For the reaction is equilibrium :
`2NOBr_((g))hArr2NO_((g))+Br_(2(g))`
If `P_(Br_(2))` is `(P)/(9)` at equilibrium and `P` is total pressure, prove that `(K_(p))/(P)` is equal to `(1)/(81)`.

Explanation

`{:(,2NOBr_((g)),hArr,2NO_((g)),+,Br_(2(g))),("P at equilibrium",p-(3P)/(9)=(6P)/(9),,(2P)/(9),,(P)/(9)):}`
`:. P_(T)=(6P)/(9)+(2P)/(9)+(P)/(9)=P`
`K_(p)=(((2P)/(9))^(2)((P)/(9)))/(((6P)/9)^(2))=(P)/(81)`