# How do I calculate the number of theoretical plates in gas chromatography?

Jun 23, 2015

There are several formulas, but the most common one is based on the assumption that the peaks are Gaussian curves.

#### Explanation:

The number of theoretical plates $n$, is the number of discrete distillations that would have to be performed to obtain an equivalent separation.

Gas chromatography columns normally have ${10}^{3}$ to ${10}^{6}$ theoretical plates.

The number of theoretical plates is related to the retention time, ${t}_{r}$, and the width of the peak containing the compound.

If the peaks are reasonably symmetric, it can be assumed that they have a Gaussian shape. Then

$n = 5.54 {\left({t}_{r} / {w}_{\frac{1}{2}}\right)}^{2}$

where ${w}_{\frac{1}{2}}$ is the peak width at half-height.

You find the peak width at half height by drawing a line vertically from the peak maximum to the baseline, measuring half-way up the peak, drawing a horizontal line, and measuring the length of the horizontal line.

You measure the retention time (designated avove as ${V}_{e}$ for elution volume) at the point where the vertical line drawn through the maximum intersects the baseline.

Both ${t}_{r}$ and ${w}_{\frac{1}{2}}$ must be measured in the same units.

EXAMPLE

A chromatogram from a certain column has a peak with a ${w}_{\frac{1}{2}}$ of 12 mm and a ${t}_{r}$ of 650 mm as measured on the chart. What is the number of theoretical plates?

Solution

n = 5.54(t_r/w_(1/2))^2 = 5.54((650 cancel("mm"))/(12 cancel("mm")))^2 = "16 250 theoretical plates"