Robert B. Smith and Edward J. Billingham, Jr.
Nevada Southern University Las Vegas 89109
Factorial Design in Undergraduate Organic Experiments
I n a recent account of the approach to element,ary orgauic chemistry instruction at this campus ( I ) , the thought was expressed that worthwhile laborat,ory work for undergraduates serves both to acquaint thcm with appropriate techniques, tools, and materials, and--more fundamentally-to introduce them to scientific investigation. Accordingly, faced with the opportunity to develop a fresh curriculum for a new campus, the chemistry faculty at. Kevada Southern has agreed that laboratory ~ ~ o ratl iall levels should prod the student t,o learn how t,o experiment. For instance, beginning with the first day of freshman laboratory there is a continual emphac sis upon error analysis and the critical and complete reporting of experimental results. By the sophomore year, the student is using the library regularly to piece t,ogether his own experimental approaches to independent projects in the organic laboratory. We have found it not just necessary, but quite feasible, to dispense completely with traditional, "cookbook" laboratory manuals. The student reaction, expressed in interest, perseverance, and accomplishment, has been astounding. An appreciation of experimental design should be onc of the fruits of this type of training, and we have sought to devise experiments which draw attention to specific design techniques. Unfortunately, most chemistry curricula and textbooks take little note of efficient experimental designs and statistical evaluation of data, although excellent discussions of these matters are mailable (2-6). A superficial statistical treatment is usually presented in the freshman chemistry and quantitative analysis courses; however, this seems to be promptly forgotten or ignored by the students in subsequent courses. We have used the experiment described below early in t,he sophomore organic course to introduce the concept of factorial design, as developed by Fisher @), utilizing statistical data evaluation. Although factorial design is commonplace in the chemical industry, it is rarely used in most academic circles. We find that busy students respond favorably to the introduction of this concept as a labor- and time-saving device. The experience appears to help instill in them a questioning attitude toward experimental procedures in subsequent studies. Our students were introduced to the factorial concept via a mimeographed discussion, including a detailed example, which proceeded generally as follows. It is usually accepted practice to divide a laboratory problem into its component parts and to proceed tediously to study each part separately. This is reasonable if one is interested in evaluating the effect of one
factor, or of two factors at no more than t v o levels. (For example, the effect of two different t,emperatures corresponds to one factor at two levels. Each experiment in which t,he factor level is changed is referred to as a t,reatment.) If, however, one is concerned ~ ~ i t h the effect of alarger number of factors at more than two levels the number of treatments necessary to obtain precise data grows exponentially, as does the time involved. Furthermore, the data obtained through this type of conventional design enable one to evaluate the effect of changing each factor, but do not directly reveal interactions between two or more factors. An interaction may best be viewed as a diierence between differences. If, for example, the effect of varying a reaction temper* ture produces a certain effect at one catalyst ratio (moles catalyst to moles reactants) and a different effect at a second catalyst ratio, there is an interadon between reaction temperature and catalyst ratio. If there were no interact.ion, a change of temperature should produce the same effect regardless of catalyst ratio. If the conventional design is employed, the effects of single fact,ors (main effects) as well as interactions beheen factors can be evaluated with a maximum of precision and a minimum of v o r k In a factorial design more t,han one factor is varied in each treatment,,~ ~ ithe t hmain effect,sand int,eract,ions being evaluated via appropriate addition and/or subtraction of treat.ment results. I n a t,ypical laboratory problem one may wish to determine the effectsof temperature and reactant addition rate on the yield in an organic reaction. The selection of three different temperatures and two rates of addition results in a set of experiment,^ with six treatments involving all combinations of the selected factors. The mean effectof changing the rate of addition may be calculated by subtracting the mean yield obtained in treatments employing the first rate of addition from the mean yield in treatments employing the second rate of addition. I n similar fashion, the effect of varying the temperature from level one to level two and from level two to level three may be determined. Interactions may then be evaluated by comparing the temperature effects at one rate of addition to t,he temperature effects at the second rate of addition. A Suggested Experiment
The organic field abounds with potential class projects to which factorial design might be applicd. Care is needed, however, in selecting a system u-hichwill give results meaningful enough to give the students a feeling for t,he utility of this approach. For example, one obvious type of problem for such study-the effects of Volume 45, Number 2, February 1968
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varying reaction conditions on absolute yield of a reaction product--appears unsuitable for beginning students. Successful systems will generally involve studies of effects which are relatively insensitive to the quality of student technique.' The system described below, Friedel-Crafts hutylation of benzene, is an extension of the experiment described by Dunathan (6),and seems to he ideal for this project. On the one hand, the striking changes in relat,ive product distribution which result from variations in reaction conditions make it amenable to simple factorial analysis. At the same time, the chemistry involved is stimulating because it forces the student to the literature to rationalize results which are incompatible with his textbook knowledge of the reaction mechanism. Finally, the student is introduced to quantitative infrared spectral analysis, a simple statistical significance test, and such practical techniques as magnetic stirring and heterogeneous cataly~is.~ The Project. Data compiled by a previous class are given in advance to the students8 These data show the butylhenzene isomer distrihut.ion resulting during alkylation of benzene by all hutyl chlorides, both at reflux and at room temperature. The students are told that the gas chromatographic and infrared spect,roscopic evidence for the occurrence of the various hutplbenzene isomers is incontrovertible, hut that the exact proportions represented in the data are unreliable, due to analytical difficulties and a limited numher of samples. Also, the distributed data reflect no effect due to the proportion of catalyst used. The students are asked to reinvestigate the reaction of 2-bromobutane, assuming that the identity of the halogen is immaterial. They are provided with standard procedure4 and individual treatment assignments. The six treatments consist of combinations of three temperature levels (25, 50, and 80°C) and two molar ratios of aluminum chloride to 2-bromobutane (1:5, 1:25). Reproducibility of the results is probably enhanced by the use of magnetic stirring for all reaction mixtures.5 The isomer distribution in each product is determined by quant,itat,ive infrared analysis (see below). All results are pooled and used as the basis for individual formal reports. The class is asked to apply factorial analysis in order to reach conclusions concerning the effects on product distribution exerted by tempera-
' This is a tentative hypothesis based on our experience with two different systems. We think that reaction yield depends heavily upon the beginning student's manipulative skill in working up the reaction mixture; this factor overshadows ang effects due to operating conditions during the actual reaction. It is worth noting that many instructors assume such a. hypothesis by using yield to grade the student's h h technique. *Our study was limited to using a single isomer, 2-hromohutane, simply to keep the scope of the project manageable far a relatively small olass. This isomer gives interesting results, and still allows the use of a straightforward analytical procedure. Alternatively, data could be adapted from Dunathan (6). 'Provision of a "cookbook" procedure is not customary in our course, but is obviously necessary in a community project of this type. ' A liberal supply of relatively inexpensive stirrers (from Henry Troemner, Inc., Philadelphia; 519.75 in kit form) was provided through NSF Instructional Scientific Equipment Grant #GY1425, and hss proven immensely useful in many organic student experiments. 1 14
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Journal of Chemical Fducafion
ture (about which they have some inlding in advance) and by catalyst proportion (ahout which they know nothing). In addition, the class is asked to estimate the reliability of its conclusions via statistical analysis (see results below). Then they are to rationalize the observed effects, if any, in terms of a proposed mechanism for the rearrangements involved and the physical significance of the temperature and catalyst effects. Attention is drawn to leading literature references (7, 8) for aid in interpretation. Analysis of The Reaction Mixture. This may he carried out on a Perkin-Elmer Model 137 Infracord spectrophotometer. Sec-hutylbenzene has an absorbance maximum a t 13.1 p while iso-hutylbenzene exhibits a maximum at 13.5 p. The quantitative determination of each component may he calculated by a direct comparison of the absorption curves of the pure components to that ohtained for the reaction mixture, as done by Roberts, et al. (8, 9); or it may he done by solving simultaneous equations, as described by Ewing (10) or Willard, Merritt, and Dean (11). The authors have adopted the latter procedure. Reagent-grade acetone is used as a solvent for the product mixture. Although precision is not crucial, 0.P0.8 g of the product mixture may be diluted to 10 ml in a volumetric flask. (Weighings can be done on a IVIettler top loading P-120 balance.) The ahsorhancy indices (e) for each of the pure components are given in Table 1. Equations (1) and (2) are used to calculate Table 1.
Absorbancy Indices for Butylbenzenes (ml/g)
the concentration of each of the butylhenzenes. Relative isomer distribution is easily derived from these concentrations. Cis. = 0.082Axs - 0.004Ax1
(1)
C., = 0 . 1 1 8 A ~-~ 0.005Ax2
(2)
where XI is 1 3 . 1 ~ ;A, the absorbance; Xz, 1 3 . 5 ~ ;and C is in g/ml. Results
A summary of class results, in terms of weight percent see-hutylhenzene in the total product ohtained under various treatments, is presented in Table 2. The Table 2.
Tempera- 7 5 ture %W/W (Ti ser,Bnd
Student Factorial Data Summary
Reactant-to-catalyst Ratio-: I----. -2.5: I-%w/w Zd' N see-Bud L'd'
N
class size was such that six replicate runs of each treatment were possible when each student made two runs under differing conditions. The results of five runs were rejected on the basis of the 4d rule, which accounts for the varying N values (number of replicates) given in the table. Fisher's (8) t-test was applied to the data to determine whether there were significant differences
between the results of various treatments. It is necessary to sum the squares of the deviations from the mean ( E d % )within each set for this test. The t-test and its associated formulas are given in any modern "Handbook of Chemistry and Physics." The students had some difliculty in performing the t-test when comparing means of means to one another (e.g., the mean of all results at the 5: 1ratio to the mean of all results at the 25: 1 ratio). The problem centered about determination of the numher of degrees of freedom. This will not be (N1 N , - 2), as in the direct comparison of simple means, but rather should be con-
+
n
sidered as C (N - 1)where N represents the number of 4 - 1
replicates used to evaluate each treatment mean used l/Ns) has the in the comparison. The term (1/N1 same meaning as in the comparison of two simple means. For all comparisons, t-test calculations indicated a significant difference at the 99y0 confidence level between the weight percents sec-hutylbenzene obtained under various treatments, except as follows: there was no difference between the results at 25°C regardless of the catalyst ratio; there was a significant diierence at only the 95% confidence level between the results at 50" and 80°C with a 25:l catalyst ratio; the overall effect of changing the temperature from 50' to 80°C, including data for both catalyst ratios, resulted in a significant diierence at only the 90% confidence level. The student results accord reasonably well with those reported by Roberts (8) and by Dunathan (6). The use of an intermediate temperature (50°C) serves to show the effect of temperature on the rate a t which equilibrium is reached among the hutylhenzene isomers. Likewise, the necessity of an adequate supply of catalyst in order to reach equilibrium in this heterogeneous svs-
+
tem is clearly indicated. The time of reaction was constant in this project, but this is undoubtedly a third factor which could he considered in a more elaborate experiment with a somewhat larger class. One slight experimental difficulty is reflected in Table 2. Temperature control is more difficult at 50°C than at reflux or ambient temperatures, and the results a t this temperature were less reproducible. (Temperature control was exerted simply by a water bath, while monitoring was done by an internal thermometer.) One anomaly in the data, which is not readily explained, is the result at 50°C and a 25:l catalyst ratio. The students worked quite enthusiastically on this project, and appeared to grasp its significance. Literature Cited
(1) SMITH,R. B.,J. CHEM.EDUC.,44,148 (1967). (2) FISHER,R. A., "The Design of Experiments,'' (4th ed.), Oliver & Boyd, Edinburgh, 1947. N. L., "Statisticd Analysis (3) BENNETT,C. A., AND FRANKLIN, in Chemistry and the Chernied Industry," John Wiley & Sons, Ine., New York, 1954, p. 493ff. (4) HOGG,R. V., AND CRAIG,A. T., "Introduction to Mathe maticill Statistics," The Macmillan Co., New York, 1959.
(5) Cox, D. R., "Planning of Experiments," John Wiley& Sonq Inc., New York, 1958. H.C., J. CHEM.EDUC.,41,278 (1964). (6) DUNATHAN, (7) M A R ~ K. I , L., AND WILEN,S. J., J. CAEM.EDUC.40, 214 (1963). D., J . Am. Chem. Sac., (8) ROBERTS, R. M.,AND SHIEGTHONG, 82,732 (1960). (9) ROBERTS, R. M., HAN,Y. W., SCHMID, C. H., AND DAVIS, D.A., J . A m . Chem. Sac., 81,640 (1958). (10) EWING.G. W., "Instrumental Methods of Analysis," McGraw-Hill Book Co., New York, 1960, p. 51. (11) WILLARD, H. H.,MERRITP,L. L., AND DEAN.J. A., "Instrumental Methods of Analysis," ( a h ed.), D . Van Nostrand Co., Inc., Princeton, 1965, p. 94.
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