D. Cabrol, D. Cachet, and J. H. Basso Universitk de Nice Parc Valrose, F 06034 N ~ c eCedex, France
Laboratory-Equivalent Minicomputer Experiments A kinetic
Computer assisted instruction is customarily conducted using time-sharing systems. However, as shown by G . L. Breneman,' small computers can conveniently be used for this task, especially for laboratory simulation. The princiDleS of computer ex~eriments have been outlined by 'Craig, et al. in this ~ o m m and l ~ it appears to us that the field of chemical kinetics lends itself particularly well to simulated experimentation. The kinetic study of chemical reaction requires numerous lengthy experiments, but in the usual conditions of teaching it is necessary as a rule to restrict an experiment to a few closely directed manipulations. This situation leaves the student no r w m for initiative in planning experiments and thus deprives him of the greatest enrichment he could gain from experimental practice. To fill this gap, we have developed programs that allow kinetic ex~erimentsto be simulated on a small computer (PDP 8 / ~with a memory of 8 K words of 12 hits). We wish to report here the principles that have guided us in the conception of these programs and to describe an instance of their application to a complex reaction. During a simulated computer experiment it is essential to allow the student a maximum of freedom in the f o m u lation and realization of his experimentation plan. Thus the program should allow the user to vary all the factors which he believes have an influence on the reaction being studied. It is desirable that the section of the program, wherein the experimental conditions are defined, be conversational and not exclusively directed by the computer. Moreover, teaching teams unspecialized in computation must be able both to program their own examples for their students and to modify them easily. These requirements have consequences on two levels
C I ~ ~ / ~ C C I ~ ~ O ~
FOCAL (Formula CALculatar-DEC Trademark) on account of its simplicity and its appropriateness to the material we use. 2) With regard to the programming itself, it is important that the formal structure of a simulated experiment be made explicit. T o simulate an experiment it is necessary to conceive a model consisting of two parts, one of them relating to the chemical reaction itself, the other to the observation conditions. Figure 1 shows the links between these different elements. In chemical kinetics the reaction model may always be represented by a system of differential equations, defined by its initial conditions (rate laws). This uniqueness of mathematical formulation allows the writing of a standard program whose structure is represented by Figure 2. In this flow chart one can distinguish 1) parts of general character which remain unchanged in all ex-
periments 2) parts of specific character which are programmed whenever needed The particular manner of labelling the instruction with FOCAL suits the division of the program into independent parts, and the interpretative nature of FOCAL facilitates modifications. Example of Minicomputer Kinetics Experiment The knowledge required for fruitful work in this field concerns: order and stoichiometry, classical methods of
1) The language used in programming must be conversational, interpretative, simple both to learn and to use. We have chosen 'Breneman, G. L., J. CHEM. EDUC., 50,473 (1913). ZCraig,N. C., Sherertz, D. D., Carlton, T. S., and Ackermann, M. N., J. CHEM. EDUC., 48,310(1911).
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Figure 1. Structure of an experiment simulation model. The input variables are those that the operator could vary during an actual experiment.
Table 1. Outout of lntroductorv Text
reaction is a simple order one. For this purpose, he selects the option WHEN THE FORMATION OF TETRAHYDROBENZALDEHYDE (THE) STARTING " C O M P and can then either use FROM BUTADIENE AND A C R O L E I N E I S REALISED BETWEEN a20 AND 600 the computer by direct commands DEGREES K , REAGENTS A N D PRODUCTS ARE GASEOUS. or call upon parts of programs corBY W O R K I N G UNDER ISOTHERMAL AND I S O C H O R I C C O N D I T I O N S r ONE CAN STUDY THE K I N E T I C BY MEASURMENT O F THE TOTAL PRESSURE. responding to diverse integrated formulas. YOU MAY SELECT THE I N I T I A L PARTIAL PRESSURES AND THE TEMPERATUREThe student cannot directly sePRESSURE I S EXPRESSED I N TORR TEMPERATURE I N DEGREES R lect a formula, hut must propose AYO T l M E I N SECONDS. one to the instructor and justify his choice. I€ the formula is convenient, CODES TO BE U S E D I N SELECTING THE EXPERIVENTAL C O N D I T I O N S : the instructor delivers a keycode PAC : I N I T I A L PARTIAL PRESSURE O F A C R O L E I N E (MAX 2 a m ) for access to the corresponding PBU : I I # BUTADIENE (MAX 2 ATH) portion of the program. Usually, TP : TEMPERATURE OF TAE EXPERIMENT the student will try second-order TlT : TOTAL TIME O F MEASUREMENT IIJTV r INTERVAL OF TlME BETVEEN TWO MEASUREMENTS with the data from the preceding ( T Y I S L I S T I S NOT EXHAUSTIVE ) experiment. As seen in Table 4 and in Figure TO GET THE RESULTS O F YOUR EXPERIMENT TYPE # G O # A C i V I N G MADE YOUR C H O I C E S , P U S H #RETURN# 3 (A), the reaction indeed follows -->?LEASE PROPOSE A REACTION SCHEME COMPATIBLE WITH YOUR OBSERVATIONS a second-order law, hut this situation results from the ratio between the rate constants (kllkz 10) and from the choice of closelv related Table 2. Definition of Experimental Conditions and initial pressures. If, lacking a critical attitude, the student Control of Inputs contents himself with this result, he is unable tu detert the WHAT VARIABLE DO Y O U WISH TO COMMAND ? existenre of the side reartion. Conversely, if he rhooses for another experiment a butadiene pressure much higher than CODE :PAC VALUE:800 CODE IPBU VALUE:700 that of arrolein, he may uhserve that the value of the total CODE rTP VALUE:350 pressure falls below that corresponding to the complete THIS VALUE I S TOO LOW Diels-Alder transformation. RATE OF REACTION I S INAPPRECIABLE BELOW b20 DEGRES K PLEASE CORRECT ERRONEOUS DATA Moreover, the graphical second-order trial (Fip. 3(B)) deviates from linearity and the value of the constant, calVALUE1 550 culated for each point, drifts away. These deviations CODE i T O T UALUE:4000 oblige the student to analyze the kinetic and stoichiometCODE :I N T V VALUE:400 CODE :GO ric results carefully and lead him to complete his first hypothesis. With the aid of complementary experiments Student entries immediately follow the mlon typed by the computer. (e.g., addition of THB, omission of butadiene or acrolein . . .) the student should be able to retain the most convincine hvoothesis. Durine each ontion nhase. the user can kinetic experimental data treatment, relationships beaslk f i r supplement&y infGmatidn (option HELP) tween physical properties and degree of reaction. The edsuggesting new experiments. (e.g. = YOU MAY INTROucational aims are to allow the free planning of an experiment, to develop a critical attitude towards the results obtained, and incidentally to give further practice in treatingexperimental data. We have chosen the gas phase reaction between acrolein and butadiene. According to G. B. Kistiakowsky and J. R. Table 3. Simulation of the Experiment and Option Phase Lacher3 the Diels-Alder reaction is second-order, hut the TEM?ESATURE = 550.0 DEGREES K simultaneous hutadiene dimerization complicates the interpretation of the data. Their model is I N I T I A L PRESSURES
-
Aerolein
+ Butadiene
-k,
2 Butadiene
Tetrahydrobenzaldehyde (THB)
k2
Dimeric
and we retain it. The rate constants kl and kz are calculated by the Arrhenius equation, using their thermokinetic results. Principal Steps of the Simulated Experiment
Using the program codes (Tahle I), the student now specifies the input variables he wishes to control and types the numerical value he has chosen. If this value does not fit into the corresponding predefined range, the computer delivers a diagnostic of error and an order to make corrections (Tahle 2). When all the commands are checked, the computer delivers a series of simulated data (Tahle 3). To give a realistic effect, a uniformly distributed random error is assigned to these values. Using these data the student will try to verify if the 3Kistiakowsky, G. B., and Lacher, J. R., J. Arner. Chem. Soc..
O F ACROLEINE; OF BUTADIENE-
TlME ( S E C . ) 0
-
= = = = =
=
= = = =
400 $00 1200 I600 2000 2400 2902 3200 3600 4000
800.0
TOR?
700.0
-. -.
TOT. P. 1500
. . .
1140 I I02
--
(TORR)
1358 1260 1191
1066
OPTION PHASE
TYPE
I F YOU HISH TO CWAYGE THE EXPERIMENTAL C O N D I T I O N S
CHANGE
TO EXTEND THE EXPERIMENT
MORE
FURTHER I N F O R M A T I O N
HELP
TO COMPUTE YOUR RESULTS
COMP
58, 123, (1936). Volume 5 2 , Number 4. April 1975
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Table 4. Result of Second-Order Trial TlME
EXPERImENTAL
COMPUTED
K
Figure 3. Secondorder plots far the initial conditions: TP = 550% ( A ) . PBu = 770 tor, and PA, = 800 torr; ( 0 ) Pgu = 750 torr and PA, = 400 t o m Line B shows the deviation from the second-order law.
On the average, about 20 trials (3 min of computing time each) are necessary in order to recognize the proposed model fully. This can he reached within a reasonable time. We feel it is undesirable to restrict the trials to a limited number, as we think that a systematic approach must not be automatically prevented. The rate constant can he determined by the method originally suggested by Kistiakowsky and Lacher and described from a pedagogical viewpoint by Frost and P e a r ~ o n . ~
I
I
I
lHQUT
I Of
V A O I A B L ~ SAND ~ 0 ~ 1 ~ 0 1
Conclusion
OUlSUl Of E R R O R MESSAGES
In spite of certain problems resulting from their small amount of core memory, minicomputers may thus be used for computer assisted instruction; they are specially helpful for fictive experiments and usefully enlarge the field of nedagoeic techniaues In particular critical attitude is developed towards anv tendencv they have to overextend the use of the laws that appear t o govern some phenomenon. But, these benefits do not replace genuine experimental courses and exercises.
.
Olfff RENTIAL CHANGt I N
I H L RfACllON I INTEGRATION I
a
Acknowledgment
We are greatly indebted to Prof. R. Luft of the Laboratoire de chimie organique-Institut Polytechnique MBditerranhen-Nice-for his cooperation, helpful discussions, and assistance. This project was supported by a grant from Ministere de I'Education Nationale-Paris-Direction des Objectifs-Mission de Recherche Pgdagogique, 1973. Further information and listing of the programs with examples are available upon request from D. Cahrol. Figure 2. General flow chart for simulating fictive experiment. Modules represented by single line rectangles are general: those represented by double line rectangles are specific to a given example.
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Journal 01 Chemical Educafion
Trost, A. A,, and Pearson, R. G., "Kinetics and Mechanism," 2nd ed., John Wiley + SonsInc., NewYark, 1961, p. 33.
