FE Chemical Practice Question Solution included after investigation
CASE E-067 · FE

The Batch Reactor That Reached 63%, Not 100%

The shortcut kt=1 suggested 100% conversion after 5 minutes. The first-order batch model gave only 63.2%.

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Case E-067 engineering failure visual
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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 constant-volume batch reactor carries out an irreversible first-order reaction A→products with k=0.20 min^-1. A note uses X=kt and predicts complete conversion after 5.0 min. Determine the correct conversion. Then determine the time required for 90% conversion at the same rate constant.

Chemical Reaction Engineering Chemical Design Verification Root Cause Analysis Safe Correction
E-067
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

A small-time approximation was treated as an exact conversion equation.

What was missed

First-order concentration decays exponentially.

Corrected model

Use X=1-exp(-kt) for the stated constant-volume first-order batch reactor.

QUICK ANSWER

For a constant-volume first-order batch reactor, X=1-exp(-kt). With k=0.20 min^-1 and t=5.0 min, X=1-exp(-1)=0.6321, or 63.2%. Reaching 90% conversion requires t=-ln(0.10)/0.20=11.51 min.

ENGINEERING TAKEAWAY

For an irreversible first-order reaction in a constant-volume batch reactor, CA=CA0 exp(-kt) and X=1-exp(-kt).

CASE QUESTIONS

Questions this case should settle.

What is the first-order batch-reactor conversion equation?

For the stated constant-volume irreversible reaction, X=1-exp(-kt).

How long does 90% conversion take when k=0.20 min^-1?

About 11.51 minutes.

NEXT FE PRACTICE QUESTION

The 70% Conversion That Produced Only 50% Yield

Chemical Reaction Engineering · 5–10 min

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