1544 Journal of Chemical Education  •  Vol. 85 No. 11 November 2008  • www.JCE.DivCHED.org  • © Division of Chemical Education

In the Laboratory

A chemist makes many decisions about the conditions under which an experiment is carried out. For example, should the temperature be held constant or varied or does it even affect the experimental outcome? We must know which variables af-fect experimental outcome and in what manner. To choose the most important variable(s), we might conduct factor-screening experiments (1). To determine whether there are synergistic effects of two or more variables, a full factorial design is used (2). The use of the technique of response surfaces allows us to maximize (or minimize) the yield of high purity products in the shortest time using a minimum quantity of reagents.

Introduction

This project was completed by students during the second semester of their second year in our educational institution.1 The students carry out the project over five weeks (three eight-hour days per week) and conduct it in parallel to other courses or other practical work. The project is done in a domain chosen by the student (organic chemistry, organometallic chemistry, analytical chemistry, process engineering, polymers, formula-tion, or catalysis). The students conduct a literature search, laboratory work and experiments, and write a technical report on the research subject.

The project described here illustrates experimental design and optimization applied to an organic reaction: the produc-tion of benzyl-1-cyclopentan-1-ol using a Grignard reaction (Scheme I). It exposes students to a combination of different chemical disciplines: practical organic chemistry, quantitative gas chromatography, and experimental design. It also prepares the student-engineer for an internship in industry.

Experiment

Students work in pairs and follow the experimental procedure adopted from the literature (3). Students start by identifying a number of factors that can influence the reaction. They then decide on a strategy to optimize the yield of the reac-tion. The students carry out 29 experiments for this study. The students begin by screening factors (8 experiments) and repeat an experiment once to calculate the standard deviation (1 experi-ment). They then carry out a factorial study (8 experiments) and finally use the response surfaces technique (12 experiments) to analyze the experimental data. Nemrod software (4) is used for all calculations and processing of data.2

At the end of each set of experiments, each pair of students combines their results to find the model of the strategy. At each step students discuss their results, their conclusions, and their plan for the next step with the professor, who gives her approval or hints for moving in a different direction. Finally, the students write a report describing the effect of all variables on the yield and discuss all the results obtained.

Hazards

Magnesium is highly flammable and contact with water liberates flammable gases. Cyclopentanone is flammable and ir-ritating to eyes and skin. Benzyl chloride is harmful if swallowed and toxic by inhalation, irritating to respiratory system and skin, and presents risk of damage to eyes. Diethyl ether is flammable and may form explosive peroxides. It is harmful if swallowed, re-peated exposure may cause skin dryness or cracking, and vapors may cause drowsiness and dizziness.

Experimental Design and Optimization: Application to a Grignard ReactionNaoual Bouzidi* and Christel GozziLaboratoire de Catalyse Organometallique de Surface (LCOMS), Ecole Supérieure de Chimie Physique Electronique de Lyon (CPE Lyon), 43, Bd 11 Nov. 1918, BP 82077, 69616 Villeurbanne cedex, France; *naoual.bouzidi@free.fr

Cl MgCl

MgCl

O

OMgCl

OMgCl OH

MgEt2O

H2O MgCl(OH)

2MgCl(OH) MgCl2 Mg(OH)2

Scheme I. Synthesis of benzyl-1-cyclopentan-1-ol by a Grignard reaction.

© Division of Chemical Education  • www.JCE.DivCHED.org  •  Vol. 85 No. 11 November 2008  •  Journal of Chemical Education 1545

In the Laboratory

Results and Discussion

The optimization study began by screening the experimen-tal factors that could have an influence on the reaction according to the experimental procedure selected.

Screening ExperimentsFor the Hadamard matrix (Plackett–Burman design) (5)

the students chose six factors, • VolumeofdiethyletherEt2O needed to prepare a solution

of benzyl chloride; x1

• Benzylchloride(BnCl)solutionadditiontime;x2

• Stirringtimetopreparethebenzylmagnesiumchloride;x3

• Excessofbenzylchloride/cyclopentanone;x4

• Excessofmagnesiumturning/benzylchloride;x5

• Reactiontime;x6

and examined each at two levels as shown in Table 1. For each factor the students define a range of variation; the low level is noted as ‒1 and the high level is noted as +1. The use of +1 and ‒1 for the factor settings is called coding the data. This helps in the interpretation of the coefficients fitted to any experimental model. Th e design matrix and the experimental results are re-The design matrix and the experimental results are re-ported in Table 2.

To estimate the standard deviation, run 4 was chosen randomly and was repeated three times, the standard deviation value found is 3.5. The coefficients of the linear polynomial were estimated and the result is as follows:

45 63 15.Y .. . .63 0 13 0 881 2 3x x x

. . .0 13 5 88 1 884 5 6x x x

The model was fitted with the variables in coded form. High values of coefficients indicate a strong influence of the variables on the dependent response (yield). The results obtained show, over the range studied, the volume of the diethyl ether (x1) and theexcessofmagnesium/benzyl chloride (x5) are significant. However, the volume of diethyl ether has a greater influence on the response. The addition time (x2), stirring time (x3), the excessbenzylchloride/cyclopentanone(x4) are the factors that have the least influence on the yield. The reaction time (x6) has an average effect on the response in comparison to the factors x1 and x5.

The Hadamard matrix design is a useful tool in any study as it is appropriate for screening the factors according to their influ-ence. The students chose to continue with the most influential factors (x1, x5). The reaction time (x6) is also an important factor for the organic reaction: the longer it is, better the formation of product (provided that a secondary product is not formed, which is not the case in this reaction). Though the screening showed that this factor has an average effect, the students de-cided to study it in the factorial design.

The students then made a more precise study to evaluate the effect of the interactions between the three factors x1, x5, and x6. They carried out a full factorial design. To conduct the experiments for this design, the factors that have a slight positive effect on the reaction (screening study) are fixed at the level +1 that is, the addition time (x2) was set at 90 min, stirring time (x3)at40min,andtheexcessbenzylchloride/cyclopentanone(x4) at 30%. The design matrix and the experimental results are reported in Table 3.

The coefficients of the linear polynomial were estimated and the result is as follows:

. .51 06 14 3Y 11 1 31 3 561 5 6x x x. .3 31 0 06 4 191 5 1 6 5 6x x x x x x. . .2 56 1 5 6x x x.

The principal effect, represented by the value of the coefficient, showed that x1 (volume of the diethyl ether) and x6 (reaction time) are the most influential factors. With the factorial model, we also obtained the effect of the interactions between two fac-tors; the most influential are the interactions x1x5 and x5x6.

Table 1. Factors and Levels for the Screening Study

Factors Level 1 Level 2

x1: Volume of (Et)2O/mL 18 50x2: Benzyl chloride (BnCl) solution addition time/min 60 90

x3: Stirring time/min 20 40

x4: Excess of (BnCl)/cyclopentanone (%) 20 30

x5: Excess of Mg/BnCl (%) 12.5 25

x6: Reaction time/min 30 60

Table 2. Hadamard Matrix Design and Results

Run

Factors Response

x1 x2 x3 x4 x5 x6

Yield (%)Vol (Et)2O/mL

Addition Time/min

Stirring Time/min

Excess BnCl/ Cyclopentanone (%)

Excess Mg/BnCl (%)

Reaction Time/min

1 50 90 40 20 25 30 72

2 18 90 40 30 12.5 60 33

3 18 60 40 30 25 30 29

4 50 60 20 30 25 60 74

5 18 90 20 20 25 60 31

6 50 60 40 20 12.5 60 52

7 50 90 20 30 12.5 30 47

8 18 60 20 20 12.5 30 27

1546 Journal of Chemical Education  •  Vol. 85 No. 11 November 2008  • www.JCE.DivCHED.org  • © Division of Chemical Education

In the Laboratory

For a better understanding of the interactions, it is neces-sarytobuildtheinteractiondiagrams(Figure1).Eachupperright quadrant corresponds to the average experimental response when the individual factors involved in the interaction term are both at level +1.Eachupperleftquadrantistheaveragevaluewhen the first factor involved in the interaction term is at level ‒1 and the second at level +1, and so on (Figure 1). As a result, all the values are the average values over all experiments (presented in Table 3). As an example of a calculation, the value 70 in the interaction x1x5 (upper right quadrant) is obtained, taking the yield values when the factors x1 and x5 are held at level +1 as follows:(68+72)/2correspondingtotheexperiments4and

Table 3. Full Factorial Matrix Design and Results

Run

Factors Response

x1 x5 x6

Yield (%)Vol (Et)2O/mL

Excess Mg/BnCl (%)

Reaction Time/min

1 18 12.5 30 28.5

2 50 12.5 30 55.5

3 18 25 30 38

4 50 25 30 68

5 18 12.5 60 49

6 50 12.5 60 66

7 18 25 60 31.5

8 50 25 60 72

xj

1

1

1 10 xi

Figure 2. Central Composite design for two factors.

Figure 1. Diagrams for the interactions x1x5 and x5x6.

x5 x6

34.75 70

38.75 60.75

1

1

1

1

1

11 1 x5x1

57.5 51.75

42 53

8, respectively. The diagrams provide preliminary suggestions about which interactions may be the most significant in deter-mining the yield.

For the interaction between factors 1 and 5, there is a somewhat large difference depending on whether factor 1 is at a high (favorable) or low level. A slightly smaller difference is seen related to factor 5. It appears that factors 1 and 5 should preferably be at a high level to obtain the best response. For the interaction between factors 5 and 6, we can apply the same rea-soning but the interaction is not as strong, taking into account the differences between the responses in the various quadrants. It appears that factor 5 should preferably be at a low level and factor 6 at a high level to obtain the best response.

The screening study (Plackett–Burman design) (5) and the full factorial design allowed the most significant factors to be chosen: the volume of the diethyl ether (x1) and reaction time (x6). It is interesting to see how the yield depends quantitatively on these significant factors. One method to optimize the syn-thetic outcome is to establish a response surface model. Then, the students have chosen a full central composite design (6).

A full central composite design consists of the following parts: a full factorial design; experiments at the center (i.e., xi = 0 for all factors); and experiments where xi = ±α and with xj ≠ xi = 0. These axial points (cross points) are situated on the axis in a coordinate system and with distance ±α from the cen-ter. The design for two factors can be graphically illustrated as in Figure 2. If we apply this composite design to this study we obtain the following matrix of experiments (Table 4). The star points are located at distance α = 2k/4 (the value of α is chosen to maintain a full rotatability of the design) (6), where k is the number of factors. In this study, k = 2 so the α value is 1.41.

The coefficients of the quadratic model were estimated (the model was fitted with the variables in coded form) and the result is as follows:

Y x x x58 38 20 71 4 28 7 881 6 12. . . .

x x x1 63 5 7562

1 6. .The quadratic model is analyzed as a whole and the quality of its fit can be checked by several criteria. The determination coef-ficient R2 = 0.900 indicates that only 10% of the total variation is not explained by the model. The Fisher test (7) demonstrates a high significance for the regression model. The comparison of the residuals calculated from Table 5 with the residual variance (s2 = 12.89; s = 3.59) indicates that no residual exceeds three times the square root of the residual variance. All of these consid-erations indicate the adequacy of the second-order polynomial model proposed to explain the optimization of the yield.

Contour plots of the response surface as a function of the two factors (x1 and x6) are helpful in understanding both the main effects and the interaction effects of these two factors. These plots can be easily obtained from the model by calculat-ing the values taken by one factor when the second varies from ‒α to +α in coded form, that is, from 11.37 mL to 56.63 mL for x1 and 9.91 min to 27.59 min for x6. A 3D representation of the response surface gives a good view of the results and is easy to interpret (Figure 3). For the two factors, volume of diethyl ether (x1) and reaction time (x6), the contour plots in Figure 3 indicate that a large volume of diethyl ether (50 mL coded for the level +1, or more) associated with a long reaction time (25 min or more) leads to a good yield (higher than 78%) in the experimental region chosen (from ‒α to +α).

© Division of Chemical Education  • www.JCE.DivCHED.org  •  Vol. 85 No. 11 November 2008  •  Journal of Chemical Education 1547

In the Laboratory

Table 4. Central Composite Matrix Design and Results

Run

Factors Response

x1 x6Yield (%)

Vol (Et)2O/mL Reaction Time/min

1 18 12.5 39

2 50 12.5 66.5

3 18 25 22

4 50 25 72.5

5 11.37 18.75 10.5

6 56.63 18.75 72.5

7 34 9.91 38

8 34 27.59 70

9 34 18.75 59

10 34 18.75 57

11 34 18.75 54.5

12 34 18.75 63

Conclusion

This experiment works well in an integrated laboratory. The students can apply the theory of the experimental designs as well as the concepts of statistics; the choice of designs was made to il-lustrate performance of different designs. The prelab discussions accompanying these experiments can include the experimental design techniques and also the chemistry of the reaction in-volved. For example, the students decided to study the factor x6 (reaction time) even though the screening study showed that x6 had an average effect. They thought that this result was unusual from their knowledge of organic synthesis.

The students receive a score for this project. The score for the experimental work is an evaluation of the student’s ability. The main aspects that are evaluated are the results obtained as a function of the objectives, the efficacy, autonomy and initiative, and the capacity to work in a team while respecting the safety rules. The score for the scientific report is an evaluation of the student’s ability to take into account the bibliographic work and experiments carried out, and being able to analyse the results using their knowledge.

Notes

1. In this institution, the students have courses, tutorial work, practical work, and projects in organic chemistry, organometallic chem-organic chemistry, organometallic chem- organometallic chem-organometallic chem-istry, analytical science, process engineering, polymers, and catalysis. They also have courses and tutorial work in physical chemistry statistics and experimental design. 2. Nemrod is commercial software; a version can be downloaded for trial with a one month time limit.

Literature Cited

1. Lazaro,R.;Mathieu,D.;PhanTanLuu,R.;Elguero,J.Bull. Soc. Chim. Fr. 1977, 11–12, 1163–1170.

2. Guervenou,J.;Giamarchi,P.;Coulouarn,C.;Guerda,M.;LeLez,C.; Oboyet, T. Chemom. Intell. Lab. Syst. 2002, 63, 81–89.

Table 5. Observed Responses and Predicted Values

RunYield

Observed Response Predicted Value*

1 39 29.63

2 66.5 59.55

3 22 26.70

4 72.5 79.62

5 10.5 13.34

6 72.5 71.91

7 38 49.07

8 70 61.18

9 59 58.38

10 57 58.38

11 54.50 58.38

12 63 58.38

*Calculated by using the mathematical model obtained.

4.65

42.33

80.00

Yield (%)

Factor x 6

Factor x1

Figure 3. Response surface contours as a function of factors x1 and x6.

3. Christol, H.; Laurent, A.; Mousseron, M. Bull. Soc. Chim. Fr. 1961, 28, 2313–2318.

4. Mathieu,D.;Nony,J.;Phan-Tan-Luu,R.NEMROD-W Software, LPRAI,Aix-Marseille IIIUniversity,France.http://www.nem-rodw.com(accessedJul2008).

5. Plackett,R.L.;Burman,J.P.Biometrika 1946, 33, 305–325. 6. Palasota, J. A.;Deming , S.N. J. Chem. Educ. 1992, 69,

560–563. 7. Box,G.E.P.; Hunter,J.S.;Hunter,W.G.Statistics for Experiment-

ers; Wiley: New York, 1978.

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