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The gaseous decomposition of ozome 2O(...

The gaseous decomposition of ozome
`2O_(3)rarr3O_(2)`
obeys the rate law `r=-(d[O_(3)])/(dt)=(k[O_(3)]^(2))/([O_(2)])`
Show that the following mechanims is consistent with the above rate law :
`O_(3)overset(K_(eq))hArrO_(2)+O" " ("fast")`
`O+O_(3)overset(k_(1))rarr2O_(2)" " ("slow")`

Text Solution

Verified by Experts

From the slow rate determining step
`=-(d[O_(3)])/(dt)=k_(1)[O][O_(3)]`
From the fast reaction.,
`K_(eq)=([O_(2)][O])/([O_(3)])`
or `[O]=(K_(eq)[O_(3)])/([O_(2)])`
Substituting the value of [O] in the above expression
`r=-(d[O_(3)])/(dt)=(k_(1)K_(eq)[O_(3)]^(2))/([O_(2)])=(k[O_(3)]^(2))/([O_(2)])`
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