A large number of chemical reactions can be made to follow apparent first or second order behavior by suitable manipulation of reaction conditions. It is therefore often necessary to test experimental data to decide whether first or second order behavior is the better representation. Quality of fit is dependent upon several criteria which can be extracted from a regression analysis of the fit of the data to the model under consideration:
Many other statistical tests can be made, but most are derivable from the criteria listed above.
You have been given a simulated data set representing the consumption of one reactant in a solution mixture. Find your data in the \CHAPMAN\Ch445\ folder on the classes drive. The data were calculated using either the first or second order rate law, with random errors applied to the concentration of the reactant as it decreased with time. Your assignment is to decide which rate law is the better model; in some cases the decision is easy, but sometimes a clear choice may not be possible, given the quality of the data.
The first step is the preparation of a Mathcad document which will provide regression analysis upon both models; your report will conclude with a commentary presenting your reasoning in making the choice; your report will conclude with a commentary setting forth your choice of rate law for the data set, explaining with direct reference to the Mathcad document how you reached your decision. Verify your findings with regard to reaction order and rate constant via the differential method.
There then follows two sections of the same general form, one each for the first and for the second order trial fits. Because we will test both models using both linear and nonlinear regression methods, much of the calculations for the first order model can be copied into the second order part of the document. Brief remarks should accompany each significant step.
The linear regression is to be done by matrix methods. The same matrix analysis can be used for both rate law tests, the only difference being the definition of the independent and dependent variables. The calculations should include the variance, the variance-covariance matrix, and the relative standard deviations of the original physical parameters in the nonlinear model. The last-named will require propagation of most probable errors analysis. Plots comparing the actual data with the best fit and a plot of the deviations are essential.
The nonlinear fit is done using three Mathcad functions: given, find, and minerr. The principles will be discussed in class. Programs are available for more extensive nonlinear regression, but an abbreviated version will meet our needs here. You will note that nonlinear regression gives the original physical parameters directly; the values found may differ from those calculated from the linearized fits because of inherent differences in weighting between the two methods. Our nonlinear method does not yield a variance-covariance matrix, but variance can be calculated, and plots corresponding to those requested for the linear regression are required.
This assignment is due Friday April 7 by 4:00.