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.

Answer

`0.4`

Explanation

`{:(,N_(2)O_(5)(g),rarr,2NO_(2)(g)+,(1)/(2)O_(2)(g)),("Initial P","PmmHg",,0,0),("Final P after time t",P-p,,2p,(1)/(2)p):}`
Total pressure `= P - p + 2p + (1)/(2)p`
`= P = (3)/(2)p`
Thus, `P prop 600 mm`
and `(P + (3)/(2)p) prop 960 mm`
Thus, `p prop 240 mm`
Mole fraction of `N_(2)O_(5)` decomposed `= (p)/(P) = (240)/(960) = 0.4`