For the equilibrium `AB (g) hArr A(g) + B (g)` at a given temperature, one-third of AB is dissociated. The equilibrium pressure of the system is

Options

A. 8 times `K_(P)`
B. 16 times `K_(P)`
C. 4 times `K_(P)`
D. 9 times `K_(P)`

Answer

A

Explanation

`{:(,AB(g),hArr,A(g)+,B(g)),(t = 0," "a,," "0," "0),(t = t_(eq)," "a,," "0," "0):}`
`rArr K_(p) = (p_(A)p_(B))/(p_(AB)) =(((x)/(a+x)P)((x)/(a+x)P))/(((a-x)/(a+x)P)) rArr K_(p) = (x^(2)P)/(a^(2)-x^(2))` and `alpha = (x)/(a) = (1)/(3) rArr P = 8 K_(p)`