CSTR arrangement effects — equal-size reactors For a first-order reaction processed in two equal-volume continuous stirred-tank reactors (CSTRs), how does overall conversion compare when the reactors are connected in series versus in parallel (same total flow and total volume)?

Introduction / Context:
For first-order kinetics, reactor sequencing significantly influences conversion for a given total reactor volume. Series CSTRs emulate a progression toward plug-flow behavior, improving performance over a single back-mixed volume or parallel operation.

Given Data / Assumptions:

• Total reactor volume and total volumetric flow rate are fixed.
• Two equal CSTRs are used.
• Isothermal, first-order reaction without mass-transfer limitations.

Concept / Approach:
For first-order reactions, conversion in a CSTR is X = kτ/(1 + kτ). Placing reactors in series increases the exit conversion because the effluent of the first (with reduced concentration) feeds the second, and the algebra of sequential back-mixed stages yields higher overall X than a single back-mixed vessel of the same total volume. Parallel CSTRs each see the same inlet concentration and shorter residence time, which lowers overall conversion.

Step-by-Step Solution:
Let θ = kτ be Damköhler for one tank; single CSTR: X1 = θ/(1 + θ).Two in series: Xseries = 1 − (1 − X1)^2 = 1 − (1/(1 + θ))^2.Two in parallel (each at half residence time): Xpar = θ/2 / (1 + θ/2).Compare: Xseries > Xpar for θ > 0 → series gives higher conversion.

Verification / Alternative check:
Levenspiel plots or numerical examples with θ = 1 give Xseries = 0.75 versus Xpar ≈ 0.333, confirming superiority of series.

Why Other Options Are Wrong:

• (a) Contradicts the series advantage.
• (c) Parallel reduces residence time per tank; conversion drops.
• (d) Not true except the trivial θ = 0 case.

Common Pitfalls:

• Assuming total residence time per path is unchanged in parallel; it halves, lowering conversion.

Final Answer:
More when connected in series