Chromatography and Height Equivalent to a Theoretical Plate (HETP)

HETP can be expressed in two ways:


1. HETP = L/N
2. HETP = A + B/u + Cu


where:


L: lenght of the coloumn


N: Number of theoretical plates


A: Eddy-diffusion parameter, related to channeling through a non-ideal packing


B: diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion


C: Resistance to mass transfer coefficient of the analyte between mobile and stationary phase


u: flux speed


regarding equation 1), N is not constant for a column, but depends on the peak. Consequently, HETP should vary depending on the chromatographic peak considered and not constant for a given column.
Concerning equation 2), instead, the parameters present are column-fixed, therefore also HETP should be a column-fixed constant.


So, is HETP constant, given a column, or does It vary with the peak being considered, as N?




You are correct, $N$ is dependent on a peak, early eluting peaks are narrow and later eluting peaks are wider in an isocratic separation. The equation $H=L/N$ is derived from distillation theory, so the height equivalent for a particular component is a constant for a fixed flow rate, at a given temperature, pressure, mobile phase, stationary phase, analyte, column packing, and particle diameter.


The second equation is called the van Deemter equation (from 1951!!). As one can readily see, it shows the flow rate dependence of $H$, because $H$ is a function of linear velocity $u$. It is highly dependent on the type of analyte being investigated.


In short, neither efficiency nor HETP are fixed for a given HPLC or GC column. You have to specify all the conditions when quoting these values.


P.S., the concept of efficiency, HETP equation, and the Van Deemter equation are not valid for gradient separations.


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