Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
An enzyme converts substrate A to product B. At a given liquid feed stream of flow rate 25 L.min-1
and feed substrate concentration of 2 mol.L-1, the volume of continuous stirred tank reactor needed
for 95% conversion will be _____________ L.
Given the rate equation: 0.1
10 . 5
A
A
A
Cr C
where ̶ rA is the rate of reaction in mol.L-1.min-1 and CA is the substrate concentration in mol.L-1
Assumptions: Enzyme concentration is contant and does not undergo any deactivation during the
reaction.
Options:
(A) Higher the bicarbonate concentration in the medium, higher should be the requirement of
gaseous CO2
(B) Lower the bicarbonate concentration in the medium, higher should be the requirement of
gaseous CO2
(C) Higher the bicarbonate concentration in the medium, lower should be the requirement of
gaseous CO2
(D) CO2 requirement is independent of bicarbonate concentration in the medium
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.50)**
**1. Governing Concept & Question Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (2 Marks)
- **Topic**: Animal Cell Culture (Bicarbonate-CO2 Buffering System & pH Homeostasis)
**2. Detailed Step-by-Step Derivation**:
- In animal cell culture media (e.g., DMEM, RPMI), physiological pH ($7.2 - 7.4$) is maintained by the equilibrium of the **sodium bicarbonate ($\text{NaHCO}_3$) - dissolved carbon dioxide ($\text{CO}_2$) buffer system**:
$\text{CO}_2\text{ (gas)} \rightleftharpoons \text{CO}_2\text{ (dissolved)} + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^-$
- Applying the Henderson-Hasselbalch equation for the bicarbonate buffer:
$\text{pH} = pK_a + \log \frac{[\text{HCO}_3^-]}{[\text{H}_2\text{CO}_3]} = pK_a + \log \frac{[\text{HCO}_3^-]}{\alpha P_{\text{CO}_2}}$
where $[\text{HCO}_3^-]$ is the dissolved sodium bicarbonate concentration and $P_{\text{CO}_2}$ is the partial pressure of gaseous $\text{CO}_2$ in the incubator.
- To maintain a constant target physiological pH ($\approx 7.2 - 7.4$):
$\frac{[\text{HCO}_3^-]}{P_{\text{CO}_2}} = \text{constant}$
- Therefore, if a culture medium is formulated with a **higher bicarbonate concentration** $[\text{HCO}_3^-]$ (e.g., $3.7\text{ g/L}$ in DMEM vs. $2.0\text{ g/L}$ in MEM), the incubator must supply a proportionally **higher gaseous $\text{CO}_2$ concentration** (e.g., $10\%\text{ CO}_2$ instead of $5\%\text{ CO}_2$) to prevent alkaline shift and maintain equilibrium pH.
- Thus: *“Higher the bicarbonate concentration in the medium, higher should be the requirement of gaseous $\text{CO}_2$”*.
- **Option-by-Option Evaluation**:
- **Option (A) [CORRECT]**: Higher bicarbonate levels require higher gaseous $\text{CO}_2$ to maintain the ratio $[\text{HCO}_3^-]/[\text{CO}_2]$ and target pH constant.
- **Option (B) [INCORRECT]**: Lower bicarbonate requires lower, not higher, $\text{CO}_2$.
- **Option (C) [INCORRECT]**: Lowering $\text{CO}_2$ while increasing bicarbonate causes dangerous alkalization.
- **Option (D) [INCORRECT]**: Bicarbonate buffering strictly depends on gaseous $\text{CO}_2$ partial pressure.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **A**
- **Scoring Criteria**: +2.0 Marks (Negative marking: -0.67 marks).
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