In the Laboratory
Hammett Parameter and Molecular-Modeling Correlations of Substituent Effects on Esterification Kinetics Jeremy B. Smith, Houston Byrd,* Stephen E. O'Donnell,* and Will Davis Department of Biology, Chemistry & Mathematics, University of Montevallo, Montevallo, Alabama 35115 *
[email protected] In organic chemistry, students learn how substituents affect equilibrium constants, the stability of intermediates, and reaction rates. However, there are relatively few experiments that quantitatively investigate this relationship (1-4). A kineticsbased experiment that demonstrates this relationship in a way that most students should be able to understand is presented. In 1979, Knipe et al. (5) published an article investigating the rates and mechanisms of esterification reactions. Knipe's work showed that esterification reactions between trifluoroacetic acid (TFA) and a variety of primary and secondary alkyl alcohols proceed via a reverse AAC2 mechanism1 established by Ingold (6). In this mechanism (Figure 1), the second step of the reaction, the nucleophilic addition of the alcohol, is the rate determining step. The rate of esterification relative to a reference alcohol depends on the presence of any substituents on the reference alcohol, especially those substituents that are electron-withdrawing groups (7). This is presumably due to a decrease in the electronic density around the oxygen atom, making the alcohol a weaker nucleophile. In 1985, Minter et al. (8) developed an excellent laboratory experiment using 1H NMR for a kinetic study of the esterification of TFA with a variety of alcohols. Although the article described the use of different alcohols, the primary focus was the determination of the rate constant. No attempt was made to look for correlations of rates and structures. Minter's work (8) combined with the dependence of the rate of reaction on the alcohol structure established by Knipe (5, 7) led us to develop a more advanced laboratory based on the esterification of TFA to probe the effect of different substituents on rates of reactions. Substituent effects on reaction rates have been extensively studied in the context of the Hammett equation (9), k ð1Þ ¼ Fσ log k0 which describes the relationship between structure of a compound and its reactivity. In this equation, k is the rate constant for reaction of the substituted alcohol, k0 is the rate constant for reaction of the unsubstituted or reference alcohol, σ is the Hammett substituent constant, and F is the reaction constant. The substituent constant is a measure of the electron-donating or electron-withdrawing properties of the given substituent. A larger value for σ indicates a stronger electron-withdrawing group. However, this relationship is not easily understood by students (10) and students do not always correlate theory presented in lecture with experiments performed in the lab. By adding a molecular-modeling component, students are able to calculate the charge on the oxygen atom of the alcohol and correlate this with observed rates. The comparison of the theoretical
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Figure 1. The reverse AAC2 mechanism for the esterification of trifluoroacetic acid.
calculations with the observed results helps students develop a more complete picture of the process. We chose the esterification kinetics of TFA because it is a well-established reaction and the necessary equipment is readily found in most undergraduate laboratories. Our results are in excellent agreement with literature values (5, 8) and the processes represent a more advanced approach to the undergraduate experiment. We find a direct correlation between the Hammett (9) substituent constant and the rate of the esterification of substituted alcohols. This observed dependence is further supported when the charge on the oxygen of the nucleophilic alcohol is compared to the rate of the esterification. Procedure All reagents were purchased from Aldrich and used without further purification. Deuterated TFA was used to minimize its NMR signal. The procedure is similar to what has been reported in this Journal (8), but the reactants are weighed using an analytical balance to allow for second-order kinetics analysis. A clean NMR tube with the cap is accurately weighed on an analytical balance. Then, a volume of the given alcohol equivalent to a mass of 50 mg is added to the NMR tube, which is then capped and reweighed. In a hood, 0.5 mL of TFA is added to the NMR tube, which is capped, mixed, and reweighed. If the weights of the alcohol and of the TFA are recorded accurately, using published densities, the actual concentrations of both can be calculated. NMR spectra are recorded at regular time intervals, typically 2-3 min for methanol and ethanol but longer for other alcohols. Measurements are made until 75-85% of the alcohol has been consumed. The protons alpha to the oxygen
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r 2010 American Chemical Society and Division of Chemical Education, Inc. pubs.acs.org/jchemeduc Vol. 87 No. 8 August 2010 10.1021/ed100212d Published on Web 06/10/2010
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In the Laboratory Table 1. Summary of the Experimental Results Substituent on the Alcohol β carbon
Alcohol
k/(103 M-1 min-1)a
log(k/k0)b
σ
Calculated O-Atom Chargec
Ethanol
H
3.18
0
0.00
-
1-Propanol
CH3
4.74
0.173
-0.04
-
1-Butanol
CH3CH2
3.64
0.059
-0.05
-
1-Pentanol
CH3CH2CH2
4.90
0.188
-0.03
-
2-Ethoxyethanol
CH3CH2O
0.909
-0.544
0.27
-0.331
2-Iodoethanol
I
0.462
-0.838
0.39
-0.326
2-Fluoroethanol
F
0.441
-0.889
0.52
-0.326
2-Nitroethanol
NO2
0.153
-1.32
0.76
-0.321
2,2,2-Trifluoroethanol
F3
0.013
-2.39
1.56d
-0.309
a Rate based on second-order analysis at 25 °C. b k is the rate constant for substituted alcohol and k0 is the rate constant for ethanol. c Charge calculated using HyperChem and the semiempirical method, AM1. d σ is approximated to be 3 times the 2-fluoroethanol value.
atom on both the alcohol and the ester are integrated to obtain concentrations for both species. An Excel template is provided in the supporting information to assist in recording and analyzing the data. It is important to note that reaction times for alkyl alcohols are approximately 1 h. Once the electronwithdrawing groups are added, the reaction times increase significantly. Hazards Standard procedures for safe handling of chemicals should be followed. The alcohols and the TFA should be measured out in a fume hood. The alcohols listed in Table 1 are flammable and are irritants to the skin and eyes. TFA is corrosive and causes burns. It is harmful if swallowed, inhaled, or absorbed through skin. TFA is extremely destructive to the upper respiratory tract, eyes, and skin. Students should wear goggles and gloves while handling all chemicals. Analysis In this experiment, the TFA is in a 10-fold excess; therefore, the reaction could be treated as pseudo-first order and the students could calculate the rate constant in this manner to compare their data to published results (5, 8). However, the students calculate the rates based on second-order kinetics because the reaction is first-order with respect to both the [TFA] and the [ROH]. The integrated second-order rate law (11) is ! ½TFA0 ½ROHt 1 ln ¼ kt ð2Þ ½ROH0 - ½TFA0 ½ROH0 ½TFAt where [TFA]0 and [ROH]0 are the initial concentrations and [TFA]t and [ROH]t are the concentrations at a given time, t. Knowing that the sum of the concentrations of the alcohol and the ester at a specific time must equal [ROH]0, one can use the relative areas of the peaks to calculate the concentration of the alcohol at each time interval. If IA and IE represent the integrals for the alcohol (A) and the ester (E), then the concentration of the alcohol at time t can be calculated using IA ½ROH0 ð3Þ ½ROHt ¼ IE þ IA
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The concentration of TFA at the same time, [TFA]t, is calculated using reaction stoichiometry: ð4Þ ½TFAt ¼ ½TFA0 - ð½ROH0 - ½ROHt Þ A plot of the left side of eq 2 versus time should yield a straight line whose slope is the rate constant, k. A summary of experiments that were conducted using this procedure is listed in Table 1. The rates of reaction for the alkylsubstituted alcohols are similar to each other. This is because substituent constants for the alkyl groups are essentially equal to that for hydrogen, the reference substituent. The primary focus of this lab is directed toward alcohols that possess electronwithdrawing groups. The data clearly indicate that the rate of reaction decreases as the electron-withdrawing substituents are added to the reference alcohol. A decrease in the rate is expected if the rate-determining step is the nucleophilic attack of the alcohol because the greater the electron-withdrawing power of the substituent results in less electron density around the oxygen atom of the alcohol. To further illustrate this point, a Hammett plot of log(k/k0) values for alcohols containing electron-withdrawing substituents versus the appropriate σ constants (eq 1) is shown in Figure 2A. A strong linear correlation (R2 = 0.994) with a derived reaction constant F = -1.4 results, which indicates that these reactions are consistent with the nucleophilic addition of the alcohol (reverse AAC2 mechanism) (7). It is important to note that a literature value for the σ constant for the trifluoro-substituted alcohol could not be found; therefore, the Hammett parameter for the trifluoro-substituted alcohol (X = F3) was estimated to be 3 times that of the monofluoro-substituted alcohol (X = F). To provide further support for this mechanism, students use HyperChem (13) Molecular Modeling System (version 7.52) to calculate the charge of the oxygen atom on the alcohol. First, the desired alcohol is drawn and optimized using the “model-build” mode in HyperChem. A further geometry optimization is performed using the AM1 semiempirical method. The charge is calculated based on this geometry. The results for these calculations are shown in Table 1. A plot of the log(k/k 0) versus the theoretical charge of the oxygen on the substituted alcohols is shown in Figure 2B. There is also a linear relationship between the calculated charge of the oxygen atom and the rate constant (R2 = 0.995). Both of the plots indicate a strong correlation between the substituted alcohol and the rate of reaction and support the reverse
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r 2010 American Chemical Society and Division of Chemical Education, Inc.
In the Laboratory
Figure 2. (A) A plot of rate constant for the alcohols with electron-withdrawing substituents versus the Hammett substituent constant, σ and (B) a plot of the rate constant of the same alcohols versus the calculated charge on the oxygen atom.
AAC2 mechanism. Further, the combination of the molecular modeling and experimental results reinforce the electronicsubstituent concepts presented throughout the undergraduate curriculum. The results of this lab clearly show a strong correlation between the electron-withdrawing substituents and the decrease in the rate of esterification. The combination of the experimental data with the theoretical calculations should increase the students understanding of substituent effects on reaction rates. Note 1. The AAC2 mechanism is an acid-catalyzed bimolecular acyloxygen cleavage mechanism.
Acknowledgment Financial support for these laboratories has been provided through the purchase of equipment. The FT-NMR upgrade was funded by a NSF grant (DUE-9950438) and the University of Montevallo. Literature Cited 1. Ikeda, G. K.; Jang, K.; Mundle, S. O. C.; Dicks, A. P. J. Chem. Educ. 2006, 83, 1341. 2. Setliff, F. L.; Soman, N. G.; Toand, A. D. J. Chem. Educ. 1995, 72, 362.
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3. Mullins, R. J.; Vedernikov, A.; Viswanathan, R. J. Chem. Educ. 2004, 81, 1357. 4. Keenan, S. L.; Peterson, K. P.; Peterson, K.; Jacobson, K. J. Chem. Educ. 2008, 85, 558. 5. Johnston, B. H.; Knipe, A. C.; Watts, W. E. Tetrahedron Lett. 1979, 20, 4225. 6. Ingold, C. K. Structure and Mechanism in Organic Chemistry; Cornell University Press: Ithaca, NY, 1953; Chapter 14. 7. Kavanagh, P.; Knipe, A. C.; Watts, W. E. J. Chem. Soc., Chem. Commun. 1979, 20, 905. 8. Minter, D. E.; Villarreal, M. C. J. Chem. Educ. 1985, 62, 911. 9. Hammett, L. P. J. Am. Chem. Soc. 1937, 59, 96. 10. Schwan, A. L. J. Chem. Educ. 1993, 70, 1001. 11. Atkins, P.; De Paula, J. Physical Chemistry, 8th ed.; Freeman, W. H.: New York, 2006; p 803. 12. (a) Hansch, C.; Leo, A. Substituent Constants for Correlation Analysis in Chemistry and Biology; Wiley-Interscience, New York, 1979. (b) Wired Chemist. http://www.wiredchemist.com/ chemistry/data/hammett_sigma_constants.html (accessed May 2010). 13. HyperChem Molecular Modeling System for Windows Release 7.52
Supporting Information Available Additional information for the instructors. This material is available via the Internet at http://pubs.acs.org.
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