Retention equation for

For the density-only retention surface, retention data were collected at 4 different densities (0.1,0.2,0.3 and 0.4 g/mL) at a temperature of 80°C. Data were fit to equation 2 via nonlinear regression, and the resulting retention equations for each solute could be used to calculate the response surface. Although the goodness of fit was difficult to estimate since there was only one degree of freedom (and it is easy for R2 values to exceed 0.999 under these conditions), the good agreement of the predicted and measured retention values at the optimum (vide infra) provided additional support for the accuracy of equation 2. 

We should note that eqn (8.5) is rigorously valid only for parabolic flow in thermal FFF the gradient in viscosity caused by the temperature gradient leads to a complex retention equation for which eqn. (8.5) is only an approximation. While the effects of the departure from parabolic flow have been treated in some detail [30], eqns (8.5) and (8.6) are adequate for present purposes. 

The retention times for solutes A and B are replaced with their respective capacity factors by rearranging equation 12.10... 

To find Kovat s retention index for isobutane, we use equation 12.29. 

Using the data from Problem 1, calculate the resolution and selectivity factors for each pair of adjacent compounds. For resolution, use both equations 12.1 and 12.21, and compare your results. Discuss how you might improve the resolution between compounds B and C. The retention time for an unretained solute is 1.19 min. 

Equations (22-86) and (22-89) are the turbulent- and laminar-flow flux equations for the pressure-independent portion of the ultrafiltra-tion operating curve. They assume complete retention of solute. Appropriate values of diffusivity and kinematic viscosity are rarely known, so an a priori solution of the equations isn t usually possible. Interpolation, extrapolation, even precuction of an operating cui ve may be done from limited data. For turbulent flow over an unfouled membrane of a solution containing no particulates, the exponent on Q is usually 0.8. Fouhng reduces the exponent and particulates can increase the exponent to a value as high as 2. These equations also apply to some cases of reverse osmosis and microfiltration. In the former, the constancy of may not be assumed, and in the latter, D is usually enhanced very significantly by the action of materials not in true solution. 

Returning to equation (13), it is now possible to derive an equation for the adjusted retention volume, (V r),... 

Scott and Beesley [2] measured the corrected retention volumes of the enantiomers of 4-benzyl-2-oxazolidinone employing hexane/ethanol mixtures as the mobile phase and correlated the corrected retention volume of each isomer to the reciprocal of the volume fraction of ethanol. The results they obtained at 25°C are shown in Figure 8. It is seen that the correlation is excellent and was equally so for four other temperatures that were examined. From the same experiments carried out at different absolute temperatures (T) and at different volume fractions of ethanol (c), the effect of temperature and mobile composition was identified using the equation for the free energy of distribution and the reciprocal relationship between the solvent composition and retention. 

The authors arrived at the following specific equations for the retention volume s(c T) R(cT) isomers. These are the same equations used in chapter... 

The equation for the retention volume of a solute, that was derived by differentiating the elution curve equation, can be used to obtain an equation for the retention time of a solute (tr) by dividing by the flowrate (Q), thus,... 

Equation (25) can be extended to provide a general equation for a column equilibrated with (q) solutes at concentrations Xi, X2, X3,...Xq. For any particular solute (S), if its normal retention volume is Vr(S) on a column containing (n) plates, then from the plate theory, the plate volume of the column for the solute (S), i.e., (vs) is given by... 

One of the most important properties of a chromatographic column is the separation efficiency. A measure of this parameter could be the difference of the retention volume for two different compounds. The result of a GPC analysis is usually, however, only one large peak, and a separation into consecutive molar mass species is not possible. Additionally there is no standard for higher molar masses consisting only of a species that is truly monodisperse. Therefore, the application of the equation to the chromatographic resolution of low... 

Normally a calibration curve—molar mass against the total retention volume—exists for every GPC column or column combination. As a measure of the separation efficiency of a given column (set) the difference in the retention of two molar masses can be determined from this calibration curve. The same eluent and the same type of calibration standards have to be used for the comparison of different columns or sets. However, this volume difference is not in itself sufficient. In a first approximation the cross section area does not contribute to the separation. Dividing the retention difference by the cross section area normalizes the retention volume for different diameters of columns. The ISO standard method (3) contains such an equation... 

This equation is based on experience with liquid chromatography of low molecular weight samples displaying single peaks. Its application for the GPC of polymers, however, contains a disadvantage, as it mixes two inseparable properties the retention difference for the separation and the peak width for the contrary effect of band broadening. Such a procedure is acceptable if both effects are accessible for an experimental examination. For the GPC experiment, we do not possess polymer standards, consisting of molecules that are truly monodisperse. Therefore, we cannot determine the real peak width necessary for a reliable and reproducible peak resolution R,. This equation then is not qualified for a sufficient characterization of a GPC column. 

Equation (20-70) is the unsteady-state component mass balance for fed-batch concentration at constant retentate volume. Integration yields the equations for concentration and yield in Table 20-19. 

The variables that control the extent of a chromatographic separation are conveniently divided into kinetic and thermodynamic factors. The thermodynamic variables control relative retention and are embodied in the selectivity factor in the resolution equation. For any optimization strategy the selectivity factor should be maximized (see section 1.6). Since this depends on an understandino of the appropriate retention mechanism further discussion. .Jll be deferred to the appropriate sections of Chapters 2 and 4. 

It is important to know from Equation 27.7 that the performance of a complete mix with recycle system does not depend on hydraulic retention time. For a specific wastewater, a biological culture, and a particular set of environmental conditions, all coefficients Ks, b, Y, and km become constant. It is apparent from Equation 27.7 that the system performance is a function of mean cell residence time. 

With just a few exceptions, there is a dearth of published information providing systematic studies of retention volumes as a function of composition of the eluent over the whole composition range of binary solvents. To rectify this situation, a general equation for HPLC binary solvent retention behavior has been proposed [59] that should help generate a chromatographic retention model to fit Eq. (15.20) ... 

The particular case of the solubilities of organic solutes in water can be dealt with by rather simple equations, based on a general equation for solvent-dependent properties, apphed to solubilities, distribution ratios, rate constants, chromatographic retention indices, spectroscopic quantities, or heats of association [4] [see Eq. (2.12) for an example of its application]. For the molar solubilities of (liquid) aliphatic solutes B in water at 25°C the equation... 

This model also assumes that the binding of unpaired cluiic to the stationary phase is negligible. Equations (96)-(98) can be combined to calculate the retention factor for the eluite as... 

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