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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

The Knox Equation During 1972 and 1973 Knox and his co-workers (18), (19), and (20) carried out a considerable amount of work on different packing materials with particular reference to the effect of particle size on the reduced plate height of a column. The concept of reduced plate height (h ) and reduced velocity  (n) was introduced by Giddings (21) and (22) in 1965 in an attempt to form a basis for the comparison of different columns packed with particles of different diameter. The reduced plate height is defined as,                                         &

nbsp;                                    Therefore,                         The ratio, (), (the column length divided by the number of theoretical plates in the column) has, for obvious reasons, become termed the Height Equivalent to the Theoretical Plate (HETP) and has been given the symbol (H). However, it is seen that (H) is numerically equal to, , which is, in fact, the variance per unit length of the column. Thus, the function, , is the variance that the Rate Theory will provide an explicit equation to define and can be experimentally calculated for any column from its length and column efficiency. It follows that the equations that give a value for, (H), the variance per unit length of the column,

Plate Saturated by Solvent Unsaturated Plate Vapor Figure 31 Effect of Plate Saturation on Plate Development Continuous Plate Development The normal development of a thin layer plate is limited by its physical dimensions but a continuous development procedure has been used employing special equipment. An apparatus used for the continuous development of a thin layer plate is shown in figure 32. The plate is held horizontal and inverted so that the stationary phase layer faces downwards and rests on a second glass cover plate. A wick transfers the solvent from the reservoir to the stationary phase coating which is sandwiched between the two glass plates. The whole system is situated in a suitable chamber to prevent solvent evaporation from the reservoir. The solvent passes along the plate by surface tension forces in the usual way until it reaches the end of the plate. A small area

;                                                Xo(e-p–1) After the addition of each plate volume of charge, a new concentration of solute exists in plate (1), and its contents will be eluted through the column in the normal manner. Consider a total of (p) plate volumes of pure mobile phase are injected onto the column followed by a further (v) plate volumes of equilibrated mobile phase. After the injection of (r) plate volumes of pure mobile phase, the new concentration of solute in plate 1 will be eluted by a further (p-r) plate volumes of sample followed by (v) plate volumes of equilibrated mobile phase. Therefore, the concentration of solute leaving the (n)th plate due to the (r)th volume of pure mobile phase will be

nbsp;                      (74) Under adiabatic conditions, b=0 and                                     Thus, when there is no heat lost from the plate, the temperature profile of the plate will take the same form as its concentration profile. When w >3, the solute band will have virtually passed through the plate and           Thus, when w >3 and the temperature of the plate is recovering, equation (39) becomes            or                &