FE Chemical Practice Question Solution included after investigation
CASE E-068 · FE

The CSTR That Needed 600 L, Not 367

The PFR-sized volume looked efficient, but the well-mixed CSTR needed 600 L to reach the same 60% conversion.

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Case E-068 engineering failure visual
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1

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2

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3

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4

Fix

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5

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Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A liquid feed enters a steady CSTR at 100 L/min with CA0=2.0 mol/L. Reaction A→products is first order with k=0.25 min^-1. The target conversion is 60%. A sizing note uses the plug-flow equation and reports about 367 L. Determine the required CSTR volume.

Chemical Reaction Engineering Chemical Design Verification Root Cause Analysis Safe Correction
E-068
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

A plug-flow equation was used for a well-mixed tank reactor.

What was missed

The CSTR reacts everywhere at the lower exit concentration.

Corrected model

Use V=FA0X/(-rA,exit) for the stated steady CSTR.

QUICK ANSWER

For a constant-density first-order CSTR, V=v0X/[k(1-X)]. With v0=100 L/min, X=0.60, and k=0.25 min^-1, V=600 L. The corresponding first-order PFR expression gives about 366.5 L, so using it would undersize the CSTR.

ENGINEERING TAKEAWAY

For a steady constant-density CSTR, V=FA0 X/(-rA at exit)=v0 X/[k(1-X)] for a first-order reaction.

CASE QUESTIONS

Questions this case should settle.

What is the first-order CSTR volume equation at constant density?

V=v0X/[k(1-X)].

Why can a CSTR require more volume than a PFR for a positive-order reaction?

A CSTR is mixed to the lower exit reactant concentration throughout, so its average reaction rate is lower.

NEXT FE PRACTICE QUESTION

The 70% Conversion That Produced Only 50% Yield

Chemical Reaction Engineering · 5–10 min

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