The decomposition of nitrogen pentoxide is given as `2N_(2)O_(5) to 4NO_(2) + O_(2)` . The rates of reaction are `([N_(2)O_(5)])/(Delta t ) =k_(1)[N_(2)O_(5)],(Delta[NO_(2)])/(Deltat) = k_(2) [N_(2)O_(5)] and (Delta [O_(2)])/(Delta t) = k_(3) [N_(2)O_(5)]`
Relate the rate constants `k_(1) , k_(2)` and `k_(3)` .

Explanation

The rate of the reaction is given as
`-(1)/(2)(Delta[N_(2)O_(5)])/(Deltat)=+(1)/(4)(Delta[NO_(2)])/(Deltat)=+(1)/(1)(Delta[O_(2)])/(Deltat)`
Substituting the given values of rate in the above expression,
`(1)/(2)k_(1)[n_(2)O_(5)]=(1)/(4)k_(2)[N_(2)O_(5)]=(1)/(1)k_(3)[N_(2)O_(5)]`
Therefore, the rate constants `k_(1),k_(2)` and `k_(3)` are related as, `2k_(1)=k_(2)=4k_(3)`.