A fermentation system has KLa = 3 s^-1 and C* = 5 ppm O2. If the bulk liquid is already saturated (CL = C*), what is the oxygen transfer rate (OTR)?

Introduction / Context:
Oxygen transfer from bubbles into liquid is driven by the concentration difference between saturation (C*) and bulk dissolved oxygen (CL). When CL equals C*, there is no driving force, and the net transfer stops regardless of the KLa magnitude. This scenario frequently occurs at low cell densities or during idle gassing.

Given Data / Assumptions:

• KLa = 3 s^-1 (system capacity).
• C* = 5 mg·L^-1; CL = C* = 5 mg·L^-1.
• Assume steady conditions with no rapid transients.

Concept / Approach:
Use OTR = KLa * (C* − CL). If CL = C*, the term in parentheses is zero; therefore, OTR is zero. Oxygen may still circulate between phases, but net transfer into the bulk does not occur until CL drops below C* due to cellular consumption.

Step-by-Step Solution:

Verification / Alternative check:
As soon as OUR > 0 lowers CL below C*, the same KLa will yield OTR = KLa * ΔC to match OUR at steady state.

Why Other Options Are Wrong:

• 3, 5, or 15 mg·L^-1·s^-1: confuse KLa or C* with OTR; ignore ΔC = 0.
• 0.2 mg·L^-1·s^-1: arbitrary nonzero value without basis.

Common Pitfalls:
Assuming large KLa always means high OTR; without driving force, capacity is unused.

Final Answer:
Zero