Question

In Capillary Electrophoresis, for a representative 50 cm capillary column operated at 30,000 V, typical net mobility for a 10 min migration time is about $2\times10^{-8}\ \text{m}^2\text{s}^{-1}\text{V}^{-1}$. Calculate the number of theoretical plates for an ion having diffusion coefficient $D = 1\times10^{-9}\ \text{m}^2\text{s}^{-1}$.

• A. 3,000
• B. 30,000
• C. 3,00,000
• D. 1,50,000

Hint:

In CE: $N = \dfrac{\mu_{\text{net}} \cdot V}{2D}$. High voltage and low diffusion coefficient give more theoretical plates (better separation).

Answer 1

The Correct Option is C

Step 1: Concept
Theoretical plate number in capillary electrophoresis (CE).

Step 2: Meaning
The number of theoretical plates $N$ in CE is given by: \[ N = \frac{\mu_{\text{net}} \cdot V}{2D} \] where $\mu_{\text{net}}$ is the net mobility, $V$ is the applied voltage, and $D$ is the diffusion coefficient.

Step 3: Analysis
Given: \mu_{net} &= 2\times10^{-8} m^2s^{-1}V^{-1}
V &= 30{,}000 V
D &= 1\times10^{-9} m^2s^{-1} \[ N = \frac{\mu_{\text{net}} \cdot V}{2D} = \frac{(2\times10^{-8})(30{,}000)}{2\times(1\times10^{-9})} = \frac{6\times10^{-4}}{2\times10^{-9}} = 3\times10^{5} = 3{,}00{,}000 \]

Step 4: Conclusion
The number of theoretical plates $N = 3{,}00{,}000$. Final Answer: (C)