For the first order decomposition reaction of `N_2O_5`,it is observed that
`N_2O_(5(g))rarr2NO_(2(g))+1//2O_(2(g)),-(d[N_2O_5])/dt=k[N_2O_5]`
`2N_2O_(5(g))rarr4NO_(2(g))+O_(2(g)),-(d[N_2O_5])/dt=k[N_2O_5]`
which of the following is true?

Options

A. k=k
B. k= 2K
C. k=k/2
D. ` k=K^2`

Answer

B

Explanation

For the reaction,`N_2O_(5(g))rarr2NO_(2(g))+1//2O_(2(g))`
Rate=`-(d[N_2O_5])/(dt)=k[N_2O_5]`
For the reaction, `2N_2O_(5(g))rarr4NO_(2(g))+O_(2(g))`
Rate=`-1/2(d[N_2O_5])/(dt)=k.[N_2O_5]`
-`(d[N_2O_5])/(dt)=2k.[N_2O_5]=k[N_2O_5]`
Since `-(d[N_2O_5])/(dt)` does not depend upon the way the chemical reaction is formulated, we have k=2K.