GATE BT 2022 • Q58 NAT • 2 Marks

Section 4: Bioprocess Engineering and Process Biotechnology

Bioreactor types, scale-up

Subtopic: Fundamentals of Bioreactor types, scale-up

Question Statement:

The amount of biomass in a reactor at the end of the batch process is 50 g. Fed- batch operation is initiated by feeding the substrate solution at a constant rate of 1 L h -1. The concentration of substrate in the feed is 50 g L -1. The maximum biomass yield (Y௑ௌ ெ) is 0.4 ୥ ୠ୧୭୫ୟୱୱ ୥ ୱ୳ୠୱ୲୰ୟ୲ୣ. Assuming the system is at quasi-steady state, the maximum amount of biomass after 5 h of feeding is _____________ g. .59 An enzyme catalyzes the conversion of substrate A into product B. The rate equation for this reaction is 5 A A A Cr C   mol L-1 min-1 Substrate A at an initial concentration of 10 mol L -1 enters an ideal mixed flow reactor (MFR) at a flow rate of 10 L min-1. The volume of the MFR required for 50% conversion of substrate to product is ___________ L.

Official Answer Key:

150 to 150

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE BT 2022 Q.58)** **1. Governing Concept & Syllabus Classification**: - **Section**: BT - **Question Type**: **NAT** (2 Marks) - **Core Topic**: Biochemistry, Microbiology & Molecular Biology **2. Detailed Step-by-Step Analytical & Scientific Derivation**: - **Mathematical & Quantitative Formulation**: - Problem Statement: *"The amount of biomass in a reactor at the end of the batch process is 50 g. Fed- batch operation is initiated by feeding the substrate solution at a constant rate of 1 L h-1. The concentration of substrate in the feed i..."* - Identifying governing bioprocess / mathematical relation: - In a continuous stirred tank bioreactor (chemostat) at steady state: $\mu = D = \frac{F}{V}$ where $\mu$ is the specific growth rate ($ ext{h}^{-1}$), $D$ is the dilution rate, $F$ is volumetric feed flow rate, and $V$ is working volume. $S = \frac{K_s D}{\mu_{max} - D}, \quad X = Y_{X/S}(S_0 - S)$ - **Calculated Quantitative Value**: **150 to 150**. **3. Final Answer / Verification Summary**: - **Official GATE Answer Key**: **150 to 150** - **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).

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