The thermal decomposition of dinitrogen pentoxide in the gas phase follows the overall stoichiometry
2 N2O5(g)⟶4 NO2(g)+ O2(g).
At 318 K, the experimentally determined rate law is
rate=k[N2O5].
Three alternative sequences of elementary steps (Mechanisms I–III) have been proposed to account for the reaction.
Mechanism I
1. N2O5→NO2+NO3 (slow)
2. NO3+NO2→N2O5 (fast)
3. NO3→NO2+21O2 (fast)
Mechanism II
1. N2O5→NO2+NO3 (fast)
2. NO3→NO+O2 (slow)
3. NO+N2O5→3NO2 (fast)
Mechanism III
1. N2O5+NO2→2NO3 (slow)
2. NO3→NO2+21O2 (fast)
3. NO3+NO2→N2O5 (fast)
Use the kinetic information given above to evaluate the plausibility of each mechanism.
(a) For Mechanism I, write the rate law that would result if the slow step controls the overall rate. Express the rate in terms of the concentration of any species present in that slow step.
(b) Repeat the procedure in part (a) for Mechanism II and for Mechanism III.
(c) Compare each predicted rate law with the experimental rate law. Identify which mechanism(s), if any, are consistent with the observed kinetics, and which are ruled out. Provide a brief justification in each case.
(d) One of the rejected mechanisms contains a species in its slow step whose concentration does not appear in the observed first-order rate law. Explain why the presence of that species in the slow step necessarily contradicts the experimental data.