Problem

The key insight is that half-life depends on initial concentration differently depending on reaction order. For zero-order reactions, $t_{1/2}$ is proportional to initial concentration; for first-order, $t_{1/2}$ is independent of concentration; for second-order, $t_{1/2}$ is inversely proportional. By checking how $t_{1/2}$ changes as pressure (a proxy for concentration) doubles, you can identify which relationship holds and determine the order.

The key insight is that half-life depends on initial concentration differently depending on reaction order. For zero-order reactions, $t_{1/2}$ is proportional to initial concentration; for first-order, $t_{1/2}$ is independent of concentration; for second-order, $t_{1/2}$ is inversely proportional. By checking how $t_{1/2}$ changes as pressure (a proxy for concentration) doubles, you can identify which relationship holds and determine the order.