Precision of Specific Rate Constants

Precision of Specific Rate Constants. For a simple reaction system of a given order, the rate constant may be calculated from data giving the state of the system at two different times. This assumes that sufficient measurements have been made to establish the order of the reaction so that the functional relation is known. 

Let us choose a simple second-order reaction as an example. The specific rate constant kx will be given by (see Table II.2) 

If we may assume that the errors made in measuring the four quantities A2, Ai, t 2, and fi are independent of each other and completely random, then AkA) the expected resultant error in the dependent quantity Aa, is given by  

For most purposes it is convenient to rewrite Eq. (IV.6A.2) in terms of the relative errors AkA/kx, Mi/h, etc., rather than in terms of the absolute errors in each of the variables. This can be done by dividing each term by kA and then in turn multiplying and dividing each term by the square of the independent variable  

Equation (IV.6A.1) can be ised to calculate the partial derivatives. On substituting these we find 

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