The decompoistion of `N_(2)O_(5)` according to the equation `2N_(2)O_(5)(g) rarr 4NO_(2)(g)+O_(2)(g)`
is a first order reaction. After `30 min`, form the start of the decompoistion in a closed vessel, the total pressure developed is found t be `284.5 mm Hg`. On complete decompoistion, the total pressure is `584.5 mm Hg`. Calculate the rate constant of the reaction.

Explanation

`{:(,2N_(2)O_(5(g)),rarr,4NO_(2(g)),+,O_(2(g))),`{:("mole"att=0,a,0,0),(t=30,(a-x),2x,x//2),(t=oo,0,2a,a//2):}
`:'` No. of mole `prop` Pressure developed
`:. a prop `P_(0)` , at `t=0`
`a+(3x)/2 prop 284.5` at `t=30 "minute"`
`(5a)/2 prop 584.5` at `t=oo`
Thus, `a prop (2xx584.5)/(5)` or `a prop 233.8` at `t=0`
`x prop 33.8` at `t=30 minute`
`a-x prop 200.0`
`:' K=2.303/t"log"_(10) a/((a-x))`
`:. K=2.303/30"log"_(10)233.8/200`
`=5.206xx10^(-3) "minute"^(-1)`