A gaseous substance A ₂ dissociates according to the reaction: A ₂( g ) 2 A ( g ) The molar mass of pure A ₂ is 80 g mol ⁻¹ . When the reaction reaches equilibrium at a total pressure of 16 atm , the average molar mass of the equilibrium mixture is found to be 60 g mol ⁻¹ . The value of the equilibrium constant K_ p for the reaction is ________.

Step-by-step solution

Let the initial number of moles of A ₂ be 1 and its degree of dissociation be . A ₂( g ) 2 A ( g ) Initial moles: 1 , 0 Moles at equilibrium: 1 - , 2 Total number of moles at equilibrium = 1 - + 2 = 1 + The average molar mass of the mixture ( M_ mix ) is given by: M_ mix = Total mass Total moles = M_ initial 1 + Given M_ mix = 60 g mol ⁻¹ and M_ initial = 80 g mol ⁻¹ : 60 = 80 1 + 1 + = 80 60 = 4 3 = 1 3 Moles of A ₂ at equilibrium = 1 - 1 3 = 2 3 Moles of A at equilibrium = 2 1 3 = 2 3 Total moles = 4 3 Mole fract