THE VELOCITY OF BROMINATION O F ACETOACETIC ETHYL ESTER. I THE WATERREACTION KAI JULIUS PEDERSEN Chemical Laboratory of the Royal Veterinary and Agricultural College, Copenhagen, Denmark Received A p r i l 2, 10%
The object of this work was to make a contribution to the theory of prototropic reactions, and with this end in view it was decided to study the enolization of acetoacetic ethyl ester by measuring the rate of bromination. In aqueous solution the equilibrium CH&OCHzCOOCzH5
CHaCOH: CHCOOCzHb
is displaced mainly in favor of the ketone, the concentration of enol being only 0.4 per cent of the total concentration of the ester. It is well known that bromine reacts practically instantaneously with the enol, while it does not affect the ketone appreciably. This fact is used in Meyer’s (1) method for estimating the enol content of the equilibrium mixture by titration with bromine water. If bromine is added to an aqueous solution of acetoacetic ester, the enol is removed by the bromine as soon as it is formed. Therefore, in the amount of bromine used we have a measure of the progress of enolization. A similar mechanism was first suggested by Lapworth (2) for the reaction between acetone and halogen in aqueous solution. Here the rate of halogenation is a measure of the velocity of enolization of acetone. In agreement with this explanation Lapworth found that the velocity was independent of the concentration and the nature of the halogen. The kinetic experiments on the reaction of acetoacetic ester and bromine described in this paper agree with the following explanation. The reaction takes place in four steps: CH3COCHzCOOCzHa
-+
+
CHsC0H:CHCOOCzHb
+ + Br-
(la)
CHsCOH:CHCOOC~Ha Brz
+ CH3COCHBrCOOC2H6 Hf
(lb)
CHaCOCHBrCOOC2H6
+ CH3COH:CBrCOOCzH5
(14
+
CHsCOH:CBrCOOCzHb Brz
-+
+ + Br-
CHsCOCBr~COOCzHs H+ 751
(Id)
752
KAI JULIUS PEDERSEN
Thus the reaction does not stop when a-monobromoacetoacetic ester is formed, but this substance takes up more bromine giving the final product a,a-dibromoacetoacetic ester. The rates of bromination of the enol forms of acetoacetic ester (lb) and of monobromoacetoacetic ester (Id) are so great compared with the rates of enolization of the keto forms, that the reactions l a and IC determine the velocity of the total reaction. In agreement with this the concentration of bromine was always found to be without influence on the velocity of bromination. From these assumptions we shall now deduce a mathematical expression for the amount of bromine used by the reaction t minutes after its start. We use the following symbols: HR HR’ R” c
keto form of acetoacetic ester, keto form of a-monobromoacetoacetic ester, u,a-dibromoacetoacetic ester, initial concentration of acetoacetic ester (ketone and enol), degree of enolization at keto-enol equilibrium, time in minutes from the start of the reaction, bromine used a t the time t in equivalents per liter, IC0 = unimolecular velocity constant for the enolization of H R (with no added catalyst), ho = the same for HR’, and r = ho/ko. * By an asterisk we denote that the velocity constant has been calculated by means of decadic logarithms. Thus IC* = 0.4343 IC. = = = = e = t = J: =
The enol concentration being always 0 after the start of the reaction, we have (HR)
+ (HR’) + (R“) = c
(2)
From equations l a to Id it follows that the bromine used by the reaction is
+ 4(R”) = r
(3)
+ +(HR‘) = c - -24
(4)
2(HR‘)
From equations 2 and 3 we have (HR)
The velocity of the consecutive reactions H R termined by the differential equations
and d(HR‘) = ko(HR) dt
- ho(HR’)
---f
HR’
-+
R” is de-
753
BROMINATION OF ACETOACBTIC ETHYL ESTER. I
At the time t = 0 we have (HR)
=
~ ( -i e)
and (HR')= ce
(7)
Integrating equation 5 and using equation 7 we obtain
(HR)= ~ ( -l e ) €-lint From equations 5 and 6, together with the abbreviation r
(8) =
ho/ko,we get
Integrating equation 9 and using equation 7 we get (except when
1'
= 1)
(HR) and (HR') are now eliminated from equations 4, 8, and 10: X
where we have used the abbreviation
Equation 11 may be written in the following way:
For special values of r the two-membered exponential expression 11 is reduced to a single-membered one. Thus, X
X
if r
= 1,
c c--
if r = 4,
4
c
c--
ifr=O,
z
-= C
X
2
(1 - e)e-liot
754
KAI JULIUS PEDERSEN
In order to show that the kinetic experiments agree with the explanation given above we find such values of the constants E , ko* and ho* that the experimental values of x and t satisfy equation 13. At first B is determined. When t is small, equation 13, or the identical equation 11, may be written c
- 2.-
4 -= A ( l C
- kot) -
(1 - hot)
t
ko
2
2
1 - - - t - (1
+
(T
- 1)e)
(18)
X
Consequently,
E
4
can be computed by plotting - against t for small c
values of t and rectilinear extrapolation to t = 0. It is more difficult to determine ko* and ho*. If ho* > > ko", the second exponential member of equation 13 will decrease rapidly for increasing c--
X
4
values of t and will soon be negligible. If we plot log - against t we C
should get a curve which approaches asymptotically to a straight line with the slope -ko* and makes an intercept log A on the ordinate axis. From these constants we easily get ho* by means of equation 12. In order to test whether all the experimental pairs of values of x and t agree with equation 13 for the values of the constants thus computed we plot
against 1. Now, all the points should fall on the straight line previously drawn. If there should be any systematic deviation we may attempt to obtain a better agreement by drawing a new straight line and repeating the operation, The method here outlined is only applicable when ho* is much greater than k ~ * . If they are of the same order of magnitude, the curve will not sufficiently quickly approach a straight line. The following method can be used in all cases. For each pair of values of x and t found by experiment and for a series of values of r we calculate by the method of trial and error the values of ICo* which satisfy equation 13. Thus, for each pair of x and t a curve through corresponding values of ko* and r is determined. We get a family of curves all going through the same point. The coordinates of this point are the values of ICo* and r which satisfy equation 13 for all the experimental values (figure 1). Actually, we do not find a single point of intersection for all the curves, owing to experimental inaccuracy. However, it is always possible to find the value of r for which the variation of ko*
BROMINATION O F ACETOACETIC ETHYL ESTER. I
755
is smallest. In the following treatment of the experimental results we shall see examples of both methods of computation here described. Owing to the mathematical form of expression 13, a small error in r and t will cause rather a great inaccuracy in ko* and ho“ (see figure 1 and table 3). If equation 13 is satisfied for all the experimental pairs of 2 and t by r = and a certain value of ko*, say ko* = y, it will, as seen from equations Y 14 and 16, also be satisfied by r = 00 and ko* = -. If (y, i)is the common 2 point for all the kO*,r-curves, they will all approach the straight line ko*
+
’
asymptotically when r 400 . Consequently, in this case it is impos2 sible to decide from the experiments whether 1’ = 3 and ko* = y, or r = =
w
and ICo* =
2.
It is seen from figure 1, that if the common point of
intersection for all the ko*,r-curves falls in the interval 3 < r < a ,each curve will cut each of the other curves in another point in this interval, but the new points of intersection are not common for all the curves. It is useful to remember this when computing the constants. Otherwise there is danger of finding a false solution, especially when using the first of the two methods. EXPERIMENTAL
Materials Kahlbaum’s best preparation of acetoacetic ester was purified in one of the following two ways. (1) With sodium bisulfite as suggested by Elion (3). The ester was dissolved in a little less than the calculated amount of saturated sodium bisulfite solution. An impurity which does not combine with bisulfite w.as removed by extraction with ether. The ester was again liberated by addition of the calculated amount of potassium carbonate and extraction with ether. After drying with anhydrous sodium sulfate the ether was distilled from the ester. Finally, the ester was distilled several times in vacuo. (2) Through the copper compound. This compound was made by shaking an ethereal solution of acetoacetic ester with an aqueous solution of copper acetate (Wislicenus (4)). The copper compound was three times recrystallized from benzene and then decomposed with hydrochloric acid. The ester was extracted with ether and, after drying with anhydrous sodium sulfate, was twice distilled in vacuo. Samples of the two preparations were left for fifteen to twenty hours with an excess of sodium hydroxide solution and afterwards titrated with hydrochloric acid. It was found that one equivalent of base hydrolyzed 130.0 g. of the first and 130.1 g. of the second preparation. The calculated molecular weight is 130.08. The bromine water was prepared from Kahlbaum’s bromine “for analysis. ”
756
KAI JULIUS PEDRIRSEN
Experimental procedure
A beaker with acetoacetic ester solution (usually 175 cc.), containing in most of the experiments varying amounts of hydrochloric acid or neutral salts, was placed in a thermostat a t 2497°C. or 17.94"C.or in an ice-water mixture. The solution was stirred mechanically. Its temperature could be read off on a thermometer. Bromine water (usually 25 cc. of 0.15 N ) was brought to the same temperature. The reaction was started by mixing the two solutions. It was stopped after some time (t minutes) by adding an excess of allyl alcohol dissolved in water. This reacts instantaneously with the remaining free bromine. The time was measured by means of a stop-watch which had been compared with an accurate pendulum clock. The corrections never exceeded 0.2 second. Immediately after the reaction was stopped, an excess of solid potassium iodide (1 to 2 9.) and a little dilute hydrochloric acid was added. Iodine equivalent to the bromine used by the reaction is liberated
+ 21- + H+
+ CH3COCHzCOOC2H6 IZ
+ + 2H+
+ CH3COCH2C0OC2H6 212
CH3COCHBrCOOCzH5
and
CHsCOCBnCOOC2H5 41-
+ + Br+ + 2Br-
The iodine was titrated with 0.05 N thiosulfate and starch solution. The liberation of iodine does not take place instantaqeously. The thiosulfate was added in small portions, and the titration was considered as finished when the solution stayed colorless for five minutes after addition of one drop of 0.05 N thiosulfate. Usually the titration took fifteen to twenty minutes. Dissolved oxygen and small amounts of impurity in the chemicals used may oxidize some iodide during the titration. I n order to correct for this error a blank experiment without acetoacetic ester was done for each series of experiments, It used always less than 0.10 cc. of thiosulfate. I n the experiments a t 0°C. the solution was slowly heated to room temperature during the titration. Both the bromination and the analysis were carried out in diffused daylight or artificial light. Neither the bromopropyl alcohol formed by the reaction between bromine and allyl alcohol, nor the excess of allyl alcohol interfered during the analysis. The former does not liberate iodine from iodide; the latter reacts too slowly with iodine. Fortunately it is unnecessary to know the exact concentration of bromine during the reaction, the velocity being independent of the amount of bromine. It was found to be important to add the potassium iodide immediately after the bromination was stopped. If the solution was left for some time before analysis, too little thiosulfate was used, and the last part of the liberation of iodine was much slower than usually. I n this case it was noticed that the solution had a sharp smell. Probably the bromo- or
BROMINATION OF ACETOACETIC ETHYL ESTER. I
757
dibromo-acetoacetic ester is slowly transformed into compounds which react more slowly with iodide. This may also explain why the results of the analysis are lower than expected in experiments where the bromine has reacted for a very long time. With extremely long times of reaction the bromine found by the analysis even decreased when the time of bromination was increased. I n such experiments the solution was cloudy after the bromination. This error adds to the difficulty in computing the velocity constants ko* and ho* from the experimental results. I n a great number of experiments it was shown that the velocity is independent of the bromine concentration. This is seen most distinctly from some experiments carried out in another way. To the solution of acetoacetic ester was added insufficient bromine water, and the moment when the reaction ceased because all the bromine had reacted was determined electrometrically. Into the beaker dipped a platinum electrode, and the solution was connected by means of an agar-agar bridge with a glass containing a solution of iodine and potassium iodide into which dipped another platinum electrode. The electrodes were connected with a galvanometer through a high resistance. As long as bromine was present the galvanometer gave a slowly decreasing deflection. When the last trace of bromine disappeared the zero was quickly passed, and the galvanometer gave a considerable deflection in the opposite direction. The time from the mixing of the solutions until the disappearance of the bromine was measured. Potassium iodide was added to the solution, and the analysis was carried out in the usual way. The time of reaction was varied by adding varying amounts of bromine water in the different experiments. Experiments carried out in this way gave exactly the same results as experiments with an excess of bromine and interruption by means of allyl alcohol. This shows conclusively that the velocity is independent of the concentration of bromine. Consequently, the reaction by which bromine is taken up is very rapid compared with the reaction which determines the actual velocity of the complete process. The allyl alcohol method, being the simplest and most accurate, was used for all the experiments whose numerical results are given below. The results of a series of experiments on the bromination of acetoacetic ester in water a t 17.94"C. are given in table 1. The initial concentration of bromine was 0.025 M , and that of the ester 0.005062 M except in experiments marked thus (?), where it was 0.01736 M . By extrapolation to 2
2 = 0 it was found that
E
= 0.0034.
c-z By plotting log -against t, the
values LO* = 0.01802 and ho" = 0.206 were found. 2
C
In order to test the
agreement with formula 13, - was calculated from the formula, using the 4
758
c =
KAI JULIUS PEDERSEN
TABLE 1 Bromination of acetoacetic ester in water at lY.9d"C. 5.062 X 10-3. In the experiments marked t, c = 17.36 X 10-3. 0.01802. ho* = 0.206. ko*
+x
t
t0.083 10.258 10.500 tl.00 1.00 t2.00 2.00 t3.00 3.00 4.00 5.00 6.00 7.00 8.00 10.00 12.00 15.00 18.00 24.00
'
5
5
-a -
103
A 10-ko't
' A - 2 +;)
10-b*
X 103 (oalod.)
e =
6
0.0034.
x 10'
C
0.063 0.132 0.240 0.470 0.140 0.993 0.286 1.540 0.454 0.618 0.786 0.943 1.118 1.277 1.575 1.851 2.226 2.552 3.090
0.9964 0.9924 0,9862 0.9729 0.9725 0.9428 0.9438 0.9113 0.9105 0.8782 0.8449 0.8140 0.7793 0,7475 0.6891 0.6345 0,5604 0.4960 0.3897
1.0406 1.0328 1.0226 1.0014 1.0014 0,9607 0.9607 0.9222 0,9222 0.8847 0.8488 0.8141 0.7809 0.7490 0.6894 0,6349 0.5604 0.4948 0,3857
0,0440
0.0405 0.0363 0.0286 0.0286 0.0177 0.0177 0.0110 0.0110 0.0069 0.0043 0.0027 0.0017 0.0011 0.0004 0.0002 0,0000 0.0000 0.0000
0.059 0.134 0.238 0.473 0.138 0.990 0.288 1.542 0.450 0.619 0.787 0.954 1,117 1.276 1.574 1 ,847 2,225 2.557 3.109
+4 -2 $2 -3 +2 +3 -2 -2 +4 -1 -1 -11 $1 +1 +l $4 +1 -5 (- 191
6, = 3.6 X
TABLE 2 Bromination of acetoacetic ester in.0.060 M potassium bromide at IY.94"C. B = 0.0040. ko* = 0.01780. c = 5.056. In experiments marked t, c = 6.275X ho* = 0.216. t
0.053 0.080
1.oo
2.00
4.00 6.00 t8.00 10.00 t12.00 t14.00 16.00
