An equimolar mixture of N ₂ O ₄ and an inert gas Neon (Ne) is introduced into a closed vessel. The system is allowed to equilibrate according to the reaction: N ₂ O ₄( g ) 2 NO ₂( g ) At equilibrium, the average molar mass of the gaseous mixture is found to be 44.8 g/mol and the total pressure is 10.0 atm. The equilibrium constant K_p (in atm) for the reaction is: [Given: Molar masses of N ₂ O ₄ = 92 g/mol, Ne = 20 g

Step-by-step solution

Let the initial mixture contain 1 mole of N ₂ O ₄ and 1 mole of Ne. Total mass of the mixture = (1 92) + (1 20) = 112 g. The total mass remains conserved during the reaction. Let be the degree of dissociation of N ₂ O ₄ . At equilibrium, the moles of each gas are: n_ N ₂ O ₄ = 1 - n_ NO ₂ = 2 n_ Ne = 1 Total moles at equilibrium = (1 - ) + 2 + 1 = 2 + . The average molar mass at equilibrium is given by: M_ avg = Total Mass Total Moles = 112 2 + = 44.8 2 + = 112 44.8 = 2.5 = 0.5 Moles of gases at equilibrium: n_ N ₂