# Concept of Theoretical Plates in Column Chromatography

As a chromatographer you would be interested in getting the maximum return from your column in terms of performance efficiency. Useful tips on care of HPLC columns have been suggested earlier to preserve the performance features and improve useful life of your column. Now the question arises as to how do you quantify efficiency and decide if you can still use your column to get reliable separations. The answer lies in keeping a track on theoretical plates over the lifespan of a column.

#### What are theoretical plates?

A chromatographic column does not consist of any physical plates which can be measured from time to time to rate a column’s performance efficiency. It is only a theoretical concept drawing similarity to the huge fractional distillation columns used in refining of crude petroleum. Such distillation column actually comprises of separator plates which help separation and isolation of different petroleum fractions which are collected as separate streams.

However no such plates exist in the chromatographic columns.You have to imagine that your column is divided into a number of sections or plates. A sample component spends a finite time in each plate as it moves the column length and this is the time required to establish equilibrium over the length of the plate between its concentration in the stationary phase and the mobile phase. The movement of the analyte is assumed from plate to plate as a series of equilibrated mobile phase plugs. In other words the greater the number of such plates the more efficient is the separation power of the column.

The number of plates (N) over the column length (L) is dependent on the plate height (H)

N = L/H

Smaller plate height implies large number of plates in the column and higher is the column efficiency. H is also referred to as height equivalent to a theoretical plate (HETP) and smaller the value of HETP the greater is the column efficiency.

#### Calculation of the number (N)

N is calculated from the peak of the injected standard under prescribed operational conditions

N = 16$$(\frac{t_r}{W_b})^2$$

where TR is the retention time of the peak and Wb is the peak width. In case peak width is measured at half height or W1/2 then the relation is expressed as

N = 5.54$$(\frac{t_r}{W_1_/_2})^2$$

In above calculations retention time and width should be expressed in the same units

Present day chromatographic softwares provide number N without the need for manual calculations but the basic assumption is that the peak shape should be Gaussian.

The number of theoretical plates is dependent on several operational parameters such as flow rate, analyte characteristics, temperature and sample size. Overloading a column rapidly deteriorates its performance.

A column manufacturer provides a certificate of column performance features along with the column and also specifies the minimum acceptable value of the number of theoretical plates. A deteriorating column should be reconditioned to improve the value and if this is not possible then it is suggested that the column be replaced.

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#### Responses

1. Very good lecture…. Easy language and easy concept transferring way..