A gas-phase reaction proceeds by the elementary steps shown below.
Overall: 2X(g) + Y(g) → products
Step 1 (slow): X(g) + Y(g) → D(g)
Step 2 (fast): D(g) + X(g) → products
At 450 K the following initial concentrations are used in a reference trial: [X]₀ = 3.0 × 10⁻³ M, [Y]₀ = 2.0 × 10⁻³ M, giving an initial rate r₀.
(a) Derive the rate law implied by the mechanism.
(b) Determine the factor change in initial rate after uniform dilution to one-half the original concentrations.
(c) Determine the factor change in initial rate when [X]₀ is tripled while [Y]₀ is unchanged.
(d) Predict and justify the factor change in initial rate when [Y] is halved and [X] is tripled simultaneously.