Answer :
The rate of disappearance of [tex]O_{2}[/tex] related to the rate of appearance of [tex]O_{3}[/tex] according to first-order reaction is [tex]4\times10^{-5}ms^{-1}[/tex].
The power dependence of rate on the concentration of all reactants can be used to define the order of reaction. For instance, the concentration of one species in a first-order reaction determines the reaction's pace entirely.
The reaction takes place in following order:
[tex]2O_{3}(g) \rightarrow 3O_{2}(g)[/tex]
Rate = [tex]-\frac{1}{2}.\frac{d[O_{3}]}{dt} = \frac{1}{3}.\frac{d[O_{2}]}{dt}[/tex]
=>[tex]\frac{d[O_{2}]}{dt} = 6\times10^{-5} m/s[/tex]
=> [tex]-\frac{d[O_{3}]}{dt} = \frac{2}{3} .\frac{d[O_{2}]}{dt}[/tex] = [tex]\frac{2}{3}\times6\times 10^{-5}[/tex]
=> [tex]-\frac{d[O_{3}]}{dt} = 4\times10^{-5} m/s[/tex]
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