For the dissociation reaction `N_(2)O_(4) (g)hArr 2NO_(2)(g)`, the degree of dissociation `(alpha)`interms of `K_(p)` and total equilibrium pressure P is:

Options

A. `alpha = (K_(P)//P)/(4+K_(P)//P)`
B. `alpha = (K_(P))/(4+K_(P))`
C. `alpha = ((K_(P)//P)/(4+K_(P)//P))^(1//2)`
D. `alpha = (K_(P)/(4+K_(P)))^(1//2)`

Answer

C

Explanation

`N_(2)O_(4)(g) rarr 2NO_(2)(g)`
`n_(total) = C + Calpha`
`K_(p) = ((2Calpha/C+Calpha) xx P)^(2)/((C-Calpha/C+Calpha) xx P)`
`K_(p) = 4alpha^(2)p/(1-alpha)(1+alpha) implies alpha = sqrt(K_(p)//P/(4+K_(p)/P))`