A reactor has a total (geometric) volume of 50,000 L and a headspace of 10,000 L. What is the working liquid volume inside the reactor?

Introduction / Context:
Specifying a reactor requires distinguishing between total geometric volume, headspace for gas handling and foam, and working (liquid) volume. Accurate working volume is essential for calculating residence times, specific power input (P/V), and mass transfer coefficients such as KLa.

Given Data / Assumptions:

• Total volume = 50,000 L.
• Headspace volume = 10,000 L (gas space above liquid).
• No internal fixtures significantly displacing volume (assumed negligible for this calculation).

Concept / Approach:
Working liquid volume equals total volume minus headspace. This simple subtraction is standard unless additional displacements (coils, internals) are specified. The resulting working volume is used in all volumetric performance metrics during operation.

Step-by-Step Solution:

Verification / Alternative check:
If the process requires 20% headspace in a 50,000 L tank, 0.2 * 50,000 = 10,000 L, confirming the same calculation.

Why Other Options Are Wrong:

• 10,000 or 20,000 or 30,000 L: incorrect subtraction or arbitrary fractions.
• 50,000 L: ignores headspace volume.

Common Pitfalls:
Confusing nominal vessel size with working volume; always confirm fill level and headspace policy for foaming systems.

Final Answer:
40,000 L