Nitrogen pentoxide, N₂O₅, decomposes in liquid dichloromethane at 25 °C according to the overall reaction
N₂O₅ → NO₂ + NO₃.
Kinetic studies give the empirical rate law
rate = k[N₂O₅].
Transient-absorption spectroscopy carried out during the first 30 ms of reaction shows a broad band centered at 350 nm that is assigned to NO₃· radicals. No spectral signatures attributable to dinitrogen tetroxide (N₂O₄) are observed.
Three competing mechanisms have been advanced:
Mechanism I
1. N₂O₅ ⇌ NO₂ + NO₃ (fast equilibrium)
2. NO₃ → NO₂ + O (slow)
3. O + N₂O₅ → NO₃ + NO₂ (fast)
Mechanism II
1. N₂O₅ → NO₂ + NO₃ (slow, unimolecular)
2. NO₃ + NO₂ → N₂O₅ (fast)
Mechanism III
1. 2 N₂O₅ → N₂O₄ + 2 NO₃ (slow, bimolecular)
2. NO₃ → NO₂ + O (fast)
Assume that any intermediates or transition states not shown are present in negligible concentrations.
(a) For each mechanism, use the elementary-step sequence to derive the rate law expressed in terms of the concentration of N₂O₅ and any measurable equilibrium constants. Clearly state any steady-state or equilibrium approximations you employ.
(b) Compare each derived rate law with the experimentally determined first-order rate law. Indicate which mechanisms are kinetically compatible with the data.
(c) Considering the spectroscopic observation of NO₃· and the absence of detectable N₂O₄, evaluate the likelihood of each mechanism. Rank Mechanisms I–III from most to least plausible and justify your ranking with explicit reference to the experimental evidence.
(d) Propose one structural modification to N₂O₅ (for example, isotopic labeling or substitution of a ligand) that would allow rapid-scan infrared spectroscopy to provide additional mechanistic insight. Explain what spectral change you would expect for the preferred mechanism.