Useful Equations for HPLC

This is a synopsis. The equations are explained in Chapters 2 and 8. Retention factor  

Practical High-Performance Liquid Chromatography, Fifth edition Veronika R. Meyer 

Linear flow velocity of the mobile phase if e = 0.65 (chemically bonded stationary phase)  

Reduced flow velocity in normal phase (hexane, analyte with low molar mass, i.e. 

Reduced flow velocity in reversed phase (water/acetonitrile, analyte with low molar mass, i.e. in 6 x lO cni /inin) if e = 0.65  

Practical High-Performance Liquid Chromatography, Fourth edition Veronika R. Meyer 2004 John Wiley Sons, Ltd ISBN 0-470-09377-3 (Hardback) 0-470-09378-1 (Paperback) 

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The updates and improvements of this new edition are mainly to be found in details such as new references and technical descriptions which match today s instrumentation. Four new sections have been written, namely on the shelf-life of mobile phases, the mixing cross, the phase systems in ion chromatography, and on measurement uncertainty. Some equations in the zeroth chapter . Important and Useful Equations for HPLC, have new numeric values because a porosity of 0.65 is more realistic than 0.8 for chemically bonded phases. 

The experimental results obtained in the laboratory by the researchers can be monitored using computer programs with help of empirical equations or models. Most of the computer-assisted procedures have been developed for HPLC separations and mainly for RPLC, and some of them are commercially available. 

Fayolle et al.12 described work done on alcoholic fermentation, wherein they studied the effects of temperature and various calibration methods. The samples were removed and submitted for HPLC and other conventional analyses. The samples were used as is for MIR spectra generation. PLS-1 was used for equation constmction. The test RSDs for glucose, fructose, glycerol, and ethanol were, respectively, 12.5,6.1, 0.6, and 2.9 g/1. The wavelengths assigned to various components were also listed. 

A more vigorous treatment similar to the van Deemter equation but developed specifically for HPLC is the Knox equation, which uses a number of reduced parameters where h is the reduced plate height (h/dp) and vis reduced velocity (V dJD. ... 

The CLD methods for HPLC using isoluminol (190) with microperoxidase catalysis, for determination of lipid hydroperoxides in clinical fluids, have been reviewed. Determination of phospholipids hydroperoxides by luminol (124) CL has been reviewed . A fast RP-HPLC method (retention times 1 to 2 min) for determination of hydroperoxides and other peroxide compounds includes UVD, which is not always effective, and CLD, attained on injection of luminol (124), the CL reagent (Scheme 3), hemin (75a), a catalyst, and NaOH to raise the pH of the solution. A FLD cell may act as CLD cell if the excitation source is turned off. The selectivity of CLD is of advantage over UVD in industrial analysis thus, for example, UVD of a sample from a phenol production line based on cumene oxidation (equation 13) shows peaks for cumyl hydroperoxide (27), unreacted cumene, cumyl alcohol and acetophenone, whereas CLD shows only the 27 peak. The... 

Since the evaluation of this parameter is very important, it was also measured using the micellar HPLC technique (9), which allows a better estimation of the partition coefficients in the presence of quite high concentrations of surfactant. The chromatographic parameter P was measured for each ligand as a function of surfactant concentration, according to Equation 2 ... 

Olefination of acylsilanes is expected to become a useful method for the preparation of vinylsilanes, which are a powerful synthetic tool . Olefination of the acylsilanes 135 with ynolates provides the -silyl-a,/S-unsaturated esters 136 in high yields with high Z-selectivity (equation 56) . In most cases, the E isomers could not be detected by H NMR and HPLC. This is the first general method for the stereoselective synthesis of tetrasubstituted olefins. 

This equation can be used to calculate the expected pressure drop across the column. The present instrumentation for HPLC usually allows for column backpressures up to 30-40 MPa, which means that short columns should be used with small-diameter particles not to exceed the pressure limits. 

Snyder s thorough model [1-5] of gradient elution provides an extremely convenient means to achieve the objectives outlined above. The model uses the general resolution equation for isocratic chromatography in terms adapted to gradient elution. This equation defines resolution between two closely resolved analytes in gradient RP-HPLC as a function of mean column efficiency N, mean selectivity a, and the effective retention factor Aavc experienced by the compounds during the elution process j 1-3,5). 

To correct capacity factors for ionization, the same equations are used as for the corresponding correction of the apparent partition coefficients. Thus for monoprotic acids and bases, Eqs. 13 and 14 are suggested for extrapolated, as well as isocratic, capacity factors derived froiUg HPLC and RP-TLC I... 

Lehtonen - used molecular connectivity indices to correlate chromatographic parameters with molecular structure for n-ethylbenzamides, amines, and dansyl-amines separated by HPLC. The best regression equation for 22 isolated amines from wines is ... 

Many different types of chromatographic methods have been used to determine pKa value, such as ion-exchange chromatography, gas chromatography, and RP-HPLC, is well placed for high-throughput analysis. A review by Hardcastle et al. [21] explains the theory behind the calculations and the derivation of equations for the determination of pKa value. It has been demonstrated that the correct determination of pH of the mobile phase is key to the determination of pKa value of an analyte from chromatographic retention [22, 23]. However, this is the pKa value of the analyte in the mobile-phase system and not in a purely aqueous environment. 

Micelle-water partition coefficients are extracted by micelle chromatography (high performance liquid chromatography, HPLC) using micelle aqueous solution as mobile phase. For determination of retention times are measured using a usual HPLC system at various concentrations of micelle in the aqueous mobile phase and then estimated from the following equation ... 

The present study reports the measurements of intracrystalline diffusion and adsorption equilibrium for ethanol, propanols and butanols from aqueous solution in silicalite using a modified HPLC technique. The unique feature of the present work is the use of a mathematical model with a nonlinear adsorption isotherm equation to obtain the intracrystalline diffusivity and adsorption isotherm parameters. The adsorption equilibrium data for alcohols from aqueous solution in silicalite measured by the conventional batch method are also reported and compared with the results measured by the HPLC technique. 

Assuming a resolution of 2 (typical value for baseline resolution), one can solve the above equation for a and find that = 10 a minimum a of 1.06 is required for baseline resolution on the HPLC system, whereas an a of 3.9 is necessary with a Sep-Pak cartridge. The HPLC column will be able to separate components within a class, whereas the Sep-Pak cartridge can separate one class from another. This explains why Sep-Pak cartridges are used most often in a step-gradient mode, because one can elute components with high a s in relatively small volumes. 

As with the van Deemter equation, there is an optimum flow rate. It is difficult to see, but the optimum flow rate for HPLC is 10,000 times slower than that for GLC. Based on theory alone, it would seem that HPLC should never be used. 

We can approach an undostanding of macromolecular HPLC in various ways, based on the present model (//, 12,28,40). On the one hand, we can use the model to carry out exact predi ons (computer simulation of HPLC runs), and see how separation varies with experimental conditions. Altema tively, we can simplify our model to provide >proximate but explicit equations for resolution, peak capacity, and peak height as functions of variables such as flow rate, column length, gradient time. 

For the calculations of reduced velocities or the prediction of an HETP we need to know the diffusion coefficient of an analyte in the mobile phase. However, this information is seldom available. We therefore have to estimate the diffusion coefficient. There are several different approaches available, but the one most frequently used in the HPLC literature is the Wilke-Chang equation. It is claimed to be accurate for small to medium-sized molecules within 10%, which is sufficient for most purposes (9) ... 

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