Consider the reaction `N_2(g) + 3H_2 (g) rarr 2NH_3 (g)`
The equilibrium constant of the above reaction is `K_p` .If pure ammonia is left to dissociated, the partial pressure of ammonia at equilibrium is given by `(x^(3//2)K_p^(1//2) p^2)/16`. The numerical value of x is ____ (Assume that `P_(NH_3) lt lt P_"total"` at equilibrium and `P_"total"` = p)

Options

A. `3^(3//2)K_(p)^(1//2)P^(2)/16`
B. `3^(3//2)K_(p)^(1//2)P^(2)/4`
C. `K_(p)^(1//2)P^(2)/16`
D. `K_(p)^(1//2)P^(2)/4`

Answer

A

Explanation

`2NH_(3)(g) rarr N_(2)(g) + 3H_(2)(g)`
`1/K_(p) = x(3x)^(3)/(p_(NH_(3)))^(2)`
`p_(total) = p = p - 2x + x + 3x = (p_(NH_(3)) + 4x )4x`
`x = p/4 :. 1/K_(p) = p/4(3p/4)^(3)/(p_(NH_(3)))^(2)`