# Column length for baseline separation

I have a GC-chromatogram with 4 retention times and peak widths and a column length.

How can I calculate the column length that I need in order to get baseline separation for all components in the sample?

I know I can calculate the resolution between the peaks and that it should be equal or greater than 1.5 for baseline separation, but in what way should I use the equation of Rs in order to calculate the best column length, using all retention times for the components?

Resolution depends on three factors (i) efficiency N (ii) alpha or selectivity $$\alpha$$ and (iii) retention factor k, which the same as the capacity factor in older texts.

Guess which factor is dependent on the column length? It is only the efficiency. If you recall the resolution equation:

$$R_s=\frac{\sqrt{N_2}}{4}\left[\frac{\alpha-1}{\alpha}\right]\left[\frac{k_2}{k_2+1}\right]$$

you need the desired resolution, say 1.5, you already know $$\alpha$$ and ks from the experimental retention times. All you need is to solve N. You would also know that N scales linearly with the column length. With these hints you can estimate the necessary column length.

Other ways to increase resolution, if it were a research problem: You would use a smaller thermal gradient, change temperatures, and lastly change the column length.

In the real world, people would use brute force, i.e. they would change the column, because it's the selectivity which affects the resolution the most. For example, pharmaceutical companies test about 8-16 columns at once (HPLC). The column which separates a given sample with their fixed mobile phases is chosen for further optimization.

• Now use simple ratio and proportion. Suppose your shorter 30 m column has an N of 1x, where x is some number. However the the equation above shows you that N must be 2x. Calculate the corresponding length. You need a column which is 2x30 = 60 m long. I just chose random numbers. Share your chromatograms and calculations if you wish to double check. – M. Farooq Jun 15 '19 at 19:26
• Alright, thanks! – Miana Jun 15 '19 at 19:27
• Miana, a very important point. All these equations are valid for ISOCRATIC separations only. Make sure that the exercise/question is clear about it. Even experienced people make this mistake. – M. Farooq Jun 15 '19 at 19:37