Collision Theory Rate Expression

Rate Equation:

$$\text{Rate} = Z_{AB} \cdot \rho \cdot e^{-\frac{E_a}{RT}}$$

Alternative Form (in terms of Rate Constant $$k$$):

$$k = P \cdot Z_{AB} \cdot e^{-\frac{E_a}{RT}}$$

Concept: According to collision theory, a chemical reaction occurs only when reactant molecules collide with sufficient kinetic energy (threshold energy) and proper steric orientation.

Notation & Key Terms: *

• $$Z_{AB}$$ = Collision frequency (number of collisions per second per unit volume between reactants $$A$$ and $$B$$) $$\rho$$ or $$P$$ = Steric factor / Probability factor (accounts for proper molecular orientation; $$P < 1$$)
• $$e^{-\frac{E_a}{RT}}$$ = Energy factor (fraction of effective collisions exceeding activation energy) Comparing with Arrhenius equation gives: $$A = P \cdot Z_{AB}$$