### Determination of Rate Laws and Nonlinear Curvefitting

You have been assigned a simulated data set representing the consumption of one reactant in a solution mixture. Find your data in the \Ch445\ folder on the classes drive. The data were calculated using order = 1/2, 3/2, or 5/2, with random errors applied to the concentration of the reactant as it decreased with time. Your assignment is to decide to what order the reaction corresponds, and to calculate and report the rate constant at 95% CI.

The first step is to derive, for the general case of a stoichiometric reaction A = B (coefficients a and b = 1), a form in which the concentration/ time data could be plotted in order to linearize the data for the cases of order = 1/2, 3/2, and 5/2.

The next step is the preparation of a Mathcad document which will provide regression analysis. 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 a section in which nonlinear curvefitting methods are used to extract the kinetic rate constant and initial concentration of reactant for the specific reaction order which corresponds to your unknown.

The linear regression is to be done by matrix methods. The same matrix analysis can be used for all 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 8 by 4:00.

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