S P E E D O F ESTERIFICATION, AS COMPARED
WITH THEORY BY ROBT. B. WARDER
Z. Intvoduction
*
T h e following paper is based upon the theory of mass action, as applied to I,ichty's' experiments on the speed of esterification. Equivalent weights of ethyl alcohol and the several chlor-substituted acetic acids were made to react for definite intervals at 8oOC. T h e alcohol, having been sealed in its own bulb, was placed in a tube containing the acid with a piece of glass rod, and the tube was then sealed. After heating in a glycerine bath to the required temperature, the bulb was broken by a blow from the rod. After a carefully timed interval, the reaction was stopped by immet'sing the tubes in water of about 15"C., and the free acid remaining was determined by ammonia, with rosolic acid. T h e work seems to be very well planned and successfully executed. From two to nine determinations were made for liiost of the intervals chosen, and the resulting means agree closely with smooth curves. Numerical result$ are given in the tables which follow, showing variations in the calculated coefficientsof speed. T h e course of the reaction is compared with that which would be expected for a reversible action, unmodified by secondary influences ; and some hints are added regarding the secondary influence, which may necessitate an extension of present theories.
11. Mathematical Epzcations aiid Methods I. Fundamentalformzilas foy mass action.-Since we are dealing with a bimolecular reversible reaction, and equivalent weights of the active bodies, we must assume
dx dt -k (a--x)'--K'x';
--
61)
'Am. Chem. Jour. 18, 590 (1896) ; Abstract i n this JOURNAL I , 67* (1896).
Robt. B. Warder
1.50
Where
a=the quantitly of active substance taken ; x = t h e quantity that undergoes change in the time, t ; k= the coefficient of speed for the direct action ; Y=the'coefficient of speed for the reverse action ; and dx dt ---the actual speed 'at any moment.
For convenience let Y be expressed as 6'k, and let X=ay. Then dx=ady, and
{
I-
*=ak (r-y)"-b'y' . dt Let y, express the limiting value of y,when the reverse reaction (between ether and water) exactly balances the direct one dx between alcohol and acid. When this condition is reached, dt=o ; hence,
)'-by,
( I - J ~ ~
6=- 1-Y
'=o, to-
I
and y, =3'w r+b Equation ( 2 ) may also take the forms
(3)
and or, making
c=---
r I'm r--6 - 2~1, -r,
Eq. (4) is useful, when b is assumed to be a very simple number or fraction, so that 3~may be readily multiplied by its coefficients without the use of logarithms. Otherwise, eq. (6) is preferable. 2. Integration.--To integrate eq. (4), write dY
{r-(1+6)y}
(I+6)dY {r-(~xm=s { 1-(1-6)y r-(r-6)y
whence, by integration from zero,
=aAdt
Speed of Ester$cation
151
.or, writing m for the modulus of common logarithms, 1
-( I -
I- (I
b )y
+b)y =zabkmt.
Also, between limits denoted by subscripts
(7) I
and
2,
If b is not a simple number or fraction, it is more convenient to integrate eq. (6) or to reduce (7) and (S), obtaining the following : C Y
3’co -Y,
(zyw-I)
CY>
} =zabkmt, =zabkm(t,-t,)
and
(9) (10)
3. Mode of using these equations.-In the last four equations, the product zabkm has been assumed to be constant, and may be computed by dividing each time interval into the corresponding logarithm. If the series of resulting quotients proves to be nearly constant, the theory is confirmed, and k (the actual coefficient of speed in any convenient system of units) is found by substituting the proper value of zabm.’ But if the series shows a marked increase or decrease, it is fair to conclude that the fundamental hypothesis is untrue, that we are not dealing simply with a bimolecular reversible reaction between equivalent masses, or (possibly) that we have assunied a false value for yco and, therefore, for the related constant b or c. I n similar investigations, it has been usual to take the entire integral from zero, or from the first determination thereafter. Values for aabkm thus computed (multiplied for convenience by IOOOO) will be found in the tables, in the third column under each acid. When k proves to be a variable, it is better to use the integral between narrow limits, as the successive observations. A series of numbers is thus obtained, expressing mean values of the coefficient of speed ’We may best express the value of a in gram-equivalents per liter, dividing the weight of one liter by the sum of the molecular weights. For this purpose it would be desirable to know the specific gravity of the various mixtures at the temperature of the experiment.
152
Robf. B. Wader
for short portions of the curve, and affording some insight into the nature of the perturbations with which we have to deal. See t h e fourth column under each acid, in the tables, where fluctuations in value are much more marked than in the third column. It is obvious that in many published investigations on the speed of chemical action (as with other dependent variables) where the fundamental equations receive a general confirmation by integration of a whole, it may be possible to detect many perturbations (and thus to modify or amplify the fundamental equations) by integrating between narrow limits, and studying such systematic Variations as may then appear. I n case of frequent observations, the inevitable errors may , accumulate so as to affect unduly the numbers derived from short intervals, accidental errors may obscure the perturbations ; more regular results are then obtained by integrating for longer intervals, as from zero to the second observed point, from the first to the third, the second to the fourth, and so on. T h e table shows values thus obtained for trichloracetic acid. Finally, if calculated values for k prove to be nearly constant for some portion of the curve, a mean for that portion may be obtained by selecting still wider limits, as illustrated in the tables.
1Zl. Tables of Narmerical Deductions Lichty’s mean results are repeated, for each acid, in the first two columns. Numbers proportional to the coefficient of speed, as obtained by integration from zero to each determination, are given in the third column ; this being the usual method of testing such experiments. There is a marked diminution in the series ; yet, since each number is (in a sense) a mean for the whole period from the beginning of the reaction, there is no clear indication of the changes. This is gained, however, by integrating between the limits of successive determinations, with results recorded in the fourth column, or those deduced for double intervals, as in the fifth column under trichloratic acid. These numbers are all calculated on the assumption of the limits assigned by Lichty himself; 68.65%, 7 1 . 2 2 % and 74% for these three acids respectively. They show the same general features for each acid ; a sfeady decrease in fhe ear&
Speed of Esterz;fication
I53
stages is followed by a moderate incrense, then by a rapid fall. T h e minimum is most remarkable during the fifth minute for trichloracetic acid, as indicated by four pairs of determinations, published in Lichty’s paper. T h e infinite value at the end of the series is a necessary result of the assumption that the result actually reached in experiment is the “limit” for indefinite time of action. T h e slight increase among the last few numbers conld be made to disappear, by assuming a higher value for the limit. .
-
~
p
~
MOKOCHLORACETIC ACID
DICHLORACETIC ACID
Assumed limit, 68.65 per cent.
limit, 71.22 per cent.
_~
Lichty’s determinations
I
3 5 IO
I5 20
I
~
120
870
0.0178 1 ,0509 I .0765 i .1338 1 .I815 i ,2223 1 -2.591 a2863 -3596 .4189 I a5733 ,6139 .6265 ! .6713 .6745
1
25 30 45 60 I80
1
1
~
Lichty Is determinations
rnbkmXzo ooo
72
71 66 61 59 57 56 54 51 50 52 44 29 24
1
I
I
1
18
72
54 52 52 42 44 46 54 30 7 I9 3
1
~
9420
.6865
1
co
I5
-3.553
40
.SI79
IO1
64 51
32 15
300 600
1
I200
I
1
28 17
5 5
4 4 4
0
4 3
,7122
1By integration between the limits for mean i s 51. 2By integration between limits for is 133.
.6495 I .6684 .6773 -6843 I .6829 1 a7042 .7095
1500 3000 4500 6000
0
7 1
2abkmX roooo
I
IO
and
and 20
120
minutes, the computed
minutes, the computed mean
Robt. B. Warder
‘54
TRICHLORACETIC ACID
Assumed limit, 74 per cent.
Lichtp’,s determinations
t,
minutes
-,,,,I I 2
3 4 5
7 9
1
1
I3 I5 I7 23 26
I
30
1
35 40 50 60 70
80
,
I I 1 1
1
90 100 I IO
I
I20
130 I 60 190 240 360 600
1540 .1S92 .2260 e2324 . 2 804
I
*3230’ * 3645 .3970 4903 .5046 ,5183 ,5302 e5438 .555I .5736 .5939 .6108 .6230 .6355 a6433 .6544 .6618 *
.6846 ~
1
For single 1 For double From intervals, by1 intervals. bv 1 by eq. (9) eq. ( 1 0 ) 1
-
*
I1
20
’
1
znbk iiz X roooo
.7008
-7223
-
339 278 238 223 185 171 163 161 I57 I57 156 I53 141 I33 I21 I11 I02
339
~
I
217
I57 I81 33 I34 I37 152 136 1.50 1.56 129 65
i I
68
’
89 SI
77 72 69 65 63 61 59 51 45 36 28 22
=BYintegration between the limits for z and mean is 140.
47 44 42 37 38 54 37 43 30 47 36 38 I3 16 3 I2
14
20
278l 187 169 107 IO1
136 I44 I44 I40 158 140 97 66 50 47 44 39 38 40 41 40 37 39 42 37 I9 I4 8 9 I3 minutes, the computed
Speed o f Esterz3cation
ZV. Possible Causes
155
of the Va~iations
The following are among the various conditions which may be considered, in searching for disturbing influences :I. Is there some secondary chemical reaction ? For example, does the water fornied react upon the acid, generating HC1 ? Some attention has already been given, by the experimentors, to such contingencies. 2. With formation of ether, does the liquid separate into nonmiscible layers? If the changing composition of such layers were determined, it would still be possible to construct a forniula for the speed of action in each portion. 3. Does electrolytic dissociation affect the speed ?‘ We may have one coefficient for the ions, and another for entire molecules, tbe observed speed resulting from both. 4. Does the reaction proceed to any considerable extent, after placing the tubes i n cold water, owing to slowness in the cooling process ? Such error in time nieasurenients would chiefly affect the shorter periods ; yet a constant error of this kind would be eliniinated by using eq. (8) or ( I O ) , and omitting the first minute. Further experiments are needed to determine the true cause.. Among other phases of the investigation, parallel determinations may be made, under the same conditions of time and temperature, to compare the action of alcohol and acid with that of ether and water. This would at least afford valuable testimony in regard to the ratio, k:K’, and therefore of b, yco and c. I n many cases this work may be more trustworthy as well as more expeditious than the prolonged action required for direct determination of the limit.
V. Comparison of the T/ljeee Acids T h e secondary iiifluence must be more fully explained, before the actual constants can be determined, in order to trace the effect of successive atoms of chlorin in acetic acid. IPerhaps this hypothesis is the most probable. See Goldschmidt’s discussion of “auto-catalysis”, and Donnan’s comment, in Ber. chem. Ges. Berlin, 29, 2208-2216, 2422-2423,which have appeared since this paper was written.
156
Robt. B. Warder
As I,ichty points out, however, the percentages of mono- di- and trichloracetic acids esterified at 80' C. in one minute are the following : 1.78 : 4.56 : 9.99=r : 2.56 : 5.61. If we were justified in applying an extrapolation formula to find the percentage speeds at the very beginning, the first two determinations would yield the following : 1.82 : 4.95 : 12.28=1 : 2.7 : 6.7.
If we compute zooooabknz from the first minute's change in each case, we find the values : 72 : 167 : 3 9 ' 1
: 2.3 : 4.7.
But if we select the middle portion of each curve, where R seems to vary comparatively little, the values of 20000abkm are
51 : 133 : rpo=r : 2.6 : 2.7. Hence, dichloracetic acid reacts about two and one-half times a s rapidly as monochloracetic ; but it is still uncertain what part of the higher curve should be taken as a suitable basis of comparison with the lower ones. I n conclusion, I wish to thank Mr. D. M. Lichty for the opportunity to discuss his interesting experimental results, and for friendly correspondence in regard to them. Howard University, Washiiigtoiz, D.C. September, 1896
