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Exercise · Q33

Q.The thermal decomposition of acetaldehyde, CH3CHO→CH4+CO\text{CH}_3\text{CHO} \rightarrow \text{CH}_4 + \text{CO}, is found experimentally to obey the rate law rate=k[CH3CHO]3/2\text{rate} = k[\text{CH}_3\text{CHO}]^{3/2}. What does this tell you about

(a) the order of the reaction, and
(b) whether this rate law could describe a single elementary step?
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(a) The rate law rate=k[CH3CHO]3/2\text{rate} = k[\text{CH}_3\text{CHO}]^{3/2} shows the reaction is order 3/23/2 in acetaldehyde -- an order that could never have been correctly guessed from the balanced equation's coefficient of 1 for CH3CHO\text{CH}_3\text{CHO}, underscoring that rate laws and orders must always come from experiment, never from stoichiometry. (b) Molecularity, by definition, counts the whole number of species colliding simultaneously in one elementary step, and can therefore only take the values 1, 2, or (rarely) 3 -- there is no physical elementary event corresponding to '1.5 molecules colliding.' Since the observed order here, 3/23/2, is not even a whole number, this rate law cannot possibly describe a single elementary step; it must instead be the net, overall outcome of a mechanism with two or more elementary steps (in this case, the decomposition of acetaldehyde is known to proceed by a multi-step f …

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