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)`.

Options

A. `1//9`
B. `1//81`
C. `1//27`
D. `1//3`

Explanation

`K_(p)=((P_(NO))^(2)(P_(Br)))/((P_(NOBr))^(2))`,
`underset(P-(3P)/(9)=(6P)/(9))(2NOBr)hArrunderset((2P)/(9))(2NO)+underset((P)/(9))(Br_(2))`
Total pressure `=(6P)/(9)+(2P)/(9)+(P)/(9)=P`
`K_(P)=(((2P)/(9))^(2)xx((P)/(9)))/(((6P)/(9))^(2))`
`K_(p)=(P)/(81)`