Two CSTRs in series: For reactions of order greater than one, which size arrangement maximizes performance at a given overall conversion, and which reactor should be placed first?

Introduction / Context:
This design question in chemical reaction engineering asks how to size and order two continuous stirred-tank reactors (CSTRs) in series when the intrinsic reaction order n > 1. The goal is to achieve a specified overall conversion with minimum volume (or, equivalently, to maximize performance at fixed total volume).

Given Data / Assumptions:

• Two mixed flow reactors (CSTRs) in series.
• Overall conversion target is fixed.
• Single, irreversible reaction with apparent order n > 1.
• Isothermal operation and identical feed composition to the train.

Concept / Approach:
For n > 1, the instantaneous rate r = k * C^n is highly sensitive to concentration. Higher concentrations at the reactor inlet provide disproportionately higher rates. Placing the larger volume first exposes more fluid to high-concentration conditions for longer residence time, harvesting the strongly concentration-dependent rate advantage and reducing the total volume needed for the target conversion.

Step-by-Step Solution:

Verification / Alternative check:
Graphical design with 1/(-r_A) versus X shows the CSTR area rectangles. For n > 1, the first rectangle area (at lower X, higher C) benefits more from larger volume, minimizing the sum of areas (i.e., total volume).

Why Other Options Are Wrong:

• Equal-sized reactors: Not optimal for n > 1; it wastes high-concentration potential.
• Smaller first: Misses the rate benefit at high C, increasing total volume.
• None of these: The recommended arrangement is the larger reactor first.

Common Pitfalls:
Confusing CSTR behavior with PFR. While a PFR naturally exploits high concentration at the inlet, CSTRs require deliberate volume placement to mimic that advantage.

Final Answer:
The larger reactor should be placed first.