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)])/(Delta t) = + (1)/(4) (Delta[NO_(2)])/(Delta t) = + (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)/(2) 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)`.