Chemistry
Chemistry
Problem
A research team is studying the gaseous reaction sequence below at 450 K. Step 1 P + Q ⇌ X (fast) Step 2 X + Q ⇌ Y (fast) Step 3 Y → Z (slow) The overall reaction is P + 2 Q → Z. Assume that no other elementary steps occur and that all species are in the same homogeneous phase. (a) Describe the experimental evidence a kineticist would seek to justify classifying Steps 1 and 2 as elementary reactions that are not rate-limiting. (b) Explain, without using any mathematical derivation, why the rate law for the overall reaction is expected to depend only on the concentrations of P and Q, even though the slow step does not contain P explicitly. (c) Experimental rate data at 450 K show that doubling [Q] while holding [P] constant leads to a fourfold increase in the initial rate, whereas doubling [P] with [Q] constant only doubles the initial rate. Relate these observations qualitatively to the elementary sequence provided.Intuitive explanation
The rate law for a multi-step mechanism is determined entirely by the slowest step and any intermediates it contains—but you can't leave intermediates in your final answer. The key is to use the fast equilibrium steps before the slow step to express those intermediates in terms of the original reactants, then substitute back into the rate expression for the rate-determining step. This transforms an answer that looks incomplete into one written only in terms of measurable concentrations.
Intuitive explanation
The rate law for a multi-step mechanism is determined entirely by the slowest step and any intermediates it contains—but you can't leave intermediates in your final answer. The key is to use the fast equilibrium steps before the slow step to express those intermediates in terms of the original reactants, then substitute back into the rate expression for the rate-determining step. This transforms an answer that looks incomplete into one written only in terms of measurable concentrations.