Collision Theory - COLLISION THEORY OF THE RATE CONSTANT...

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COLLISION THEORY OF THE RATE CONSTANT CHEMISTRY 213 The simplest collisional model for the rate constants in bimolecular elementary reactions, e.g., A + B Products , is to assume that reaction occurs every time an A and B molecule collide. Thus the rate becomes: RATE = Z A , B (1) where Z A , B is the number of AB collisions occurring per unit time, per unit volume of the sys- tem. The kinetic theory of gases gives Z A , B = π ( R A + R B ) 2 c AB n A n B , (2) where R A and R B are the van der Waals radii of A and B, respectively, n A and n B are their num- ber densities, and c AB is the mean relative speed of A with respect to B; i.e., c AB 8 k B T π μ AB 1/2 . (3) In Eq. (3), k B is Boltzmann’s constant and μ AB m A m B /( m A + m B ) is the AB reduced mass ( m A , B denotes the mass of A or B). Equation (2) is obtained by considering how many B molecules will lie in the cylinder swept out by an A molecule in time dt. The radius of the cylinder is the maximum distance and A and B can be in order to collide, i.e., R A
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