Chromatograms column efficiency calculation from

Using equation (10), the efficiency of any solute peak can be calculated for any column from measurements taken directly from the chromatogram (or, if a computer system is used, from the respective retention times stored on disk). The computer will need to have special software available to identify the peak width and calculate the column efficiency and this software will be in addition to that used for quantitative measurements. Most contemporary computer data acquisition and processing systems contain such software in addition to other chromatography programs. The measurement of column efficiency is a common method for monitoring the quality of the column during use. 

Equation (20) allows the efficiency of any solute peak, from any column, to be calculated from measurements taken directly from the chromatogram. Many peaks, if measured manually, will be only a few millimeters wide and, as the calculation of the column efficiency requires the width to be squared, the distance (x) must be determined very accurately. The width should be measured with a comparitor reading to an accuracy of 0.1 mm. 

Primarily the Plate Theory provides the equation for the elution curve of a solute. Such an equation describes the concentration of a solute leaving a column, in terms of the volume of mobile phase that has passed through it. It is from this equation, that the various characteristics of a chromatographic system can be determined using the data that is provided by the chromatogram. The Plate Theory, for example, will provide an equation for the retention volume of a solute, show how the column efficiency can be calculated, determine the maximum volume of charge that can be placed on the column and permit the calculation of the number of theoretical plates required to effect a given separation. 

A measure of the efficiency of the chromatography column is the height equivalent to a theoretical plate or plate height H [19]. The plate height for an experimental chromatogram is calculated from... 

TABLE 2.8 CALCULATION OF COLUMN EFFICIENCY FROM CHROMATOGRAMS... 

Equation (5) allows the efficiency of any solute peak, from any column, to be calculated from measurements taken directly from the chromatogram. 

For the quantitative determination of the column efficiency a small amount of a retained test component is injected into the column. From the resulting chromatogram the column efficiency can be calculated. 

The hodograph transform is valid only within the framework of the ideal model. It has been shown, however, that the hodograph plots derived from actual chromatograms are very similar to those predicted by the ideal model [18]. If the column efficiency exceeds 100 to 200 theoretical plates, there is no significant difference between the hodograph plot obtained with the ideal model and the plot derived from the profiles calculated with the equilibrium-dispersive model, except very near the axes of coordinates (Figure 8.13). Figure 8.14a compares the... 

Figure 11.24 Qualitative demonstrations of the displacement and tag-along effects. Left set Influence of the feed composition. Left column Chromatograms obtained with 200 mg of a mixture of two of the epimers of a 1,1,1-trisubstituted cyclohexanone on a 250x21.4 mm column packed with 12 im silica, with 40 mL/min of a solution of n-hexane and ethyl acetate (97.5 2.5). Composition as indicated. Right column results of computer calculations. Right set Influence of the column efficiency. Top two rows, experimental data under the same experimental conditions as in (a), except average particle size of silica particles, and mixture composition 1 3. Bottom row, results of computer calculations. Reproduced with permission from ]. Newburger and G. Guiockon,. Chromatogr., 484 (1989) 153 (Figs. 6 and 8).

Figure 13.22 Influence of the additive concentration in the mobile phase on the chromatogram of a binary mixture. Experimental conditions. Column length, 25 cm efficiency, 5000 theoretical plates phase ratio, 0.215 mobile phase flow velocity, 3.0 mL/min to = 68.4 s. Langmuir isotherm coefficients cfs = 3.0 ai = 60 fl2 = 75 Us = 120 bi = 20 bi = 25 bs = 40 a = 1.25. Sample size, 16.7 mmol 2-phenylethanol (2PE, curve 1) and 60 mmol 3-phenylpropanol (3PP, curve 2) (1 3.6). Curve 3 is the sum of curves 1 and 2. Mobile phase composition dichloromethane with 0.017 M 2-propanol, (a) Experimental chromatogram, (b) Calculated chromatogram. Reproduced with permission from S. Golshan-Shirazi and G. Guiochon, Anal. Chem., 61 (1989) 2380 (Fig. 3). 1989 American Chemical Society.

The fundamental criteria for assessing a column s capabilities relate to its separating capabilities in terms of the retention characteristics, column efficiency and the stationary phase at OPGV, and temperature cycle. Retention characteristics of a component are indicated by its retention ratio, k (k = t f /tM)- Dead time, is an indication of the OPGV and is readily determined by introducing a sample of methane onto the column. Column efficiency, N or Veir, can be calculated using data from the chromatogram... 

The % dose (or fraction metabolized) for each metabolite is calculated by summing the % dose calculated for each excretion pathway (urine or feces) of the metabolite and any subsequent secondary metabolites. The % dose for each excretion pathway is calculated by multiplying the percent abundance of a characterized metabolite on a radiometric chromatogram by the total radioactivity present in the evaluated sample (once extraction and column efficiencies have been taken into account). More detailed analysis would be required to calculate the fraction metabolized if secondary metabolites were formed from more than one primary metabolite (Bu et al., 2005, 2006). 

The value of N calculated from one peak in a chromatogram should be the same for each of the other peaks. Another way to characterize the efficiency of a column is to calculate the quantity N/L, called H, the height equivalent per equivalent plate (L is the length of the column). N and H will depend on the number of equilibrium stages in the process, as we have seen above in our discussion of CCD. The actual band widths observed are always larger than ideal because of the nonequilibrium but reproducible processes accompanying mass transfer, such as diffusion of various sorts. 

For the actual HPLC assay, equal volumes (about 20 p,l) of the standard preparations and the assay preparations are injected into the chromatogr h, the chromatograms recorded, and the peak responses measured. From the peak responses of the standard versus the assay preparations, the quantity, in mg, of rifampin (C43H5gN40i2) and isoniazid (C6H7N3O) in the product is calculated. If the assay is performed correctly, the relative retention times are about 2.6 and 1.0 for rifampin and isoniazid, respectively the column efficiency is not less than 50,000 and not less than 6000 theoretical plates for rifampin and isoniazid, respectively the tailing factors are not more than 2.0 and the relative standard deviation for replicate injections is not more than 2.0%. 

TABLE 2.11 Calculation of Column Efficiency from Chromatograms... 

Figure 13.3. LC/ESI chromatograms and sampling efficiencies obtained at different split ratios from a 2.1-mm column operating at 500pL/min and the resulting calculated sampling efficiency. The same amount of Reserpine was injected on column in each case. The amount entering the ion source was reduced proportionally as a result of the split. An example of the efficiency calculation for case C is as follows (1) Ions hitting detector = 60,000. (2) Analyzer transmission efficiency on product ion miz 195 = 5.12%. (3) Ions entering analyzer (QO) = 60,0007.0512= 1.1 x 10 ions. (4) 5pg Reserpine = 4.9 x 10 molecules x 0.001 split ratio=4.9 x 10 molecules. (5) Sampling efficiency = 1.1 x 10 /4.9 x 10 = 22%.

The data of Table III represent calculated bandwidths and efficiencies. Actual realized efficiencies were measured for the four chromatograms of Figure 4. For the 10-ym gel column, the conventional system produced an effective efficiency of 11,000 plates, compared with an effective efficiency of 16,000 plates for the optimized systems. These values are in excellent agreement with the calculated values shown on the top line of Table III. Similar measurements on chromatograms obtained from the 5-vim gel columns yielded values of 16,000 and 20,000 plates, respectively, for the conventional and optimized systems. This also represents good agreement with calculated effective efficiencies at total exclusion for a 24,000 plate column. 

Solute equilibrium between the mobile and stationary phases is never achieved in the chromatographic column except possibly (as Giddings points out) at the maximum of a peak (1). As stated before, to circumvent this non equilibrium condition and allow a simple mathematical treatment of the chromatographic process, Martin and Synge (2) borrowed the plate concept from distillation theory and considered the column consisted of a series of theoretical plates in which equilibrium could be assumed to occur. In fact each plate represented a dwell time for the solute to achieve equilibrium at that point in the column and the process of distribution could be considered as incremental. It has been shown that employing this concept an equation for the elution curve can be easily obtained and, from that basic equation, others can be developed that describe the various properties of a chromatogram. Such equations will permit the calculation of efficiency, the calculation of the number of theoretical plates required to achieve a specific separation and among many applications, elucidate the function of the heat of absorption detector. 

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