I455
HYDROLYSIS O F TRIACETIN.
the oven. A metal loop on the front engages the handle C with which they are lifted while hot. ‘his equipment has been in use for several years in the writer’s laboratory and has proved its worth. In laboratories used by students its value is especially high because the rule, one tsay to a student, can be followed and one student in inserting or removing his material need not interfere x i t h the work of the others. Since the trays rest on the original shelves of the oven, it takes but a minute t o remove them all and again convert the oven interior into one large compartment. ialthough this equipment increases the amount of metal subject to corrosion it cannot be said to increase the danger of contamination beyond C. W. POULK. what any increased use of the oven would involve. OHXOSTATEUNIVERSITY, COLUMBUS, OHIO.
~ ~ o r ~ ~ c t ~ ofigures ~ . - - for ~ h the e ordinates of Fig. 5, in our article on ““%he Transference Numbers of Lithium Chloride, etc.” in the June 1920 JBIJRNAL, have been printed one division too high in each case; for D. A. MACINN~S, instance, the figure 0.270 should be 0.280. JAMES A. BEATTIE. [COXTRIBUTXON FROM THE CREMICAL INSTITUTE, SCIEXCE COLLEGE, TOHOKU IMPERIAL UNIVERSITY. 3
SUCCESSIVE STAGES OF THE HYDROLYSIS OF TRIACETIN. EY EIICHIYAMASAKI. Received March 22, 1920.
Introduction. The various acetins, or glycerin esters of acetic acid, some of them, however, being still unknown, are as follows : Triacetin CM2AC
1 i
CHAC CHzAc (A)
Diacetin CHAc
I I CHzAc
CHQH
CH20H
Monoacetin CH2OH’ CHzOH
CHAc
GHOH
I
I
CH~AC
I
I
CHA
I i CI-IIOH CHAc
(B) (C) (U) (E) If the ester A is hydrolyzed, the reaction will proceed successively by the fcllowing steps to glycerine, C8Ha(OH)8(G) 1
Esters (C) and (D) have one asymmetric carbon atom, respectively. Hence both
of them must have 3 modifications,i. e., the racemic and the optically active antipodes,
Evidently such a reaction is very complex and its chemical kinetics almost hopelessly involved. However, according to the investigation of A. de Hemptinel and R. I,dwenherz,2 the esters oi the same acid have one property in common, namely, the rate oi hydrolysis is independent 01 the nature of the alcoholic radicals : that is, esters of primary, secondary and tertiary alcohols have the same velocity constant h of hydrolysis when the acid is the same. If this holds true in the case of the esters of polyvalent alcohol such as glycerin, the kinetics of the triacetin hydrolysis i s simplified and can be ascertained by a suitable method.
Previous ~ ~ v e ~ t i ~ a t ~ o ~ ~ . Geite13 prepared triacetin (A), diacetin (€3) and monoacetin and studied their rates oE decomposition with various reagents. found that the hydrolysis of acetins with dil. hydrochloric acid takes place as follows. I Monoacetin (D) decomposes normally as a monomolecular reaction. 2 . The constants for diacetin, calculated as a reaction of the first order, do not show a sufficient concordance. 3. The velocity constants for triacetin increase steadily (results obtained a t 40’). Re expressed these results by the following differential equations a
whae e is the initial concentratioii of triacetin; z, y and x are, respectively, the amounts of tri,- di- and monoacetin decomposed a t the moment under consideration. e transformed these Equations I into h -
d?, I
e-z.
74-
z-y’
dz --7$1ax
e -z. Y-X’
9dx= n 2 -xy ---yx )
(2)
de Hemptine, Z. p h y d . Chem , 13,56r (1894)~
* Lawenherz, ibid., 15, 389 (r894). a
Geitel, J . prakt. Chem., 55, 417 (1897);57, 113 (1898).
4
He gave only the chemical formulas C&Ts(OH)(Ac)zand CaHa(0H)zAc. The
above constitutional formulas are given according to the Reilstein.
not important lor this investigation.
But the point is
7457
HYDROLYSIS OP TRIACETIN.
when n = ki/kz, n~= kJ&, and z as fo1lo.w~:~ x = e _.
-+
Iu. 1_1
(w -- I)I.( u
31=e---------
74--
--
I)
n-
=
Ict2e(++-
($4
kz/Ka; and he integrated Ecpations I)/%
- I ) (MI - Ict)
-
n,u1/ m x_______I_I_
($2.1-
i)(nl-Ict)e”n’
p-l ) / w u l / x
74
I
~2
I
(3)
$111
where u is the concentration of the triacetin at any moment. Then, assuming that the regularity observed by Hemptine and Lowenherz, that the decomposition constants of the esters of a single acid are independent of the nature of the alcoholic radicals, also holds good in the case of the esters of polyvalent alcohols, he put k l : k z : ks = 3 : 2 : I. (4) Introducing Relation 4 into Equations 3 and simplifying them by putting e = I , Z==T---U
+ +
y = x =
I E
1- 221.- 3(4i4>2 - 7.1 - 3.q; -t- 3 ( 4 4 ) 2
x y 8 = 3 - 3.q;. (5) Consequently, if the function u = f ( t ) were solved, x, y and 8 would be also obtained as known functions of t. So he gave the arbitrary value o .os to the constant k l , and calculated u from €%quations 3 and 4 between the limits u = x (= e) and u = o; that is, from the initial Concentration (= x) to the complete hydrolysis. From the value of u, he deduced the corresponding values of x , y and z hy means of Equation 5 and expressed u, x, y and z graphically to explain the course of the reaction. Unfortunately, he could not find tlie real value of the velocity constaBt AI. Consequently, he could not make use of his experimental results to explain quantitatively the actual co~irseof the reaction. Recently Treub2 made an interesting investigation of the successive kiydrolysis of trilaurin with sulfuric acid. He gave the following reaction scheme
(TI)
I
2
LOC. cit. ’Sxeub, J. clzim p h y , x6, 107 (1918);Proc. Akad. Sci. Amterdatn, aQ,343 (rgr7).
r458
EIICHI YAMASAICI.
where A is trilaurin and PI glycerin; B, C, and D are, respectively, dilaurin, and E, P and G monolaurin. When r, x and y are, respectively, the concentrations of tri-, di- and monolaurin, and s and x are the concentrations of glycerin and acetic acid, their relative concentrations, R,X ,Y,S and Z are, respectively,
where a is the initial concentration of trilaurin. He also assumed that each radical 01 the ester is decomposed at the same rate, and gave the following differential equations,
where k is the uniform vnlue that the decomposition constants of the various esteric radicals are assumed to have, according to de Hemptine and Lowenhen. Eqcations 7 he transformed to dr -- -____ d X - _____ dY elx --- b (8) 3r r----2x zx- y 3y 3(r 2% y)' After an ingenious mathematical treatment of the above equation, he found the relation _I
I
I__
s
=
+ +
ll_____l__
23;
that is, the relative concentration of glycerin is always equal to the cube of the relative concentration of lauric acid throughout the course of the reilctions, and this relation is quite independent of the progress of the reactions. Re sought to confirm the above relation by the direct determination of the concentration of the lauric acid and glycerin produced by the hydrolysis of trilawin. Contrary to expectations, he could not obtain sufficient confirmation.2 This can probably be attributed to the dimculty of a quantitative determination of glycerin. Besides, he did not determine nmnerically the value of the velocity constant k and evaluate r, x , y, a and s as known functions of the time dz/dt, the rate of the formation of the lauric acid is not directly given, as is the velocity of formation of the other comporients, in the original paper. But the above equation will be easily -mderstood iE we count the number of esteric radicals decomposed by the formation of x , y and s. 2 He found actually that the relative concentration of glycerin is smaller than the cube OF the concentration of its arid. Consequently, he assumed further that the velocity constants of the hydrolysis of the esters o€ primary and of secondaryalcohols have dijereni values and gave the following differential equation according to Scheme III (below), --drldt = (p 4- 2)kY; h l d t = Kr __ ( p r)kxl; d x z / d t = p k x s - 2 k x 1 : dyJ/dt L- kk3~1 Kxp --h y ~ ;dyrldt = 3kx1 p k y ~ ;dS/dt = aky: 4- pkyL, where k' i s thc
+
-
+.
HYDROLYSIS OF TRIACETIN.
1459
and of the initial Concentration of trilaurin. Consequently, the present problem, the hydrolysis of the polyvalent ester is not yet in a way of oettlement from the point oil view of chemical kinetics. The present writer has, however, evaluated the constant k of the reaction for triacetin numerically and has given the concentration of the components of the system under consideration as known functions of the time and of the initial concentration of triacetin. The results will be given in order. Theoretical Part. "%he successive hydrolysis of triacetin takes place according to the following equations. GHs(Ac)I CaHrj(OH)(Ac)* HAC, Cd%(Ac)2(0H) C ~ H ~ ( O H ) ~ ( A CHAC, ) CaHs(0H)s HAC. C3Hs(OH)z(AC) Consequently, each reaction must be separately carried out as one of the first order, having, respectively, the velocity constants kl,kz and k8. In the initial stage of the reaction (t = 0)acetic acid is formed only by
2
Fig.
1.
+ + +
Pig.
2.
~ e l ~ c iconstant tv of the ester of the secondary alcohol which is equal t o kp, i. e., h'/k = p.
I3y a skilful computation, he obtained the relation, S < P , t o explain his experimental aesults. But he did not definitely determine whether the constants k, and k' actually differ or riot in the polyvalent esters. Consequently the treatment must be said to %Emere assumption.
E I ICH1. YAMASAICI.
1460
the hydrolytic decomposition of triacetin. Hence, the velocity constaBlt kl can be accurately determined, if the exact value of the initial velocity of the formation of acetic acid (C,) is obtained. Then the relative initial velocity or the velocity constant k can bc determined graphically, bccause, if C, and C are the relative concentrations of acetic acid and triacrtin, respectively,
Such a graphical method is not adapted for obtaining a very exact value of the velocity constant kl, but the value of kl olAaiiaed by it k sufficiently accurate to verify the theory. Again returning to the data of Geitel's expcriments, I drew the diagram ( V ,Y, t ) instead of (c, 17, t ) , where I7 is the volume of barium hydroxide used t o neutralize the acetic acid. Prom the initial tangents, the following are obtainetl,
Cor triacetin, and
for diacetin, where a denotes the initial concentration of triacetin and a' that of diacetin. Taking the mean value of the constants kl and kz, respectively, from these two diagrams, we obtain kl L= 0.00638 and kz = 0.00423. Now kd is the velocity constant of the hydrolysis of monoacetin, whjcla is, of course, a monomolecular reaction. Hence, the constant k3 call be easily determined from the equation,
I take the mean value
oC two series of experiments given by Geitel a i d
obtain
kB =
0.002213.
I€ each alcoholic radical of acetin has an equal rate of hyd~olysisa? supposed, the following relation exists among them 1/3 kl = x/z kz = i / r k? = k. In agreement with this, the experimental values are found to be closely
equal k1/8 == 0.002127
mean'k = o.nozrga. ka/t
Q
002213
This confirms the assuniption made by Geitel and Treub that each alcoholic radical of the polyvalent esters has an equa! rate of hydrolysis irrespective of whether the radical be primary or secondary. Then the successive hydrolysis of triacetin given by Scheme I is simplified to MI + Mz + Ma + Mq. And the differential equations which express the progress of (he reaction are giveril as follows:
iw
where a is the initial concentration of triacetin, ami XI, xz anti x3 are, respectively, the concentration of MI, Mz and Ma decomposed a t any time 1. The above equations are integrated according to Rakowskil and C0 i s substituted for a! as usual: cMl= ~ , e - - ~ ' cMZ = 3c, (x -- eVkt)e--22ki C,, 3c0 (1 -- ,-kt)ze-+t cM4 = ~ ~ -(e--kt'B 1I (1 1) As the concentration of acetic acid C A ,formed by the reaction i s expressed as follows, @A = CMz I- Gfl 3. 3cm it becomes C A = 3C, (I - rP) (12) from lfjquation I I . When CM4and C A are compared the following relation is easily found,
Now both terms of Equation xg express the relative concentrations of acetic acid and glycerin which were denoted as Z and S, respectively, by Treub. That is, S = Z3, which i s the relation deduced by him. Experimental Part. Un€ortianately, the number of experimental results given by Geitel are few. In addition to this, the degree oi hydrolysis ol triacetin at. 25' only amounts to 10%. Therefore, I prepared triacetin according to his method and undertook the hydrolysis with N hydrochloric acid at 35O. As a result, I obtained sufficient confirmation cE the theory above enunciated. 1 Rakowski, Z.physik. Cltenz., 57, 3 2 1 (1907).
2462
EIICHI YAMASAKI.
Mode of Experiment.-Triacetin was dissolved to make a 0.25 N solution. 5 , IO, 15 and 2 0 cc. of the solution were made up to 2 0 cc. in a, thermostat a t 35 O and mixed with IO cc. of 3 AT hydrochloric acid of the same temperature. Two cc. of the solution was drawn off with a pipet from time to time and titrated with a 0,05 N solution of barium hydroxide. The concentration of hydrochloric acid was determined by the volume of barium hydroxide solution used for the titration immediately after the reacting mixture had been prepared as above. The initial concentration of the ester was determined from the concentration of the acetic acid obtained a t t = *, i. e., ( C A / J ) ~ -=~ C,. In order to determine the concentration of acetic acid, (CA),= at the end of the reaction, 5 cc. of the same hydrochloric acid was mixed with the same volume of ester solution in a sealed tube. The solution in the tube was heated in a water bath for a long while until the titrations of the solution became constant, independent of the time of heating. The concentration of acetic acid (C,), m, corresponding to the former series of experiments, was determined by calculation from that of the latter experiment. xplanation of the Experimental Results.--The concentrations of acetic acid C A obtained from the reacting mixtures-namely, 4 different initial concentrations of esters-were divided by the corresponding coneentrations of the acetic acid a t infinite time. The series of relative concen-
Fig. 5 .
trations of acetic acid QZ),a r t e expressed by the ordinates of Fig. 3 and the corresponding times (in minutes) by the abscissas. As the concentration of the hydrochloric acid is constant and equal to 0.961,the respective curves must coincide with one another in spite of the fact that thc initial concentrations of the ester C, differ, because
=
CA
(I
- g-kl)
(14)
3co from Equation 12, and the right side of the above equation is quite independent of the value of C,. e results obtained in the 4 different series of experiments do indeed coincide sufficiently well to verify our expectations. The tangent line drawn a t the starting point of the axes of the coijrdinates gives
Consequently, k or 0,4343 k = k’ = 0.00373 is determined graphically. Z, given in Fig. 3, is calculated back with this k‘ by Equation 14, and compared with the observed results to show their sufficient agreement. Tables of Experimental Data.-The experimental data are summed up in the following tables, in which t is the interval of time in minutes; Z, the relative concentration of acetic acid; C A(obs.), the concentration of acetic acid; CA(calc.),that calculated from Equation 1 2 ; and C,, CM,, and CMsare the concentrations of tri-, di-, and monoacetins at any time and CM4,the concentration of glycerin. The experimental conditions, with the exception of those for the initial concentration of triacetin, were exactly the same for all 4 series of results. That is, CwcI, the concentration of hydrochloric acid, was 0.961 IV and the temperature of the observation, 35O“ C, = 0.0442. d.
2.
CA(obs.).
CA(ca1c.).
CMP
x0.00
0.104
0.0138 0.0268 0.0440 0.0680 0.0833 0.. 1061
0.0108 0.0256 0.0424 0.0637 0.0842 0.1036
0.0342 0.0231
25.18 47.00 76.37 116.94 177.17
0.202
0.332 0.513 0.629 0.800
0.0132
0.0062 0.0022 0.000.5
CMp.
CMr
0.oogz o.ooo8 0.0167 o.oo$o 0.0196 0.0098 O.OI72 0.0159 0.0113 0.0195 0.0049 0.0177
0.0000
0.0003 0,0016 0.0049 0.0113 0.0211
TABLE 11.
C = 0.0883. t.
6.67 15.50
33.00 58.67 88.22 IK7.52 157.45 213.37 283.62
2.
CA(obs.).
cA(calc.).
CMI.
CMP
0.058 0.135 0.246 0.386 0.513 0.620 0.730 0.809 0.867
0.0154 0.0357
0.0152
0.0744 0.0593 0.0377 0.0195 0.0091 0.0043
0.0132 0.0254 0.0371 0.0383 0.0309
0.0652
o
I
1024.
0 , I359
0.1642 0.1934 0.2143 0.2300
0.0332 0.0654 0.1050 0.1405 0.1680 0.1960 0.2227 0.2415
0.0015
0.0004 0.0001
CMS 0.0009 0.0036 0.0122
0.0251
0,0350 0.0389 0.0131 0.0376 0.0057 0.0299 0.0019 0.0193 0.0224.
CM4. 0.0GQO 0.0002
0.0013 0,0055 0,0132 0.0226
0.0359 0.0524 0.0670
ELICHI YAMASAKI.
C A cobs.) ,
CMr
CMp.
0.0234 0 ,0464
0.0153 0.0322 0.0479 0.0587 0 .o563
0.0007 0.0036
0.0720
Cm. 0.0000
0.000I
0.0105
0.000s
o 0038 0.0097
0.2189 o .2681
O.0453
0.0262 0.0404 0.0534
0 I032 I
0.0588
~ G(IO-- ,-In 3/21e-2 I n 3 / 2 -- 4/9 c o and (CMJ = 3Co(r -. @ - y 2 @ + 3 =4/9 I
c,
e., (Gd = (&fa) = 4/9 co. (17) That is, the maximum concentrations of M2 and M3are equal in numerical value, but the corresponding times, of course, differ.2 The relations above entmciated are satisfied in the diagrams. Further, the curve if C,,, has one inflection point at t'i = I / k In 9/4 (18) 1.
1 e-2kt = o when f = 03 the same foi e-kt = o ; and I -- e-k1 = when t = o The times have no relation to the maximum values of CBI~and CM~. Such results are due 2 Such a simple relation does not hold, of course, generally. to the fact that the 3 constants have a simple ratio, k , kz : ks = 3 z : I. ~
where
And the curve of CmMs has two inflexion points at tPzand tI3, respectively, t'z = I / k 1~ a, and t13 = a/k lut p, where
in which times,
NOW,t t l , is greater that t t , and tr3 greater than tz, but t'z isless than The last time, t'z, suggests that the nature of the increase of CMeand CaIvra is quite different lip to their maximum concentrations. That is, dCm,/dt always decreases from t = o to t = tf1, and the curve Cm2is always concave to the t-axis till t = PI. But dCMl,/dtincreases at first till it reaches t ' ~ ,then it begins to decrease steadily to the second inflection point l'g. The curve CM3is convex to the axis t in the initial stage up to t ' ~ then , it becomes concave to the same axis till t increases up to 8'3. Now, when we investigate the curve Cnl, dCM,fdt = gkCO( I - e-k')>ze-kt kc,,. The curve C, has no maximum, but has one inflexion point a t the lime when the curve CMohas them aximum concentration, i. e., t S -- I / k 1% 3. Lastly consider the curve C,, dCA/dt sCoe-K' =-=k(3C0 - - A ) . Rut the value 3 6 , is the concentration of acetic acid a t t = 0 0 . Consequently dC,/dt = k(CAcO- CA). (19) That is, the curve must be a logarithmic one which has neither a maximum nor an inflexion point. Furthermore, the rate dCA/dt is the same as that of the chemical reaction, A1 = 3AB where GA corresponds to the concentration oi Ai.
Conclusion. The hydrolysis of the ester formed by a polyvalent alcohol and a monobasic acid, such as triacetin, takes place according to the simple rule that each ester radical has an equal rate of hydrolysis. Consequently, theis rates are simply expressed in the same way as those of the successive reactions MI -+ Mz -+ MB-+ Mq, which have, respectively, the velocity constants gk, 2 k and k, though the actual reactions would be carried out according to the following scheme,
ElYDRULYSTS 3F TRIACETIN.
Conseq.uent1.yan explanation in detail of the results of experiment would give a clear idea of the course of the successive chemical reactions.
A ~ ~ ~ ~ ~ For the sake of comparison, the results obtained a t 40' by Geitel flor triacetin are calculated by the same method and are given in Table V. I.
TABLBV. ,
