For the reaction: `N_(2)O_(5)(g)rarr2NO_(2)(g)+(1)/(2)O_(2)(g)` Calculate the mole fraction of `N_(2)O_(5)(g)` decomposed at constant volume and temperature, if the initial pressure is 600 mm Hg and the pressure at any time is 960 mm Hg. Assume ideal behaviour

Explanation

The given reaction is :
`" "N_(2)O_(5)(g)rarr2NO_(2)(g)+(1)/(2)O_(2)(g)`
`{:("at"t=0,P,0,0),("at"t=t,P-p,2p,0.5p):}`
`therefore"At "t=t, " the total pressure"=P-p+2p+0.5p=P+(3)/(2)p=960"mmHg"`
Given : P = 600 mm Hg.
`thereforeP+(3)/(2)p=960 ` mmHg or, p = 240mm Hg
`therefore` The mole fraction of `N_(2)O_(5)` decomposed `=(p)/(P)=(240)/(600)=0.4`