The Preexponential Factors of Bimolecular Reactions

The preexponential factor predicted by the hard sphere collision theory is given by (Table XII. 1) Z abP in which we can evaluate Z ab from kinetic theory (Table VII.2) Z b = 4.57 X 10 o B(T/ny cc/molecule-sec = 

This simple collision theory thus predicts preexponential factors of about 10 cc/mole-sec, since we expect P 1. Values of P 1 are interpreted kinetically as due to improperly oriented collisions ( steric hindrance) or thermodynamically as a negative entropy of activation, i.e., a loss of freedom of A and B in forming the collision complex. As we shall see, these results are in good qualitative agreement with observations and Zab does indeed seem to be an upper limit for bimolecular frequency factors.  

Let us compare this with the preexponential factors Z, predicted by the other theories, writing them in terms of partition functions  

The detailed theory differs from the transition-state theory in replacing kT /h by v, a specific molecular constant, and in using (zJB(vib), the true vibrational partition function of AB rather than AB(vib), which has one less vibrational degree of freedom. However, since v is expected to be about 10 sec and kT/h = 6 X 10 scc at 300°K and the extra vibrational term in gJn contributes a factor of less than 10, it can be seen 

Theory Specific rate const A b Exp. activation energy E ny) Eq. (XII.5.2) Preexponential factor 

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There have been many attempts made to calculate the preexponential factors of bimolecular reactions from molecular constants based on the considerations of the transition-state theory. Such efforts depend on a number of educated guesses as to the vibrational properties and structure of the transition-state complex, an assumption about the transmission coefficient for the reaction, and the assumption of the validity of the normal coordinate treatment for computing the thermodynamic properties of polyatomic molecules. 

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