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Using Dynamic Simulation Software in the Physical Chemistry Laboratory Robert W. Ricci and Jane M. Van Doren College of the Holy Cross, Worcester, MA 01610 The availability of modeling software has given today’s chemistry instructor a wealth of new teaching tools. Several examples of these have appeared in the Computer Series section of this Journal over the past several years. Among them was a report on the use of dynamic simulation software that allows for the modeling of chemical kinetics schemes (1). Dynamic simulation software numerically integrates differential equations rather than evaluating the integrated equation, as does equation-solving software such as Mathcad (2). We have found that many of these software programs are best introduced as analysis tools in the laboratory course rather than in the accompanying lecture course. At Holy Cross, undergraduates gain experience with spreadsheet, graphing, and molecular modeling programs; in addition, however, we wanted to include a dynamic simulation software program as part of our instruction in kinetics for students enrolled in physical chemistry. Our goal was to emphasize graphical analysis of kinetic data through computer simulation rather than traditional integration techniques (3). Such simulations are important research tools of the chemical kineticist and are readily accessible to the chemistry undergraduate. We use a simulation package that allows students to build models of reactions pictorially and intuitively rather than mathematically. As a result, students focus on the dynamic behavior of the species involved and quickly become adept at modeling complex reactions. The experiment described here incorporates real-time data gathering with kinetic modeling and does so in a way that does not presuppose any prior knowledge of kinetics. Consequently, the experiment serves as an introduction to chemical kinetics and at the same time gives students a powerful tool for understanding reaction mechanisms. We chose Powersim (ModellData AS) as our dynamic simulation program because it is a versatile Windows-based program with an interface familiar to students already trained on Excel and Microsoft Word. A similar program, originally written for Macintosh computers but now available for PCs as well, is STELLA (academic version) or ITHINK (commercial version).
Figure 1. Diagram of apparatus used in this experiment. Students monitor water level as a function of time as water flows from the top reservoir.
bottles marked off in 50-mL intervals—were attached to a rack with chain clamps and connected to each other with plastic tubing. Because the containers have a constant cross-section, the volume markings are proportional to height. Students fill the top container with water and monitor the water height in all three containers as a function of time. The data are then entered into a graphing or spreadsheet program and plotted. Typical student results are seen in Figure 2. Dynamic Simulation Before coming to the simulation lab, students are given a demonstration on the use of Powersim and must complete a self-directed tutorial. They model the three-container flow process as illustrated in Figure 3. The boxes labeled A, B, and C are Powersim symbols representing the water containers. Water flow between containers is represented by the large arrows going from A to B and B to C. The circles attached
The Experiment Liquid flowing from an opening at the bottom of a cylindrical container represents a first-order process:
– dh = kh dt where h is the height of the liquid above the opening and k is the rate constant for flow from the container. Now if three containers are placed one below the other and if the output of the first container is allowed to flow into the second container and the flow from the second is in turn allowed to flow into the third, then we have created a physical analog of consecutive first-order processes (4). A diagram of the apparatus is seen in Figure 1. The containers—1000-mL aspirator
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Figure 2. Typical student data for the volume of water in reservoirs A, B, and C as function of time. Data were plotted in a graphing program. Students can also graph the data directly in Powersim.
Journal of Chemical Education • Vol. 74 No. 11 November 1997
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Figure 3. (a) Powersim diagram for two consecutive first-order processes. “A”, “B” and “C” represent the three reservoirs; K_AB and K_BC are the rate constants for the flow processes, and RATE_AB and RATE_BC represent the first-order rates for the two flow processes. (b) Graph of the water levels of reservoirs A, B, and C as a function of time, as generated by Powersim.
Figure 4. (a) Powersim diagrams for isothermal and adiabatic firstorder processes. (b)The graph of the concentration of reactant as a function of time for an isothermal reaction and the same exothermic reaction carried out adiabatically. (See text.)
to the large arrows are symbols representing the rates of flow of the water from one container to another. The rates of flow are dependent upon the water levels and the flow constants, which are represented by the diamond-shaped symbols in the diagram. This dependency is illustrated by the small linking arrows seen in the model connecting the water container symbols and flow constants to the flow rate. In addition to the diagram view, as illustrated in Figure 3, Powersim has an equation mode in which the actual mathematical values and relationships among the various rates, water levels, and constants are introduced. In this mode, for example, the initial height of the water in reservoir A and the value of k_AB are entered and Rate_1 is set equal to the first-order expression k_AB × A. The simulation process involves numerical integration using Euler’s algorithm. If we define the height of the water in reservoir A at time t as At then the rate of water loss from the reservoir is R = k_AB × At. The computer program repetitively calculates the derivative water flow using R and the height of the water at t = t + dt based upon At and R, using the relationship At+dt = At – dt × R. In Powersim the results of the model can be displayed graphically (Fig. 3) or in tabular form. Having constructed the appropriate model the student’s task is to adjust the flow constants in the model so that the simulation curves fit the data obtained in the laboratory. Once they have obtained the appropriate rate constants from their model, we have them compare K__AB to the experimental value of the rate constant for the loss of water from the first container, which can be obtained from a first-order plot of ln (water height) vs. time. If time permits, one can continue this experiment by having students model the behavior of four reservoirs connected in series or perhaps one reservoir simultaneously
flowing into two other reservoirs (parallel first-order reactions) and then return to the lab and carry out the experiment. We believe the experiment serves two purposes. One, it introduces students to a dynamic simulation program using real laboratory data and second, it serves as an introduction to rates of reactions. The similarity between successive firstorder processes in kinetics and the flow of water through the three reservoirs is impressive. Students can be asked to model reactions in which kAB >> kBC or the converse case kBC >> kAB. The latter case is a particularly interesting example, since it leads to the concept of the steady state. Once students have mastered the program and are studying kinetics, they can use Powersim to explore other reactions. Of course, dynamic simulation software is not a substitute for the traditional methods of kinetics analysis but it does complement those methods. Additional Exercises We are particularly interested in encouraging students to integrate concepts learned throughout the physical chemistry curriculum. Current physical chemistry texts discuss the difference between isothermal and adiabatic processes in depth in thermodynamics but only rarely in kinetics. This is true even though in practice most kinetic reactions occur adiabatically to some degree. The reason for this is probably the mathematical challenge of attempting to find analytical solutions to differential equations in which both the rate constant and the concentration of reactants are variables. The use of a dynamic modeling program simplifies the mathematics and makes exploration of this system relatively straightforward. Figure 4 illustrates the difference in models and equations between adiabatic and isothermal first-order reactions.
Vol. 74 No. 11 November 1997 • Journal of Chemical Education
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Information • Textbooks • Media • Resources In the isothermal case, the rate depends upon kisoth and the concentration of the reactant whereas in the adiabatic firstorder reaction, kadiab is defined in terms of the Arrhenius expression,
k adiab = Ae
–
Ea RT
so an additional temperature variable, TEMP, is introduced and linked to kadiab . TEMP is defined in terms of the heat of the reaction, the heat capacity of the system, C p, and the extent of reaction. For simplicity’s sake, Cp is assumed to be independent of the extent of reaction. It is also assumed that no heat is lost to the surroundings during the reaction. Referring to Figure 4, one observes that the rate of loss of the reactant with time is the typical exponential decay in the isothermal reaction, whereas the decay of reactant with time in the adiabatic reaction is S-shaped. This is expected, since kadiab increases with time while the reactant concentration decreases.
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This example on the treatment of adiabatic reactions is just one of several that appear in a tutorial on “Powersim for Scientist”. The tutorial was written for our students as a self-guided introduction to Powersim. Interested readers may obtain a copy by writing to the author (JMVD). Acknowledgment We would like to acknowledge the National Science Foundation Grant, “New Traditions: Revitalizing the Curriculum”, DUE-9455928, for support in developing this work. Literature Cited 1. Steffen, L. K.; Holt, P. L. J. Chem. Educ. 1993, 70, 991– 993. 2. Zielinski, T. J. J. Chem. Educ. 1995, 72, 631–638. 3. Gellene, G. I. J. Chem. Educ. 1995, 72, 196–199. 4. Davenport, D. A. J. Chem. Educ. 1975, 52, 379.
Journal of Chemical Education • Vol. 74 No. 11 November 1997
