For the gaseous reaction PCl ₅( g ) PCl ₃( g ) + Cl ₂( g ) 2 mol of PCl ₅ is taken in a closed vessel. At equilibrium, 1 mol of PCl ₅ remains. If the equilibrium constant K_ p for the reaction is 4 , the total pressure of the system at equilibrium is ________ atm .

Step-by-step solution

The given reaction is: PCl ₅( g ) PCl ₃( g ) + Cl ₂( g ) Initial moles: 2 mol, 0 , 0 At equilibrium: 2 - x , x , x We are given that equilibrium moles of PCl ₅ = 1 . 2 - x = 1 x = 1 Moles at equilibrium: n_ PCl ₅ = 1 n_ PCl ₃ = 1 n_ Cl ₂ = 1 Total number of moles at equilibrium = 1 + 1 + 1 = 3 Let the total pressure at equilibrium be P . Partial pressures of the components are: P_ PCl ₅ = 1 3 P P_ PCl ₃ = 1 3 P P_ Cl ₂ = 1 3 P The equilibrium constant K_ p is given by: K_ p = P_ PCl ₃ P_ Cl ₂ P_ PCl ₅ Substituting