Question

Which column is more efficient: plate height = 0.1 mm or plate height = 1 mm?

Short answer

The solution is

the column with a lower plate height of 0.1 mm would be preferred. Because there would be less band dispersion, it would be more efficient.

Step-by-step solution

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In this job, we'll see whether column is more efficient: one with a plate height = 0.1 mm or one with a plate height =1 mm.

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Consider the van Deemter equation, which explains how plate height is affected by column and flow rate:

$\mathrm{H}=\mathrm{A}+\frac{\mathrm{B}}{{\mathrm{u}}_{\mathrm{x}}}+\mathrm{C}\times {\mathrm{u}}_{\mathrm{x}}$

where denotes numerous pathways, $\frac{\mathrm{B}}{{\mathrm{u}}_{\mathrm{x}}}$denotes longitudinal diffusion, and denotes equilibration time.

- In addition, the following is the formula for plate height:

$$\begin{gathered} \mathrm{H}=\frac{\mathrm{L}}{\mathrm{N}} \\ \mathrm{N}=\frac{\mathrm{L}}{\mathrm{H}} \end{gathered}$$

1. The value of H = 0.1 mm is inversely proportional to the value of (lower H=larger N ).

2. The size of H = 1.0 mm is inversely proportional to the size of N (larger H=smaller N ).

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Examine the Purnell equation for resolution now:

Resolution =$\frac{\sqrt{\mathrm{N}}}{4}\frac{\left(\alpha -1\right)}{\alpha }\left(\frac{{\mathrm{k}}_2}{1+{\mathrm{k}}_2}\right)$

1. The resolution is proportional to$\sqrt{\mathrm{N}}$ (the larger the N , the higher the resolution).

2. Resolution is proportional to$\sqrt{\mathrm{N}}$ (lower N = lower resolution).

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As a result, the column with a lower plate height of 0.1 would be preferred. Because there would be less band dispersion, it would be more efficient