Height of a theoretical plate

In their original theoretical model of chromatography, Martin and Synge treated the chromatographic column as though it consists of discrete sections at which partitioning of the solute between the stationary and mobile phases occurs. They called each section a theoretical plate and defined column efficiency in terms of the number of theoretical plates, N, or the height of a theoretical plate, H where... 

A column s efficiency improves with an increase in the number of theoretical plates or a decrease in the height of a theoretical plate. 

Assuming a Gaussian profile, the extent of band broadening is measured by the variance or standard deviation of a chromatographic peak. The height of a theoretical plate is defined as the variance per unit length of the column... 

Gombining equations 12.13 through 12.15 gives the height of a theoretical plate in terms of the easily measured chromatographic parameters and w. 

A chromatographic analysis for the chlorinated pesticide Dieldrin gives a peak with a retention time of 8.68 min and a baseline width of 0.29 min. How many theoretical plates are involved in this separation Given that the column used in this analysis is 2.0 meters long, what is the height of a theoretical plate ... 

Solving equation 12.12 for H gives the average height of a theoretical plate as... 

Equations 12.21 and 12.22 contain terms corresponding to column efficiency, column selectivity, and capacity factor. These terms can be varied, more or less independently, to obtain the desired resolution and analysis time for a pair of solutes. The first term, which is a function of the number of theoretical plates or the height of a theoretical plate, accounts for the effect of column efficiency. The second term is a function of a and accounts for the influence of column selectivity. Finally, the third term in both equations is a function of b, and accounts for the effect of solute B s capacity factor. Manipulating these parameters to improve resolution is the subject of the remainder of this section. 

If the capacity factor and a are known, then equation 12.21 can be used to calculate the number of theoretical plates needed to achieve a desired resolution (Table 12.1). For example, given a = 1.05 and kg = 2.0, a resolution of 1.25 requires approximately 24,800 theoretical plates. If the column only provides 12,400 plates, half of what is needed, then the separation is not possible. How can the number of theoretical plates be doubled The easiest way is to double the length of the column however, this also requires a doubling of the analysis time. A more desirable approach is to cut the height of a theoretical plate in half, providing the desired resolution without changing the analysis time. Even better, if H can be decreased by more than... 

To determine how the height of a theoretical plate can be decreased, it is necessary to understand the experimental factors contributing to the broadening of a solute s chromatographic band. Several theoretical treatments of band broadening have been proposed. We will consider one approach in which the height of a theoretical plate is determined by four contributions multiple paths, longitudinal diffusion, mass transfer in the stationary phase, and mass transfer in the mobile phase. 

Putting It All Together The net height of a theoretical plate is a summation of the contributions from each of the terms in equations 12.23-12.26 thus. 

Plot of the height of a theoretical plate as a function of mobile-phase velocity using the van Deemter equation. The contributions to the terms A B/u, and Cu also are shown. 

The chromatogram in Problem 4 was obtained on a 2-m column with a column dead time of 50 s. How long a column is needed to achieve a resolution of 1.5 What height of a theoretical plate is needed to achieve a resolution of 1.5 without increasing the length of the column ... 

Height of a theoretical plate (HETP) Height of packing in a distillation column that gives a separation equivalent to one theoretical stage. 

The efficiency of a plate can be predicted with more certainty than the equivalent term for packing (height of a theoretical plate [HETP] or heights of transfer units [HTU]). 

The height of a theoretical plate, in which the distribution equilibrium of sample molecules between stationary and mobile phases is established, is related to the plate number via the length of the separator column ... 

The equivalent height of a theoretical plate H, as already defined (expression 1.5), is calculated for reference compounds to permit a comparison of columns of different lengths. H does not behave as a constant, its value depends upon the compound chosen and upon the experimental conditions. 

For a long time in gas chromatography an adjustment value called the effective height of a theoretical plate H g was calculated using the true efficiency. 

Up to now only the number of theoretical stages was determined for dimensioning an extraction. The connection between the theoretical stage model and real separation column was established through the plate efficiency for a plate column or the height of a theoretical plate FIETP for a packed column. Hereby, the actual mass-transfer pro-... 

DAE differential-algebraic equations EQ equilibrium HETP height of a theoretical plate MS Maxwell-Stefan NEQ non-equilibrium RD reactive distillation... 

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