Theoretical Plates

The separation process in gas chromatography can be compared to a multiple distillation or a fractional distillation using a reflux column.

Gas chromatography uses relatively long packed or open tubular capillary columns and is subsequently far more efficient at separation than fractional distillations with short reflux columns. In addition, gas chromatography uses packing or stationary phases that can be liquid or solid and may exhibit an affinity toward the compounds being separated.

The column efficiency of a gas chromatography column is gauged by the number of theoretical plates, n.

The concept of a plate is a carry-over from the first fractionating columns which used discrete plates for separation. The chromatography column does not have discrete plates.

The number of theoretical plates is the number of discrete distillations that would have to be performed to obtain an equivalent separation. This number is commonly used as a measure of separation efficiency and is a useful number to use when comparing the performance of various chromatographic columns.

Gas chromatography columns normally have 1,000 to 1,000,000 theoretical plates as opposed to fractionating columns which normally operate in the range of 5-100 plates.
The number of theoretical plates, n, is a dimensionless number, which is related to the ratio between the retention time, tr, and the width of the peak containing the compound. If the peaks are reasonably symmetric, it can be assumed that they are Gaussian in shape. In this case, n is found from:
n=5.45(tr/W1/2)2.

The peak width at half height, W1/2, is found 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.

The retention time, tr, is measured at the point where the vertical line drawn through the maximum intersects the baseline. Both tr and W1/2 must be measured in the same units. Since the measurement is usually made from a recorder chart, the units are usually in cm, mm, or in.

n varies depending on the compound as well as the column packing material. So a column does not have a single n value. n also varies with the flow rate, and the column length. It is good practice to specify the column conditions and the compound used to determine n.