T H E VELOCITY OF BROMINATION O F ACETOACETIC ETHYL ESTER. I1
THE GENERALBASICCATALYSIS KAI JULIUS PEDERSEN Chemical Laboratory of the Royal Veterinary and Agricultural College, Copenhagen, Denmark Received October $7, 1933
In Part I (10) the bromination of acetoacetic ethyl ester was studied in pure water and solutions of hydrochloric acid. It was found that the reaction may be expressed by the schemes la-ld (Part I, p. 751). Thus four consecutive reactions could be distinguished: (a) the acetoacetic ester is enolized, and (b) brominated to the keto form of a-monobromoacetoacetic ester; (c) this is enolized, and (d) brominated to a,a-dibromoacetoacetic ester. Only reactions la and ICtake place with measurable velocity. Hydrogen ions do not catalyze to any perceptible degree. In this part of the investigation the bromination of acetoacetic ethyl ester is studied in buffer solutions containing a weak acid (HB) and its sodium salt (NaB), or, if we use Bronsted’s definition (3) of acids and bases, an acid (HB) and its corresponding base (B-). The hydrogen-ion concentration was as a rule greater than The measurements agree with the mechanism expressed in the schemes la-ld when we assume that the enolizations of acetoacetic ester and a-mono-bromoacetoacetic ester are catalyzed by the base B-. We use the following symbols in addition to those given in Part I, p. 752.‘ k B and h g , catalytic constants for the catalysis by B- of the enolization of acetoacetic ester (HR) and a-monobromoacetoacetic ester (HR’), respectively. a, stoichiometrical initial concentration of the acid HB. b, stoichiometricsl initial concentration of the salt NaB. It will be shown that the velocity of bromination can be explained by assuming that it is determined by two consecutive reactions with the velocities [ko k~ (B)-] (HR) and [ho hB(B-)] (HR’). Owing to the
+
+
1
+/z
In Part I, page 759, line 6, the following misprint occurs:
?!
n-1
should read 601
602
KAI JULIUS PEDERSEN
hydrobromic acid formed by the bromination, the concentration of the catalyst will decrease during the reaction. From these assumptions we shall first deduce a mathematical expression for the course of the reaction. Then we shall show that the expression agrees with the experiments. When the subscripts 0 and co denote that the concentration corresponds with t = 0 and t = C O , respectively, we have for the concentration of the catalyst (B-)o = b
+ (H+)o, (B-)oo = b
(B-)
=
b
+ (H+) .- -X2
+ (H+)cc - 2~
(19)
(H+) varies so little during reaction that it is sufficient to assume that its increase is proportional t o x. From a rou'gh value of the dissociation constant KEBwe calculate (H+)oand the hydrogen-ion concentration (H+)m X
corresponding ,to2 the equation
= c.
We calculate the proportionality factor K from
(H+)m - (H+)o= K~
2
We then have
which we introduce into equation 19:
In some cases the increase in (H+)is so small that we can disregard it and put K = 0. The course of the reaction is determined by the differential equations
a.nd
BROMINATION O F ACETOACETIC ETHYL ESTER.
I1
603
While the expressions in square brackets are not constant we may with good approximation consider the ratio
as constant. Provided that one of the following conditions holds, r is a constant :
and (3) b > >
X
They all hold approximately. From the equations 21,22, and 23 we get d(HR') (HR') =r----l d(HR) (HR)
which is identical with expression 9 in Part I, p. 753. By integration we get expression 10. When r > 1, equation 10 approaches the following equation as t increases (HR') (HR)
- 1 r -1
By introducing this into equation 4, we get
If r is sufficientslygreat, equation 24 will only fail for very small values of t . If we eliminate (HR) from equation 21 and 24 we get
By introducing (B-) from equation 20 we get
If we integrate and use equation 20 we obtain k*t = f(x)
+ log,, s
604
KAI JULIUS PEDERSEN
where we have used the abbreviations
and
and S is an integration constant. I n order to test the agreement between expression 25 and the experiments, we introduce the observed values of z intof(z). (B-) is calculated from z by means of equation 20. For a first approximation we may use ko/kB = 0 or a preliminarily estimated value. We now plot f(z) against t. When 2 is sufficiently great the points fall on a straight line, whose slope determines a preliminary value of k". From expression 26 we find the corresponding value of k ~ and * of i i ~ / k ~We . repeat the computation with the new value of k0/iiB and continue in the same way until a new repetition does not alter the value of k". The intercept on the ordinate axis of the straight line is -log S. Equation 25 does not hold for the observed values of z during the first part of the experiment. Owing to mathematical difficulties we must refrain from testing the explanation for this part of the reaction. If instead of using the observed values of z we use those determined by means of equation 24, equation 25 will hold for the whole experiment. When t = 0,we have (HR) = c (1 - E ) , and, consequently, by equation 24 when we use the abbreviation 12 c
-4
= c(l
- €1 (1+2&)=-4c
If we introduce this expression together with t = 0 into equation 25 we get
By means of this expression we calculate A from X,determined from the experiment as mentioned above. From A we find T, and, by introducing * equation 23, we find this and the known values of ko*, ho*, and k ~ into hB*. Owing to the.approximate character of the calculations we can not ex-
BROMINATIOX O F ACETOACETIC ETHYL ESTER.
605
I1
pect to get a great accuracy in the determination of the catalytic constant, especially in the case of AB*. T H E HYDROLYSIS O F BROMINE
In an aqueous solution of bromine we have the following equilibria Bra
+ H20 +
HBrO
+ H+ + Br-
and Brz
+ Br- e
Br3-
We neglect a possible formation of the ion Br6-. The hydrobromic acid formed by scheme 29 will cause a decrease in the concentration of the catalyst. In order to repress the hydrolysis all experiments were done in 0.05 M potassium bromide. We shall here see that this is sufficient to make the error negligible. The equilibrium constants of the reactions in scheme 29 determined by Bray and Connolly (2) and in scheme 30 determined by Jakowkin (7) are (H+)(Br-) (HBrO)/(BrJ
= 5.2
X 10-8.
and (Br-) (Brz)/(Bra-) = 0.063
The normality of the bromine is d (HBrO) =
=
2(Br2) 1.6
(0.063
x
+ 2(Br3-).
We get
10-lOd
+ (Br-)) (H+)(Br-)
I n the experiments (Br-) was 0.05, d usually about 0.02, and (H+) > For these values we get (HBrO) < 6 X The hydrobromic acid formed by the hydrolysis is equivalent to the (HBrO). Whenb > 0.01 the formation of 6 X N strong acid is without importance. EXPERIMENTAL
The bromination of acetoacetic ester was examined in the following five sodium acetate; (2) glycolic acid sodium solutions: (1) acetic acid sodium chloroacetate; (4) phosphoric glycolate; (3) chloroacetic acid primary potassium phosphate; (5) acid sodium sulfate normal acid sodium sulfate. Kahlbaum’s acetic acid “for analysis” was used without purification. Glycolic acid was purified as described in reference 9. Chloroacetic acid (pure, “Rilerck”) was distilled. The buffer solutions were made by adding sodium hydroxide to solutions of the acids. The phosphate mixtures were made from Kahlbaum’s primary potassium phosphate (for Sorensen’s buffer solutions) and hydrochloric acid. The sulfate mixtures were made
+
+
+
+ +
606
KAI JULIUS PEDERSEN
from sulfuric acid and sodium hydroxide. The hydrogen-ion concentration was always so great that it was unnecessary to keep the solutions carbon dioxide-free. Sufficient potassium bromide solution was added to make the solutions 0.05 M with respect to this substance during the bromination. The initial concentration of bromine was always about 0.02 N , except in experiments carried out in order to show that the concentration of bromine has no influence on the velocity. The volume of the reacting solution was always 200 cc. The experimental procedure was the same as described in Part I. In computing the catalytic constants kB* and hg* we have used the values of E , ko*, and ho* found for the water reaction (the "uncatalyzed" reaction) in 0.05 M potassium bromide by the experiments given in table 4 (Part I, p. 761). Other salts present in the catalytic experiments may also have an effect on the water reaction. It has already been shown that the kinetic salt effect of sodium chloride on k0* and ho* is small, and the effects of the other salts are probably also small. Since, further, the water reaction usually plays a rather insignificant part compared with the catalytic reaction, we have always neglected a possible salt effect on ko* and ho* in the calculation of k ~ and * hB*. The error thus committed is probably insignificant, except in the experiments in sulfate mixtures. Here the salt effect on the water reaction is probably greater than in the other experiments, and it has an especially great influence on the value of the catalytic constant, because the sulfate ion catalysis is only a small part of the total react ion.
Acetate ion catalysis
It was first shown that even a great variation in the concentration of bromine did not affect the velocity of bromination in the acetate buffers. This is seen especially clearly from four series of preliminary experiments in acetate buffers (8). Here an insufficient amount of bromine was added and the moment when the reaction ceased because all bromine had reacted was determined electrometrically by means of the arrangement described in Part I, p. 757. The mean value of kB* found here was 7.47 (at 18"C.), while kg* = 7.41 was found by the experiments with an excess of bromine in this paper. The velocity is independent of the concentration of undissociated acetic acid (table 1) and thus also independent of the hydrogen- and hydroxylion concentration of the acetate buffer, when the acetate ion concentration is kept constant. Table 4 gives a summary of ten series of experiments in different mixtures of acetic acid and sodium acetate a t the temperatures 0.03, 17.94, and 24.97"C. The results of two of the series are given in more detail in tables 2 and 3.
BROMINATION OF ACETOACETIC ETHYL ESTER.
607
I1
The constant k* has been computed by plotting f(x) against t as described above. I n the last column of tables 2 and 3 6 = f(x) - (k* t - log S ) has beenTtabulated. The agreement with formula 25 is always good when
> (c - X-4) / c > 0.5.
X
I n the first part of the reaction, when (c - -)/c 4 > 0.8, too great values of f(z) are obtained. This is in qualitative agree-
0.8
TABLE 1 Bromination of acetoacetic ester in acetic acid-sodium acetate mixtures at 18°C. b = 0.04008 a = 0.110
1
b = 0.02004 a = 0.080
a = 0.060
I
I
1
a
0.030
t
0.8584 0.7246 0.5114
0.250 0.495 1.005
0.8584 0,7246 0.5117
1.500 3.000
0.6001 0.3674
0.6009 0.3725
TABLE 2 Bromination of acetoacetic ester in a m i x t u r e of acetic acid and sodium acetate at 0.0S"C. a = 0.0600; b = 0.04008; c = 5.291 X (KBr) = 0.050; KHB = 3 X 10-6; (B-)= X
0.04013 - -; 2 t
@-)a
=
0.02955; k* = 0.05144; log &' = 0.0113; k g = 1.621; hB* = 23 X 109
le*$
1.003 1.997 2.497 2.997 3.497 4.000 4.502 5.003 5.997
0,633 1.261 1.553 1.808 2.052 2.275 2.419 2.667 2.998
0.0421 0.0915 0.1177 0.1426 0.1688 0.1947 0.2199 0.2460 0.2950
- log s
0.0403 0.0914 0.1171 0.1429 0.1686 0.1945 0.2203 0.2461 0.2972
zx
104
+18 fl $6 -3 +2 +2 -4
-1
-22
ment with the theory, but owing to mathematical difficulties we cannot test the agreement quantitatively. Later in the reaction, when (c
- :4) / c
< 0.5, we get greater and greater discrepancies, corresponding to too small values of x. This was also found in experiments in pure water and hydrochloric acid and is probably due to a secondary reaction. In this period of the reaction the solution acquired a peculiar sharp smell and, toward the end of the reaction, it turned cloudy.
608
KAI JULIUS PEDERSEN
From the summary of all the experiments in acetate mixtures given in table 4 it is seen that the constancy of kg* at constant temperature is good even when the acetate concentration is varied considerably. The mutual TABLE 3 Bromination of acetoacetic ester in a mixture of acetic acid and sodium acetate at 1y.@"C. a = 0.0900;b = 0.06012;c = 6.275X 10-3; (KBr) = 0.050;K H B= 3 x 10-6; (B-)=
0.06017- ? * (B-)w = 0.04762;k* 2'
= 0.3718; log S = 0.0099;k
X 108
t
0.103 0.200 0.300 0.398 0.500 0.595 0.700
0.514 1.049 1,552 2.003 2.411 2.759 3.084
f (2)
- logs
6 x 104
0.0284 0.0645 0.1016 0.1381 0.1760 0.2113 0.2504
+15 +1 -2 $2 -2 $2 - 18
k*t
0.0299 0.0646 0.1014 0.1383 0.1758 0.2115 0.2486
~ =* 7.43;h ~ = * 121
TABLE 4 Bromination of acetoacetic ester in mixtures of acetic acid and sodium acetate at 0,28, and 85°C. (KBr) = 0.050in all experiments MEAN VALUES
TEMPER-
(B-)~
ATURE
(B-)o1
'k
kB*
hB* kB*
degrees C.
0.03
{
I
0.04013 0.02955 0.05144 0.1002 0.08967 0.1488
1.621 1.620
23 27
0.1208 0.0912 0.2691 0.4162 0.3718 0.5645
7.46 7.38 7.42 7.39 7.43 7.39
121 112 127 121 137
0.02009 0.01513 0.2222 0.04013 0.03020 0.4170
12.62 12.77
214 207
0.02009 0.02009 0,04013 17' 94 0.06017 1 0.06017 [ 0.08021 24.97
{I
0.01381 0.00998 0.03385 0.05389 0.04762 0.07393
98
1
'I
1.620
hB'
25
I
1
7.41
119
12.70
210
agreement of the values of hg" is not very good. However, when we remember that we can only obtain a rough value of this constant, we might . not expect a better agreement.
609
TI
BROMINATION OF ACETOACETIC ETHYL ESTER.
Glycolate ion catalysis Table 5 gives the results of a single series of experiments, and table 6 a summary of all the experiments in mixtures of glycolic acid and sodium TABLE 5
Bromin,ation of acetoacetic ester in a mixture of glycolic acid and sodium glycolate at 0.03"C.
(KBr) = 0.050; ~
a = 0.0136; b = 0.05550; c = 3.056 X 0.05555
- 1.99
H B =
2.2
x
104; (B-) =
X ;: (B-)m = 0.04948; k* = 0.02630; log S = 0.0128; k ~ = * 0.460;
4
h ~ *= 6.87
ax
t
3.00 5.00 5.00 7.00 9.00 11.00
I (x)
103
0.474 0.788 0.790 1.064 1.307 1.516
k*t
0.0666 0.1187 0.1189 0.1710 0,2241 0.2764
- log s
6 x 104
0.0661 0.1187 0.1187 0.1713 0.2239 0.2766
+5
0 +2 -3 +2 -1
TABLE 6
Bromination of acetoacetic ester in,mixtures of glycolic acid and sodium glycolate at 0, 18, and 25'C. (KBr) = 0.050 in all experiments
1 TEMPERATURE
degrees C .
0.03 17.94 24.97
@-)a
{
{I {I
(B-)
~
k*
kB*
hB*
i
XEANVALUES
kB*
0.05555 0.09256
0.04948 0.08645
0.02630 0.04357
0.460 0.463
0.05555 0.09256
0.04948 0.08645
0.1197 0.1958
2.06 2.06
29'4 27.3
1 1
0.05555 0.09256
0.04948 0.08645
0.2032 0.332
3.48 3.48
53'6 53.2
1
6'87 6.36
0.462
hB'
6.62
2.06
28.4
3.48
53.4
glycolate. The dissociation constant K H B a t different salt concentration has been taken from a yet unpublished determination. The agreement of the kinetic experiments with the theory is as good as in the experiments on acetate ion catalysis.
610
KAI JULIUS PEDERSEN
Monochloroacetate i o n catalysis Table 7 gives the results of a single series of experiments, and table 8 a summary of all the experiments in mixtures of monochloroacetic acid and sodium monochloroacetate. The dissociation constant of monochloroaceTABLE 7 Bromination of acetoacetic ester in a mixture of monochloroacetic acid and sodium monochloroacetate at 17.94"C. a = 0.1018; b = 0.1002; c = 3.382 X 10-8; (XBr) = 0.050; KHB= 0.0023; (B-) = 0.1024
- 1.92 X
I;
(B-)m = 0.0959; k* = 0.0709; l o g s = 0.0145; k g = 0.554; hB* = 7.8 k*t
1.000 2.000 2.500 3.000 3.500 4.000 5,000 6.000
0.446 0.893 1.092 1.274 1.447 1.601 1.880 2.098
0.0586 0.1276 0.1626 0.1974 0.2535 0.2685 0.3408 0.4046
- log s
6 x 104
0.0564 0.1273 0.1627 0.1982 0.2337 0.2691 0.3400 0.4109
+22 +3 -1 -8 -2 -6
+8
-63
Bromination of acetoacetic ester in mixtures of monochloroacetic acid and sodium monochloroacetate at 0, 18, and 85°C. (KBr) = 0.050 in all experiments TEMPERATCRE
degrees C.
{ 17.94 { 24.97 { 0.03
k*
kB*
I
0.06226 0.1024
0.05597 0.0959
0.01001 0.01470
0.1158 0.1168
0.06226 0.1024
0.05597 0.0959
0.0488 0.0709
0.554 0.554
0.04218 0.1024
0.03611 0,0959
0.0669 0.1250
0.989 0.978
1 1 ''" 1) 1.54
8'o 7.8
12.3
0.1162
1.62
0.554
7.9
0.983
1
12.0
tic acid a t 2OOC. and in infinite dilution KHBO = 1.41 X 10-3 has been determined by Grove (6). From this value and the assumption that the relative increase of K H B by addition of salt is the same as for glycolic acid, it is estimated that the value K H B = 2.3 x 10-3 is sufficiently accurate
'
BROMINATION O F ACETOACETIC ETHYL ESTER.
for calculation of (H+)in all the experiments. good.
611
I1
Also here the agreement is
Primary phosphate ion catalysis Table 9 gives the results of a single series of experiments, and table 10 a summary of all the experiments in mixtures of phosphoric acid and priTABLE 9 Bromination of acetoacetic ester in a mixture of phosphoric acid and primary potassium phosphate at 2g.07"C. (KBr) = 0.050; (KCl) = 0.015; K H B= a = 0.01520; b = 0.06085; c = 3.056 X 0.0089; (B-) = 0.06274 - 1.69 X :; (B-)m = 0.05758; k* = 0.0817; log S = 0.0160; 4 kp,* = 0.877; h ~ = * 10.6 t
0.0575 0.0914 0.1206 0.1456 0.1672
1.253 2.000 2.752 3.500 4.253
0.0863 0,1475 0.2089 0,2701 0.3314
0.0864 0.1474 0.2088 0.2700 0.3315
-1 $1 +1 +1 -1
TABLE 10 Bromination of acetoacetic ester in mixtures of phosphoric acid and primary potassium phosphate at 0, 18, and 25°C. (KBr) = 0.050 in all e mimente TEMPERATURE
(BWa
(B-)
1
OTAL S A L T CONCENTRATION
ki3*
hg*
1 I
MEAN V A L U E S
-
kB* -degrees C .
0.06311 0.05807
0.126
0.00907
0,0954
17.94
1I
0.03596 0.04716 0.07003 0.09259
0.03122 0.04214 0.06468 0.08705
0.094 0.114 0.145 0.170
0.03320 0.03882 0.0491 0.05944
0.493 0.499 0.484 0.478
5.6 5.4
24.97
{
0.06274 0.05758 0.05641 0,05143
0.126 0.125
0.0817 0.07616
0.877 0,874
'O" 11.7
0.03
o*88
hB*
5.6
0'.876
11.2
, mary potassium phosphate. The values of the first dissociation constant of phosphoric acid used for the calculation of (H+) have been calculated from the measurements of Bjerrum and Unmack (1) at 18°C. and 25°C. These measurements have been carried out in solutions containing sodium
612
KAI J U L I U S PEDERSEN
ions instead of potassium ions and a t salt concentrations 5 0.1 N , while the solutions for the catalytic experiments were usually somewhat more concentrated. Nevertheless, the values obtained from the interpolation formulas given by Bjerrum and Cnmack are considered to be accurate enough for the rather rough calculation of (Ht). For the experiments at 0°C. the values of -log K H at~25°C. and 18°C. have been extrapolated to 0°C. It is assumed that the concentration of the secondary phosphate ion is always negligible. Formula 25 holds well within the single series of experiments. The part of the total reaction which is caused by the catalysis is only one to two times as great as the part caused by the water reaction. Nevertheless, the constancy of kB* when the concentration of primary phosphate ion is varied is good. Naturally, the accuracy of hB* is much smaller, but also here the constancy is fairly good.
T h e second dissociation constant of suyuric acid For the calculation of the experiments on the bromination of acetoacetic ester in mixtures of acid and normal sodium sulfate it is necessary to have some knowledge of the second dissociation constant of sulfuric acid a t different salt concentrations. Sherrill and Noyes (13) have calculated this constant K a t 25°C. from measurements of the electric conductivity of solutions of sulfuric acid and of acid sodium sulfate. By extrapolation t o infinite dilution they find the activity dissociation constant KO = 0.0115. Here we shall compute KO from their determinations of K in a slightly different way. According to the theory of Debye and Hiickel the activity coefficient f i of an ion in dilute solution may be expressed by the formula
- log fi =
AZ
fi- Pip
where x is the number of electric charges on the ion, p the ionic strength of the solution, a is a constant, the same for all ions (at 25°C. in water a! = 0.504), and pi approaches a constant value, when p --+ 0. By means of this formula we may express the second dissociation constant o€ sulfuric acid as follows
- log K = - log KO - 2.016 4;+ P,u K + 2.016 &, calculated from the values of
We now plot -log Sherrill and Noyes, against p . The points fall on a straight line which determines the constants -log KO and /?. We thus find for the solutions of sulfuric acid
- log K
= 1.988
- 2.016 d;+ 0.62p
6 0.0844)
(31)
(P 5 0.1056)
(32)
(p
and for the solutions of acid sodium sulfate
- log K
= 1,984
- 2.016 4 ;
+1.27~
. 613,
I1
BROMINATIOR' O F ACETOACETIC ETHYL ESTER.
The agreement is seen from table 11 where the dissociation constants K found by Sherrill and Noyes are given in the third column, while those calculated from the formulas 31 and 32 are given in the last column. By this extrapolation we get KO = 0.0103 a t 25°C. In order to get an idea of the variation of KO with temperature we make the following considerations. Thorvaldson, Brown and Peaker (14) have found calorimetrically that the heat evolved by mixing 1 -V HzS04 and an equivalent amount of NaOH, 100 HzO a t 20°C. is 16.984 kg-cal. per equivalent HzS04. Richards and Hall (12) have determined the heats of neutralization of different strong acids and sodium hydroxide. They NaOH, 100 HzO at 20°C. 13.924 kg-cal. and found for HCl, 100 HnO for HBr, HJ, and "03 nearly the same value. Thus sulfuric acid in
+
TABLE 11 Second dissociation constant of sulfuric acid at 25°C. S O L U T I O N 8 O F SULFURIC ACID
SOLUTION8 OF ACID 8 O D I U M S U L F A T E
- log K = 1.988 - 2.01G &P + 0 . 6 2 ~ Stoichiometric concentration of
- log K
= 1.984
- 2.016 4; f
Stoichiometric K (oalcd.) concentration of NaHSOd
p
1.27~
K (calcd.)
~~
0.00025 0.001 0.005 0.00625 0.0125 0.0250 0.0500
0.0007 0.0027 0.0116 0,0141 0.0225 0.0461 0.0844
0.0118 0.0130 0.0168 0.0175 0.0208 0.0260 0.0352
0.0116 0.0130 0.0167 0.0175 0.0208 0.0260 0.0352
0.000391 0,000781 0,001562 0.003125 0,00625 0.0125 0.0250 0,0500
0,0011 0.0022 0.0044 0.0084 0.0160 0.0302 0.0564 0.1056
0.0107 0,0121 0.0135 0.0153 0.0178 0,0213 0.0265 0,0348
0.0121 0.0128 0.0139 0,0155 0.0178 0.0213 0.0265 0.0344
approximately the same molar concentration gives 3 kg-cal. more per equivalent than the strong acids. We may assume that the first dissociation of 1 N HzS04 is practically complete. The difference in the heat of neutralization is probably caused by the second dissociation HS04- H20 -+ S04-H30+. If the second dissociation constant of sulfuric acid is not many times as great in 1 N HzS04 as by infinite dilution, only few per cent of the acid is present in form of the normal sulfate ion. We thus get from the above measurements that the heat of dissociation of the ion HSOeis approximately 3 kg-cal. per h mole or 6 kg-cal. per mole. If we use this value also at infinite dilution and in all the temperature interval 0-25°C. we get from KO at 25°C. by means of the formula
+
+
u = 4.575 x
10-3
d log KO d (T-I)
. ,6 14
KAI JULIUS PEDERSEN
where U is the heat of dissociation in kilogram-calories per mole per liter and T is the absolute temperature, the following values of KO: 25°C. 18°C. 0°C.
- log KO = 1.99 = 1.88 = 1.58
- log KO - log KO
KO = 0.0103 KO = 0.013 KO = 0.026
Sulfate i o n catalysis Experiments on the bromination of acetoacetic ester were carried out in solutions of sodium sulfate containing a little acid sodium sulfate and 0.050 M potassium bromide (0.16 < p < 0.34). K was found from equation 32. F o r experiments a t 18°C. and 0°C. the values of -log KO found a t these I
TABLE 12 Bromination of acetoacetic ester i n a mixture of acid and normal sodium sulfate at 24.9'7"C. a = 0.00035; b = 0.07644; c = 3.039 X IOT3;(KBr) = 0.050; K H B = 0.053; (B-)= 0.07658 - 1.16 X
X
4;( B - ) W
=
0.07306; le* = 0.03785; log S = 0.0164; k ~ = * 0.091;
k*t - 1 o g s
1.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00
0.189 0.616 0.817 1.002 1,175 1.330 1.475 1,603
0.0277 0.0976 0.1350 0.1725 0.2109 0.2484 0,2867 0.3235
0.0214 0.0972 0.1350 0.1728 0.2107 0.2486 0.2864 0.3242
I
ax
104
+63 +4 0 -3 +2 -2 $3 -7
temperatures were substituted for 1.984 in equation 32. Owing to the great ionic strength of the solution we can only get very rough values of K in this way. However, we consider the accuracy sufficient for the following reasons. Firstly, the correction for the variation of (H+) is here very small, and secondly, there is, as we shall see, another source of error which makes it of no use to attempt to determine the concentration of the catalyst with great accuracy. As seen from table 12 tlie agreement with formula 25 is as good as in experiments with other catalysts. I n table 13 is given a summary of all the experiments in sodium sulfate. It is seen that k" is only 11 to 24 per cent greater than ko*. Thus the velocity is not much increased by the presence of the sodium sulfate. The kinetic salt effect on ICo* is probably not negligible compared with the increase. However, the increase can not be explained only by the salt effect. We have found in Part I, that 0.1 M
BROMINATION O F ACETOACETIC ETHYL ESTER.
615
I1
sodium chloride or potassium chloride gives a decrease of the velocity of 1 to 2 per cent. It is therefore most unlikely that the salt effect of 0.1 M sodium sulfate can give an increase of 24 per cent. However, the effect of the salt being unknown, it is disregarded. In the other catalytic experiments the error thus introduced is probably of no importance. Here it makes the values of kB* less reliable. I n addition, the experimental error in k" is of greater importance here, where the water reaction is 80 to 90 per cent of the total reaction. In spite of these possible errors, the values of kg" a t different catalyst concentrations agree fairly well among themselves. Naturally, the values of hg* are only very rough. We have now examined the bromination of acetoacetic ester in solutions containing one of the following bases,-acetate, glycolate, monochloroaceTABLE 13 Bromination of acetoacetic ester in mixtures of acid and normal sodium sulfate at 0, 18, and 26°C. (KBr) = 0.050 in all experiments TEMPERATURIS
I.r
k*
kg?
degrees C .
0.0767
0,0744
0.28
0.004012
0.0065
1
0.6486 0.0766 0.0961
0.0455 0.0734 0.0928
0.195 0.28 0.34
0.02012 0.02111 0.02205
0.0510 0.0452 0.0458
i
0.0383 0.0766
0.0355 0.0731
0.16 0.28
0.03475 0.03785
0,100 0.091
0.03
17.94
24.97
hB*
-1
0.09
1
MEAN VALUES
Izg'
1
:::
I
hg'
1 0.047
0.5
0.4
tate, primary phosphate, and sulfate ions-together with the corresponding acid. We have always found agreement with formula 25 for the part of the reaction where a comparison was possible. From this we conclude that the mechanism is as given in scheme 1 (Part I, p. 751), and that the enolization of acetoacetic ester And of a-monobromoacetoacetic ester is catalyzed by bases in general. The theory of general acid and basic catalysis and of prototropic isomerization has recently been discussed in another paper ( l l ) , where references to the literature on the subject will be found. The water reaction studied in part I is explained as the result of the basic catalysis of the water. If we neglect the effect of the association of the water molecules, the concentration of water is (HzO) = 55.5, its basic strength 55.5-1 and the catalytic constants kHtO = k0/55.5 and hH20 = ho/55.5. The catalytic constants for the six bases examined are given in table 14
616
KAI JULIUS PEDERSEN
together with the strengths of the acids which correspond to the bases. In the paper (11) mentioned above we have discussed the forniula (33)
where KBo is the strength of the catalyzing base a t infinite dilution, p and p are statistical factors, and and G are constants for a given reaction a t a given temperature (0 < fl < 1). In order to test the validity of this
FIG.1. BASICCATALYSIS OF
THE ENOLIZATION OF ACETOACETIC ESTER The dependence of catalytic constant upon basic strength
1 1 formula for the reaction examined here we plot log (AB*) and log (-hB*) P 4
against log (FKBO) (figure 1 and 2). The points for acetate, glycolate, 4 and monochloroacetate ions fall very close to a straight line. If we draw the line through the points for acetate and glycolate ions we get in the case of acetoacetic ester the following values of p : 0.602, 0.605, and 0.599 at 0, 18, and 25"C., respectively. p is here independent of the temperature. In figure 1 we have drawn all the straight lines with the slope p = 0.60. This value has also been used for the calculation of G* from formula 33 (see table 14). For a-monobromoacetoacetic ester, where the accuracy is
BROMINATION O F ACETOACETIC ETHYL ESTER.
I1
617
much smaller, we get from the catalytic constants of acetate and glycolate ions p = 0.64, 0.68, and 0.63 a t 0, 18, and 25"C., respectively. We have used the value p = 0.64 for drawing the straight lines in figure 2 and for calculating G* (table 14). While the agreement with formula 33 is always good for the three carboxylate bases, the catalysis of the primary phosphate ion is a little too strong, and that of the sulfate ion much too weak. This latter deviation of the base with two negative charges is qualitatively in agreement with the theory (11). The points for water fall below the lines. However, the deviation is not unreasonably great when
FIa. 2. BASICCATALYSIS O F T H E EWOLIZATION O F CY-&~OXOBROMOACETOACETIC The dependence of catalytic constant upon basic strength
ESTER
we reinember that we have neglected the effect of the association. As seen both from the figures and the table, the deviation from formula 33 for a given base is approximately independent of the temperature. From the experimental values of kB* a t the three temperatures we get the expressions for log kg* given in table 15. This table also contains the heats of activation Q in kg-cal. calculated from the formula Q
=
- 4.575 y 10-3
d log k R d (T-l) ~
The basic strength of a catalyst generally varies with the temperature. The increase in velocity when the temperature rises may therefore formally
I
618
KAI JULIUS PEDERSEN
3
0 0 0 0 0 0
M
o 0 0 0 0 d
*
d
, 9
'
.L---.,-------~ 4
t
m
z
u)
m
0
3
0 0 0 0 0 0
2
-_y___
t-
Q: , N
619
11
BROMINATION O F ACETOACETIC ETHYL ESTER.
be divided in two parts: (1) the increase in velocity a t constant basic strength, (2) the change in velocity owing to the change in basic strength. It may be of some interest to consider the first part separately. From formula 33 we find, when we assume that /3 and KBQare constant, the "heat of activation" QG =
log G - 4.575 x 10-3 dd(T-1)
The values of QG calculated from this formula are given in table 15. For monochloroacetic acid we have assumed that the dissociation constant is independent of the temperature. QG is approximately constant for all the bases. When we compare bases which have a t constant temperature the
CATALYST
I log kg'
CHsCOzCHZOHCOZCHzCICOzHzPOa-
so,--
HzO
a-MONOBROMOACETOACETIC ESTER
A C E T O A C E T I C ESTER
(Oocc. - 25'C.)
10.905-2.921 X 10.166. 2.868 X 10.125-3.021 X IO. 487-3.143 X 11.788-3.817 X 7.130-3.093 X
103/T lO3/T lo3/T 103/T 10S/T 103/T
Q
QG
Q
13.4 13.1 13.8 14.4 17.5 14.2
13.5 13.6 (13.8) 13.0 13.7 14.2
14 13.5 13 16 14
same G* this must naturally be so. However, QG has nearly the same value also for the last three bases, although G" here varies considerably. It is interesting that the sulfate ion, which has an especially great heat of activation (Q), has the same QG as the other bases. The mechanism of prototropic isomerization was discussed a t length in the theoretical paper (11). As shown there the enolization of acetoacetic ester follows the scheme 0:CCH3
I
B
+ HCHCOOCzHs
*
0 :CCHs I
A
I
+
-CHCOOCgHs
-lr -0. CCH3
A
4-
/I
CHCOOCzHs
HOCCHs
--+ B
ll + CHCOOCsH6
where the equilibrium between the two forms of the ion is attained practically instantaneously. It follows from the theory that the transference
620
KAI JULIUS PEDERSEN
of protons from the keto-ester to the base determines the velocity of the total reaction, if the tautomeric ion by taking up a proton from a n acid forms predominatingly the enol-ester. It was shown that this is probably the case here, because the enol form is a much stronger acid than the keto form. However, we may also test this condition experimentally in the following way. The apparent dissociation constant of acetoacetic ester a t 25°C. is 2.0 (Goldschmidt and Oslan (4)). It is therefore easy to prepare a X solution which is so alkaline that the ester is completely ionized. To this solution we suddenly add a mixture containing an excess of hydrochloric acid and bromine water. If only enol is formed this will instantaneously react with bromine (one mole per mole ester). After this the a-monobromoacetoacetic ester formed will react slowly with more bromine. The excess of bromine was removed by adding allyl alcohol immediately after the hydrochloric acid, and the solution was titrated in the ordinary way. It was always found that about one mole of bromine had reacted per mole of ester. However, the experiments were not quite reproducible. When the excess of bromine was small, less than the theoretical amount was used. Similar experiments have been carried out by Grossmann (5). H e also finds that acetoacetic ester in sufficiently alkaline solution behaves as if it were exclusively the enol form of the ion. From these considerations we conclude that the velocity of enolization which we have measured in this work is actually the velocity of transference of protons from the keto form to the bases, or, in other words, the velocity of dissociation of the keto form, which is an extremely weak acid. SUMMARY
This paper contains an experimental study of the rate of bromination of acetoacetic ester in solutions of weak bases and their corresponding acids. It has been shown that the velocity of bromination is determined by the consecutive enolization; of acetoacetic and a-monobromoaceto$cetic ester, which reactions are catalyzed by bases in general. The catalytic constants of the six bases acetate, glycolate, monochloroacetate, primary phosphate, sulfate ions, and water a t 0, 18, and 25°C. have been determined and compared with the strengths of the bases. Evidence has been given in favor of the view that the velocities of enolization are determined by the velocities of dissociation of the keto forms, which are extremely weak acids.
I wish to thank the head of the laboratory, Professor Niels Bjerrum, for valuable advice and kind interest in my work.
BROMISATIOS O F ACETOSCETIC ETHYL ESTER.
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REFERENCES (1) BJERRUM, N., AND UNMACK, A.: Kgl. Danske Videnskab. Selskab Math. fys. Medd. 9, No. 1 (1929). (2) BRAY,W. C., A N D CONNOLLY, E. L.: J. Am. Chem. SOC.33, 1485 (1911). (3) BROXSTED, J. N.: Rec. trav. chim. 42,718 (1923); Chem. Rev. 6, 231 (1928). (4) GOLDSCHMIDT, H., AND OSLAN,L.: Ber. 33, 1146 (1900). (5) GROSSMANK, P.: Z. physik. Chem. 109,305 (1924). (6) GROVE,C.: J. Am. Chem. Soc. 62, 1404 (1930). (7) JAKOWKIK, A. A.: Z. physik. Chem. 20, 19 (1896). (8) PEDERSEN,K. J. : Beret. Skand. Naturforskermede, 18th Meeting, Copenhagen, p. 451 (1929). (9) PEDERSEN, K. J.: J. Am. Chem. SOC.63, 23 (1931). (10) PEDERSEN, K. J.: J. Phys. Chem. 37, 751 (1933). (11) PEDERSEN, K. J.: J. Phys. Chem. 38, 581 (1934). (12) RICHARDS, T. W., AND HALL,L. P.: J . Am. Chem. Sor. 61,731 (1929). (13) SHERRILL, M. S., A N D NOYES,A. A.: J. Am. Chem. SOC.48, 1861 (1926). T., BROWN, W. G., AND PEAKER, C. R.: J. Am. Chem. SOC.61, (14) THORVALDSON, 2678 (1929).
