A suggested mechanism for the decomposition of ozone is as follows: O3 O2 + O fast equilibrium O + O3 2O2 slow step What is the rate law predicted by this mechanism?
For a reaction, mechanism follows the next elementary steps:
Here, intermediate is O as it forms in one elementary step and it is consumed in next steps.
Rate law comes from slowest step that is,
"rate = k_2[O][O_3] \\;\\;\\;(1)"
For fast step at equilibrium, rate of forward and reverse reactions are equal.
"k_1[O_3] =k_{-1}[O_2][O] \\\\\n\n[O] = \\frac{k_1[O_3]}{k_{-1}[O_2]} \\;\\;\\;(2)"
Substitute [O] in rate law (1).
"rate = k_2[O][O_3] \\\\\n\n= k_2\\frac{k_1[O_3]}{k_{-1}[O_2]}[O_3] \\\\\n\n= \\frac{k_1k_2[O_3]^2}{k_{-1}[O_2]}"
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