Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Temperature of a reaction with an activation energy value of
115 .kcal mol - is
increased from 300 K to 310 K. If the value of the ideal gas constant (R) is
111.9872 . .cal mol K--
, the ratio of the reaction rate constants
310
300
k
k
(rounded
off to two decimal places) is ___________.
Official Answer Key:
2.24 to 2.26
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2023 Q.47)**
**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: *"Temperature of a reaction with an activation energy value of
115 .kcal mol - is
increased from 300 K to 310 K. If the value of the ideal gas constant (R) is
111.9872 . .cal mol K--
, the ratio of the reaction rate con..."*
- Identifying governing bioprocess / mathematical relation:
- For heat transfer across a heat exchanger:
$q = U A \Delta T_{lm}$
$\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}$
- **Calculated Quantitative Value**: **2.24 to 2.26**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **2.24 to 2.26**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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