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) Write the rate law corresponding to the mechanism.
(b) In a second trial, the system is diluted by adding inert gas at constant pressure and temperature so that both [X] and [Y] become one-half of their original values. Determine the factor by which the initial rate changes relative to r₀.
(c) In a third trial, additional X is injected so that [X]₀ becomes 9.0 × 10⁻³ M while [Y]₀ remains 2.0 × 10⁻³ M. Determine the factor by which the initial rate changes relative to r₀.
(d) In a fourth trial the chemist simultaneously halves [Y] and triples [X] compared with the reference trial. Predict the net factor change in the initial rate and justify your reasoning.
(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.