The elementary, gas phase reversible reaction 𝑨 ↔ 𝑩 is carried out in two identical packed bed reactors

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The elementary, gas phase reversible reaction
𝑨 ↔ 𝑩
is carried out in two identical packed bed reactors connected in
series with interstage cooling. The operation of each packed bed
reactor (PBR) is adiabatic and the pressure drop is negligible.
You are required to evaluate the following 2 proposed
configurations for the reactor system in order to determine which
configuration achieves a higher conversion.
Configuration 1:
Pure A enters the first reactor at 300 K and 12 mol/min. The
catalyst weight in each reactor is sufficient to achieve 90% of the
equilibrium conversion. An interstage cooler cools the effluent
(outlet) from the first PBR back to 300 K. Determine the outlet
temperatures and conversions in each stage.
Configuration 2:
Pure A enters the reactor at 300 K and 12 mol/min. The catalyst
weight in each reactor is sufficient to achieve 90% of the
equilibrium conversion. Direct cold injection of inerts is used to
cool the effluent from the first stage back to 300 K. The flow rate
of the cold inerts is 1.5 times the feed flow rate of A entering
the first stage. Determine the outlet temperatures and conversions
in each stage.
Note: You may find it useful to determine the appropriate values
for the following temperatures: 300, 350, 400, 450, 500 K.
Additional Data
Heats of Formation at 300 K (J/mol): Ho A = -43400 Ho B =
-127000
Specific Heat Capacities (J/mol.K): CpA = 240 CpB = 240
Equilibrium Constant: Kc = 1.2 x 105 at 300 K
Gas Constant, R = 8.314 J/mol.K
All calculations must be done manually and written. Do not use
any program or software