A protein is to be purified using ion-exchange column chromatography. The relationship between
HETP (Height Equivalent to Theoretical Plate) and the linear liquid velocity of mobile phase is
given by:
A
H
Bu
C
u
where H is HETP (m) and u is linear liquid velocity of mobile phase (m.s-1). The values of A, B and
C are 3×10-8 m2.s-1, 3 s and 6×10-5 m, respectively. The number of theoretical plates based on
minimum HETP for a column of 66 cm length will be ___________.
Official Answer Key:
1000.0
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.61)**
**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: *"A protein is to be purified using ion-exchange column chromatography. The relationship between
HETP (Height Equivalent to Theoretical Plate) and the linear liquid velocity of mobile phase is
given by:
A
H
Bu
C
u
..."*
- Identifying governing bioprocess / mathematical relation:
- Calculating retention/retardation factor ($R_f$) in planar chromatography:
$R_f = \frac{\text{Distance migrated by solute}}{\text{Distance migrated by solvent front}}$
- **Official Answer Key Interval**: Evaluated numerical range is **1000.0 to 1000.0** (Target value: **1000.0 to 1000.0**).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **1000.0 to 1000.0**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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