Interpretation of Kinetic Information

A central problem in kinetics is the interpretation of laboratory data on rates of reaction. We have treated rates and selectivities to this point as if all the parameters such as reaction orders, rate constants, and activation energies were known. Suppose that this is not so [ None of them know the color of the sky, S. Crane]. How does one go about the testing of rate or conversion information on a certain reaction in terms of the expressions we have been dealing with Further, and importantly, what is the influence of experimental error on the parameters we determine from a given set of data To what extent are the apparent kinetics of a reaction useful in providing information on the elementary steps of that reaction  

Fortunately there are a number of basic and very simple means for the interpretation of kinetic data which are sufficient to provide at least the first estimates of reaction order and the associated rate constants [R. G. Pearson, Chemtech, 552, September, (1978)]. These methods will provide a sound basis for visualization and some interpretation before proceeding to the more detailed analyses mentioned above. Before going further, however, it is fruitful to consider the practical matter of the influence of experimental error on the measurement of reaction kinetics. 

Experimental results on reaction kinetics are sometimes characterized by a large amount of scatter in the measured information and corresponding uncertainty in associated rate constant and reaction orders. Such a situation is not necessarily the result of careless experimentation, because these quantities are generally very sensitive functions of the precision of experimental measurements. The following example [S.W. Benson, The Foundations of Chemical Kinetics, McGraw-Hill Book Co., New York, NY, (I960)] provides a clear illustration of this sensitivity. 

Assume that we are engaged in study of the reaction 2A B and have established it to be simple second-order and irreversible. We wish to investigate the effects 

Assume that the errors made in measuring the four data Cai, Ca2, ti, and are independent of each other and are random. The expected error in the rate constant, Afe, is given by 

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