Determining Hammett Sigma and Rho Values Improvements on a Published Student Experiment Bruce A. Hathaway and Bjorn Olesen Southeast Missouri State University, Cape Girardeau, MO 63701 In a recently published organic chemistry laboratory text, a series of experiments are described in which students are able to relate the structure of a compound to its reactivity ( I ) . The experiments are 1. Determining the pK,'s of substituted benzoic acids. 2. Preparing the henzoie acid methyl esters. 3. Measuring the rates of base hydrolysis of the methyl esters. The rate constants for the hydrolyses are determined, and the Hammett relationship between acidity and rate of hydrolysis can be demonstrated. As we began doing this series of experiments, we encountered some problems. In the first experiment our measured pK,'s were not linear with literature values. In the given text procedure, the acids were dissolved in a 48% (vlv) ethanol-water mixture, then titrated with aqueous base. Because equimolar amounts of each acid were not used, each titration required a different amount of base. Therefore, the proportions of ethanol and water a t the end of each titration were different. Since pK.'s are quite solvent de~endent(2). this could account for our deviations from liiearity. wehave overcome this difficulty by titratine with base dissolved in the same ethanol-water mixture as the benzoic acids, yielding more linear results. For the preparations of methyl benzoates, the lab text recommended refluxing the benzoic acids with excess methanol in the presence of sulfuric acid for 1-2 h. This gave us low yields of the esters (10-30%). We were able to increase the yields to about 50% by allowing the reaction flasks to stand for a week (capped with a drying tube) after the reflux time. Alternatively, refluxing the benzoic acid with a slight excess of thionyl chloride for two hours, followed by pouring the crude acid chloride into methanol, resulted in isolated yields of about 80%. For the rate measurements, the lab text called for the reaction to be maintained at 0 'C, with aliquots to be removed a t unspecified time intervals, quenched with HCl, and titrated with NaOH. After examining the literature (3) and performing a number of trials, we found suitable time intervals for use with methyl benzoate, methyl 4methylbenzoate, and methyl 4-methoxybenzoate. We discovered that, even though the ester and base solutions were precooled to 0 'C, the temperature still heated up to about 10 T when the solutions were mixed. Since we couldn't easily wntrol the temperature, to simplify the pmcedure, we elected to perform the hydrolyses a t mom temperature. At room temperature, the rates of hydrolyses of the methyl esters of Cnitro, 4-chloro, and 4-bromobenzoic acids were too fast to measure accurately. Reducing the concentrations of ester and base helped for the halobeuzoic acid esters, but hydrolysis of the nitro compound was still too fast. Therefore, we developed a "Quench" method (see procedure section). Briefly, several identical ester solutions are prepared, base is added to one, the whole reaction is quenched with acid a t an appropriate time interval, and the reaction mixture is titrated with NaOH. Each ester solution is reacted, varying the time interval at which the reaction is quenched. This worked so well with the nitro
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compound and was much easier for the students to do, that this method was adapted for use with the other esters also. By appropriate choices of time intervals, the same concentrations of ester and base can be used for all of the esters, except the 4nitro ester. We have written a BASIC computer program for IBMcompatible computers to calculate the rate constant for hydrolysis of an ester. The published program LLSQ (4) was modified for the least-squares analysis. The user is prompted to input the reaction conditions and the data from the titrations of the reaction mixtures. The concentration of ester remaining in each reaction mixture is calculated, and the best straight line is calculated from the data of l/[esterl versus time. The slope of the line is the rate constant. Pearson's correlation coefficient, r, is used to report the fit of the line. The program also calculates the concentrations of ester a t each time interval from the calculated straight line. The average values of the pK:s and rate constants obtained by our Organic I1 lab students in the spring semester of 1992 are reported in Table 1. Simple linear regression of pK,'s in 48% ethanol versus pK,'s in water produced the following equation: pK,(48% ethanol) = 0.14(M.08)+ 1.32(M.10)x pKJwater) For this equation, r = 0.99. Finally, to see if a Hammett relationship existed, simple linear regression of the log relative rates (log of the ratio of the rate-constants of the X-substituted benzoic esters to methyl benzoate itself) versus sigma [pK,(benzoic acid). pK,(4-X-benzoic acid) in water] was performed. The following equation was produced: log (relative rates) = 0.13(M.16) + 2.45(?-0.19)x sigma For this equation, r = 0.98. The slope, 2.45, is the Hammett reaction constant, rho, for this reaction. The literature value of rho for this reaction in 60% acetone at 25 T is 2.382 (5).Given that the temperature was not rigorously controlled, this agreement is gratifymg. Table 1. Experimentally Determined pK;s (in 48% ethanol), Literature pKa's (in water), and Experimentally Determined Rate Constants for Ester Hydrolyses (in 60% acetone) Substituent
PK~
PK~
(48% Ethanol) Water (Ref. ZJ &NO2
4 4
4-Br
H 4-CH3 4-OCH3
4.29 4.94 5.01 5.45 5.51 5.63,
3.42 3.98 3.97 4.20 4.37 4.47
Rate Constant (M-I s 8 ) 9.20 x lo-' 8.74 x 10.' 5.40 x 10-' 1.03x 10-' 5.86 x lo4 2.54 x I oil
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Table 2. Reagents and Time Intervals for Kinetic Runs for Substituted Methyl Benzoates
Substituent
Quench Flask Vol (mL) HCI
M HCI
Stock Solution moles ester1 50 mL acetone
Reaction Flask Volume (mL of Stock Soh)
Conclusion The modifications we have developed represent a set of workable procedures that allow this series of experiments to be performed in three, 3 4 hour lab periods. During the first period, the preparations of the esters are begun, and the pK;s of the benzoic acids are determined. In the second period, the esters are isolated and purified. In the fmal period, the rate studies are run. We had each student make one ester and determine one pK., and let the students work in pairs for the rate studies. All of the class results were given to each student. This allowed the students to see that those groups that increase acid strength also increase the rate of base hydrolysis of the corresponding methyl ester. Groups that decrease acid strength decrease the rate of ester hydrolysis. These results can be related to the electronic effects of these groups in electrophilic aromatic substitution (p-nitro: strongly electron-withdrawing; p-chloro and p-bromo: electronwithdrawing by induction, which outweighs any electrondonation by resonance; p-methyl: electron-donating by induction andlor byperconjugation; andp-methoxy: strongly electron-donating by resonance, which outweighs the inductive electron-withdrawal). We plan to use meta-substituted benzoic acids in the future, which would eliminate resonance effects, thus changing the methoxy into an acidstrengthening and rate-enhancing substituent. Procedure Determination of pKa's
Three, 100 mg samples of the substituted benzoic acid are weighed out to the nearest tenth of a milligram. Each sample is dissolved in 25 mL of 95% ethanol, and diluted with 25 mL of distilled water. Each solution is titrated with 0.03 N sodium hydroxide in 48% ethanol using a pH meter. A blank of 25 mL of 95% ethanol and 25 mL of water is titrated also with the 0.03 N NaOH in 48% ethanol. A graph pH versus milliliters of base for each titration is prepared, and the blank is subtracted manually. The inflection point of each corrected curve (the point at which the slope of the curve reaches its maximum and changes direction) is marked, and the volume of base a t that point is determined. The pH reading a t one-half that volume of base should be equal to the pK, of the acid. Preparation of Methyl 4-X-Eenzoates
Normal Esterification Approximately 5.5 g of the 4-Xbenzoic acid, 50 mL of anhydrous methanol (Caution: Poison), and 1mL of conc. H2S04(Caution: Strong Acid) are combined in a 100-mL round-bottomed flask, which is fitted with a water-cooled condenser and a calcium chloride drying tube. The mixture is heated a t reflux for 23 h, allowed to cool to room temperature, then allowed to stand 954
Journal of Chemical Education
Vol (mL) Acetone
Vol (mL) NaOH
M NaOH
Reaction Times (min)
a t room temperature until the next lab period, either corked or protected with a drying tube. The reaction mixture is poured into about 75 mL of water, and extracted with three, 50-mL portions of ether. The combined ether solutions are extracted with 25-mL portions of 5% sodium bicarbonate solution until there is no appreciable gas evolution (three times is usually enough), then extracted once with 25 mL of saturated sodium chloride solution, and dried over sodium sulfate or maenesium sulfate. The drvine agent is filtered off and the " ether removed by simple distillation or with a rotary evaporator. The esters are ~urifiedeither bv distillation or recrystallization, as app;opriate. ~solatedyields were in the 4 0 5 0 % range. Thionyl Chloride Method Approximately 5.5 g of the 4X-benzoic acid and 1drop of pyridine are placed in a 100mL round-bottomed flask. A condenser is attached, and a gas trap is attached to the top of the condenser. The apparatus is taken to the fume hood, and 5 mL of thionyl chloride (Caution: Corrosive. Lacrymator) are added through the top of the condenser, after which the gas trap is immediately reattached. The mixture is heated a t reflux for 1-2 h (or for about 10 min after all of the acid has dissolved), allowed to cool to room temperature, and then cooled in a n ice-bath. Methanol (50 mL) is also cooled in an ice-bath. The acid chloride and the methanol are taken to the hood, and the acid chloride is cautiously added to the methanol dropwise, with stirring. After the addition is complete, the methanol solution is allowed to stand for a t least 1 h (or until the next lab period in a corked container), then worked up as above. Isolated yields ranged from 7683%.
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Rate Measurements
Quench. For each kinetic run, five identical quench flasks are prepared by adding the prescribed amount of HCI and two drops of phenolphthalein to each of five, 125mL Erlenmeyer flasks. Reaction Flasks. Four identical reaction mixtures are prepared from a stock solution. To prepare the stock solntion the prescribed amount of ester is weighed out and placed in a 50-mL volumetric flask, and diluted to the mark with acetone. Then 5.0 mL of the stock solution is pipetted into each of four, 125-mL Erlenmeyer flasks. Finally 10.0 mL of acetone is pipetted into each Erlenmeyer flask, and the flasks are stoppered until the kinetic runs are made. n'tmlion of Blank. One of the quench flasks from step 1 is taken and 10.0 mL NaOH iconcentration ofNaOH should be the same as that added &the reaction flask), and 15 mL of acetone are pipetted into the quench flask. This is titrated to a faint pink endpoint. Kinetic Run. When everything is ready, the prescribed amount of NaOH is added to one of the four reaction flasks
and the time is recorded. At the prescribed time interval, the contents of the quench flask is poured into the reaction flask. The quench flask is rinsed with a small amount of distilled water and this is added to the reaction flask. The solution is titrated immediate,,, to a persistent pink endpoint with 0,01 NaOH,The process is repeated with the other reaction mixtures, varvinc . - the time as prescribed in the Table 2.
Literature Cited
o. R.; wen, C. E., JI; clnh A. K.olgonle c h m i s t ~kbornloq standard and ~lemscalp~lperimpnts; saundem:~ h i ~ a d d ~1880. h i ~ chapters , 22 & 23. 2. Thusire, R.C. R. h d . Sci. Paris 1BBs.267, W33-994. 1. m i , ,
3. T m d a , E.;Himhd"mod. C. N. J Chm. Soc (London) I%%,1801-1810. 4. Rogers, D. W Computotio~lChmlptry U s i n g f h P C : VCH:NewYorL, 1880: Chap t e r ~
5. wells,p.R
.
C RPU ~ 1 ~ s . 6 3I~I-ZI~. ,
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