`PCl_(5)(g)hArrPCl_(3)(g)+Cl_(2)(g).` If 1 mole `PCl_(5)` was put in a container of volume V litre and at equlibrium, x moles of it was decomposed, find its `K_(p) and K_(c)` at equlibrium pressure of P atm.

Explanation

`K_(p)=(P_(PCl_(3))P_(Cl_(2)))/(P_(PCl_(5)))and K_c=([PCl_(3)][Cl_(2)])/([PCl_(5)])`
`PCl_(5)hArrPCl_(3)+Cl_(2)`
`{:("Initial moles",1,0,0),("Moles at equlibrium",1-x,0,0),("Concentration at equlibrium",(1-x)/(v),x/v,x/v):}`
Total moles at equlibrium `=1-x+x+x=1+x`
`K_(c)=(((x)/(v))^(2))/(((1-x)/(v)))=(x^(2))/((1-x)v)`
`K_(p)=(((x)/(1+x)P)^(2))/(((1-x)/(1+x))P)=(x^(2)P)/(1-x^(2))`