Half-integer kinetics

This agrees with experimental findings on the decomposition of acetaldehyde. The appearance of the three-halves power is a wondrous result of the quasisteady hypothesis. Half-integer kinetics are typical of free-radical systems. Example 2.6 describes a free-radical reaction with an apparent order of one-half, one, or three-halves depending on the termination mechanism. 

In addition to the usual terms of kinetic energy and potential energy, quantum mechanical particles possess another property called spin, which has the dimensions of angular momentum. The values of spin are quantized to half integer or integer multiples ofB. In the following we omit the factor of ft when we discuss spin values, for brevity. If the total spin of a particle is s then there are 2s -k 1 states associated with it, because the projection of the spin onto a particular axis can have that many possible values, ranging from +s to -s in increments of 1. The axis of spin projection is usually labeled the z axis, so a spin of s = 1/2 can have projections on the z axis = +1 /2 and = -1/2 sl spin of s = 1 can have = -1,0, +1, and so on. 

As seen in Table 2.1, the overall order of an elementary step and the order or orders with respect to its reactant or reactants are given by the molecularity and stoichiometry and are always integers and constant. For a multistep reaction, in contrast, the reaction order as the exponent of a concentration, or the sum of the exponents of all concentrations, in an empirical power-law rate equation may well be fractional and vary with composition. Such apparent reaction orders are useful for characterization of reactions and as a first step in the search for a mechanism (see Chapter 7). However, no mechanism produces as its rate equation a power law with fractional exponents (except orders of one half or integer multiples of one half in some specific instances, see Sections 5.6, 9.3, 10.3, and 10.4). Within a limited range of conditions in which it was fitted to available experimental results, an empirical rate equation with fractional exponents may provide a good approximation to actual kinetics, but it cannot be relied upon for any extrapolation or in scale-up. In essence, fractional reaction orders are an admission of ignorance. 

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