To determine the order of the reaction, we can use the relationship between the half-life of a reaction and its order. The half-life (t1/2) of a reaction varies with the initial concentration or pressure of the reactant in a manner that depends on the order of the reaction:
- Zero-order reaction: t1/2 = [A]0/2k. The half-life is directly proportional to the initial concentration.
- First-order reaction: t1/2 = 0.693/k. The half-life is independent of the initial concentration.
- Second-order reaction: t1/2 = 1/k[A]0. The half-life is inversely proportional to the initial concentration.
Given that at 300 K, the half-life is 350 s when the pressure is 40 kPa, and the half-life is 175 s when the pressure is 20 kPa, observe the relationship:
For zero-order: t1/2 = [A]0/2k. If the initial pressure is halved (from 40 kPa to 20 kPa), the half-life should also halve if the reaction is zero-order, which matches the given data: 350 s to 175 s.
Thus, the reaction is zero-order.