J. C. Merrill, 1. D. Spicer,' R. Brown, and C. Walling University of Utah saltLake City, 841 1 2
A Computer Simulated Experiment in Complex Order Kinetics
Computer simulation can 6 e a valuable adjunct to lahoratory experience in chemical e d u c a t i ~ n . Experiments ~.~ which would otherwise he unfeasible for students due to time limitations, expense of reagents, or degree of difficulty can he programmed on a wide variety of programmable calculators and larger computers in interactive languages. One particular area in which this is true is in the field of chemical kinetics.' While several undermaduate phvsical chemistry laboratory experiments nre available in this tieln. most do not ha\,e the complete generalit y of requiring the student to determine all-of the kinetic parameters of the reaction such as order of reaction with respect to each reagent, forward and reverse rate constants for the overall reaction, and forward and reverse activation energies for the reaction.5 We have prepared a computer simulated experiment in Basic which allows a student to generate the data needed to determine all of these parameters using conventional kinetic analysis or additional computer programs de. ~ generalized reaction scribed e l ~ e w h e r eThe
characterized in this "experiment," and data is generated i l l the form of concentrations of variw.. reagents or products a s a function of time. Since the computer program developed for this experiment has what we feel are several unique features, we wish to describe it in detail. The program is sufficiently short to run in a mini-computer with the equivalent of 4K of programmable core in Basic language. In particular, we have run it on a PDP 11/10 with8K of total memory, a Wang 2200 with 8K of memory, as well as on the campus Univac 1108 computer operating in realtime Basic. Only minor modifications to the program are required to allow it to operate on these three different systems, and we feel that this will he true for any computer which will operate in the Basic language. IS
Generation of Parameters and Student Input One objective of this computer program was to make the "experiment" totally interactive and personalized. Thus extensive use of alphanumeric information was incorporated. Upon activating the program, the computer asks the student "what is your social security numher?" When he inputs his social security numher, the computer uses it both to identify the student and to generate the various kinetic parameters for the reaction. This means that each student will have his own unique rate parame-
' Camille and Henry Dreyfus Teacher-Scholar 1971-1976. 2See, e.g., Tabbutt, F. D., Chem. and Eng. News, 48, 44 (Jan. 1-, 4 iwni .-,. McWilliam, I. G., J . CHEM. EDUC., 51,482 (1974). An annotated hihlio~aphyof computer programs for chemical kinetics has recently appeared in this Journal. Hogg, J . L., J. CHEM. EDUC., 51. 109 (1974); Seyse, R. J., and Rose. T. L., J. CHEM. EDUC., 51. 112 (1974). 5Shoemaker, D. P., Garland, C. W., and Steinfeld, J . I., "Experiments in Physical Chemistry," 3rd Ed., McGraw-Hill Book Co., New York, 1974. pp. 273-320, and references cited therein. A
528 / Journal of Chemical Educatbn
ters to determine, and thus his own personal "reaction" to run. These parameters are determined by examining the social security numher digit by digit. Since in most institutions, a great majority of the students are in the same age group and come from within the same state, the first three digits of many of their social security numbers will be identical. For this reason the computer ignores the first three digits of the numher. The fourth digit is used directly in a subroutine to find the order of the reaction with respect to the first component, A. Similarly, the fifth, sixth, and seventh digits determine the order with respect to the other components, B, C, and D. The reaction may be half., first., or second-order with respect to each component. Pre-exponential factors in the Arrhenius rate expression then are assigned values based upon the eighth and ninth digits of the numher. The computer next operates on the social security numher as a whole with various arithmetic expressions to generate the forward and reverse rate constants a t 25°C. These are adjusted in magnitude according to the overall orders of the forward and reverse reactions in order to ensure that "reaction" will occur in a reasonable period of time. The rate constants and pre-exponential factors are then used to calculate the values of the Arrhenius activation energies for the forward and reverse reaction. The cwnputer nexr informs the student This is a simulated kinetics experiment in which you will proceed as if you were investigating the following reversible reaction in the laboratory A
+
B +--*C
+
D
Your objective is to 1) Find the values of the forward and reverse rate constants, kr and kb, at 25%. 2) Find the values of the forward and reverse activation ener-
gies, Er and Eb, in calories per mole. 3) Find the order of reaction with respect to each of the components A, B. C, and D. thisrxpo~rnentas many time.3ns you uant. The renrtim of mereit proceeds at constant iemprmlurr and i i rnntndled b y hut plnre4 and rre harhs which permit a temperature range of 0-100°C. Sou ma) r u n
T h e computer then asks the student a t what temperature he would like to run the reaction and what he would like the initial concentrations of various reactants to he. If the temperature falls outside the specified range, or if the student selects physically unrealistic concentrations, the computer so informs the student and queries him again for better information. Next the student is asked a t what time intervals he would like to measure the concentration of A, B, C, and D and the numher of measurements to he made. At this stage the student input is complete and the computer begins calculating simulated data to he used by the student. Method of Calculating Simulated Data In calculating the data to he output to the student the computer first determines the initial rate of the reaction
Summary of Undergraduate Physical Chemistry Student Performance on the Simulated Kinetics Experiment During Spring of 1974 Kinetic Parameter Reaction Order of
Number of Students Finding Correct Answer"
A
B
20 20
P
19.
D Rate constants Forward Back Activation Enere'es Forward Back
13
-
Answers found to be within 5% of the tme value were considered eorreet.
Twenty-onestudents participated in the experiment.
These are adjusted relative to the actual concentrations so that the fluctuation is less than 2% if the concentration is greater than or equal to 0.05 M, or less than 5% if the concentration is less than 0.05 M. Thus, a true "scatter" is introduced. The error is not allowed to propagate, however, since the fluctuations in the output for one of the sampling intervals are not introduced into the next measurement interval, i.e., the scatter in each output is independent of that preceding it. For each measurement requested by the student, the computer calculates and outputs time (in min) starting a t zero and the concentration of each snecies A. B. C. and D. After all the measurements requestkd by the student are generated, he is queried as to whether or not he wishes to run another experiment. If so, the computer transfers to the temperature input question and proceeds from there. If not, an exit from the program is executed.
according to the equation
Student Results
where dX is the instantaneous concentration change, 'using the student's input concentrations. This is then compared with the smallest of the concentrations greater than zero. The student's frequency of measurement is suhdivided hv five and further subdivided hv factors of ten until t h e smallest nonzero concentration~changesby no more than 0.5% during one integration cycle. The integration loop, initiating atfive cycles, is sim~ltaneouslyincreased by factors of ten for each subdivision. These steps are important to assure accuracy of the simulated data over a wide range of initial concentrations. After the size of the integration cycle is determined, the computer calculates the initial rate for the beginning of the first cycle. Concentrations for the end of the cycle are calculated using this initial rate, and then the rate for the end of the cycle is computed. The average of the two rates is then used to calculate a more accurate concentration a t the end of the cycle. The cycle is then incremented and the nrocess continued until the looo is satisfied. After the loo^ is satisfied, four random numbers are generated to introduce statistical fluctuations into the concentration data.
The program was made available as an optional experiment to the students in our junior-level physical chemistry laboratory course spring term, and 21 students elected to perform the experiment. The results are tabulated in the table. In summary 88% of the students obtained the correct orders, 79% the proper rate constants, and 67% the proper activation energies from the data for the "reaction" associated with their social security number. Typical student comments obtained on an anonymous course evaluation form indicated that this "experiment" was beneficial both in providing insight into chemical kinetics and stimulating interest in computer applications in chemistry. Somewhat different kinetics problems using the same general computer simulation techniques have also been assigned quite successfully in our graduate kinetic course a t Utah over the past three years. The program described above appears to work well, without bugs, and we feel it to be very useful as a supplement to our ohvsical chemistrv laboratorv. L.D.S. or . J.C.M. will be happy to provide listings or punched paper taoes of the oroeram including instructions for outouttiue thk individual rate associated with an; social security number for grading purposes.
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Volume 52. Number 8, August 1975 / 529
