A continuous stirred tank reactor (chemostat) contains biomass at 20 g dry weight per litre. Under ideal mixing, what is the biomass concentration in the effluent stream?

Introduction / Context:In a continuous stirred tank reactor (CSTR/chemostat), perfect mixing is assumed: composition is uniform throughout the vessel and identical to the effluent. This principle is crucial when estimating productivities, washout risk, and downstream loading on separators.

Given Data / Assumptions:

• Reactor biomass concentration X = 20 g L^-1 (dry weight).
• Ideal mixing (no concentration gradients).
• Steady operating conditions (no abrupt transients).

Concept / Approach:Mass balance for a well-mixed tank gives Cout = Creactor for any component that is neither selectively retained nor phase-partitioned. Cells are suspended and exit with the same concentration unless cell retention devices are used (e.g., membranes, settlers).

Step-by-Step Solution:

Verification / Alternative check:Residence-time distribution for a CSTR and tracer studies show effluent composition equals mixed bulk fluid composition, validating the equality.

Why Other Options Are Wrong:

• Greater than/More than 30: would imply enrichment or phase separation not present here.
• Less than 20: contradicts perfect mixing without retention.
• Zero: only true if a perfect cell retention barrier is used or at washout with X ≈ 0.

Common Pitfalls:Confusing chemostats with perfusion or immobilized-cell systems where effluent cell concentration may differ.

Final Answer:Approximately 20 g dry weight per litre