Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

384 TREATMENT OF EXPERIMENTAL DATAtion of the k; values is obtained. Alternatively, it may be decided that the uncontrolledfactors operate in a purely random fashion from run to run and that theobserved variations in the k; values are small for the required purpose; if this is so,the comparison of different groups of experiments carried out at different initialconcentrations can be undertaken as described in the previous section. However,if the uncontrolled factors influence the k; values from replicate experiments insome systematic way, it is not useful to compare one group of experiments withanother if the object is to decide whether or not the data fit a given rate expression.Such data would fail the first of the F-tests described previously [see eqn. (73)], butthe reason would not necessarily be that the rate expression under investigation wasan inappropriate representation of the data; the whole set would be subjectto systematic errors just like the group of replicate experiments and a value ofF greater than the critical could be obtained on this account alone. There is nochoice but to eliminate factors which operate in this way. An example might beuseful. Suppose a set of experiments were carried out in which known volumes ofthe reactant A were withdrawn from a stock solution. Furthermore, suppose that,unbeknown to the investigator, the reactant A was slowly decomposing in the stocksolution giving inert products. Then, assuming that the quantity k; was dependenton the initial concentration of A, the values of k; obtained from a group of replicateexperiments would vary systematically as the stock solution became weaker; if theexperiments were performed in the order of decreasing formal initial concentrations,the values of k, (not k;) would show significant differences even thoughthe rate expression under test were correct. If the decomposition of the reactantA were the sole factor affecting the results and if the experimental procedure couldnot be modified in any way to eliminate its influence, it is clear that merely randomizingthe order in which the experiments were carried out would permit a validcomparison of the ki values to be made. This is yet another example of the closelink between the methods employed to process the data and the design of theexperimental procedure.It is obvious that these calculations are greatly facilitated by using a digitalelectronic computer. Indeed, it is because these machines have become so accessiblein recent years that the procedures described have been given such prominence.(0) Further comments on replicationIt can be argued that the extensive replication of the kinetic experiments for allvalues of the initial concentrations is unnecessary. Suppose, for example, that noreplicate experiments at all are carried out so that each run corresponds to differentinitial conditions. It is possible to. modify the previous test for the homogeneityof the rate coefficients within a group of replicate experiments to examine thehomogeneity of such a set. Since the experiments correspond to different initialconditions, we have to compzre the distribution of the rate coefficients themselvesabout their weighted mean with the scatter of the points about the family of lines