M. 1. Corrin Department of Chemistry University of Arizona
Tucson
Lecture Demonstrations
with an Analog Computer
T h e analog computer can serve as a striltingly graphic and effective tool for the presentation of important concepts in first year college chemistry. We have found illat computer demonst,rations have the fouowing advantages: 1. The actual mathematical processes are handled by the computer. The attention of the student is focused on the physical model and the quantitative relations obtained from it rather than the mathematical details involved. 2. The quantitative effect of pertinent variables is dearly denionstrated. 3. Our experience has indicated that students consider relations demonstrated by the computer more significant than similar functions drawn on the blackboard. They also rcmenrher the conlputer conclusions longcr. 4. Wc have found that 10-15% of the students arc willing to spend a portion of their free time in learning the principles of the computer and its programming. We have used analog computer demonstrations in first year chemistry a t the University of Arizona for both the honors and standard classes in lecture and laborat,ory sessions. The demonstrations have greater impact in the laboratory, perhaps because of the relatdve informality. The bas~cprohlem is dealt with first in terms of a physical model. A mathematical relation is deduced from the model (the notation of calculus is used with the honors groups), a computer (black box) solution of the mathematical problem is set up, and finally the graphic relation between physical variables is displayed. The computer solutions may be shown with repetitive operation on an oscilloscope. This is suitable with small groups and allows a rapid display of the effects of variable changes. An X-time recorder, which is more satisfactory with large groups, may also be used. We have used a 14 X 17 in. X-Y recorder with a time sweep and replaced the standard pen with a broad marking pen. Using this technique, we have presented demonstrations before groups as large as 250. Operating of the recorder in real time reduces the speed, of course. A discussion of two first year chemistry computer demonstrations follows. The first deals with the development of the concept of equilibrium and equilibrium constant from the kinetic approach. This demonstration has been given to both standard and honors groups and with both oscilloscope and recorder readout. The second involves the solution of the Schrodinger equ* tion for a particle in a one dimensional box and the origin of the quantum restrictions on the total energy. This demonstration has been used with the honors groups only and with osciUoscope readout. The follo~v-
ing discussion and computer diagrams are based on the use of an Electronic Associates TR-10 analog computer. The principles of analog computation and simulation are discussed in several texts.' Application of the analog computer to the kinetic problem of consecutive first-order reactions was discussed by Osburn in THE JOWRNAL.~ This paper also presents the basic elements of analog simulation. A handbook published by Electronic Associates entitled "Bzwics of Analog Computation" is an excellent introduction to the subject. I t will be supplied without charge to interested individuals on requesLa
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Figure 1. Computer diagrom for kinetics-equilibrium demonstration. All values unity unless otherwire specified.
Chemical Kinetics and Equilibrium
It is necessary to develop the notion of the rate of a chemical process as the rate of change of concentration with time. The analogy with velocity and an automobile speedometer is useful. I t is then postulaled (with some simple mechanism discussion added for the honors group) that the reaction rate should be a function of concentration. For simplicity, the first-order --
' ASHLEY,J. EL., "Introdu~ti~n to Anslog Campotation," John \Iriley Xi Sons, h e . , New York, 1963. 1:. It., "Analog Computation and Simulation: JENIVESR, Lahuratory Approach," Allyn and Bacon, Ine., Boston, 1965. JACKSON,A. S., "Analog Computation," XcOrav--Hill Book Company, Inc., New York, 1960. OSBUKN,J. O., J. CHEM.EDUC., 38, 492 (1961). 8 Electronic Associates, h e . , 185 Monmouth Parkway, West Long Branch, New Jersey. Volume 43, Number 1 7 , November 7966
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is emphasized that the reaction under consideration is irreversible. The effect of initial concentration is illustrated by means of potentiometer P5 and that of reaction rate constant by 2'6. The concept of a reversible reaction i q thm drveloped and illustrated in termsof
It is shown that (Standard)
Rate [A]
Rate [B] Figure 2. O3cillowape trace for irreverribie R"., order reaction. COI oiir-concentrotion of reactant; horizontoi oxir-lime.
verti-
~ ~ itrace l for i ~reversible ~ ~ tint ~ order ~ ~ reaction. Curve Figure 3. O !.--concentration of reoctont verrur time. Concentrotion of products "..."I time.
Figure 4. Orciiiorcope troce for reversible 6.5, order reo
