The decomposition 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 minutes from the start of the decomposition in a closed vessel, the total pressure developed is found to be 284.5 mm Hg and on completion, the total pressure is 584.5 mm Hg. Calculate the rate constant of the reaction.

Options

A. `5.2 xx10^(-3) min^(-1)`
B. `10.1 xx10^(-3) min^(-1)`
C. `8.3 xx10^(-3) min^(-1)`
D. `2.2 xx10^(-3) min^(-1)`

Answer

A

Explanation

`2N_(2)O_(5)rarr4NO_(2)+O_(2)`
Initial pressure of `N_(2)O_(5),P_(0)=2/5xx58.5 =233.8 mm Hg`
After 30 minutes the total pressure =2805 mm Hg
`2n_(2)O_(5) rarr4NO_(2)+O_(2)`
`p_(0)-2p 4p p`
pressure of `N_(2)O_(5)` after 30 minutes =`233.8 -(2xx16.9) =200 Hg`
`k=(2.303)/(30)log_(10)(233.8)/(200.0)=5.2xx10^(-3) min^(-1)`