Ozone reacts with nitric oxide in the stratosphere according to the overall reaction

CHEMISTRY · Multi-part · A Level · Chemistry · Rate equations · Rate equations

Problem

Ozone reacts with nitric oxide in the stratosphere according to the overall reaction O3(g)+NO(g)→O2(g)+NO2(g)O_3(\text{g}) + NO(\text{g}) \rightarrow O_2(\text{g}) + NO_2(\text{g}). Experimental studies at 250 K250\,\text{K} and 1.0×10−6 atm1.0 \times 10^{-6}\,\text{atm} total pressure give the rate law rate=k[O3][NO]\text{rate} = k[O_3][NO]. Two alternative mechanisms have been proposed. Mechanism A (two-step): Step 1: O3(g)⇌O2(g)+O(g)O_3(\text{g}) \rightleftharpoons O_2(\text{g}) + O(\text{g}) (fast equilibrium) Step 2: O(g)+NO(g)→NO2(g)O(\text{g}) + NO(\text{g}) \rightarrow NO_2(\text{g}) (slow, rate-determining) Mechanism B (single-step): O3(g)+NO(g)+NO(g)→O2(g)+NO2(g)+NO(g)O_3(\text{g}) + NO(\text{g}) + NO(\text{g}) \rightarrow O_2(\text{g}) + NO_2(\text{g}) + NO(\text{g}) (termolecular elementary step) Complete the tasks below. (1) Part 1: a) Derive the rate law predicted by Mechanism A, expressing the rate solely in terms of the measurable concentrations [O3][O_3] and [NO][NO]. (2) Part 2: b) Write the rate law that would result if Mechanism B were the correct single elementary step. (3) Part 3: c) Using your results from parts (a) and (b), identify which mechanism is consistent with the experimentally observed rate law and justify your choice. (4) Part 4: d) Beyond the rate-law comparison, evaluate the intrinsic likelihood of the elementary step in Mechanism B at 250 K250\,\text{K} and 1.0×10−6 atm1.0 \times 10^{-6}\,\text{atm}. Your answer should refer explicitly to the statistical probability of simultaneous three-particle collisions under the given conditions.

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