Prove `alpha=sqrt((K_(p)/(P+K_(p))))` for
`PCl_(5) hArr PCl_(3)+Cl_(2)`
where `alpha` is the degree of dissociation at temperature when equilibrium constant is `K_(p)`.

Explanation

`{:(,PCl_5hArr , PCl_3+ , Cl_2),("Initial mole", 1, 0,0),("Moles at equilibrium" , 1-alpha , alpha , alpha):}`
where `alpha` is degree of dissociation
`therefore P'_(O_2)=[alpha/(1+alpha)]xxP , P'_(PO_2)=[alpha /(1+alpha )]xxP , P'_(PO_5)=[(1-alpha)/(1+alpha)]P`
`therefore K_P=(P'_(PCl_3 ) xx P'_(Cl_2))/(P'_(PCl_5))=([(alpha xx P)/(1+alpha)][(alpha xx P)/(1+alpha)])/([(1-alpha)/(1+alpha)]P), K_P=(alpha^2P)/(1-alpha^2), alpha = sqrt((K_P/(P+K_P)))` Hence proved .