Standard deviation chromatographic peaks

First, excellent control and repeatability of the injection volumes was confirmed with over 100 injections of a peptide mixture consisting of glycine-tyrosine, valine-tyrosine-valine, methionine enkephalin, leucine enkephalin, and angiotensin II. The overall relative standard deviation for peak area and retention time was 3.9% and 3.6%, respectively. Chromatographic performance of the chip in reversed-phase mode was then tested with a mixture of proteins (insulin, antibiotin, and a-lactalbumin). Repeated separations of these compounds are shown in Figure 47.2. ... 

A pyrolysis - gas chromatography method has been described [44-46] for the determination of the composition of an ethylene-butene-1 copolymer containing up to about 10% butene. Pyrolyses were carried out at 410 °C in an evacuated gas vial and the products swept into the gas chromatograph. Under these pyrolysis conditions, it is possible to analyse the pyrolysis gas components and obtain data within a range of about 10% relative standard deviation. The peaks observed on the chromatogram were methane, ethylene, ethane, combined propylene and propane, isobutane, 1-butene, trans-2-butene, ds-2-butene, 2-methyl-butane and w-pentane. 

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... 

When a chromatographic peak has a Gaussian shape, its width at the baseline, w, is four times its standard deviation, T. 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

It is now necessary to attend to the second important function of the column. It has already been stated that, in order to achieve the separation of two substances during their passage through a chromatographic column, the two solute bands must be moved apart and, at the same time, must be kept sufficiently narrow so that they are eluted discretely. It follows, that the extent to which a column can constrain the peaks from spreading will give a measure of its quality. It is, therefore, desirable to be able to measure the peak width and obtain from it, some value that can describe the column performance. Because the peak will be close to Gaussian in form, the peak width at the points of inflexion of the curve (which corresponds to twice the standard deviation of the curve) will be determined. At the points of inflexion... 

The small peak volumes typical of samples eluted from small bore columns and short small diameter particle columns used in high-speed liquid chromatography place severe demands on the dispersion characteristics of all components of the liquid chromatograph. The standard deviation of a peak eluting from a column is given by... 

Chromatographic system (See Chromatography <621 >.) The liquid chromatograph is equipped with a 230 nm detector and a 4.6 mm x 30 cm column that contains packing L7. The flow rate is about 2 mL/min. Chromatograph the Resolution solution and the Standard preparation, and record the peak responses as directed under Procedure the resolution, R, between the dibutyl phthalate and miconazole peaks is not less than 5, the tailing factor for the miconazole peak is not more than 1.3, and the relative standard deviation for replicate injections of the Standard preparation is not more than 2%. The relative retention times are about 0.7 for dibutyl phthalate and 1 for miconazole. 

Chromatographic system. (Follow the method described in the general procedure <621 >.) The gas chromatograph is equipped with a flame ionization detector and a 1.2 m x 2 mm column packed with 3% phase G32 on support S1A. The injection port, detector, and column temperatures are maintained at about 250, 300, and 250 °C, respectively, and helium is used as the carrier gas, flowing at rate of about 50 mL/min. The relative retention times for cholestane and miconazole nitrate are about 0.44 and 1, respectively. Chromatograph the Standard preparation, and record the peak responses as directed for procedure The resolution, R, between cholestane and miconazole nitrate is not less than 2 and the relative standard deviation of replicate injections is not more than 3%. 

The liquid chromatograph is equipped with a 254 nm detector and a 3.9 mm x 30 cm column that contains packing LI. The flow rate is about 2 mL/min. Chromatograph replicate injections of the Standard solution and record the peak responses as directed for procedure the relative standard deviation is not more than 3%. 

Chromatographic system. The gas chromatograph is equipped with a flamioniza-tion detector and a 2 mm x 1.8 m glass column packed with 10% phase G34 on 80- to 100-mesh support SI A. The column temperature is maintained at about 150 °C, and the injection port and the detector block temperatures are maintained at about 250 °C. Dry helium is used as the carrier gas at a flow rate of about 40 mL/min. Chromatograph the Standard preparation, measure the peak responses, and calculate the ratio, Rs, as directed for procedure the relative retention times are about 0.5 for valproic acid and 1.0 for biphenyl the resolution, R, between valproic acid and biphenyl is not less than 3.0 the relative standard deviation for replicate injections is not more than 2.0%. 

As readily observed in most chromatograms, peaks tend to be Gaussian in shape and broaden with time, where W, becomes larger with longer This is caused by band-broadening effects inside the column, and is fundamental to all chromatographic processes.The term, plate number (N), is a quantitative measure of the efficiency of the column, and is related to the ratio of the retention time and the standard deviation of... 

Bandwidth. Column efficiency may also be expressed in terms of a bandwidth. The bandwidth is defined as the volume of mobile phase containing 95% of an eluted compound, or, equivalently, four standard deviations of a statistical distribution of the same shape as the chromatographic peak ... 

The analysis of chromatographic data is usually performed on normalized chromatograms, which is an attempt to account for the mass injected. However, the closure of analytical data is a problem with normalized data which has been described elsewhere (11). We examined our data for this problem by plotting the grand mean variation over all 368 peaks versus the standard deviations of these peaks. Closure did not occur in the unnormalized data. 

Bromate near its detection limit gave the following chromatographic peak heights and standard deviations. The blank is 0 because chromatographic peak height is measured from the baseline adjacent to the peak. For each concentration, estimate the detection limit. Find the mean detection limit. 

The suitability of the system is determined by chromatographing the Standard solution, and recording the peak responses as directed under Procedure. The tailing factor is not more than 2.0, and the relative standard deviation for replicate injections is not more than 4.0%. 

In chapter 1 (section 1.4) we have expressed the width of a (Gaussian) chromatographic peak in terms of the standard deviation o. Using the additivity of variances, we may... 

The spread of data about the mean is usually measured with the standard deviation ct, but another common parameter is the range. (In our discussion of Gaussian chromatographic peaks, we have used peak width.) By definition,... 

Standards were prepared by injecting known amounts of freshly distilled vinyl acetate into 1.00 mL of solvent. Calibration curves were obtained by injecting 5.0-yL aliquots of standards and diluted standards into the gas chromatograph and plotting the peak areas versus concentrations. These calibration curves were linear over the range of 5-5000 yg/mL. The precision for replicate injections of a standard at 5 yg/mL was 3 relative standard deviation. 

When the various instrumental and chromatographic factors are set for optimum performance, extremely good quantitation is possible, as shown in Table 7-3. The data represent nine replicate runs of the separation described in Figure 7-5. The values reported are average retention time and peak area along with their corresponding percent relative standard deviation (% RSD). These results are excellent by any standard of performance. 

Chromatographic System (See Chromatography, Appendix IIIA.) Set up the system with reference to High-Performance Liquid Chromatography. The chromatograph has a 254-nm detector and a 15-cm x 4.6-mm column that contains 5-to 10-mm porous microparticles of silica bonded to octylsilane (Zorbax 8, or equivalent). Set the flow rate to about 2 mL/ min. Chromatograph three replicate injections of the Standard Preparation, and record the peak responses as directed under Procedure. The relative standard deviation is not more than 2.0%, and the resolution factor between nitrilotriacetic acid and Calcium Disodium EDTA is not less than 4.0. 

Procedure Inject, in triplicate, 5.00 mL of the Standard Preparation into the gas chromatograph, record the chromatograms, and average the peak area responses. The relative standard deviation does not exceed 5.0%. 

Procedure Inject in triplicate 1.00 mL of the Standard Preparation into the gas chromatograph, and average the peak area responses. The relative standard deviation should not exceed 5.0%. Similarly, inject in triplicate 1.00 mL of sample, sum the average peak areas of the individual peaks, except for the Carbon Dioxide peaks, and calculate the ppm v/v in the sample by the equation... 

Standard Curve Chromatograph aliquots of each Standard Preparation as directed under Procedure. Measure the peak areas for each Standard Preparation. Plot a standard curve using the concentration, in milligrams per kilogram, of each Standard Preparation versus its corresponding peak area, and draw the best straight line. To ensure that the relative standard deviation does not exceed 2.0%, chromatograph a sufficient number of replicates of each Standard Preparation, and record the areas as directed under Procedure (below). 

Chromatograph five injections of equal volume, up to 25 pL, of the Standard Solution, and measure the peak response. The relative standard deviation, calculated by the formula... 

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