Q.28 A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is 0.5 g biomass/g substrate. The initial concentrations of biomass and substrate are 2 g L-1 and 200 g L-1, respectively. Assuming that there is no endogenous metabolism, the maximum biomass concentration that can be achieved is ________________ g L-1.
Apparent growth yield determines biomass production from substrate in microbial batch cultures. With 0.5 g biomass/g substrate, initial 2 g/L biomass, and 200 g/L glucose, the maximum biomass reaches 102 g/L under no endogenous metabolism.
Growth Yield Basics
Apparent growth yield (YX/S) measures grams of biomass produced per gram of substrate consumed. In batch culture, total substrate (S0 = 200 g/L) converts to biomass increase via YX/S = 0.5. Maximum biomass Xmax = initial biomass X0 + YX/S × S0.
Step-by-Step Calculation
Start with batch mass balance: ΔX = YX/S × ΔS. Since substrate depletes to zero (Sf ≈ 0), ΔS = S0 = 200 g/L. Biomass gain = 0.5 × 200 = 100 g/L. Thus, Xmax = X0 + 100 = 2 + 100 = 102 g/L.
No maintenance or endogenous metabolism means all substrate supports growth, simplifying to true yield application.
Common Options Explained
This numerical answer type (GATE BT 2022) expects 102 (range 101.5-102.5 often accepted).
| Possible Answer | Explanation |
|---|---|
| 100 g/L | Error: Ignores initial 2 g/L biomass; assumes X0 = 0. |
| 102 g/L | Correct: Accounts for X0 + yield-based gain. |
| 200 g/L | Error: Assumes 1:1 yield, not 0.5 given. |
| 50 g/L | Error: Misapplies yield as total Xmax / S0. |
Batch Culture Assumptions
Closed system exhausts limiting substrate (glucose). Yield stays constant; no product formation or decay specified. Real yields <0.5 for glucose due to energy needs, but problem uses apparent value directly.
