The plate theory assumes that the solute is, at all times, in equilibrium with the two phases. Due to the continuous exchange of solute between the mobile and stationary phases as it progresses down the column, equilibrium between the phases is, in fact, never actually achieved. As a consequence, an approach is taken similar to that used in distillation column theory and the column is considered to be divided into a number of cells or plates. In fact, the term "plate" evolved from Martin's studies on distillation theory.
Each cell is allotted a finite length and, thus, the solute can be assumed to spend a finite time in each cell. The size of the cell is considered to that would allow sufficient "dwell time" for the solute so that, theoretically, the solute would achieve equilibrium with the two phases. Hence, the smaller the plate, the more efficient the solute-exchange between the two phases and the more plates there would be in the column. This is why the number of Theoretical Plates in a column has been termed the column efficiency.
(K), the distribution coefficient is defined by the equation,
(1)
where (Cm) is the concentration of solute in the mobile phase and (Cs) is the concentration of solute in the stationary phase.
(K) is a dimensionless constant and, thus, in GLC and LLC systems, (Cs) and (Cm) are conveniently measured as mass of solute per unit volume of phase.
Equation (1) merely indicates that the general distribution law applies (i.e. the adsorption isotherm is linear) which, at the very low concentrations normally employed in chromatography separations, will be true.
Differentiating equation (1), dCs = KdCm (2)
Consider three consecutive plates in a GC column, the (p-1), the (p) and the (p+1) plates and where there is a total of (n) plates in the column. The three plates are depicted diagrammatically below.