The gas phase reaction A $---7$ B$+$C follows an elementary rate law and is to be carried out fir t in a PFR and then in a separate experiment in a CSTR$.$ When Pure A is fed to a l $0$ dm $3$ PFR at $290$K and a volumetric flow rate of $5$ dm $3/$s$,$ the conversion is $80\%.$ When a mixture of $50\%$ A and $50\%$ inert $($I$)$ is fed to a I $0$ dm $3$ CSTR at $330$K and a volumetric flow rate of $5$ dm $3/$s the conversion is also $80\%.$ What is the acti$-$ vation energy in cal$/$mol$?$