The following elementary reversible reaction, A+BC+D is carried out in a series of staged packed-bed reactors with inter-stage cooling. The lowest temperature to reactant system may be cooled is 300K. The feed is equal molar in A and B and the catalyst weight in each reactor is sufficient to achieve almost the equilibrium conversion. The feed enters at 300K and the reaction is carried out adiabatically. Additional information HRx=30,000molAcalCp,A=Cp,B=Cp,C=Cp,D=25molKcalKe(50C)=500,000,andFAo=10minmolA a- Derive an expression for the rate law b- Derive an expression for the reaction temperature c- Derive an expression for the equilibrium conversion from energy balance d- Given that the equilibrium conversion depends on the temperature as Xe=1+KCKC, plot equilibrium conversion versus reaction temperature (between 300 and 600K ). e- What would the reaction temperature and conversion be at equilibrium if the reactant enters at 300K ? f- How many reactors and interstage coolers are required to achieve 90% conversion