For the dissociation reaction `N_(2)O_($) (g)hArr 2NO_(2)(g)`, the degree of dissociation `(alpha)`interms of `K_(p)` and total equilibrium pressure P is:

Options

A. `(2alpha)/(1-alpha^2)`
B. `(alpha^2P)/(1-alpha)`
C. `(4alpha^2)/(1-alpha^2)`
D. `(4alpha^2P)/(1-alpha^2)`

Answer

D

Explanation

`{:(,N_2O_4 hArr , 2NO_2),("Initial conc", 1,0):}`
Let `alpha` is the degree of dissociation of `N_2O_4`
Conc. At equ. `1-alpha " " 2alpha`
Total moles =`1-alpha +2alpha =1+alpha`
`p_(N_2O_4)=(1-alpha)/(1+alpha).P`
`p_(NO_2)=(2alpha)/(1+alpha).P`
`K_p=(p_(NO_2))^2/(p_(N_2O_4))`
`=((2alpha)/(1+alpha). P)^2/((1-alpha)/(1+alpha).P)`
`=(4alpha^2P)/((1+alpha)(1-alpha))=(4alpha^2.P)/(1-alpha^2)`