For the equation
`N_(2)O_(5)(g)=2NO_(2)(g)+(1//2)O_(2)(g)`, calculate the mole fraction of `N_(2)O_(5)(g)` decomposed at a constant volume and temperature, if the initial pressure is `600 mm Hg` and the pressure at any time is `960 mm Hg`. Assume ideal gas behaviour.

Explanation

(i) `E_(a) =22 kJ A=5.42 xx10^(10) s^(-1)` (ii) x=0.375
(i) `"In "(k_(2))/(k_(1)) =(E_(a))/(R ) ((T_(2)-T_(1))/(T_(1)T_(2)))`
`rArr" In "((4.5xx10^(7))/(1.5xx10^(7)))=(E_(a))/(8.314) ((50)/(323xx373)) rArr E_(a) =22 kJ`
Also In k = In `A -(E_(a))/(RT)`
At `50^(@)C` : In `A=" In "(1.5xx10^(7)) -(22xx1000)/(8.314xx323)=8.33 rArr A=4.15xx10^(3) s^(-1)`
(ii) `N_(2)O_(5) (g) rarr 2NO_(2) (g) +(1)/(2) O_(2) (g)`
`600-p" "2p" "(p)/(2)`
Total pressure `960=600+(3)/(2) p rArr p =240` m m
`rArr ` Partial pressure of `N_(2)O_(5)(g)` remaining =600-240 =360 m m
Mole fraction `=(360)/(960) =0.375`