Order Of Reaction

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 (t_1/2) 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: t_1/2 = [A]₀/2k. The half-life is directly proportional to the initial concentration.
• First-order reaction: t_1/2 = 0.693/k. The half-life is independent of the initial concentration.
• Second-order reaction: t_1/2 = 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: t_1/2 = [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.