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Study Notes: Theoretical Plates

Methods for Describing Column Efficiency
There are two related terms used as quantitative measures of chromatographic efficiency:

  • Number of ‘theoretical plates’ N
  • Plate height H.

These parameters are used to measure a column’s resolving power (ability to differentiate between closely migrating peaks - sometimes called efficiency). The two parameters are related by the following equation:

N equals L divided by H

where L is the length of the column packing (usually in cm - this is a constant for a given column).

The term theoretical plates refers to an early explanation of the resolving power of a column where the column was viewed as a ‘stack’ of closely related but discrete layers (or plates). The more plates in the column the greater the resolving power of the column but as the column has a definite length, more plates equals thinner plates. In other words N and H are inversely proportional. As N increases (for a given column) H decreases.

There are great differences in the plate height and numbers of theoretical plates between columns due to differences in the column type as well as the stationary and mobile phases used.

Thus variations of the following magnitudes exist:

Plate height: 0.1 to 0.001 mm or smaller
Plate numbers: 100 to 100 000

There are a number of complex methods for determining N but a simple approximation of N is given by:

N equals 5.54 times (tg divided by W over 2) squared.

where W/2 = half of the width of the peak at its base, which is also equal to the width of the peak at half its maximum height and tg = retention time (time taken for the peak to come off the column) of the analyte.

A peak on chromatogram showing a vertical line through the top of the peak and a horizontal line accross the peak at its base. The W/2 label on the chromatogram represents half of the base width.

Sample problem:
Calculate the number of theoretical plates N and the plate height H, when the retention time is 20.40 minutes, half of the base width (given in minutes) is 0.65 minutes and the column length is 30 cm.

Solution
N equals 5.54 times (tg divided by W over 2) squared, which equals 5.54 times (20.40 divided by 0.65) squared, which equals 5.54 times (31.38) squared, which equals 5.54 times 984.70 which equals 5455 plates.

N equals L divided by H, so H equals L divided by N, which equals 30 cm divided by 5455 which equals 0.05 mm.

Practical application of N
N is usually used to measure and verify the performance of a column.
Measurement of N can be used to:

  • measure the resolving power of a column
  • measure that the resolving power of a new column is to specification
  • monitor the resolving power of a column over time
  • determine if column replacement is required due to deterioration in performance
  • troubleshoot problems.

 

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