How to Calculate Theoretical Plates

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How to Calculate Theoretical Plates
Chromatogram sketch (Personal collection)

Chromatography is a method of substance separation. It is implemented using a narrow tube (column) packed with a specific material. A mixture of compounds is forced through the column using pressure. Each compound comes out from the column during certain times, graphically representing a peak on a chromatogram. The position of the peak maximum, called a retention time, is specific for each compound. Performance of chromatographic columns is expressed as a number of theoretical plates. A theoretical plate is an imaginary layer within a column that helps to interpret the separation process. A higher number of theoretical plates corresponds to better column efficacy.

Skill level:
Moderately Easy

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Things you need

  • Calculator
  • Metric ruler

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Instructions

  1. 1

    Obtain a chromatogram chart from your chromatographic column.

  2. 2

    Draw a vertical line from the peak maximum to the baseline.

  3. 3

    Measure the length of this line and divide it by 2 to find the centre of the line. In these steps, make all measurements in millimetres (mm).

  4. 4

    Draw a line passing through the line's centre and parallel to the baseline.

  5. 5

    Measure the length of the line from Step 4 to get the peak width at the half-height. For example, the peak width is 12mm.

  6. 6

    Measure the distance from 0 to the peak maximum to obtain the retention time. For example, the retention time is 650mm. Note that the retention time is normally expressed in minutes, but it also proportional to the measured length.

  7. 7

    Divide the retention time by the peak width and raise the quotient in the power of 2. Then multiply the result by 5.55 to calculate the number of theoretical plates:

    Number of theoretical plates = 5.55 * (Retention time / Peak width)^2

    In our example, it would be 5.55 * (650 mm / 12mm)^2 = 16,284 theoretical plates. The result is rounded to the whole number.

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