For the gas-phase conversion of acetaldehyde to methane and carbon monoxide,
CH3CHO⟶CH4+CO,
the experimentally determined rate law at 750 K is
rate=k[CH3CHO]3/2.
Four sequences of elementary steps (A–D) are presented below. In each sequence, one step is rate-determining and all other steps are elementary and much faster.
Sequence A
1. 2CH3CHO→CH3CHO∗+CH3CO (slow)
2. CH3CHO∗→CH4+CO (fast)
Sequence B
1. CH3CHO→CH3CO+H (fast)
2. CH3CO+CH3CHO→CH4+CO+CH3CO (slow)
Sequence C
1. CH3CHO+H→CH3CHOH (fast)
2. CH3CHOH+CH3CHO→CH4+CO+CH3CHOH (slow)
Sequence D
1. 3CH3CHO→2CH3CO+CH4 (slow)
2. CH3CO→CH3+CO (fast)
3. CH3+H→CH4 (fast)
Assume that any reactive intermediates (e.g., H, CH3CO) do not appear in the initial reaction mixture.
(a) For each sequence, write the rate law that would result if the designated slow step controls the overall rate. Express the rate only in terms of species present in that slow step.
(b) Using the experimentally observed rate law, eliminate any sequence(s) that are inconsistent with the data. Clearly state the reasoning for each elimination.
(c) One of the remaining sequences contains a step whose molecularity does not match an integer order in the experimental rate law. Explain how the non-integer overall order could still arise from that sequence.
(d) From your analysis, identify the single most plausible sequence and justify your choice with reference to both molecularity and agreement with the rate law.