Determining the rate law?
O3 ->O2 + O (slow)
O + O3 ->2O2 (fast)
2O3 -> 3O2 (net reaction)
If this is the mechanism, what is the reaction's rate law?
Could someone explain to me how to determine the rate law? I know you use the reactant of the slower reaction, but I'm not sure how to determine the order?
Thanks so much, in advance :)
Answer:
The overall rate of the reaction to produce diatomic oxygen is:
r =k1[O3]+k2[O][O3], where
k1 is the rate constant for the slow step,
k2 is the rate constant for the fast step, and the values in brackets are the concentrations of each species
Notice that the only undefined quantity is [O], b/c it's an intermediate which gets produced and consumed. Because its rate of production by the slow reaction is slower than its rate of consumption by the fast reaction, its concentration at any time is zero, so the rate equation simplifies to
r=k1[O3], which is pseudo-first order in ozone and psuedo-first order overall.
The order is determined by the stoichiometric coefficient of the reactants in the slow step.
The slow step here is the first step, so that makes it easy. The rate of the reaction depends on the concentration of ozone, and because ozone is decomposing in a unimolecular process (its stoichiometric coefficient is 1 in the slow step) then the order of ozone (and the overall order) are both 1.
rate = k [O3]
PS the next guy's answer is not even wrong. It's nonsense.
First you'll have to come up with an overall reaction, which would be 2O3 -> 3O2 as you did.
The rate law will consist of a rate constant "k". The rate law can either be expressed as the rate of the disappearance of the ozone or as the rate of formationof the oxygen. These are expressed as R= -k [O3] squared or R= k[O2] cubed.
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