In the Laboratory
Kinetic Solvent Isotope Effect: A Simple, Multipurpose Physical Chemistry Experiment Omar A. El Seoud,* Reinaldo C. Bazito, and Paulo T. Sumodjo Instituto de Química, Universidade de São Paulo, C.P.26077, 05599-970, São Paulo, SP, Brazil Isotopic substitution may affect reaction rates in a number of ways, all of which can yield valuable mechanistic evidence. The power of this technique lies in the fact that isotopic substitution is the least disturbing structural change that can be made in a system in order to gain the required information. Since all isotope effects ultimately depend upon relative masses of the two nuclei involved, and this ratio is greatest for the hydrogen isotopes, the largest number of studies have involved comparison of substrates containing deuterium with their protium-containing analogues (1–4). Several mechanistic uses of the kinetic isotope effect are given in any introductory organic chemistry course— for example, in discussing the mechanisms of elimination by the E2 pathway, and electrophilic aromatic substitution (2, 5). A quiz given to our undergraduate chemistry students showed, however, that they regard the isotope effect as a topic for graduate research. This may be because their contact with isotopic substances is practically limited to the study of isotope effect on molecular vibrations (IR of gaseous H 35Cl and H 37Cl) and their use of deuterated solvents in NMR experiments. Surprisingly, physical chemistry laboratory textbooks do not contain any experiment on the kinetic isotope effect (6–12). To remedy this situation, we introduced a new experiment in our physical chemistry laboratory. Instead of using the primary kinetic isotope effect, which would require synthesis of an isotopically labeled compound (13), students investigate the spontaneous hydrolysis of acetic anhydride in H2O and D2 O, whose equation in the former solvent is given by: (CH3CO)2O + H2O → 2 CH3COOH
(1)
This reaction is an example of the kinetic solvent isotope effect, KSIE, which has been used in teaching in a qualitative manner (14). KSIE is observed if any or all of the following undergo change on going from reactant to transition state: (i) differences in bulk solvent properties, (ii) differences in solute–solvent interactions, (iii) differences in zero-point energy of the O–L bonds (where L is an unspecified isotope of hydrogen) of reacting solvent water molecules, or (iv) differences in zero-point energy of solute bonds to (exchangeable) H that have become labeled by rapid exchange with solvent (15). Quantitative treatment of KSIE is simplified if the effect is primary in nature—that is, if the reaction involves rate-determining proton (deuteron) transfer from either reactant water or solute. This simplification applies to the present case because acetic anhydride does not exchange hydrogen with the solvent, so that this “water reaction” involves rate-limiting hydrogen transfer between “nucleophilic” water (which attacks the anhydride acyl group) and “general base” water, as shown in the following representation of the transition state (16):
In this structure, H a contributes a primary isotope effect and Hb contributes a secondary isotope effect, whereas Hc does not contribute an isotope effect. The resultant KSIE is conveniently large, ca. 2.9 at 25 °C (17–20). The students determine rate constants by two experimental techniques, namely, UV-vis spectroscopy and conductance measurement. In the former experiment, the rate constant is determined by following the disappearance of the reactant, acetic anhydride, at 228 nm. In the latter one, they follow the increase in conductance of a solution of the anhydride in H2O due to dissociation of the reaction product, acetic acid. The UV-vis experiment is carried out in a differential manner, that is, the H2O reaction cuvette is inserted in the reference beam, whereas the D2 O reaction cuvette is inserted in the sample beam of a double-beam spectrophotometer. By using this novel approach, they are able to calculate both rate constants, kH2 O and kD2 O from a single kinetic run, with commercially available software. The conductance experiment introduces the students to a new technique to study chemical kinetics, and the obtained kH2O allows them to evaluate the quality of rate constants calculated by the curve-fitting procedure. Results and Discussion The spontaneous hydrolysis of acetic anhydride is a convenient experiment for the undergraduate physical chemistry laboratory because the reactants are inexpensive; the solution of the anhydride in acetonitrile is stable and can be safely handled; and the reaction kinetics can be followed by different instrumental methods. The experiment requires very little preparation and uses only readily available equipment (a spectrophotometer and a conductimeter), and the reaction proceeds at convenient rates in both solvents. (At 25 °C, the half-lives are ca. 4.5 and 13 min for the reactions in H 2O and D2O, respectively).1 The “infinity” conductance reading is stable (22) and can be taken during the same laboratory period, thus permitting ready access to kH2O. This contrasts with the “classic” experiment of hydrolysis of sucrose, whose infinity reading is taken after 48 hours, and is usually a source of error in the calculated rate
*Corresponding author. fax: 55-11-8183874; email:
[email protected].
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In the Laboratory constant (23). The usual procedure to determine kH2O and kD2 O spectrophotometrically is from two separate experiments, one in each solvent, against KCl solution as a reference. Instead, students measure the difference between absorbances of experiments in both solvents, as given in “Experimental Procedure”. This new approach allows the simultaneous determination of two rate constants from a single kinetic run, and has the following attractive features. First, speed: the time required to carry out both experiments is that of the slow reaction. Note that no infinity reading is needed to calculate rate constants from the differential absorbance data (see below, under Experimental Procedure). This time saving is crucial in today’s crowded undergraduate laboratories, especially when the experiment requires use of medium-sized instruments. Second, novelty: the students calculate two rate constants from a single set of absorbance data by iteration, using commercial software. Figure 1 shows a typical curve-fitting result of the differential spectroscopic experiment. The following average values were obtained by a group of 48 students: 2.6 ± 0.1 × 10{3 s{1 and 8.9 ± 0.1 × 10{4 s{1 for kH2 O and kD2O, respectively, in excellent agreement with literature values of 2.6 ± 0.1 × 10{3 s{1 and 9.0 ± 0.1 × 10{4 s{1, respectively (16–20). In principle, curve fitting of a set of experimental results may generate, for reasons beyond the scope of the present paper, more than one answer. Although students can compare their rate constants with those published in the literature (16–20), it is instructive and much more interesting that they determine these constants by a procedure that does not rely on curve fitting. Independent determination of a rate constant is required, however, when the reaction has not been previously studied or has been studied under different experimental conditions. Determination of kH2O by conductance measurement, therefore, allows students to obtain this rate constant without curve fitting and introduces them to the use of a different experimental technique for determining reaction rates. Our students do not determine kD2O by conductance measurement because (i) much more D2 O would be needed (at least 5 mL per run), and (ii) they would not be able to finish all three experiments (one using UV-vis spectroscopy, and two using conductance) in a single 4-hour laboratory period. From eq 4 (see Experimental Procedure) it is clear, however, that if kH2O determined by curve fitting is correct (as indicated by the agreement between rate constants determined by UV-vis and conductance experiments), then the associated kD2 O must also be correct. Figure 2 shows a typical plot for the determination of kH2O by conductance. The values obtained by the students were in the range 2.6 ± 0.1 × 10 {3 s{1, in excellent agreement with the value obtained by curve fitting, and literature results (see above).
determined with great accuracy by two independent experimental techniques. Experimental Procedure
Materials The following chemicals were from Aldrich and Merck: acetonitrile (99.5+%, ACS reagent), potassium chloride (ACS reagent), D2O (99.9% D), and acetic anhydride (99%+). Acetonitrile was purified by distillation from P 2O5 , and the anhydride by distillation from P 2O5 , then from 1% quinoline (24). The stock solutions are acetic anhydride, 2.0 M in acetonitrile; KCl, 0.02 M and 1 × 10{4 M in H2O; and KCl, 0.02 M in D2O. Apparatus An SLM AMINCO DW-2000 double-beam UV-vis spectrophotometer was used for measuring kH2O and kD2O by the differential absorbance method. The apparatus is provided with thermostated cell holders. It is interfaced to a microcomputer for data acquisition and subsequent rate constant calculation. The reactions were carried out at 25 °C in 1-cm path-length quartz semi-micro cells equipped with Teflon stoppers. Conductance measurements were carried out with a Fisher Accumet-50 pH-meter equipped with a Fisher conductivity cell (cell constant 1.0 cm{1) and interfaced to a microcomputer. The output of this pH meter permits data acquisition only at a preselected fixed-time intervals. This feature is not convenient, particularly toward the end of the reaction, because the variation of the conductance/time interval is small. We wrote an acquisition program in which conductance data are saved by the microcomputer only if the difference between two successive readings (taken at 5s intervals) is ≥ 1 µS. The reaction was carried out in a 30mL Pyrex glass tube immersed in a thermostated water bath. The reaction solution was stirred with a small magnetic bar, and its temperature was adjusted to 25 °C before
Conclusions The spontaneous hydrolysis of acetic anhydride in H2 O and D2O is a chemical kinetics experiment that is much more convenient than the “classic” experiment given in most laboratory physical chemistry textbooks, namely, the acid- or base-catalyzed hydrolysis of methyl or ethyl acetate (6, 7, 12). An important functional derivative of carboxylic acids, the anhydride, is used to demonstrate the deuterium isotope effect, without resorting to use of specifically labeled reagents. The differential absorbance method results in an efficient use of spectrophotometer time and introduces students to the use of curve fitting. The rate constants can be
Figure 1. Typical plot for the determination of kH2O and kD2O by the differential absorbance method. For this experiment, the results of curve fitting are: k H2 O = 2.59 × 10{3 s{1, k D2 O = 8.9 × 10{4 s{1, α = 0.637, β = 0.645, A∞ = 0.011. The KSIE is 2.9. The points are experimental and the solid line is calculated by curve fitting. For clarity, we show only a fraction of the total number of ∆At vs. t points (15% of a total of 691) that are provided by the microcomputer, based on the A-vs.-t curve.
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In the Laboratory guesses for α, β, kH2O and kD2O and calculate the resulting ∆At vs. t curve. Adjust the guesses manually until the shape of the generated curve resembles that of the experimental one; then apply the curve fitting routine, Fit, to obtain the final parameter results by iteration. In principle, curve fitting can be done with any set of initial guesses, except for α or β = 0. The number of iterations, but not the final result, depends on the values employed. Reasonable initial guesses are α = β = 0.5, and kH2O = 2 kD2O (e.g., 0.001 and 0.0005, respectively). Any other suitable curve-fitting program can be employed. For example, the students successively used Enzyfitter (Elsevier-Biosoft, New York). Determination of k H2O by Following Formation of Acetic Acid by Conductance Measurement Figure 2. Representative plot for the determination of kH2O by conductance measurement. The rate constant for this experiment is 2.57 × 10{3 s{1.
starting the run.
The Experiment All stock solutions are provided by the instructor. In a laboratory period of 4 hours, each pair of students easily finishes both experiments. Calculation of kH2 O and kD2O from differential absorbance measurement and kH2O from conductance measurement takes, at maximum, an additional 2 hours. Determination of k H2O and kD2O by Differential Absorbance Measurement Pipet 1 ml of each of the 0.02-M KCl solutions (in H2 O and D2 O) into two cuvettes and mark them by H and D, respectively. Place the H2O cell in the reference beam and the D2 O cell in the sample beam. Leave them in the thermostated holder for 15 min. To start the reaction, inject 5 µL of the 2.0-M acetic anhydride stock solution in each cuvette, shake the cuvettes by hand, and return them to the cell holders.2 Record the absorbance difference between the two cells, ∆At , at 228 nm as a function of time, t, for 80 min (> 6 half-lives for the reaction in D2 O). Calculation of Rate Constants In terms of absorbance of the solution, A, the equations for the reaction in D2O and H 2O are given by, respectively: (AtD – A∞D ) = (AoD – A∞D ) · exp ({kD2O t)
(2)
(At H – A∞H ) = (AoH – A∞H ) · exp ({kH2O t)
(3)
where Ao , At , and A∞ refer to absorbance of the solution at the beginning of the reaction, at time t, and at the end of the reaction, respectively. The subscripts D and H refer to reaction in D2O and H2O. Subtraction of eq 3 from eq 2 yields ∆At = (AtD – AtH ) = (AoD – A∞D ) · exp ({kD2O t) + (AoH – A∞H ) · exp ({k H2O t) + (A∞D – A∞H )
Calculation of Rate Constant The solution conductance readings are transformed into the corresponding acetic acid concentrations and kH2O is obtained from a plot of log {[AcOH]∞ – [AcOH]t} vs. time, where [AcOH]∞ and [AcOH]t refer to the “infinity” concentration of acetic acid and that at time t, respectively. These concentrations are determined as follows. From Ostwald’s dilution law, the conductance of the solution is related to the concentration of the weak electrolyte by: KAcOH = Λ 2 [Ac OH] / Λο(Λ ο – Λ)
(5)
Λ = 10 3 κ / R [Ac OH]
(6)
By definition, where Λ, Λο , κ, and R refer to the equivalent conductance, the limiting equivalent conductance (of the hydronium and acetate ions), the cell constant (unity in our case), and the resistance of the cell (ohms), respectively. Combining eqs 5 and 6 we get the following expression for the concentration of acetic acid at any time, t: [Ac OH] t = (103 κ / ΛοR t ) {1 + (10 3 κ / KAcOH Λ ο Rt )} (7) [AcOH]∞ is calculated in a similar way. At 25 °C the values of KAcOH and Λο are 1.76 × 10{5 and 390.55 cm2 S mol{1, respectively (25).3 For calculation of acetic acid concentrations, one needs to subtract the initial conductance of the backing electrolyte solution from conductance values measured as a function of time (i.e., those due to KCl and acetic acid). Although it is possible to calculate kH2O from conductance measurements by a weighted least-squares program, which determines [AcOH]∞ by iteration (see, e.g., 23), it is instructive for students to follow the reaction to completion, measure the infinity reading, and use it to calculate kH2O. Acknowledgment
or ∆At = α · exp ({kD2O t) + β · exp ({kH2O t) + ∆A∞
(4)
where α = (AoD – A∞D) , β = (AoH – A∞H ), and ∆A∞ = (A∞D – A∞H). Values of α, β, kH2 O, kD2O, and ∆A ∞ in eq 4 can then be computed by curve-fitting values of ∆At versus t, using a commercial program (e.g., Origin, version 3.0, MicroCal Software, Inc., Northampton, MA). A simple procedure to do curve fitting is as follows: introduce a set of suitable initial
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Pipet 10 mL of a 1 × 10{4 M KCl solution into the reaction tube, insert the conductivity cell, and start magnetic stirring. After 15 min, initiate the reaction by injecting 50 µL of a 2.0-M acetic anhydride stock solution. The increase in solution conductivity is then recorded as a function of time for ca. 25 min (> 5 half-lives), and the infinity reading is taken after 40 min.
We thank the FAPESP and FINEP foundations for financial support, and CNPq for a research fellowship to R.C.B. Notes 1. In contrast, at 25 °C, the half-lives in the acid-catalyzed hydrolysis of ethyl vinyl ether range from 10 to 27.7 s (catalysis
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In the Laboratory by HCl) and from 18.6 to 64 s (catalysis by DCl [21]). As their first kinetic experiment, undergraduate students may not be able to get reproducible rate data for such fast reactions 2. Starting the reaction simultaneously in both solvents is not required because if the reaction in D2O is started a few seconds, ∆t , after the reaction in H2O, then ∆t is incorporated in the constant term of eq 4. This does not affect the values of computed rate constants. 3. Equation 7 is similar to that derived by Robertson et al. (19, 20) except that there is a serious misprint in these articles: the expression (103 κ / KAcOH ΛoRt) was reported as (κ / KAcOH ΛoRt)!
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8. Salzberg, H. W.; Morrow, J. I.; Cohen, S.R.; Green, M.G. Physical Chemistry Laboratory: Principles and Experiments; Macmillan: New York, 1978. 9. Matthews, G. P. Experimental Physical Chemistry; Clarendon: Oxford, 1985. 10. Halpern, A. M.; Reeves, J. H. Experimental Physical Chemistry: A Laboratory Textbook; Scott, Forresman: Glenview, NJ, 1988. 11. Shoemaker, D. P.; Garland, C. W.; Nibler, J.W. Experiments in Physical Chemistry, 5th ed.; McGraw-Hill: New York, 1989. 12. Sime, R. D. Physical Chemistry: Methods, Techniques and Experiments; Saunders: Philadelphia, 1990. 13. Zollinger, Hch. J. Chem. Educ. 1957, 34, 249. 14. Binder, D. A.; Ellason, R.; Axtell, D. D. J. Chem. Educ. 1986, 63, 536. 15. Schowen, K. B. In Transition States of Biochemical Processes; Gandour, R. D.; Schowen, R. L., Eds.; Plenum: New York, 1978; p 225. 16. Davis, K. R.; Hogg, J. L. J. Org. Chem. 1983, 48, 1041–1047. 17. Butler, A. R.; Gold, V. J. Chem. Soc. 1961, 2305–2312. 18. Batts, B. D.; Gold, V. J. J. Chem. Soc. A 1969, 984–987. 19. Robertson, R. E.; Rossall, B.; Redmond, W. A. Can. J. Chem. 1971, 49, 3665–3670. 20. Rossall, B.; Robertson, R. E. Can. J. Chem. 1975, 53, 869–877. 21. McGuiggen, P.; Eliason, R.; Anderson, B.; Botch, B. J. Chem. Educ. 1987, 64, 718–720. 22. El Seoud, M. I.; El Seoud, O. A. Educ. Chem. 1994, 105–107. 23. Holt, M. J.; Norris, A. C. J. Chem. Educ. 1977, 54, 426–428. 24. Perrin, D. D.; Armarego, W. L. F. Purification of Laboratory Chemicals, 3rd ed.; Pergamon: New York, 1988. 25. Handbook of Chemistry and Physics, 73rd ed.; Lide, D. R., ed.; CRC: Boca Raton, FL, 1992.
Acetic Anhydride
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