A chemist studies the gas-phase decomposition of substance X at 600 K according to the elementary process
X(g) → products
Two separate trials are carried out under otherwise identical conditions. The measured initial concentration of X and the time required for the concentration of X to decrease to one-half of its initial value are recorded in the table.
Trial
[X]₀ (mol L⁻¹)
t₁/₂ (min)
1
0.10
22.4
2
0.40
22.6
Answer the following questions. Assume the reaction proceeds by a single rate law in which the temperature remains constant.
(1) Identify the overall order of the reaction with respect to X. Provide reasoning that explicitly connects the data in the table to your conclusion.
(2) Without performing a numerical calculation, predict whether the half-life for an initial concentration of 1.60 mol L⁻¹ would be less than, equal to, or greater than 22 min. Explain your reasoning in terms of how the half-life depends on initial concentration for the order you identified in part (a).