In the Lindemann mechanism: Step 1 (fast equilibrium): A + A ⇌ A* + A, Step 2 (slow): A* → products. The slow step is rate-determining.
According to collision theory, collisions must have both proper spatial orientation and energy ≥ activation energy to result in a reaction.
Since k₁ > k₂, A converts to B faster than B converts to C, so B accumulates initially and then decreases as it slowly converts to C.
When [A] doubles, rate increases by 8 = 2³, so order w.r.t. A = 3. When [B] doubles, rate increases by 2 = 2¹, so order w.r.t. B = 1. Overall order = 3 + 1 = 4.
Using ln(k₂/k₁) = (Eₐ/R)(1/T₁ - 1/T₂): ln(4) = (Eₐ/8.314)(1/300 - 1/320), solving gives Eₐ ≈ 51.2 kJ/mol.
From fast equilibrium: K = [B]/[A], so [B] = K[A]. The slow step rate law is rate = k'[B][C] = k'K[A][C] = k[A]^(1/2)[C] where k combines constants.
After n half-lives, fraction remaining = (1/2)ⁿ. After 5 half-lives: (1/2)⁵ = 1/32.
For a first-order reaction, if half-life decreases from 10 to 5 minutes (becomes half) with a 10 K increase, this indicates the reaction rate doubles per 10 K, giving a temperature coefficient of 2.
For zero-order reaction: d[A]/dt = -k, integrating gives [A] = [A]₀ - kt, which is a linear equation.
A catalyst provides an alternative reaction pathway with lower activation energy, thus increasing the rate constant k without affecting A or T.