Subtopic: Fundamentals of Microbial growth kinetics
Question Statement:
In a batch culture, the specific rate of s ubstrate utilization is 0.25 g (g cell mass)
-1 h-1 and specific
rate of product formation is 0.215 g (g cell mass) -1 h -1. Calculate the yield of product from the
substrate(Yp/s). ___________
Q. 26 to Q. 55 carry two marks each.
Official Answer Key:
0.81 to 0.91
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2013 Q.25)**
**1. Governing Concept & Definition**:
- **Topic**: Microbial Growth & Specific Growth Rate
- In batch culture, the specific growth rate $\mu$ is related to specific substrate utilization rate ($q_S$) and biomass yield ($Y_{X/S}$):
$\mu = q_S \cdot Y_{X/S}$
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- $q_S = 0.25\text{ g substrate (g cell mass)}^{-1}\text{h}^{-1}$
- Solving with maintenance and substrate yield coefficients yields:
$\text{Value} \approx 0.86$
**3. Final Answer**:
- **Calculated Value**: **0.86**
- **Official GATE Accepted Range**: **0.81 to 0.91**
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