Simple Collision Theory SCT of Bimolecular Gas-Phase Reactions

1 Simple Collision Theory (SCT) of Bimolecular Gas-Phase Reactions 

In this section, we consider the total rate of molecular collisions without considering whether they result in reaction. This treatment introduces many of the concepts used in collision-based theories the criteria for success are included in succeeding sections. 

Consider a volume containing c A molecules of A (mass mA) and c B molecules of B (mass mB) per unit volume. A simple estimate of the frequency of A-B collisions can be obtained by assuming that the molecules are hard spheres with a finite size, and that, like billiard balls, a collision occurs if the center of the B molecule is within the collision diameter dAB of the center of A. This distance is the arithmetic mean of the two molecular diameters dA and dB  

This simple calculation gives a result close to that obtained by integrating over the three-dimensional Maxwell velocity distributions for both A and B. In this case, the same expression is obtained with the characteristic velocity of approach between A and B 

The collision frequency of like molecules, ZAA, can be obtained similarly, but the collision cross-section is a = itdA, the reduced mass is jU, = mAl2, and we must divide 

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