Q.48 E. coli is cultivated in a chemostat operated at a dilution rate of 0.2 h−1. The values of biomass yield due to oxygen consumption and the steady state biomass concentration are 0.2 g.g−1 and 10 g.L−1, respectively. The oxygen transfer rate (in g.L−1.h−1) is ____________.
Chemostat Basics
A chemostat maintains steady-state microbial growth by balancing dilution rate (D) with specific growth rate (μ). Here, D = 0.2 h−1 equals μ at steady state, as μ = D in continuous culture without maintenance effects dominating. Biomass concentration (X) remains constant at 10 g.L−1, set by limiting substrate feed. No options exist in this numerical answer type (NAT) question; instead, compute the value directly.
Key Parameters Explained
- Dilution rate (D = 0.2 h−1): Flow rate divided by reactor volume; controls growth rate.
- Biomass yield on oxygen (YX/O₂ = 0.2 g.g−1): Grams biomass produced per gram oxygen consumed.
- Steady-state biomass (X = 10 g.L−1): Total biomass per liter.
Oxygen uptake rate (OUR) equals oxygen transfer rate (OTR) at steady state, as dissolved oxygen stays constant.
Step-by-Step Calculation
Volumetric biomass production rate = D × X
0.2 h−1 × 10 g.L−1 = 2 g.L−1.h−1
Oxygen consumption rate (OUR) = (D × X) / YX/O₂
2 / 0.2 = 10 g.L−1.h−1
Thus, OTR = 10 g.L−1.h−1, matching OUR in steady-state chemostat.
Common Misconceptions
Trainees often confuse yield coefficients or neglect D × X as production rate. YX/O₂ is substrate-specific (oxygen here), not general YX/S. No cell death or maintenance terms apply, as problem simplifies to steady-state balance. For IIT JAM/GATE prep, memorize OUR = (μ × X) / YX/O₂, with μ = D.
Exam Relevance
This mirrors GATE BT 2023 Q48, emphasizing bioprocess mass balances for E. coli bioreactors. Practice similar problems on chemostat yields and OUR/OTR equivalence to score in biotechnology entrances.
