Spectrophotometric Estirnation of Ester HydroIysis R. S. Roy P. G . Chemistry Department, Sambalpur University, Burla, U.C.E., Orissa, India A NEW METHOD for studying the kinetics of hydrolysis of alkyl esters was recently developed (I). General equations were proposed for first and second order reactions ( I , 2 ) and consecutive reactions (3), and applied to the acid hydrolysis of methyl acetate and alkaline hydrolysis of ethyl acetate. Further considerations led to the idea of the suitability of the method for the kinetics and the equilibrium constant study of any chemical reaction, in general, in which both the product(s) and the reactant(s) absorb at the same wavelength. In chemical reactions there may result either an increase or a decrease in the number of entities in the system at equilibrium; in some reactions both the product(s) and the reactant(s) may absorb at one wavelength. The overall reaction may be studied spectrophotometrically by observing the total absorbance due to the entities in the reaction. The generalized theory for studying the kinetics and the equilibrium constant of a homogeneous chemical reaction is presented in this article. Theory. Generalizations are easily achieved from References J and 2 as follows, considering the general reaction represented by the equation, A+ B+
Equal Initial Concentrations. Let the initial concentration of each of the reactants (A, B, . . . ., K) be a, and if x be the concentration of each of the products (L, M, . . , ., Z) at a time t, then the amount of each of A, B, . . . , , K left unreacted would be (a - x ) . Assuming that all the entities in the reaction absorb at the same wavelength, absorbance A , is given by
A
= (a
- X)(ea
+
+ + + +. +
f ...
eb
- a(€,
[(el
+
Ern
+ f
eb
f ...
+ et)]/
. f e,)
- (ea
, ,
em
, ,
€2)
(1)
= (a
- X)E,
+ (b (k
f
eb
f ., ,
+
Ek)]
(2)
X)ED
+ ... +
- X)BR
+
X(EZ
+ ern + . . . +
e,>
(3)
Then, on rearranging Equation 3 x
=
[A [(El
+ kc,)]/ + - + +
-(UE+ ~ be0 + . . .
+ + ern
, ,
,
€2)
(Ea
Eb
,
..
+
Ek)1
(4)
At the equilibrium stage, the equilibrium constant of the general reaction K, is defined by (1) R. S. Roy, ANAL.CHEM., 40, 1724 (1968). (2) R. S. Roy and H. N. A. Jallo, ibid.,p 1725. ( 3 ) R. S. Roy, Tulantu, 16, 109 (1969). 2096
0.8
m 4
200
250
225 WAVELENGTH
mp
Figure 1. Spectra for tert-butyl acetate saponification at different time intervals
+
A . 0.02M ester. B. 2 ml 0.02M ester 1 ml0.03Malkali. (1) 70 sec; (2) 167 sec; (3) 667 sec; (4) 3367 sec; (5) 4325 sec; (6) 5854 sec; (7) 7218 sec
K
=
[(L)(W . . . (Z)I/[(A)(B) . . . (K)1
For the equal initial concentration of the reactants, we have K
=
[(xe)dxe)m .
,
(xe)zI/
- xe>a(a - X e h . .
(a
- xe)tl
(5)
and for different initial concentrations of the reactants it has the form K
Different Initial Concentrations. Let the initial concentrations of A, B, , . , , K be a, b, . . . , k , respectively, and x that of L, M, . . , , Z at time t ; then concentrations of A, B, . . . , K are (a - x ) , ( E - x ) , . . ., ( k - x ) , respectively. Assuming absorbance of all the entities at the same wavelength, A is given by
A
p v) 0
[(a
Rearrangement of Equation 1 shows [A
u e z
ek)
X(EZ
X =
Y
M + ....+ Z
+K+L+
, . . .
1.2
=
[(xe)dxe>rn . .
(xe)zI/
[(a
- xe)a(b - x e ) b .
'
(k
- x e > k l (6)
where ( x e ) ~ ( x & ( x ~represent ) ~ the concentration x at equilibrium of L, M, Z , respectively, and(a - x , ) ~(b , - x,)b, (c - X e ) c at equilibrium of A, B, K, respectively. General kinetic expressions can be derived by introducing values of x obtained through Equations 2 and 4 into the respective rate equations. The concentrations of both reactant(s) and product(s) at various times under non-equilibrium conditions could be obtained with Equations 2 and 4 or some of their modified equations, suitable for the evaluation of the kinetic parameters. This provides a simple method for determining the concentrations, and the course of the reaction is followed by measuring the absorbance at one wavelength, the absorbance being a simple function of the composition of the system. The novelty of this method lies in the fact that the kinetics of a reaction, both reversible and irreversible, can be studied without measuring at infinite time interval. Further, from the consideration of the general reaction at its equilibrium stage, the equilibrium constant can be evaluated through Equation 5 if the initial concentrations of the reactants are equal, or Equation 6 if the initial concentrations
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
Table I. Values of A and k at 30 "C for Allyl Acetate-Alkali Solution (A = 215.5 mp, 6, = 46.7, ea = 6.5, a = 0.015M, b = 0.015M) Time, sec 104 170 240 315 410 520 0.560 0.500 0.455 0,410 0.370 0.335 A k=t00.004 0.190 0.190 0.196 0.196 0.196 0.197 (1. mol-' sec- 1) Average k = 0.194 1. mol-' sec-l Table 11. Values of A and k at 55 "C for Ethyl p-Hydroxy Benzoate-Alkali (A = 297 mp, ea = 14200, e, = 4744, a = 0.000088M, b = 0.08M Time, sec 422 738 1197 1505 1895 1.150 1.135 1.170 1.195 A 1.215 0 0011 k i O.OOO1 0.0015 0.0013 0.0012 0.0012 (1. mol-' sec- l) Average k = 0.0013 1. mol-' sec-l
'0 WAVELENGTH
mp
Figure 2. Spectra for methyl acrylate saponification at different time intervals
are different, using concentrations obtained under equilibrium conditions.
A . 0.0003M ester. B. 1.5 ml 0.0003M ester 1.5 mi O.OO5M alkali. (1) 68
EXPERIMENTAL
sec; (2) 270 sec; (3) 465 sec; (4) 680 sec; (5) 945 sec; (6) 1168 sec; (7) 86400 sec
Analar grade sodium hydroxide and Analar grade acetic acid were used in this work. All esters were freshly prepared by the general procedure of esterification ( 4 ) . In the case of acetates, B.D.H. grade chemicals were purified before use and a large excess of acetic acid was used for the preparations. The esters used in this work had boiling and melting points in good agreement with literature values. Spectrophotometric measurements were made with a double beam Unicam SP 800 Ultraviolet Spectrophotometer fitted with a thermostat a t 200-350 mp with matched 1-cm cells. Solutions of esters and alkali, and reaction mixtures of ester and alkaline hydrolyzing agent were prepared and experiments carried out by the general procedure adopted by Roy et al. (2).
+
RESULTS AND DISCUSSION
The saturated aliphatic esters studied were n-butyl, isobutyl, sec-butyl, and tert-butyl acetates. The general feature of the spectra is almost the same as reported earlier except in the case of tert-butyl acetate, presented in Figure 1. The unsaturated esters studied were allyl acetate, methyl acrylate, methyl crotonate, methyl tiglate, and methyl dimethyl acrylate. Methyl acrylate hydrolysis was studied up t o infinite time interval and its spectra are presented in Figure 2. The general feature of spectra of the unsaturated esters is almost the same as that of methyl acrylate. The only aryl ester studied was ethyl para-hydroxy benzoate and is presented in Figure 3. The rate of saponification of each ester was measured in aqueous solution at 30 "C except in the case of sec- and tertbutyl acetate, and ethyl para-hydroxy benzoate when the temperatures were maintained a t 37 and 5 5 "C, respectively. The figures contain the spectra due to the ester solution and the ester-alkali solution in different ratios at different time intervals during hydrolysis. The maximum absorbance of the bands due to the acetate esters as well as the acetic acid shifts to (4) A. I. Vogel, "A Text Book of Quantitative Inorganic Analysis," 2nd ed., Longmans, Green, New York, N.Y., 1954; p 234; A. I. Vogel, J . Chenz. Soc., 1948, 624, 654, and 658.
m
325
WAVELENGTH
0
mp
Figure 3. Spectra for p-hydroxy benzoate saponification at different time intervals
+
B . 1 ml0.000265M ester 2 ml 0.12M alkali. (1) 422 sec; (2) 738 sec; (3) 1197 sec; (4) 1505 sec; (5) 1895 sec
the longer wavelength owing to the production of acetate ions in solution. However, in both cases the right wing of the bands remains partially unaffected. Values of E , and represent the correct observed extinction coefficients of the ester and sodium acetate, respectively. Although the alkali partially affects the absorption of the acetate esters and the acetic acid, the rate of reaction remaining unchanged, the correct observed extinction coefficients would yield a correct estimate of the rate constant. Observed values of E,, e,, and A at the absorbance where spectrophotometric analysis was carried out for allyl acetate and ethyl para-hydroxy benzoate are summarized in Tables I and 11, respectively, which also contain the values of k cal-
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
2097
Table 111. Spectral and Rate Constant Data for the Alkaline Hydrolysis of Saturated and Unsaturated Alkyl Esters and an Aryl Ester Time T Temp range, k f 0.004 "C Ester sec (1. mol-' sec-1) Ea E. a( M ) NM), X(m/.l) 0,020 n-Butyl acetate 30 0,010 40.3 5.2 215.0 788 0.080 30 Isobutyl acetate 0,010 0.020 5.2 215.0 38.7 384 0.061 0.005 37 0.0133 5.2 215.0 sec-Butyl acetate 42.3 825 0.073 37 0.0133 0,010 tert-Butyl acetate 51.5 9.3 216.0 7218 30 0.015 0.015 Allyl acetate 46.7 6.5 215.5 520 0.194 0.020 0.020 215.5 46.7 Allyl acetate 6.5 37 0.243 550 30 0.00015 0.0025 00 208.5 Methyl acrylate 5867 0.133 1813 30 9700 0.oooO75 0.015 210.5 Methyl crotonate 8100 1500 0.048 o.oooO91 Methyl tiglate 30 11430 0.018 220.0 2985 7866 0.038 Methyl dimethyl 0,0076 3 0 O.ooOo6 0.015 11708 8533 222.0 9975 acrylate Ethyl p-hydroxy 55 14200 4744 O.ooOo88 0.080 297.0 1895 benzoate (fO.oo01)
i
culated at different time intervals in the manner described previously (2). A plot of the ratio (a€, - A ) / @ - ma)us. t in each case gives straight line passing through the origin, and yields rate constants in agreement with the average value obtained in respective tables. Spectral and kinetic values thus obtained for all the esters studied are consolidated in Table 111. It can be seen from Figure 1 that the value of A unlike that in other acetate esters to begin with, increases with time passing through a maximum at about 670 sec followed by a steady decrease, and this may partly be due to its high reactivity and molecular structure. Kinetic study of allyl acetate hydrolysis does not seem to have been carried out earlier. This study presents the rate constant of 0.194 1. mol-] sec-' at 30 "C for the first time. The rate constant of 0.243 1. mol-' sec-I at 37°C obtained from this measurement for the 2 :1 ester-alkali solution is in reasonable agreement with k obtained at 30 "C, considering the temperature difference. The rate constant value obtained from this work of 0.133 1. mol-' sec-l at 30 "C for the methyl acrylate hydrolysis is in reasonable agreement with that reported earlier of 0.0779 1. mol-' sec-' at 25 "C, titrimetrically (5). The rate constant value obtained from this work for the methyl crotonate hydrolysis of 0.048 1. mol-' sec-l at 30 "C is in reasonable agreement with the reported value of 0.0245 1. mol-' sec-* at 25 "C (6). A review of the literature shows that the hydrolysis of ethyl p-hydroxy benzoate has not been studied. The isosbestic (5) E.Halonen, Act. Chem. Scand., 9, 1492 (1955). (6) Chem. Abstr., 30, 12888(1936).
2098
ANALYTICAL CHEMISTRY, VOL. 44,
point appears at 286 mp during hydrolysis. A comparison of the rate (7) constant of 0.0013 1. mol-' sec-' at 55 "C for this reaction with those of earlier investigations on similar reactions (8), Le., rate constant of 0.0010 1. mol-' sec-' for the phenyl benzoate and of 0.0023 1. mol-' sec-l for the phenyl methoxy benzoate at 59.2 "C, shows that the agreement is generally good. The equilibrium constant for the methyl acrylate hydrolysis was determined using Equation 6 with K = 0.028 + 0.001 at 30 "C. The absorbance value for this reaction at the wavelength of 208.5 as is shown in Figure 2 is 0.455 at infinite time interval. NOTEADDEDIN PROOF. This principle has been extended to study the reaction kinetics conductometrically (9). ACKNOWLEDGMENT
The experimental part of this work was carried out at the Chemistry Department, Science College, University of M o d , Iraq; grateful acknowledgment is made of the assistance rendered by H. N. A1 Jallo and I. Nazar in carrying out the experiments. RECEIVED for review January 6,1972. Accepted June 14,1972. (7) R. S. Roy, Proceedings Indian Science Congress, Bengalore Session, 1971. (8) B. Capon and B. C. Ghosh, J. Chem. Soc., 1966,473. (9)R. S.Roy and M. M. Misra, "Conferinte Nationale De Chimie Analitica, Romania, 1971,Part I, pp 279-286.
NO. 12, OCTOBER 1972
