# Column Efficiency

The column efficiency is defined as the number of theoretical plates in the column. As discussed in the plate theory, the faster the equilibrium process, the smaller the plates and thus, the greater the number of plates in the column. It is therefore important to know how to determine the number of plates a column possesses and the relationship of the number of theoretical plates in the column to the properties of the chromatogram.

Starting with the Poisson form of the elution equation, the peak width at the points of inflexion (which corresponds to twice the standard deviation of the normal elution curve) can be found by equating the second differential of the elution equation to zero and solving in the usual manner. Thus, at the points of inflexion,

Now,

Thus,

At the points of inflexion,

Hence,

The points of inflexion occur after  and  plate volumes of mobile phase has passed through the column. Thus, the volume of mobile phase that has passed through the column between the inflexion points will be,

(47)

Consequently, the peak width at the points of inflexion of the elution curve will be  plate volumes. Converting this to milliliters  of mobile phase by multiplying by the plate volume