Analysis of Multicomponent Ester Mixtures by Dual Temperature Differential Kinetics T. I. Munnelly Dicision of Food Chemistry, Food and Drug Administration, Department of Health, Education, and Welfare, Washington, D. C. 20204 Analysis of ternary ester mixtures, ranging in content over the series of acetates from methyl to phenyl, was performed by the graphical extrapolation form of differential kinetics. For these mixtures, secondorder saponification was found to be more advantageously investigated at a temperature of either 15 or 30' C. In addition, four- and five-component solutions were analyzed by the incorporation of reaction rate measurements at both these temperatures. Through this procedure the individual reactions of compounds with appreciable difference in reactivity were separated into time periods of measurable length. Mathematical extrapolation of the res ective linear plots gives individual concentrations o r the order of 0.0010.002M.
IN SOME CASES, methods of analysis based on chemical kinetic principles present very favorable alternatives to separation procedures involving several steps. Consequently, the development of suitable reaction schemes and appropriate means for detection of reactions in progress have been of primary interest in this field. Yet the use of the temperature parameter to facilitate some aspects of kinetic determinations has been the subject of only a few investigations, and those not of general application. Many reactions involving binary mixtures are readily adaptable to determination at a single operating temperature. Instances in which reaction rates differ considerably in magnitude, or a number of compounds are to be analyzed, justify more than one temperature level for effective measurements. The present study, which involves the secondorder extrapolation approach, was initiated in an attempt to expand the limits of differential kinetic analysis by using temperature variation reactions. Kinetic methods for analysis of binary mixtures have been devised to treat a great number of systems. These have included such procedures as the single point method ( I ) , originally applied to ester mixtures; first-order reaction method of proportional equations ( 2 ) ; and various functional group analyses by graphical logarithmic extrapolation (3, 4 ) . Individual criteria dictate the advantages to be gained by selection of one technique over the others. In extreme situationse.g., the reaction of anthrone with fructose and glucose mixtures (5)-the reactivity difference between compounds is substantial enough so that by working at each of two quite different temperatures, individual compositions may be determined directly from measurements at the time each reaction is complete. For some mixtures, the use of temperature itself as the driving force to effect concentration changes as a function of time, such as in distillation of unresolvable compounds (6), has illustrated a significant role of temperature in kinetic quantitative determinations. (1) T. S. Lee and I. M. Kolthoff, Ann. N . Y. Acad. Sei., 53, 1093
(1951). (2) R. G. Garmon and C. N. Reilley, ANAL.CHEM., 34, 600 (1962). (3) 3 . G. Hanna and S. Siggia, ibid., 34, 547(1962). (4) S. Siggia, J . G. Hanna, and N. M. Serencha, ANAL.CHEM., 36, 227 (1964). (5) S. L. Bonting, Arch. Biochem. Biophys., 52,272 (1954). (6) S. Siggia, J. G. Hanna, and N. M. Serencha, ANAL.CHEM., 35, 365 (1963). 1494
ANALYTICAL CHEMISTRY
Attempts at analyzing ternary mixtures have proved successful in kinetic studies on alkyl bromides (7), alcohols (8), diazonium compounds (9), and sugars ( I O ) , and on the determination of only one constituent among two or more socalled spectator species ( 2 ) . In this latter study, contrary to the usual method of rate measurements over most of the entire reaction period, data collection is minimized by a proper choice of two reaction times equivalent to solution changes involving essentially the desired component. However, in more complicated systems the more general extrapolation procedure promoted by Siggia appears preferable; it eliminates the evaluation of exact rate constants, it too can be applied to mixtures of low rate constant ratios, and it is found to be effective for mixtures in which synergistic effects are present. Thus in an effort to extend differential reaction analysis into the area of four- and five-component solutions, the author investigated a dual temperature reaction sequence in conjunction with the extrapolation form of composition evaluation. Such an approach offers a potentially practical solution to analysis of complex mixtures in which the constituents vary both in number and in relative reactivities. THEORY
The dependence of reaction rate, expressed in terms of rate constant, k, upon temperature, T , is stated by the Arrhenius equation as Ink=
-E* RT
~
+ constant
where E* signifies the activation energy of the reaction. Now in a reaction medium containing two closely related compounds that undergo a similar type of reaction at different rates, a change in temperature affects the rate constant of component A by
and of B
(3) This presumes a constancy in activation energies, a usually valid assumption for simple reactions over a small temperature range. If the reaction rates of the constituents a t TI are related in the manner (7) R. T. Dillon, W. G. Young, and H. J. Lucas, J. Am. Chem. Soc., 52, 1953 (1930). (8) F. Willeboordse and F. E. Critchfield, ANAL.CHEM.,36, 2270 (1964). (9) S. Siggia, J . G. Hanna, and N. M. Serencha, ibid., 35, 575 (1963). (10) S. Siggia, J. G. Hanna, and N. M. Serencha, ibid., 36, 638 (1964).
kA = hkB
(4)
h being some number, then Equation 2 may be expressed as
Rearranging Equation 3 in terms of kBand substituting into the above: kal = XkBl e E ~ * A T / R T ~ T l e - E ~ * A T / R T I T l (6) which upon consolidation results in
(7) The variation of the rate constant ratio is therefore related to both the temperature change and the magnitude difference in activation energies of the constituents. In evaluating relative rate constant changes with temperature, consider the following example. If 11,300 cal/mole is taken as the activation energy required for reaction of component A , which is a reasonable value for ester hydrolysis (II), a two-component system with kA = 4kB would have an EB* of approximately 12,140 callmole. This value is based upon the assumption that the Arrhenius collis'on constants are similar; in many of those cases where they differ, the divergency is such that the actual value of EB* would deviate only slightly from the calculated value. Nevertheless, a 15 "C decrease in temperature, while slowing down the respective reactions considerably, would correspond to a rate ratio increase of about 7z (see Eq 7). In a multicomponent mixture, the relative tendency of each component to react would also be altered from that expected at a higher temperature. Such an effect, however, is of minor importance when considering differential analysis via the logarithmic extrapolation approach which requires no determination of k values but relies essentially on graphically exploiting rate differences. In fact, any effect which increases the respective rate ratios enhances this technique. Alternatively, a temperature increase resulting in a substantial decrease in the ratio at the initial temperature lessens the relative variance in slopes and may in turn diminish the accuracy of an analysis. With proper selectivity, the introduction of more than one temperature level to a reaction scheme does not interfere with the underlying basis of this analytical method. In relating the experimental data with the individual reactions undergone, the second-order expression describing the saponification of, for instance, a four-component mixture may be formulated as
+ +
where M O= AO BO CO4- D O = initial ester content, Ro is the initial concentration of base, and x refers to the decrease in concentration after a lapse of time t. While each constituent is reacting at the time of mixing of reactants, though to different degrees, various points are reached in the process where a component has reacted completely and the remaining compounds continue reacting. Now by separating the total reaction into limited schemes involving two temperature runs, each of the two experimental plots will show linear portions (11) A. A. Frost and R. G. Pearson, "Kinetics and Mechanism," Wiley, New York, 1961, p. 148.
t
I
I
IbO
I
300
+,MINUTES
Figure 1. Saponification of n-propyl, isopropyl, and tert-butyl acetate mixture
which are mainly associated with either the two fastest or two slowest reacting components. These lines may be directly correlated to Equation 8 for the case at Tl and
[Ro -
log [Mo -
(A0 (A0
++ Bo) Bo) --
iRo - ( A o
XI XI
f
-
ekd[Ro
-
(Ao
+ Bo) - Dol
DO
}
(9)
at T2where TI < T2 and kl > kp > kS > kq. These equations, in a much simpler form, are actually applied in the numerical determination of compositions. Thus within limitations on the extent and direction of the temperature spread, a binary temperature form of differential analysis presents a general approach for studying mixtures in which the various individual reactions may be conveniently partitioned into reasonable time periods. EXPERIMENTAL All chemicals were of reagent grade except for 2-hydroxyethyl acetate, which was purified by passage through an activated alumina column and then distillation. Saponification of the samples was monitored by removal of suitable aliquots; these aliquots were quenched by addition of a known excess of standard acid and titrated with standard sodium hydroxide, using phenolphthalein as indicator. Specifically, a solution of each component was prepared and aliquots of each were mixed together. For mixtures of four and five components, the resulting solution was then divided into two portions, one to be studied at each of the operating temperatures. When reactants were combined, the concentrations of the individual acetates were on the order of 0.0010.002M. For phenyl acetate, it was necessary to add alcohol in a preparative step for dissolution; therefore in mixtures containing phenyl acetate R 98p7, water-2z alcohol reaction medium was established. A solution of 0.02M NaOH was employed as the titrant. Temperature was controlled to 1 0 . 1 "C at both 15.0 and 30.0 "C by a Blue M Magic Whirl temperature bath with an VOL. 40, NO. 10, AUGUST 1968
0
1495
Table I. Threecomponent Ester Analysis a t 30 "C Acetate %A mixturea Found Present 20.0 A. Methyl 19.6 43.4 B. Isopropyl 44.1 C . tert-Butyl A. Ethyl 24.7 25.1 35.9 35.7 B. Isopropyl C . tert-Butyl A. rz-Propyl 26.3 27.8 B. Isopropyl 38.9 39.2 C . tert-Butyl A. Phenyl 39.5 40.1 B. Isopropyl 24.6 23.8 C . tert-Butyl A. 2-Hydroxyethyl 33.6 33.0 B. n-Butyl 24.0 22.3 C . tert-Butyl 4 Relative saponification rates are in the order A > B > C.
%B
%C
Found 40.3 22.3
Present 39.8 21.7
Found 40.1 33.6
Present 40.2 34.9
26.1 27.7
25.0 28.6
49.2 36.4
49.9 35.7
29.0 29.9
27.8 29.4
44.7 31.2
44.4 31.4
24.0 38.8
23.9 40.6
36.5 36.6
36.0 35.6
36.7 30.2
38.3 33.2
29.7 45.8
28.7 44.5
Table 11. Three-Component Ester Analysis a t 15 "C
A.
B. C. A.
B. C.
A. B. C.
A. B. C. A.
B. C.
%A Acetate Found Present mixtures Phenyl 22.3 23.2 2-Hydroxyethyl 42.7 42.1 Isopropyl Phenyl 32.7 33.4 2-Hydroxyethyl 23.7 25.0 n-Propyl Phenyl 22.8 23.1 2-Hydroxyethyl 36.7 37.4 Ethyl 2-Hydroxyethyl 22.5 24.1 Ethyl 35.2 35.7 Isopropyl Phenyl 40.7 41.7 Methyl 42.4 43.5 Isoamyl Relative saponification rates are in the order A > B
ZB Present 35.2 31 .O
Found 42.8 28.8
Present 41.6 26.9
35.0 48.7
33.5 48.4
32.3 27.6
33.1 26.6
35.2 36.4
33.3 36.3
42.0 26.9
43.6 26.3
27.4 26.3
26.4 27.2
50.1 38.5
49.5 37.1
20.3 33.7
21 .o 33.7
39.0 23.9
37.3 22.8
> C.
automatic dual microtol. The latter device made it possible to switch quickly from one temperature level to the other preselected setting. RESULTS AND DISCUSSION
Three-Component Solutions. Initial investigsltion of threecomponent mixtures showed a number of systems suitable for analysis by differential reaction kinetics-Le., possessing sufficiently different rate constants. Of the ten acetate mixtures studied here, each was examined either at 15 or 30 "C. When the experimental data were plotted, as illustrated in Figure 1 for a mixture comprised of n-propyl, isopropyl, and tert-butyl acetate, the overall curve obtained consisted of three straight lines of varied slope, corresponding t o the relative reactivity of each component. Upon graphical extrapolation of the intermediate line to zero time, the determined intercept, y , was equated to the total concentrations of ester, M o (evaluated by allowing the rate reaction to go to completion), and hydroxide, Ro,by (10)
1496
ANALYTICAL CHEMISTRY
%C
Found 34.9 28.5
Evaluation of x yielded the concentration of the fastest reacting component. Similar extrapolation and calculation involving the final line gave the additive composition of constituents A and B; on taking differences the amount of the intermediate and slowest reacting compounds present was determined. Tables I and I1 list the molar percentages of the various analyzed mixtures and the relative tendencies toward saponification. Selection of the temperature level to be used for each mixture was necessarily prescribed by the composition. The presence of the reactivity extremes for these esters, phenyl/ hydroxyethyl acetate on the one hand and isopropylltert-butyl acetate on the other, requires measuring temperatures of 15 and 30 "C, respectively, for effective analysis. One mixture containing both phenyl and tert-butyl acetate, encompassing a reactivity differential of almost one thousandfold, was analyzed at 30 "C. By working at this temperature, no data are collected on the individual reaction undergone by phenyl acetate; only the other two reactions are of measurable length, showing up in a two line plot. Of course, the initial linear portion is useful in judging slope differences and, in mixtures of unknown character, vital in
0.90
= p 0.70
&I& 0
s
0.50
I
IbO I
1
I00
I
I
t,MINUTES
300
+,MINUTES
Figure 2. Saponification of 2-hydroxyethyl, ethyl, isopropyl, and tert-butyl acetate mixture
deciding the appropriateness of differential analysis. However, as applied here, the quantitative aspect of the approach is dependent only upon the actual correlation of the latter reactions to composition. No accuracy of the determination is sacrificed as long as rate differences are known to exist. Four-Component Solutions. Introduction of another compound into a ternary mixture, such as 2-hydroxyethyl acetate
I
I
300
Figure 3. Saponification of phenyl, 2-hydroxyethyl, n-propyl, isopropyl, and tert-butyl acetate mixture
to a mixture of ethyl, isopropyl, and tert-butyl acetate, creates a system in which the range of reactivities has increased noticeably. This mixture could be analyzed completely at 15 "C but would require an extremely long time. By operating at two temperatures the reactions were separated into two stages. As shown in Figure 2, low temperature measurements yielded mainly the reaction sequence of 2-hydroxyethyl and ethyl acetate up to the relatively short time of 30 minutes, while at the higher temperature, saponifi-
Table 111. Four-Component Ester Analysis
Acetate %A %B mixturea Found Present Found A. Methyl 16.0 17.3 22.0 B. Isoamyl 27.6 29.7 26.7 C. Isopropyl D. tert-Butyl A. 2-Hydroxyethyl 29.2 30.7 32.2 B. Ethyl 16.0 17.6 18.3 C. Isopropyl D. tert-Butyl A. 2-Hydroxyethyl 29.9 30.8 21.8 B. n-Propyl 18.1 19.6 22.5 C. Isopropyl D. tert-Butyl A. Phenyl 37.8 39.7 20.6 B. Methyl 16.5 17.4 32.8 C . n-Amyl D. Isopropyl A. Phenyl 30.2 28.4 27.7 B. 2-Hydroxyethyl 15.8 14.3 29.8 C . Ethyl D. Isopropyl A. Phenyl 27.9 28.4 19.1 B. Ethyl 17.0 16.6 34.3 C . Isopropyl D. tert-Butyl = Relative saponification rates are in the order A > B > C > D.
%D
%C
Present 22.5 26.5
Found 27.6 24.7
Present 27.7 23.5
Found 34.4 21.0
Present 32.5 20.3
31.4 18.6
19.0 32.5
18.8 31.9
19.6 33.2
19.1 31.9
22.1 20.2
15.5 18.6
15.6 20.3
32.8 40.8
31.5 39.9
20.0 34.3
22.7 32.7
20.3 31 . O
18.9 18.0
20.0 17.3
28.6 28.6
28.0 25.1
28.5 28.7
14.1 29.3
14.5 28.4
18.2 32.6
17.3 21.4
17.9 22.9
35.7 27.3
35.5 27.9
VOL. 40, NO. 10, AUGUST 1968
1497
Acetate mixturea
%A Found
Present
A. Phenyl 15.1 14.2 B. 2-Hydroxyethyl 26.1 27.3 C. n-Propyl D. Isopropyl E. fert-Butyl A. Phenyl 19.0 18.5 B. Methyl 24.1 22.8 C. Isoamyl D. Isopropyl E. tert-Butyl A. Phenyl 21.6 20.0 B. 2-Hydroxyethyl 19.5 21.4 C. )?-Butyl D. Isopropyl E. fert-Butyl A. Phenyl 14.9 14.3 B. 2-Hydroxyethyl 27,2 25.8 C. Ethyl D. Isopropyl E. tert-Butyl Relative saponification rates are in the order A Q
Table IV. Five-Component Ester Analysis Z B ZC %D Found Present Found Present Found Present
Found
Present
12.4 13.9
14.3 15.0
23.0 16.9
21.5 15.1
20.1 14.7
21.4 15.3
29.4 28.4
28.6 27.3
24.6 16.1
26.1 15.0
13.8 15.3
15.5
16.7
17.9 21.8
16.9 24.3
24.7 22.7
23.0 21.2
17.1 15.3
20.0 14.3
21.8 31 .O
20.0 28.6
18.9 11.5
20.0 14.2
20.6 22.7
20.0 21.5
14.7 21.9
17.2 25.7
21.2 16.3
19.9 14.2
21.9 15.5
22.9 14.3
27.3 19.1
25.7 20.0
> B > C > D > E.
cation of isopropyl and tert-butyl is essentially taking place. Raising the higher temperature level may have advantageously shortened the overall time, but limitations were important in this type of reaction system because of volatility of compounds and concern over vessel calibrations. After the data were plotted to ascertain the respective linear portions, the points in each linear series were treated by a least squares method for determining intercepts in order to minimize any inherent errors in correlating data from two runs. As in the above, successive concentration values were determined and differences taken. In Table I11 the calculated and experimentally determined compositions are compared. Data for one of these mixtures indicate an average deviation (error) in concentrations of between 4 and 6%. Five-Component Solutions. Extension of the dual temperature method t o mixtures of five esters, again of sufficient reactivity difference, resulted in the successful separation of the extremely fast reacting constituents from the slow ones. As illustrated in Figure 3 for the acetates of phenyl, 2hydroxyethyl, n-propyl, isopropyl, and fert-butyl alcohol, measurements showed adequate reaction monitoring at 15 "C for three components and at 30 'C for the remaining two. The rapid rate of saponification occurring for phenyl acetate produced a minimal number of points, as low as two in some instances, and at very short time increments. Any linearity associated with this region is somewhat arbitrary and as a result it may be difficult to differentiate particular lines with respect to the major component reacting. Lowering the temperature to 5 or even 10 "C would have given more detailed information on this reaction section. But over a limited concentration range, as studied here, and from preliminary studies
1498
a
ANALYTICAL CHEMISTRY
ZE
on these mixtures, it was found that the individual reactions covered a time interval within certain limits. Besides setting the regularity of performing measurements, this facilitated the assignment of the various linear portions to composition. In this case, the advantage of shorter measuring times outweighed the merits of increased data collection. Table IV shows the results obtained for five-component mixtures, calculated in an analogous manner to four-component mixtures but with an additional numerical extrapolation carried out. Although the graphs show a total of six linear segments, only four (the more comprehensive) are actually applied to the composition determinations. OTHER APPLICATIONS
Applicability of this technique to analyze selected multicomponent mixtures of any functional group is evident from its general conditions. Even though ternary mixtures composed of two very fast reacting constituents and an extremely slow one were not studied here, analysis by this dual temperature approach would most likely prove to be an effective method. I n addition, this method offers a means for determination of one component among many through selective separation of rate periods in second-order reactions. ACKNOWLEDGMENT
The author thanks Professor W. J. Svirbely, Department of Chemistry, University of Maryland, for his constructive comments o n the original manuscript.
RECEIVED April 22, 1968. Accepted May 14, 1968.
