Q.46 The maximum cell concentration (g l−1) expected in a
bioreactor with initial cell concentration of 1.75 g l−1
and an initial glucose concentration of 125 g l−1
(Yx/s = 0.6 g cell/g substrate) __________.
Maximum Cell Concentration in a Bioreactor Using Biomass Yield Coefficient
Estimating the maximum cell concentration in a bioreactor is a
fundamental concept in bioprocess engineering and is frequently tested in
competitive examinations such as GATE and NET.
Problem Statement
The maximum cell concentration (g l−1) expected in a bioreactor with:
- Initial cell concentration = 1.75 g l−1
- Initial glucose concentration = 125 g l−1
- Biomass yield coefficient,
Yx/s = 0.6 g cell / g substrate
Calculate the maximum cell concentration.
Concept Used
The biomass yield coefficient is defined as:
Yx/s = (Biomass formed) / (Substrate consumed)
Step-by-Step Solution
Step 1: Calculate biomass formed from glucose
Biomass formed = Yx/s × Substrate concentration
= 0.6 × 125
= 75 g l−1
Step 2: Add initial cell concentration
Final cell concentration = Initial cells + Cells formed
= 1.75 + 75
= 76.75 g l−1
Correct Answer
76.75 g l−1
Common Mistakes Explained
Mistake 1: Ignoring initial cell concentration
Considering only biomass formed (75 g l−1) and not adding the
initial biomass leads to an incorrect answer.
Mistake 2: Dividing by Yx/s
Yx/s should be multiplied with substrate concentration,
not divided.
Mistake 3: Assuming incomplete substrate utilization
The question asks for maximum cell concentration, which implies
complete glucose consumption.
Final Conclusion
By correctly applying the biomass yield coefficient and accounting for
the initial biomass, the maximum achievable cell concentration in the
bioreactor is:
76.75 g l−1
