JOURNAL OF CHEMICAL EDUCATION
as to why the work was done or what it proved, if anything. After the second conference these questions can usually be answered easily. Then the questions become more searching. The author of the published research obviously had a problem and a plan and he got certain results. His plan, however, was based upon certain interpretations of structure or reactivity, let UF say. Are these interpretations reasonable, or, if they are open to reasonable doubt, what alternatives are there? On the basis of the student's new interpretations where would the author's plan of attack lead'? Would the expected result be compatible with the experimental results which the author found? Could it be used to explain, possibly, some results which the author was forced to overlook? Likewise, the autho~ found he had to make certain assumptions in order t o reduce his idea to experimental verification. Can the student find and state these assumptions? What are the bases for the assumptions? Are they reasonable'? Assuming one does not wish to grant them, is there any way to establish them more firmly? The author has obviously credited previous workers with successfully carrying out certain basic operations or reactions. Does the student agree with the author that the prohlems which these involve are really adequately settled? If not, in the estimation of the student what more would be required? In a problem in organic chemistry, having to do, let us say, with a natural product, the student should always be asked to name the structure and to identify its component parts. Very often it is helpful if he is made to identify the states of oxidation of the various atoms and to relate these states with the changes involved in a chemical reaction described in the paper. At this point it is sometimes possible for the student to recognize that the overall operation just described is really just afamiliar name reaction (somewhat disguised) that he has known for some time. As the student proceeds to name the parts and to recognize the chemical processes in terms of familiar operations he often sets in motion thechain of associations which leads him to ask questions that may have no answers presently available. At this point he has, with the instructor's considerable assistance, developed a research problem for himself. Depending upon the student and his individual needs, the instructor may require him to fill in the background for the problem by exhaustively examining the related literature, or he can suggest that the student do that later and proceed immediately to a new topic. Since one can never tell what sort of paper a student will read it follows that his development is less likely to be centered around the special field of activity of his instructor. He is less of a carbon-copy of his research director and finds no difficulty whatever in making an independent beginning for himself in other fields of research.
The student is required (as a part of the course) to enter the problem on a page in a bound book, properly dated, labeled, signed, and witnessed. The students are encouraged to use the same book to record all unusual reactions, structures, or items which they do not undentand. By keeping the notebook up to date, by consulting it frequently, by puzzling over its contents and attempting to construct new relationships to any other facts, the student establishes a continuity of thought and development which may easily become the most important and satisfying element in his selfeducation. The function of the instructor should be expect,ed to change perceptibly during the course. Less and less should he he the inquisitor in routine mat,ters as the student begins to take on this function for himself. His task must always be accomplished with finesse. Very often he must lead without seeming to lead, and he must refrain from impatiently reverting to the simpler but inadequate lecture system. So far we have considered the effect on the student, but the instructor, as usual, profits considerably also. In the first place, he finds that he is obliged to maintain a fairly complete coverage of current literature. It should also be admitted that he, too, gains much in understanding of this literature by his questioning of tlhe student. Perhaps of greatest importance to a teacher, however, is the insight gained into the thinking operations of the student. Quite occasionally, too, the instructor can witness the development in the student of methods of reasoning and their fruition in the recognition of inadequately explored areas of knowledge. This is indeed a thrilling experience for anybody. While not all students are equally teachable by this or any other method the author has found that these "classes" are never dull and he heartily recommends the experience to all who will try it. Perhaps in this way we can, in part, at least, meet the challenge recently voiced by J. D. Porsche' who stated: It would seem, however, that much could be gained if marc of our professors of chemistry would impart to their students not, only the knowledgo and techniques which are the tools of research but also the mentd processes and habits which are research.
The author makes no claim for the originality of either the t,eaching method outlined herein (which is as old as education itself) nor the subject matter of the course described. He simply believes that the personalized training described is important and deserves more attention in the graduate curricula of our universities. Although the accomplishment of research is important it cannot he doubted that the main task of graduate education is the training of thinking men.
' PORSCHE,J. D., Chem. and Eng. News, 28,245 (1950).
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JOURNAL OF CHEMICAL EDUCATION
However, a new comhination of factors was tested as shown in Table 4. TABLE 4 P~essure,mm.
Temperature, "C.
Yield
800
200
25.20 25.15 25.10 25.15 25.10
Average yield = 25.14 Cdoulated yield = 33.90 (The celculeted yield sss determined from Equation 1 using PI = 400, T I = 25%, Y L= 31.40)
where Yl is the yield under condition PI, TI;Y2is the predicted yield when conditions are changed to P1,T2. TABLE 1 Effect of Pressure on Yield
LOO
Pressure, mm.
Av. yield 31.40
finn
800
20.81
15.75
TABLE 2 Effect of Temperature on Yield
Under this combination of factors Equation 1 does not hold since the observed yield of 22.14 is grossly lower than the 33.90 value predicted from the equation. This failure to account for combinations of factors is bound to occur whenever the experimental method of conventional control is applied to situations where interactions or "preferential responses" exist between variables. A more efficient design for experiments here interactions may be involved has been developed. This design is known as the "factorial" design and simply consists in the requirement that each variation of every factor be combined in one of the experimental batches with each variation of all the other factors. A factorial combination can he selected from the above experiments which points the way to obtain more reliable results with less expenditure of effort when dealing with interacted factors. Table 5 shows this factorial combination of the pressure and temperature factors a t two levels, the data being selected from Tables 1. 2, and 4. he analysis of tl; factorial combination in able 5 shows the interaction between pressure and temperature in their effect on yield to be highly significant.
@M 0,-
Av. yield 31.40
39.34
49.46
This equation fits the exoerimental facts verv well as shown in-Table 3 where P; is taken as 400 mm., T1 as 25°C. TABLE 3 Pressure, mm.
Temperatwe, "C.
Amrage Observed Yield
Calcdated Yield
25
200
100
T E M P E R A T U R E in Fig"..
'C
2
Interactions in experiments in chemistry usually can he classified into one of three types of mathematical functions or a combination of these:
42 1
AUGUST. 1950
1. Hyperbolic (cross product) relationship between variables (e. g., Y = KPT or Y = KTIP). 2. Power function relationship (e. g., Y = KIP2 K2T2,etc.). 3. Exponential function relationship (e. g., Y = K, logP K2log T,etc.).
+
TABLE 5 ----Pressure,
Temvemture. 'C.
mm.--
+
The data in these experiments fits the form
+
+
31.40 Av.
a) - K ( T 273) Y = K(T P P
which is not surprising since the investigation consisted in measuring t,he volume of air in a mercury manometer tube under various conditions of temperature and pressure. From this experiment involving only the simple gas laws it is apparent that our "conventional control" type of experiment is not designed to deal with the complex situation encountered in experimental investigations and is applicable only when the variables involved are independent and linear functions of the effect measured. This situation is the exception rather than the rule in chemical work. Reaction rates are exponential or power funct,ions of concentration of reactants. Equilibrium constants and rate constants are exponential functions of the inverse of absolute temperature. Reaction kinetics involve complex hyperbolic and power functions of the concentration of reactants. It is this peculiar complexity of interrelationships which makes the task of the chemist so baffling, and which makes the powerful tool of statistically designed experiments and statistical analysis of data a critical need for anyone engaged in this field. The primary difficulty in bringing statistical methods to hear on experimental problems in a widespread fashion is the lack of chemists trained in this field. The chemical educators are not, in general, aware of the existence, potentialities, or applicability of statistical methods in chemical experimental investigations and, as a consequence, students are not given courses in the application of the new probability developments to experimental problems Persons trained in mathematical statistics alone are not too useful since the chemical aspects of experimental problems usually outweigh the purely statistical considerations. I t therefore appears that two kinds of attacks should be made with the ohjective of increasing the use of statistical methods in chemical experimental work, one attack being directed toward the chemists now practicing their profession, the other toward providing this training in our schools. So far as the present chemists are concerned, the most effective approach appears to be to demonstrate first the utility
49.69 Av.
Soume of Variation Temperature Pressure Tem~erature
Sum of Spllares
Degrees of Freedom
957.7280 2020.0500
1 1
15.75 Av.
25.14 Av Mean Square
F"
957.7280 259,547 2020.0500 547,439
X
"This method for analyzing data is described in any of the references given at the end of this paper. F is the ratio of the "hean square" for a factor divided by the mean square for error. Chance fluctuations will give an F value as high aas 4.49 once in 20 times and as high as 8.53 once in 100 times in this experiment. A factor may be oonsidered significant at the 0.05 probability level if it gives an F value in excess of 4.49.
of the methods and then set up seminars within the schools and industrial concerns to provide guidance in mastering the principles and techniques. The most important objective, however, is to so arouse the interest of the academic chemists that they will provide the student chemist with training in the principles of experimentation so that he may better cope with the complex problems he is likely to encounter in any line of chemical work. REFERENCES (1) FISHER,R. A,, "Stati&icd Methods for Reseamh Workers," Oliver and Boyd. (2) . . FISHER.R. A,. "The Desixn of Ex~eriments!' Oliver and ~oyd. (3) FREEMAN, H. A,, 'Tndustdal Statistics," John Wiley & Sonn. (4) GOULDEN, C. H., "Statistical Methods,'' John Wiley & Rnns
(5) BROWNLEE, K. A., 'Tndustnal Experimentation," Chemical Rubber Publishing Co. (6) PETERS AND VANVOORHIS, "Stati~ticdProcedures and Their Mathematical Bases," MeGraw-Hill Book Co.
