Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
Which of the following statements is ALWAYS CORRECT about an ideal chemostat?
P. Substrate concentration inside the chemostat is equal to that in the exit stream
R. Biomass concentration increases with increase in dilution rate
Q. Optimal dilution rate is lower than critical dilution rate
S. Cell recirculation facilitates operation beyond critical dilution rate
Options:
(A) P and Q only
(B) P, R and S only
(C) P and S only
(D) P, Q and S only
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2019 Q.53)**
**1. Governing Concept**:
- **Topic**: Biochemical Thermodynamics & Standard Free Energy Changes
- Thermodynamic definitions:
- $\Delta G^\circ$ is the standard Gibbs free energy change (under standard $1\text{ M}$ reactant concentrations).
- $\Delta G$ is the actual prevailing Gibbs free energy change in vivo:
$\Delta G = \Delta G^\circ + RT \ln Q$
where $Q = \frac{[\text{Products}]}{[\text{Reactants}]}$.
- A reaction is **spontaneous in the forward direction if and only if the actual $\Delta G < 0$**, regardless of whether $\Delta G^\circ$ is positive or negative. A reaction with positive $\Delta G^\circ$ can be driven forward in a metabolic pathway by maintaining high substrate-to-product ratios ($Q \ll 1$) such that $\Delta G$ remains negative.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Negative $\Delta G^\circ$ does not guarantee spontaneity if products accumulate ($Q \gg K_{\text{eq}} \implies \Delta G > 0$).
- **Option (B) is INCORRECT**: Endothermic reactions ($\Delta H > 0$) can be spontaneous if entropy change is positive and large ($T\Delta S > \Delta H$).
- **Option (C) is INCORRECT**: Exothermic reactions with large negative entropy changes may be non-spontaneous.
- **Option (D) [Reaction is spontaneous if actual ΔG < 0] is CORRECT**: The universal, unexceptioned thermodynamic criterion of spontaneity.
**3. Final Answer**:
- **Correct Choice**: **D**
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