Statistical methods in kinetic analysis

Any experimentally measured set of (at, ti) values for an isothermal reaction contains errors including (inter alia) inaccuracies in yield and time determinations and departure of temperature from the constant value temporarily and locally. In any quantitative kinetic analysis, several interdependent factors must be considered. 

These steps may be completed separately or together, statistical methods can be employed and the computational labour reduced through the use of high speed computers. 

There have been few discussions of the specific problems inherent in the application of methods of curve matching to solid state reactions. It is probable that a degree of subjectivity frequently enters many decisions concerning identification of a best fit . It is not known, for example, (i) the accuracy with which data must be measured to enable a clear distinction to be made between obedience to alternative rate equations, (ii) the range of a within which results provide the most sensitive tests of possible equations, (iii) the form of test, i.e. f(a)—time, reduced time, etc. plots, which is most appropriate for confirmation of probable kinetic obediences and (iv) the minimum time intervals at which measurements must be made for use in kinetic analyses, the number of (a, t) values required. It is also important to know the influence of experimental errors in oto, t0, particle size distributions, temperature variations, etc., on kinetic analyses and distinguishability. A critical survey of quantitative aspects of curve fitting, concerned particularly with the reactions of solids, has not yet been provided [490]. 

Green [491] has given a general account of the applications of statistical methods to kinetic analyses and, without mentioning specific examples, suggests the approach could be of value in rate studies of solid phase reactions. The steps in his treatment are given below [492,493], 

Statistical methods used in kinetic analyses have generally been based on a least-squares treatment. Reed and Theriault [494] have considered the application of this approach to data which obeys the first-order 

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