The liquid-phase, dimer-quadmer series addition reaction 4 A 2A2 A4 can be written as 2AA2r1A=k1ACA2HRx1A=32.5kcalmol

The liquid-phase, dimer-quadmer series addition reaction 4 A → 2A2 → A4 can be written as
2A→A2−r1A=k1ACA2ΔHRx1A=−32.5kcalmol A2A2→A4−r2A2=k2A2CA22ΔHRx2A2=−27.5kcalmol A2
and is carried out in a 10-dm³ PFR. The mass flow rate through the heat exchanger surrounding the reactor is sufficiently large so that the ambient temperature of the exchanger is constant at T_a = 315 K. The reactants enter at a temperature T₀, of 300 K. Pure A is fed to the rector at a volumetric flow rate of 50 dm³/s and a concentration of 2 mol/dm³.
(a) Plot, compare, and analyze the profiles F_A, F_A2, and F_A4 down the length of the reactor up to 10 dm³.
(b) The desired product is A₂ and it has been suggested that the current reactor may be too large. What reactor volume would you recommend to maximize F_A2?
(c) What operating variables (e.g., T0, Ta) would you change and how would you change them to make the reactor volume as small as possible and to still maximize F_A2? Note any opposing factors in maximum production of A2. The ambient temperature and the inlet temperature must be kept between 0°C and 177°C.
Additional information:

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k1A=0.6dm3mol-Sat 300 K with E1-4000calmolk2A2=0.35dm3mol Sat 320 K with E2-5000calmolCPA=25calmolA K,CPA2-50calmolA2 K,CPA4=100calmolA4 KUa=1000caldm3 S K Turn in your recommendation of reactor volume to maximize and the molar flow rate at this maximum.