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WebED Education, Outreach and TrainingModeling Chemical Kinetics with StellaThe models below were contributed by Shawn Sendlinger, Associate Professor of Chemistry at North Carolina Central University. The basics of each of the models is described below. The Stella models are in a zip file that can be downloaded by clicking on the link below. You will need Winzip for Windows or Stuffit Expander for the Macintosh to unpack the file. Chemical Kinetics using STELLA A simple chemical equation can be described as: A→B The rate at which this reactions proceeds depends on a number of things. These factors include k (the rate constant), and Ao (the initial amount of compound A). In differential form, the rate equations are:
These equations can also be written as integrated rate equations:
The STELLA software program can readily be used to build a model of this reaction. The stock icon is used to represent the chemical species “A” and “B”. A flow icon represents the conversion of stock A into stock B. A converter icon is used to hold a value for the rate constant k. Finally, the connector icon is used to show the mathematical dependence shown in the above equations. The STELLA model (SimpleAtoB.STM) would look like:
Notice that the flow out of stock “A” represents a decrease in the stock, so the negative sign from the above equation is taken into account. Similarly, the flow into stock “B” is automatically considered an increase (a positive sign in the above equation). To give good results that reflect those determined experimentally, the best integration method available (Runge-Kutta 4) should be used in conjunction with a small “dt” value (0.01 or smaller). Try setting the initial amount of “A” to 1000, “B” to zero, and a small value for the rate constant k (1 x 10-3). A graph of A will show the expected exponential decrease, while the graph of B will show the expected exponential increase. The above model can be easily modified in a number of ways. These are enumerated below. Modification #1: Equilibrium(A ↔ B) In addition to the forward reaction where “A” turns into “B”, now the reverse is also true: “B” can turn back into “A”. Now we have forward (kf) and reverse (kr) rate constants. The differential form of the rate equations look like:
The above STELLA model now includes a second flow in the opposite direction, as well as a second converter for the additional rate constant. This model is shown below (AequilB):
To check if this model is working properly, the sum of “A” and “B” at any time should be a constant. Modification #2: Consecutive Reactions (A → B → C) It is quite easy to modify the first model to include an additional reaction step by adding another stock and another flow. A second converter for the new rate constant is also required. The equations for the consecutive reaction model look like (A to B to C):
The model is shown here:
Again, note that the direction of the flows automatically takes care of the signs from the differential equations shown above. If needed, each of the reactions steps in this model could be made reversible. Additional chemical species could also be added (“D”, “E”, “F”, etc.). Modification #3: Parallel Reactions from One Reactant Sometimes, a given reactant might form two different products, as shown below: A → BandA → C In differential form, the rate equations are:
The STELLA model will now have two flows originating from the “A” stock, and each flow will have its respective rate constant:
Modification #4: Parallel Reactions to Form One Product This situation is opposite to that of Modification #3 shown above. In this case, reactants “A” and “B” combine together to form one product “C”: A → C ← B The rate equations are:
The STELLA model is shown below:
Be careful to notice the directions of the flows in the above model. Summary: STELLA is a convenient and easily understood tool for constructing and studying chemical kinetics. All of the simple models here can have “real” chemical names substituted for “A”, “B”, etc., and experimentally determined rate constants can be entered. The resulting models accurately predict the concentration of the various chemical species at any time of interest. In their “general” form, the models can be experimented with to gain an understanding of the important factors that govern kinetics. Acknowledgements: Shodor Education Foundation Bibliography: K.J. Laidler, Chemical Kinetics (3rd Ed.), Benjamin Cummings, San Francisco, 1987. Model Files to Download: kinetics.zip |
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