Plate Theory Equation for Chromatographic Elution

Appendix 3.1 Derivation of the Plate Theory Equation for Chromatographic Elution 

Plate Theory is based upon a approximation of discrete sequential partitioning equilibria of analyte between mobile and stationary phases (Eigure 3.3), so it is convenient to define a partition coefficient for analyte A as  

Firstly, it is necessary to consider the limiting case of the first plate, that for convenience will be designated plate 0 (p = 0). Assume that injection of the analyte A onto the column is restricted to this first plate to create an initial concentration in the mobile phase of c ni(o) = when V = 0 = V, i.e., elution has not yet started, so that c m(p) = 0 for p 0 at this initial point. Then, since there is no plate (p — 1) for p = 0, for this case Equation [3.6] becomes  

The left side of this equation is the derivative with respect to u of the product [c ni(i).exp(v)]  

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