal t o about twenty." Therefore, from equation ( 2 i ) , it follows that
~ 5 2 y1 Referring to Keefer's evaluated
+o
FURUKAWA
K E N - I C H I S.\SAKI AND JUNJI
13
n and 3
(28)
Vol. 74
iodine. The authors' rate expression can account quantitatively for the existence of a maximum point; there, (dv/d Y ) xshould be equal to zero and hence from equation (5)13 v7c7n
1
d(dCl3I')X
+ C"'(dd/d17)X = 0
(29,
Therefore, froin equations (7)) (12) and (14))a t the Inaximum point of reaction rate, the following relation between X and Y is obtained
+
+
1'= [ ( 1 ~ a / ( K l r J ) ) ( 1 1 2 * / (lm) }
(Il?/(nt
are easily
+ l)]]X
(30,
Equation (30) means that optimum relative titer of iodine with respect to bromine should be influenced i i =. I f /\. = 2 0 4 not only by the order (m)of reaction of iodine mono bromide, but by the equilibrium constants K I , ,: = I A q = 2 72 (is,k'? and Kt. Since equilibrium constants are = 1.0-I1?andIiJ= 1.i2.I' where4 = 1 , Inserting these values into equation (%), it id- subjected to variation, for instance, by change in tcniperature or solvent, the optimum relative titer lows that y = 15.i and herice K4 = 14.i. Although any datx on the equilibriuiii constant of iodine should change in response to various exIC4for the complex forination between benzene and perimental conditions even if the same aromatic iodine inonobroinide have never been presented, its hydrocarbon is used as reactant. For example, with benzene as reactant, since ftz value may be much larger than K J or K?,just as is equal t o three, equation (30) is transformed to that of iodine monochloride has been shown t o be equation (3 1). several times larger.'Ji) I = ~~4cY!3/(A~-p)}(9/41 + (.3'4)1\ (?{I) The results of these calculations are of significance in the sense that every series of points plotted .is it has been seen, a@' y 2 is less than unity and in response to the various values of and IO lies on a K l is equal to about 400 in an indifferent solvent, so straight line, regardless of whether this was calcu- the first term is negligibly small compared with the lated from the changing values of S during a bru- second when ;I solvent, in which K1 is sufficiently mination process in an experiment or from the vari- large, is used. Therefore, from equation (31) i t is ous initial concentrations of halogens in several ex- expected that the optimum point should exist in the periments. vicinity of 1- = ( 3 '4)X which has been observed it1 This is t u be expected, but there have been pre- Bruner's data. sented not a few rate expressions which have been Results of several series of experiments on the tested only by the initial velocity of the reaction. bromination of toluene in the dark, which are in progress at the author's laboratory, will be conMaximum Point of the Reaction Rate trihuted before long. As Robertson has already indicated, it is one uf Acknowledgment.---'The authors wish to acthe characteristics of iodine-catalyzed bromination knowledge the suggestive discussions made by Prothat there exists a maximum point of the reaction fessor Ryohei Oda, Kyoto University, in this rerate with respect to the relative titer of bromine to search ~
(12) There are found w n i e ~jueitirinahlepoints d h u t the d C C U r a c \ of the absolute valuea of I
