25-3 What length of column packed with$\mathbf{2}\mathbf{}\mathit{\mu }\mathit{m}$particles is needed to yield the same plate number as in Fugure 25.12? How long woald the separation take?

Interpretation:

The length of the column that has to be packed with particles to have the same plate number has to be identified and the time taken for separation has to be calculated.

Concept Introduction:

Plate number is measure of peak dispersion on a HPLC column. This reflects the column performance. We can also find the efficiency of the column with this. Plate number can be calculated using the formula given below,

$N\approx \frac{3000)\cdot 1.(cm)}{d_p\left(\mu m\right)}$

where

L is the length of column

$d_p$is the size of the particles that is packed.

The length of the column to be packed is 10cm and the time taken for the separation is only 40%.

The plate number (N) is given as 15000. The size of the particle that is packed in the column is given as .The length of the column that has to be taken to give the same plate number can be calculated using the formula

$$\begin{gathered} N\approx \frac{3000\cdot 1.\left(cm\right)}{d_p\left(mm\right)} \\ 15000\approx \frac{3000\cdot L\left(cm\right)}{2\left(\mu mi\right)} \\ L\left(cm\right)=\frac{15000\cdot 2}{3000} \\ =\frac{30000}{3000} \\ =10cm \end{gathered}$$

The length of the column is found to be 10 cm.

The time taken for separation using the 10 cm column instead of 25 cm column can be found by finding the ratio

$\frac{10}{25}\times 100=40\%$

Therefore, the separation using a 10cm column will take 40% as much time as using a 25cm column.