A research team studies the reaction:
Overall: 2M(aq) + N(aq) → products
The mechanism is believed to be:
Step 1 (slow): M(aq) + N(aq) → F(aq)
Step 2 (fast): F(aq) + M(aq) → products
Five separate kinetic trials are planned, each starting at 298 K with the reference concentrations [M]₀ = 0.050 M and [N]₀ = 0.025 M (producing an initial rate r₀). For each trial, the concentrations are modified as indicated below. No other conditions change.
Trial 1: [M] multiplied by 4; [N] unchanged
Trial 2: [M] multiplied by 0.50; [N] multiplied by 0.50
Trial 3: [M] multiplied by 2; [N] multiplied by 3
Trial 4: [M] multiplied by 0.25; [N] unchanged
Trial 5: [M] unchanged; [N] multiplied by 5
(a) Derive the rate law predicted by the mechanism.
(b) Calculate the factor change in initial rate for Trials 1–5 relative to r₀.
(c) Rank the trials from fastest to slowest initial rate, justifying your order quantitatively.
(d) Recommend which trial should be chosen to maximize initial rate and defend your choice.
(e) Discuss one practical limitation of dramatically changing reactant concentrations in an industrial context.