Day6n7 - CE 561 Lecture Notes Fall 2009 Days 6 and 7:...

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CE 561 Lecture Notes Fall 2009 p. 1 of 20 Days 6 and 7: Sensitivity Analysis and Data Fitting to Extract Rate Parameters Extracting rate parameters from concentration vs. time profiles A common task in chemical kinetics and reaction engineering is to perform laboratory experiments to measure rate parameters for a reaction, under carefully controlled conditions, then use these rate parameters in modeling some other process. Here, we consider how to extract useful rate parameters from experimental data. Concentration vs. time is the most common kinetic measurement, but the methods discussed here are also applicable to concentration vs. position in a plug-flow reactor, and are mostly applicable to concentration vs. residence time in a well-mixed stirred tank reactor at steady state. Before we can extract rate parameters, we must have a postulated functional form for the reaction rate in terms of species concentrations. For given values of the rate parameters this function predicts the concentration vs. time profiles. We can calculate the best rate parameters for several functional forms and discriminate between them based on how well they reproduce the experimental results. If none of the forms fits the experimental results to within experimental error, we must look for a different form (or larger error estimates due to systematic errors that were overlooked). If more than one of the functions fits the data to within experimental error, then we require more experiments to distinguish between them. If we postulate a mechanism in terms of elementary reactions (which will individually obey the law of mass action) then the mechanism will imply a functional form for the reaction rates. In chemical kinetic experiments, we may use all reactants except one in large excess so that their concentrations are effectively constant during the reaction. If we can do this separately with each species, then we can isolate the concentration dependence of the rate of the overall reaction. Suppose we observe the overall reaction A + 2 B products We might do some experiments with a large excess of B and assume that the rate has a power- law dependence on the concentration of A. Then we have r = k eff C A n where the B concentration dependence has been lumped into the effective rate constant. Now we would like to determine n , the reaction order with respect to A. One method of doing this is to measure the reactant half-life (the time it takes for half of the A to disappear) for various initial concentrations of A. It can be shown that, for an arbitrary value of n , ( ) ) log( ) 1 ( ) 1 ( 1 2 log log 1 2 1 o A eff n C n n k t = So, a log-log plot of 2 1 t vs. C Ao will have a slope of –( n -1). Note that for n = 1 the half-life is independent of the initial concentration. Once n has been determined from the slope of this plot, k eff can be determined from the intercept. The reaction order with respect to B can be determined in the same way or
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Day6n7 - CE 561 Lecture Notes Fall 2009 Days 6 and 7:...

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