`3 g` mol of phosphorus is heated in a flask of `4 L` volume. At equilibrium, it dissociates to give `40%` of phosphorus trichloride and chlorine. Calculate the equilibrium constant.

Explanation

Degree of dissociation `=0.4`
`PCl_(5)(g)hArrPCl_(3)(g)+Cl_(2)(g)`
`{:(a(1-alpha),aalpha,,aalpha,("at equilibrium")),(,,,,):}`
Given, `a=3, alpha=0.4`, and `V=4`
So at equilibrium
`[PCl_(5)]=(3(1-0.4))/4=(3xx0.6)/4 "mol" L^(-1)`
`[PCl_(3)]=(3xx0.4)/4 "mol" L^(-1)`
`[Cl_(2)]=(3xx0.4)/4 "mol" L^(-1)`
Applying the law of mass action,
`K_(c )=([PCl_(3)][Cl_(2)])/([PCl_(5)])=(3xx0.4xx3xx0.4)/(4xx3xx0.6)=0.2 "mol" L^(-1)`