MEASUREMENT OF REACTION RATEBY COMPETITIVE REMOVAL OF REACTANT
of the results obtained, however, a definitive value for the AF, for this reaction can be considered established
977
from which tentative values for the AH* and So of BeOH(g) can be obtained.
Measurement of Reaction Rate by Competitive Removal of Reactant
by George B. Smith and George V. Downing, Jr. Merck Sharp & Dohme Research Laboratories, DCiswn o j Merck & Co., Inc., Rahway, New Jersey (Receined M a y 17, 1966)
Measurement of reaction rate ordinarily involves either quantitative chemical analysis or measurement of some physical property during reaction. A method has been devised in which the quantitative measurement is measurement of time. The technique is useful in measurement of rates of reactions with half-lives of about 1 min. Rate constants can be evaluated if the kinetic behavior of the system is known. The method has been illustrated by the reactions of thiosulfate with methyl chloroacetate, methyl bromoacetate, and methyl iodoacetate.
Introduction Classical methods of determining the rates of reaction involve removing samples at definite times and analyzing them for one or more of the reactants and products. Variations of this technique in which some property such as conductance, optical rotation, or absorbance is monitored continuously have greatly facilitated the determination of kinetic data. However, in general, these have been applied to relatively slow reactions, often by diluting the reactants. Special techniques must be used when the time required to sample or make a measurement is a significant part of the total reaction time. In the case of very fast reactions, elegant techniques have been developed. The intermediate case, in which the half-life of the reaction is on the order of a few minutes, is a difficult one because sampling or measurement time is a significant part of the total, and the very fast techniques are not easily applied. The method described here is related to the “clock” reactions‘ in which the rate constant is calculated from the time required for the generation of an amount of product equal to a known amount of a second reagent which reacts very rapidly with the product. I n the
method used in this work, competition is established for one of the reactants according to the scheme
A
+ B --% C (reaction under study) R(t) + A -+ products fast
R is generated electrochemically and reacts with A as fast as it is generated. The net result is that A is removed by two reactions, and the time required to remove all of A is a measure of the rate of the reaction under study. The time at which all of A is removed is determined by detecting the presence of R. To illustrate the method the reaction of thiosulfate with methyl bromoacetate, which has previously
+ S20a2-+
CH2BrCOOCH3
+ Br-
CH2(S2O3)COOCH3-
been investigated by La Mer and Kamner,2was chosen. They analyzed aliquots of the reaction by adding excess iodine and back-titrating with thiosulfate. In the (1) G. S. Forbes, H. W. Estill, and 0. J. Walker, J. A m . Chem. Soc., 44, 97 (1922). (2) V. K. La Mer and M. E. Kamner, ibid., 53, 2832 (1931).
Volume 70,Number 4 April 1966
GEORGE B. SMITHAND GEORGEV. DOWNING, JR.
978
Table I: Data for 7/7B
=
T/T=
(l/C) In (C
c
+ 1).
Firsborder Reaction: C =
~TB.
7/7B
C
7/7B
Pseudo-Firsborder Reaction: C = ~ B T B
c
7/7B
c
0.01 0.02 0.03 0.04 0.05
600 290 170 120 90
0.26 0.27 0.28 0.29 0.30
8.7 8.2 7.8 7.3 6.9
0.51 0.52 0.53 0.54 0.55
2.4 2.3 2.2 2.1 2.0
0.76 0.77 0.78 0.79 0.80
0.69 0.65 0.61 0.58 0.54
0.06 0.07 0.08 0.09 0.10
71 58 49 42 36
0.31 0.32 0.33 0.34 0.35
6.5 6.1 5.8 5.5 5.2
0.56 0.57 0.58 0.59 0.60
1.90 1.81 1.73 1.66 1.58
0.81 0.82 0.83 0.84 0.85
0.50 0.47 0.44 0.40 0.37
0.11 0.12 0.13 0.14 0.15
32 28 25 23 21
0.36 0.37 0.38 0.39 0.40
5.0 4.7 4.5 4.3 4.1
0.61 0.62 0.63 0.64 0.65
1.51 1.44 1.38 1.31 1.25
0.86 0.87 0.88 0.89 0.90
0.34 0.31 0.28 0.26 0.23
0.16 0.17 0.18 0.19 0.20
18.6 17.0 15.6 14.4 13.3
0.41 0.42 0.43 0.44 0.45
3.9 3.7 3.5 3.3 3.2
0.66 0.67 0.68 0.69
0.70
1.19 1.13 1.07 1.02 0.96
0.91 0.92 0.93 0.94 0.95
0.21 0.18 0.16 0.13 0.11
0.21 0.22 0.23 0.24 0.25
12.3 11.4 10.7 10.0 9.3
0.46 0.47 0.48 0.49 0.50
3.0 2.9 2.8 2.7 2.5
0.71 0.72 0.73 0.74 0.75
0.91 0.86 0.82 0.78 0.73
0.96 0.97 0.98 0.99 1.00
0.09 0.06 0.04 0.02 0.00
present work the same reaction was carried out in the titration cell of a coulometer. The reaction was initiated by addition of thiosulfate to a solution of the ester. At the same time addition of iodine generated at constant current was started. Thiosulfate was depleted by reaction with ester and reaction with iodine simultaneously. Rate of reaction of thiosulfate with iodine was constant and equal to the rate at which iodine was generated because the thiosulfate reaction with iodine is very rapid. The end point was observed with the appearance of free iodine (disappearance of thiosulfate), and the time at which the end point occurred was a measure of the thiosulfate-ester reaction rate. Second-order rate constants for reactions of thiosulfate with methyl chloroacetate, methyl bromoacetate, and methyl iodoacetate were measured.
responding species, and IC is the second-order rate constant. For the pseudo-first-order case with B present in large excess, the integrated form of eq 1 is easily obtained.
where A . is the initial concentration of A. The time required for A to disappear is T = - 1l n ( FkAoB +1) JGB
K = -Ao
-dA dt
= ICAB
+K
where A and B represent concentrations of the corThe Journal of Physical Chemdstyl
(3)
The rate K can be expressed as the quotient of A. and the blank time TB, which is the time required for A to disappear when B is absent.
Theory Suppose that during the second-order reaction of A and B a further constant rate of disappearance K is imposed on A. Then
T
TB
(4)
From eq 3 and 4 -
1
(5)
where C = ICBTB. The rate constant can thus be calculated from the experimental quantities B, TB, and
MEASUREMENT OF REACTION RATEBY COMPETITIVE REMOVAL OF REACTANT
979
Amounts Table 11: Data for Second-Order Reaction Where f = ~ A O T BEquivalent : +/TB
f
7/78
20, 4,000 2,000 1,000 640
ooo
0.26 0.27 0.28 0.29 0.30
19.4 17.9 16.4 15.0 13.8
0.51 0.52 0.53 0.54 0.55
0.06 0.07 0.08 0.09 0.10
440 330 250 190
154
0.31 0.32 0.33 0.34 0.35
12.8 11.9 11.0 10.2 9.6
0.11 0.12 0.13 0.14 0.15
126 105 89 76 66
0.36 0.37 0.38 0.39 0.40
0.16 0.17 0.18 0.19 0.20
57 50 44 39 35
0.21 0.22 0.23 0.24 0.25
32 29 26 23 21
7/7E
I
0.01 0.02 0.03 0.04 0.05
T/TB
f
3.5 3.3 3.1 2.9 2.8
0.76 0.77 0.78 0.79 0.80
0.79 0.74 0.70 0.65 0.60
0.56 0.57 0.58 0.59 0.60
2.6 2.5 2.3 2.2 2.1
0.81 0.82 0.83 0.84 0.85
0.56 0.52 0.48 0.44 0.40
9.0 8.4 7.8 7.3 6.8
0.61 0.62 0.63 0.64 0.65
1.97 1.86 1.76 1.66 1.57
0.86 0.87 0.88 0.89 0.90
0.37 0.34 0.31 0.28 0.24
0.41 0.42 0.43 0.44 0.45
6.4 6.0 5.6 5.3 5.0
0.66 0.67 0.68 0.69 0.70
1.48 1.39 1.31 1.23 1.16
0.91 0.92 0.93 0.94 0.95
0.21 0.19 0.16 0.14 0.11
0.46 0.47 0.48 0.49 0.50
4.7 4.4 4.2 3.9 3.7
0.71 0.72 0.73 0.74 0.75
1.09 1.03 0.97 0.91 0.85
0.96 0.97 0.98 0.99 1.00
0.09 0.06 0.04 0.02 0.00
Equation 5 is also the solution for a firstorder reaction with C = ~ T B . The function T / T B has been evaluated for chosen values of C. Values of C corresponding to T / T B between 0.01 and 1.00 at intervals of 0.01, obtained by graphical interpolation are shown in Table I. The case of the second-order reaction with equal initial concentrations has also been developed. In this case T/TB.
(6)
B=A+Kt
where A is the concentration of the reactant which is removed at constant rate. Then -dA = kA(A
dt
+ Kt) + K
With the changes of variable eq 7 becomes da -dt'
=
1
CY
=
A/& and t' =
(7) t/TB
+ fa2 + fatt
where f = k A b 7 B . Times T' = T / T B required for CY to become zero have been calculated with a computer for various values of f. Values o f f corresponding to
f
from 0.01 to 1.00 at intervals of 0.01, obtained by graphical interpolation, are given in Table 11. Of course, relative reaction rates for any mechanism can be observed as relative end point times without evaluating rate constants.
T/TB
Experimental Section Materials. Merck reagent grade potassium iodide and sodium thiosulfate, conforming to ACS specifica,tions, were used. Matheson Coleman and Bell methyl chloroacetate, bp 128-130", and methyl bromoacetate, bp 38-39' (10 mm), were used as purchased. Methyl iodoacetate was prepared as follows. Equal volumes of ethyl ether and 40% KOH in water were mixed and cooled in an ice bath. N-Nitrosomethylurea was added to make diazomethane. The ether layer containing the diazomethane was decanted and dried with KOH pellets. An ether solution of iodoacetic acid was mixed with an excess of diazomethane in ether to form methyl iodoacetate, and the ether was removed by vacuum distillation. The pale yellow product, n 2 7 . 1.5167, 2~ had an infrared spectrum in chloroform with a single carbonyl band. Purity of the esters was demonstrated by vapor phase chromatography with a Burrell Kromo-Tog Model K2, Volume 70,Number 4 April 1966
GEORGEB. SMITH AND GEORGE V. DOWNING, JR.
980
equipped with a thermal conductivity detector. The column was 2.5 m long and 6 mm in i.d., packed with 20% DC-200 on Gas Chrom Z, -80 100 mesh. Helium carrier flow rate was 60 ml/min, and column temperature was 115". Retention times of 3, 5 , and 9 min were observed for the chloro, bromo, and iodo esters, and purities by area per cent were 99.99, 99.97, and 99.0%, respectively. Impurities were not identified. Prowlure. Reaction rates were measured with a Fisher Coulomatic Titrimeter. The titration cell (reaction vessel) was a 250-ml beaker equipped with a magnetic stirrer. Platinum electrodes were used to generate iodine externally from 1 M K I solution in a buret using a delivery tip with an internal electrode (Sargent 5-29703). Iodine was generated at constant current of 5 ma, and an electric clock in the circuit indicated the generating time. The presence of free iodine at the end point was detected by polarized platinum electrodes as a "dead stop" end point. Distilled water, 150 ml, containing 1vol % methanol, was placed in a 250-ml beaker, and the temperature of the liquid was adjusted to 25.0'. The methanol was used to dissolve the esters. The beaker was placed on the titrimeter, and flow of K I solution from the buret at about 1 ml/min was started. The solution was titrated to an initial end point to provide a slight excess of iodine to which the following runs were titrated. Ester was then added in high excess to the amount of thiosulfate to be titrated. At the initial reaction time sodium thiosulfate solution was added, and the generating current and clock were started. The titration time r was observed and compared with the blank time T B obtained similarly in the absence of ester. Amounts of thiosulfate were used to make T B about 4 min. Rate constants corresponding to observed values of T / T B were obtained from Table I.
+
Results and Discussion The present method is useful in measurement of reaction rates as opposed to mechanism elucidation. The method is particularly suited for measurement of reaction rates of related compounds in a given reaction. Rate constants can be evaluated if the rate law is known. La Mer and Kamner2 showed that reaction of thiosulfate and methyl bromoacetate in water at 25' is second order and free from side reactions. Secondorder rate constants have been evaluated in the present work on the basis of this prior knowledge. Experimental data and calculations are summarized in Table 111. Each run includes successive titrations of three portions of thiosulfate in the same solution of The J o u T of ~ Physical ~ ~ Chemistry
excess ester at 25.0'. The ester used in each run is shown in Table I11 along with ester molarity B, titration time r , r / r ~C, = ~ B T corresponding B to T / T B from Table I, and finally the value for the secondorder rate constant measured in each titration. Blank times T B obtained from four titrations of thiosulfate in absence of ester were 215.4, 217.6, 217.2, and 214.9 sec. The average time of 216.3 sec was used in the calculations. Volume of reaction mixtures increased slightly throughout each run as potassium iodide solution flowed from the buret into the beaker, and ester concentration decreased accordingly. Ester molarities used in the calculations are concentrations at halftime of each titration. Salt concentration also increased during each run to about 0.1 M after the third titration. I n each run the rate constants for titrations 1, 2, and 3 are the same. This shows that rate is independent of salt concentration, as reported by LaMer and Kamner. Second-order behavior is verified by the fact that the observed rate constant for reaction of methyl bromoacetate is independent of ester concentration in the range 0.033 to 0.136 M . LaMer and Kamner reported values of 0.21 to 0.25 M-' sec-' for this rate constant at 25 A 0.01", in agreement with the present data. They used lower ester concentrations and followed reactions for several hours. With the apparatus used an interval of about 2 sec was required for iodine generated externally to pass into the reaction mixture. This was the source of the most important error in the rate measurement. During the 2-sec interval thiosulfate reacted with ester but not with iodine. As a result of the time delay titration times increased, and observed rate constants were slightly low. Reproducibility of rate constant values was about &5%. This method should find use in a variety of applications. Addition of a reagent at constant rate can be accomplished conveniently by electrochemical means, as in the present example. Also, mechanical devices can be arranged to deliver liquids at constant flow rate. Detection of end points can be done in many ways, depending on the application. This kinetic method offers several distinct advantages. First, the method is most accurate in measurement of rates of reactions with half-lives about 1 min. Such rates are often difficult to measure by analysis of aliquots during reaction or by observation of physical parameters. It should be noted, however, that the method as applied here is not useful for rate measurements of very slow or very fast reactions. Second, rate data are obtained rapidly. Rates are determined
MEASUREMENT OF REACTION RATEBY COMPETITIVE REMOVAL OF REACTANT
981
Table 111: Summary of Data and Calculations Run
Eater
1
Methyl chloroacetate
Titration
1
k,
B, M
I , 080
I/
7B
C = kBig
M-1
Bec-1
2 3
0.414 0.403 0.395
195.0 193.5 194.3
0.902 0.895 0.898
0.23 0.24 0.23
0.0026 0.0028 O.OO27
2
Methyl bromoacetate
1 2 3
0.0342 0.0334 0.0326
130.4 133.3 135.1
0.603 0.616 0.625
1.56 1.47 1.41
0.21 0.20 0.20
3
Methyl bromoacetate
1 2 3
0.0345 0.0337 0.0328
133.9 133.1 134.6
0.619 0.615 0.622
1.45 1.48 1.43
0.19 0.20 0.20
4
Methyl bromoacetate
1 2 3
0.0683 0.0667 0.0651
100.9 101.4 104.1
0.466 0.469 0.481
2.94 2.91 2.79
0.20 0.20 0.20
5
Methyl bromoacetate
1 2 3
0.0683 0.0667 0.0651
97.4 100.0 101.6
0.450 0.462 0.470
3.20 2.98 2.90
0.22 0.21 0.21
6
Methyl bromoacetate
1 2 3
0.135 0.132 0.129
69.0 71.6 75.1
0.319 0.331 0.347
6.1 5.8 5.3
0.21 0.20 0.19
7
Methyl bromoacetate
1 2 3
0.136 0.132 0.130
68.4 70.9 74.1
0.316 0.328 0,343
6.3 5.8 5.4
0.21 0.20 0.19
8
Methyl iodoacetate
1 2 3
0.0195 0.0189 0.0186
150.5 150.4 153.0
0.696 0.695
0.99 0.99 0.93
0.23 0.24 0.23
by titration times of a few minutes. Third, a wide range of rate constants can be measured conveniently for cases such as second-order reactions by variation of initial concentrations. The second-order rate constants for reactions of thiosulfate with methyl bromoacetate and methyl iodoacetate are about 100 times larger than the rate constant for methyl chloroacetate. This was determined without difficulty by using different concentrations of the esters. I n the present example, methyl bromoacetate was used in 3000fold excess to initial thiosulfate. This means that a
0.707
rate constant 3000 times larger could have been measured with about the same accuracy if ester equivalent to initial thiosulfate were used, without changing initial thiosulfate concentration or generating current. Table I1 would be used in that case instead of Table I. Acknowledgments. The authors wish to express their appreciation for the assistance of Dr. I. Schoenewaldt in the preparation of methyl iodoacetate and Mr. M. Zirrith in the computation of the table for the second-order reaction with equimolar initial concentrations.
volume 70,Number
4 April 1966
