A sealed cylindrical container with a moveable piston is initially filled with 10 moles of pure A below the piston (compartment 1 ), and 10 moles of an inert gas, I, above (compartment 2). The piston can freely move up, or down, in response to any pressure imbalance, thus the compartments always have equal pressures (but not constant in time). The total volume of the cylinder (for both compartments) is 500 liters. Initially the pressure is 1 atm. The elementary reversible gas-phase reaction A2B takes place in compartment 1 under isothermal conditions. a) Develop a model for this process in terms of moles (NA and \( \left.\mathrm{N}_{\perp} ight) \) as state variables. b) Develop a stoichiometric table for this reaction. c) Derive an expression for the volume of compartment 1 as a function of X and show that it is expressed as ( V is the total volume): V1=(2+X)(1+X)V d) After a very long time of operation, the piston stopped moving. The volume V1 at that time was 315 liters. Calculate the equilibrium conversion X and the equilibrium constant Kc of the reaction. e) What is the final pressure in the reactor. Do not write in this area