LABORATORY EXPERIMENT pubs.acs.org/jchemeduc
Study of the Kinetics of an SN1 Reaction by Conductivity Measurement Elaine M. Marzluff,*,† Mary A. Crawford,*,‡ and Helen Reynolds‡ † ‡
Department of Chemistry, Grinnell College, Grinnell, Iowa 50112, United States Department of Chemistry, Knox College, Galesburg, Illinois 61401, United States
bS Supporting Information ABSTRACT: Substitution reactions, a central part of organic chemistry, provide a model system in physical chemistry to study reaction rates and mechanisms. Here, the use of inexpensive and readily available commercial conductivity probes coupled with computer data acquisition for the study of the temperature and solvent dependence of the solvolysis of 2-chloro-2-methylpropane is described. Students obtain rate constants and activation parameters for a range of solvent compositions. This experiment takes advantage of curricular reform pedagogies by utilizing modern equipment and building linkages with earlier coursework. KEYWORDS: Upper-Division Undergraduate, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Conductivity, Kinetics, Laboratory Computing/Interfacing, Nucleophilic Substitution, Rate Law
S
ubstitution reactions provide a model system to study reaction rates and mechanisms in physical chemistry. In this experiment, students determine rate constants as a function of temperature and solvent composition for an SN1 solvolysis reaction. Activation parameters (A, Ea, ΔHq, ΔSq) are determined using both Arrhenius and Eyring analysis. By varying solvent composition, the impact of solvent polarity on the rate and activation parameters can be explored. A simple conductivity probe is coupled with inexpensive, commercially available computer data collection interfaces. This experiment fits with the ACS guidelines for physical chemistry by making connections to material studied in organic chemistry and using modern techniques of computer data collection and analysis.1 Analysis of the results requires students expand and enhance their understanding of a familiar reaction at a mechanistic level. Students in organic chemistry study in detail nucleophilic substitution reactions where one atom or group is substituted for another RX þ Nu f RNu þ X
propane by conductance, reported in 1960 by Chesick and Patterson using alternate current (ac) bridges.3 The adaption of a home-built ac conductivity probe was suggested by Cyr and co-workers in 1973,4 and an early report using computer data acquisition to monitor pH to follow the reaction kinetics was reported in 1991.5 The use of specialty equipment is understandable given that the vast majority of articles investigating the kinetics of the SN1 reactions appear in this Journal prior to 1979. This experiment can be easily updated to use commercial conductivity probes interfaced with a variety of computer data acquisition devices. The method described here was developed using an inexpensive computer data acquisition interface coupled with a commercial conductivity sensor and then adopted using a different computer data acquisition interface, demonstrating the ease of transferability of the described techniques.
’ EXPERIMENTAL PROCEDURE Conductivity was measured either with a Markson (Honolulu, HI) model 1054 electrical conductivity meter connected to Pasco (Roseville, CA) Science Workshop 500 computer data acquisition box or Vernier (Beaverton, OR) with a LabPro computer data acquisition box interfaced with Vernier CON-BTA conductivity probe. Ethanol/water mixtures (15%30%) were prepared
ð1Þ
where X denotes the leaving group, Nu represents the electron rich nucleophile, and R is an alkyl group or H. There are many types of examples of substitution reactions in organic and inorganic chemistry textbooks.2 This article describes an update and expansion of a classic kinetic experiment, the rate of solvolysis of 2-chloro-2-methyl Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
Published: September 12, 2011 1586
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LABORATORY EXPERIMENT
Table 1. Summary of Classroom Data for Various Ethanol/ Water Mixtures Compared to Literature Values at 25 °C k/s1 Ethanol/Water (%v/v)
Figure 1. Block diagram for conductivity apparatus.
Class Avg
Lit Valuea
Difference (%)
15b
0.013
0.01431
18c
0.0161
n/a
—
20b 20c
0.0087 0.0128
0.01043 0.01043
16.6 22.7
22c
0.00952
n/a
—
25b
0.0061
0.0075
18.7
25c
0.00675
0.0075
10
30b
0.0039
0.00488
20.1
9.1
a
Data from ref 6. b Results using a LabPro computer data acquisition box interfaced with Vernier CON-BTA conductivity probe. c Results using a Markson model 1054 electrical conductivity meter connected to Pasco Science Workshop 500 computer data acquisition box.
respiratory, and eye irritant. Ethanol is harmful if inhaled or absorbed through skin.
’ RESULTS AND DISCUSSION The reaction (eq 2) is first order in 2-chloro-2-methylpropane ðCH3 Þ3 CCl þ C2 H5 OH=H2 O f ðCH3 Þ3 COR 0 þ Hþ þ Cl-
Figure 2. One student’s results using the LabPro Conductivity Probe for 15% ethanol/water mixture at 290 K: (A) a nonlinear regression analysis with eq 5 with fitted parameters L∞ = 299.6 ( 0.6 μS cm1, (L∞ Lo) = 244.7 ( 0.2 μS cm1, and k = 0.00615 ( 0.00002 s1 and (B) a linear regression fitted to eq 3 that gives k = 0.00695 ( 0.00002 s1.
by volume. 2-Chloro-2-methyl-propane was obtained from Sigma-Aldrich (St. Louis, MO) and used as received. Temperature control was maintained using variable temperature water baths. The ethanol/water mixture was thermally equilibrated in a test tube containing the conductivity probe. Then, ∼0.10 mL (2 to 3 drops) of the 2-chloro-2-methyl propane was added, the solution was mixed well, and conductivity measurements commenced. Data points were sampled every 15 s. The reaction was considered complete once the reaction mixture reached a plateau. The experiment can be done in one 3-h laboratory period, with students working in groups of two, and each group responsible for collecting rate data for one solvent composition over a range of temperatures. Alternatively, two laboratory sessions allows students to further explore and refine their experimental plan, determining if any additional trials are required.
’ HAZARDS Ethanol and 2-chloro-2-methyl propane are flammable. In addition, the latter may be harmful if inhaled and is a skin,
ð2Þ
where R0 is H or C2H5 from the solvent, an ethanol/water mixture. The reaction is followed by measuring the conductivity, L, due to the formation of hydrochloric acid. A diagram of the experimental setup is shown in Figure 1. Because a strong electrolyte is produced from a nonelectrolyte, the conductivity, L, at any time is proportional to the amount of (CH3)3CCl used up and the conductivity at infinite time, L∞, is proportional to the initial (CH3)3CCl concentration, [(CH3)3CCl]0. The rate of increase in conductivity is then a measure of the rate of reaction, k. The integrated rate law is given by ln½L∞ L ¼ ln½L∞ L0 kt
ð3Þ
ðL∞ LÞ ¼ ðL∞ L0 Þ ekt
ð4Þ
where L0 is the initial conductivity and t is time. Equation 4 can be rewritten for nonlinear regression analysis L ¼ L∞ ðL∞ L0 Þ ekt
ð5Þ
Sample data with fitting parameters are shown in Figure 2. The rate constant, k, for each reaction mixture was determined from the data by fitting the curve to eq 5 (Figure 2A) or eq 3 (Figure 2B). Both methods yield excellent fits with good agreement between the values for the rate constant. Instructors can choose to have students explore just one type of analysis or compare the two. Alternatively, in cases where the reaction is not followed to completion, eq 5 gives good results. A summary of classroom data for various solvent compositions and the known literature values6 is given in Table 1. Good agreement is seen between both methods and with literature. A plot of the rate constant at 298 K as a function of solvent composition is shown in Figure 3 and demonstrates the decrease in the rate constant as the percent ethanol increases. 1587
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Figure 3. The rate constants at 25 °C as a function of solvent composition using the Markson model 1054 electrical conductivity meter connected to Pasco Science Workshop 500 computer data acquisition box.
where R is the gas constant, T is the temperature, h is the Planck constant, and kB is the Boltzmann constant. Sample Eyring and Arrenhius plots are shown in Figure 4. When high quality data is obtained, results agree well with literature. Typical student values have ΔH q ranging from 70 to 90 kJ/mol and relatively insensitive to solvent. By contrast, ΔS q is highly solvent dependent, ranging from 40 to 40 J/(mol K) as the solvent polarity changes. The trends and values are similar to those in the literature,7 though the agreement is sensitive to the care the students take when carrying out the experiment. This experiment provides several opportunities for students to consider the accuracy and deal with error and propagation of error. Typical error for rate constants from a regression analysis is less than 1% whereas the standard error from reproducing the measurement is around 10%, permitting discussion of the different types of error. When determining Arrhenius and Eyring parameters, students propagate the error determined from their linear regressions into the error in the activation parameters.
’ ASSOCIATED CONTENT
bS
Supporting Information Student handout and instructor notes. This material is available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail: (E.M.M.) marzluff@grinnell.edu; (M.A.C.) mcrawfor@ knox.edu
’ ACKNOWLEDGMENT E.M.M. would like to thank Grinnell College for financial support and Luther Erickson for helpful discussions; M.A.C. would like to thank the Knox College Richter Foundation and the Glen Nagel Fund for financial support. This collaboration was funded by the Midstates Consortium for Math and Science for funding this collaboration. We would also like to thank the students in our physical chemistry courses. ’ REFERENCES Figure 4. Temperature dependence of solvolysis in 15% ethanol/ water mixture using the LabPro computer data acquisition box interfaced with Vernier CON-BTA conductivity probe: (A) Arrhenius plot yielding parameters Ea = 76 ( 3 kJ/mol and A = (2.4 ( 1.2) 1011 s1 and (B) Eyring plot yielding parameters ΔHq = 73 ( 3 kJ/mol and ΔSq = 35 ( 11 J/(mol K).
The temperature dependence of the rate constant for a given composition is used to calculate the activation energy, Ea, and frequency factor, A, in the Arrhenius equation, k ¼ A eEa =RT
ð6Þ
or the enthalpy of activation, ΔH q, and entropy of activation, ΔS q, from the Eyring equation, k¼
kB T ΔSq =R ΔH q =RT e e h
ð7Þ
(1) American Chemical Society, Committee on Professional Training. Undergraduate Professional Education in Chemistry: ACS Guidelines and Evaluation Procedures for Bachelor’s Degree Programs, Physical Chemistry Supplement; American Chemical Society: Washington DC, 2008. (2) Wade, L. G. Organic Chemistry, 7th ed.; Pearson Education: Upper Saddle River, NJ, 2009. (3) Chesick, J. P.; Patterson, A., Jr. Determination of Reaction Rates with an A.C. Conductivity Bridge. J. Chem. Educ. 1960, 37, 242–244. (4) Cyr, T.; Prudhomme, J.; Zador, M. Stabilized Linear Direct Reading Conductance Apparatus. Solvolysis of tert-Butyl chloride. J. Chem. Educ. 1973, 50, 572–574. (5) Allen, A.; Haughey, A. J.; Hernandez, Y.; Ireton, S. A Study of Some 2-Chloro-2-methylpropane Kinetics Using a Computer Interface. J. Chem. Educ. 1991, 68, 609–611. (6) Fainberg, A. H.; Winstein, S. Correlation of Solvolysis Rates. III. tert-Butyl Chloride in a Wide Range of Solvent Mixtures. J. Am. Chem. Soc. 1956, 78, 2770–2777. (7) Winstein, S.; Fainberg, A. H. Correlation of Solvolysis Rates. IV. Solvent Effects on Enthalpy and Entropy of Activation for Solvolysis of tert-Butyl Chloride. J. Am. Chem. Soc. 1957, 79, 5937–5950.
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