Question

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

Answer 1

Hint: There are several methods to calculate the theoretical plates in gas chromatography but the common method used is based on the assumption that the peaks obtained during the process are Gaussian curves.

Complete step by step answer:
The Gas chromatography also known as GC is an analytical technique used to separate the chemical component from its mixture. The chemical components are organic compounds or gases.
The Gas chromatography columns consist of ${10^3}$ to ${10^6}$ theoretical plates. The number of theoretical plates is denoted by n which is defined as the number of discrete distillations which is done to obtain equal separation.
The number of theoretical plates have relation with the retention time which is denoted as ${t_r}$ and the peak width.
When the peaks obtained are symmetric, then it is assumed that it has Gaussian shape.
The number of theoretical plates is calculated as shown below.
$n = 5.54{\left( {\dfrac{{{t_r}}}{{{w_{\dfrac{1}{2}}}}}} \right)^2}$
Where,
n is the number of theoretical plates.
${t_r}$ is the retention time
${w_{\dfrac{1}{2}}}$ is the peak width
The peak width is obtained as half height by drawing a line vertically from the peak maximum to the baseline, measuring half-way up the peak then drawing a horizontal line and measuring the length of the horizontal line.
The retention time is measured at the point where the vertical line is drawn.
Both the values are measured in the same units.

Note:
Theoretical plate numbers are affected by a number of variables. For a specific column, the same gas chromatography conditions and compound is used while calculating the theoretical plate numbers. If it is not done different values will be obtained for each set of conditions or compound.