Q.61 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:
H = A/u + Bu + C
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 __________.
Final Result: Minimum HETP yields
Van Deemter Equation Basics
The modified van Deemter equation describes the dependence of
HETP (Height Equivalent to a Theoretical Plate)
on the linear velocity (u) of the mobile phase:
H = A/u + Bu + C
where:
- A = 3 × 10-8 m2·s-1 (eddy diffusion)
- B = 3 s (longitudinal diffusion)
- C = 6 × 10-5 m (mass transfer resistance)
A lower HETP corresponds to higher column efficiency.
Finding the Minimum HETP
To find the optimal linear velocity, differentiate H with respect to u
and set the derivative to zero:
dH/du = −A/u2 + B = 0
Solving for u:
u = √(A/B)
Substituting values:
u = √(3 × 10-8 / 3) = √(10-8) = 1 × 10-4 m·s-1
Calculation of Minimum HETP
Substitute u into the van Deemter equation:
Hmin = (3 × 10-8 / 1 × 10-4) + (3 × 1 × 10-4) + 6 × 10-5
Hmin = 3 × 10-4 + 3 × 10-4 + 6 × 10-5
Hmin = 6.6 × 10-4 m
( = 0.066 cm )
Calculation of Theoretical Plates
The number of theoretical plates (N) is given by:
N = L / H
Column length:
L = 66 cm = 0.66 m
Therefore:
N = 0.66 / (6.6 × 10-4) = 1000
Final Answer
The minimum HETP corresponds to
1000 theoretical plates for the 66 cm column.
Applications in Protein Purification
In ion-exchange chromatography, operating at the minimum HETP
ensures maximum separation efficiency, sharper peaks, and higher resolution.
This principle is critical for protein purification, analytical chromatography,
and scale-up in biotechnology laboratories.
Exam Relevance
- Commonly tested in chromatography and bioprocess engineering exams
- Requires understanding of van Deemter optimization
- Important for interpreting column efficiency
