Fractional-life methods

Integral Methods for the Analysis of Kinetic Data—Fractional Life Methods. The... 

Fractional Life Method The half-life method can be extended to any fractional life method in which the concentration of reactant drops to any fractional value F = C /Cao in time The derivation is a direct extension of the half-life method giving... 

Guess nth-Order Kinetics. Let s plan to use the fractional life method with F = 80%. Then Eq. 336 becomes... 

Example 3.1c showed how to find a rate equation by using the fractional life method where F = 80%. Take the data from that example and find the rate equation by using the half-life method. As a suggestion, why not take Cao = 10, 6, and 2 ... 

The half-life method (in general, the fractional-life method) is very useful in preliminary estimates of the order of the reaction. A series of experimental runs is carried out with different initial concentrations. If an irreversible reaction is considered ... 

Fractional-life methods. If a reaction is known to be first order and at constant fluid density, its apparent rate coefficient can be found very quickly. For batch and differential recycle reactors, the relationship between the rate coefficient and the time ty required for all but a fraction y of the reactant to be consumed is... 

Some texts describe fractional-life methods for reactions other than first order and with more than one reactant. However, the effort their application requires is not in proportion to the limited objectives of the evaluation in the present context. 

Fractional life method (7). It follows from either eqn. (18) or (19) that 6 is fixed for a given value of a and (a+b). Therefore, if, in a series of experiments at different values of the initial concentrations of A and B throughout which the ratio... 

Fractional life method (II). If, for some reason, it is not possible to cover a wide range of initial concentration conditions as is clearly necessary for the application of the above method (this could happen when one of the reactants has a limited solubility), essentially the same method can be applied to the data of a single experiment. We select a series of values of a (ao, ai, a2,.... ..) such that... 

The fractional life methods can also be used to determine a. As already indicated, the fractional life method of treating the data of a single experiment has few advantages over the superimposition method and consequently need not be considered further. On the other hand, the measurement of a particular fractional life of the reactant A in a series of experiments in which its initial concentration is varied provides a means by which a can be determined which sometimes offers experimental advantages. The only point to remember is that throughout the series of experiments [BJo must be kept constant at such a value that [BJo/[A]o,i Vb/Va. From the condition that... 

The time necessary for a given fraction of a limiting reagent to react will depend on the initial concentrations of the reactants in a manner that is determined by the rate expression for the reaction. This fact is the basis for the development of the fractional life method (in particular, the half-life method) for the analysis of kinetic data. The half-life, or half-period, of a reaction is the time necessary for one-half of the original reactant to disappear. In constant-volume systems it is also the time necessary for the concentration of the limiting reagent to decline to one-half of its original value. 

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