Reactor Inventory — Which expression correctly calculates the total mass of substrate present in the reactor at a given moment?

Introduction:
Inventory calculations convert measured concentrations into total masses for material balances and yield estimation. The key is to multiply concentration by the system volume at the same instant, ensuring consistent units.

Given Data / Assumptions:

• Known reactor volume at the snapshot of interest.
• Measured substrate concentration inside the reactor (not the feed).
• Uniform mixing so concentration is spatially uniform.

Concept / Approach:

Mass = concentration * volume. If concentration is in mass per volume (for example, g/L) and volume is in liters, the product yields mass units (g). Flow rate terms are used for rates, not for instantaneous inventory, and should not appear in the simple inventory expression.

Step-by-Step Solution:

Verification / Alternative check:

Check dimensional consistency: (L) * (g/L) = g. Any expression involving flow rate (for example, L/h) would produce rate units, not mass, and is therefore unsuitable for inventory.

Why Other Options Are Wrong:

A: Flow rate multiplies concentration to provide a mass flow rate, not an inventory. C and D: Unit mismatch; these do not yield mass. E: Feed concentration is not the reactor inventory unless reactor equals feed line volume, which it does not.

Common Pitfalls:

Using nominal working volume instead of actual time-varying volume in fed-batch; always use the correct instantaneous volume.

Final Answer:

Reactor volume * substrate concentration in the reactor