A sealed cylindrical container with a moveable piston is filled with pure A on one side of the piston (compartment 1), and pure I (and inert gas) on the other (compartment 2). Initially, both compartments are at the same volume (V0) and pressure (P0). ‘A’ is a reactive gas that can undergo the elementary gas-phase reaction A → 3B. As the reaction proceeds the piston will move such that the pressures in both compartments are equal at all times (yet they are not necessarily constant).
a) Derive a model equation that can be used to calculate the conversion of A as a function of time (Do not solve or integrate this equation).
b) Develop an expression relating the normalized volume of compartment 1 (V1n = V1/V0) to the conversion.
c) What is the maximum volume obtainable in compartment 1? What is the maximum normalized pressure (P/P0)?
d) If the reaction is stopped at 80% conversion, what are the normalized volumes and pressure?