The rate of reaction.
`2N_(2)O_(5) to 4NO_(2) + O_(2)`
can be written in three ways.
`(-d[N_(2)O_(5)])/(dt) = k[N_(2)O_(5)]`
`(d[N_(2)O_(5)])/(dt) =( k^(')[N_(2)O_(5)])`
`(d[O_(2)])/(dt) = (k^(')[N_(2)O_(5)])`
The relation between k and `k^(')` are:

Options

A. `k'=2k`, `k''=2k`
B. `k'=k`, `k''=k`
C. `k'=2k`, `k''=k`
D. `k'=2k`, `k''=k//2`

Answer

D

Explanation

`-(1)/(2)(d[N_(2)O_(5)])/(dt)=(1)/(4)(d[NO_(2)])/(dt)=(d[O_(2)])/(dt)`
`(1)/(2)k(N_(2)O_(5))=(1)/(4)k.(N_(2)O_(5))=k..(N_(2)O_(5))`
`(k)/(2)=(k.)/(4)=k..`
`k.=2k`, `k..=(k)/(2)`.