The following gas-phase reaction is carried out in a pfr operating isothermally at 650 k and a constant pressure of 3 atm.
a -> 2b, ra = -kca where k = 4.08*10^9[s-1]*e^(-27000[cal/mol]/r t)
the feed consists of a mixture of a and an inert that is twice the molar flowrate of a.
there is a disruption in the upstream process and the inlet molar flowrate of a is now reduced by a factor of 2 (i. e. fa0, new = 0.5 fa0), but the flowrate of inert (fi0,new = fi0) remains constant. you must keep the conversion of a in the reactor at 90%. you cannot change the pressure or the reactor volume so you decide to change the temperature.
a) what temperature do you recommend to maintain a constant conversion of a?
b) qualitatively explain your answer to part (a). in other words, why should the temperature be reduced or raised to maintain x = 0.9?