GATE BT 2025 • Q62 NAT • 2 Marks

Section 4: Bioprocess Engineering and Process Biotechnology

Bioreactor types, scale-up

Subtopic: Fundamentals of Bioreactor types, scale-up

Question Statement:

A 2 L bioreactor is being operated as a chemostat, at a flow rate of 0.8 L/h and sterile feed of 10 g/L substrate. The bacterial growth follows Monod kinetics at a maximum specific growth rate of 0.6 h-1 with a Monod constant of 0.5 g/L and a biomass yield coefficient of 0.4 g/g. The exit biomass concentration is _______ g/L. (Round off to one decimal place)

Official Answer Key:

3.4 to 3.8

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2025 Q.62)** **1. Governing Concept & Definition**: - **Topic**: Continuous Bioreactor Kinetics & Steady-State Chemostat Operation - In a sterile-feed chemostat without cell death: $D = \frac{F}{V} = \mu$ where $D$ is the dilution rate, and $\mu = \frac{\mu_{\max} S}{K_s + S}$. - At steady state, biomass concentration $X$ is given by substrate balance: $X = Y_{X/S} (S_0 - S)$ **2. Detailed Step-by-Step Calculation**: - **Given**: - Reactor volume $V = 2\text{ L}$, Flow rate $F = 0.8\text{ L/h}$ - Dilution rate: $D = \frac{F}{V} = \frac{0.8}{2} = 0.4\text{ h}^{-1}$ - Feed substrate concentration $S_0 = 10\text{ g/L}$ - $\mu_{\max} = 0.6\text{ h}^{-1}$, $K_s = 0.5\text{ g/L}$, $Y_{X/S} = 0.4\text{ g/g}$ - **Step 1: Calculate residual substrate concentration $S$**: $D = \mu = \frac{\mu_{\max} S}{K_s + S} \implies 0.4 = \frac{0.6 S}{0.5 + S}$ $0.4(0.5 + S) = 0.6 S \implies 0.2 + 0.4 S = 0.6 S \implies 0.2 S = 0.2 \implies S = 1.0\text{ g/L}$ - **Step 2: Calculate steady-state exit biomass concentration $X$**: $X = Y_{X/S} (S_0 - S) = 0.4 \times (10 - 1.0) = 0.4 \times 9.0 = 3.6\text{ g/L}$ **3. Final Answer**: - **Calculated Value**: **3.6 g/L** - **Official GATE Accepted Range**: **3.4 to 3.8**

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test