Corrected concentration dependence

For the simplest possible systems, in which ED and v are both independent of temperature and n, the slope of a single evolution curve at different times (temperatures) yields the rate law of desorption. The correct concentration dependence (x = 1 or 2) may be ascertained by plotting In n x dn/dt vs 1/RT. A linear relation with slope —ED will be obtained for the correct value of the order of the reaction. The preexponential can then be determined by substituting and n in Eq. (13). 

The order of the desorption reaction, as well as its activation energy, can be determined from a logarithmic plot of either (n(tx) — n)/en n(t ) or (l/ )ln[7i(straight line with slope - ED will be obtained for the plot of the correct concentration dependence. The correction factor e itself depends upon Eu, but for a temperature range from 1000-2000°K and a heat on the order of 50 kcal/mole it is small, and can be conveniently accounted for by successive approximations. 

If the concentration of effective aromatic species does vary with acidity, as sometimes happens if the compound is substantially proto-nated, then the acidity-dependence of the rate will be less steep than usual, because the concentration of the active free base diminishes significantly with increasing acidity. This situation has been observed in certain cases ( 8.2). The fall in the concentration of the active species can be allowed for from a knowledge of its pK and the acidity function which, for the particular compound, gives the best measure of the acidity of the medium. Then the corrected acidity-dependence of the rate resembles that observed with compounds the concentration of which does not change significantly with acidity. The nitration of minor species is discussed later ( 8.2). 

As noted above, all of the partial molar quantities are concentration dependent. It is convenient to define a thermodynamic concentration called the activity aj in terms of which the chemical potential is correctly given by the relationship... 

As with the diffusion coefficient, sedimentation coefficients are frequently corrected for concentration dependence and reduced to standard conditions ... 

A rapid increase in diffusivity in the saturation region is therefore to be expected, as illustrated in Figure 7 (17). Although the corrected diffusivity (Dq) is, in principle, concentration dependent, the concentration dependence of this quantity is generally much weaker than that of the thermodynamic correction factor d ap d a q). The assumption of a constant corrected diffusivity is therefore an acceptable approximation for many systems. More detailed analysis shows that the corrected diffusivity is closely related to the self-diffusivity or tracer diffusivity, and at low sorbate concentrations these quantities become identical. 

Since the infinite dilution values D°g and Dba. re generally unequal, even a thermodynamically ideal solution hke Ya = Ys = 1 will exhibit concentration dependence of the diffusivity. In addition, nonideal solutions require a thermodynamic correction factor to retain the true driving force for molecular diffusion, or the gradient of the chemical potential rather than the composition gradient. That correction factor is ... 

Competitive antagonists affinity of, 261-264 description of, 75 IC50 correction factors for, 223 Schild analysis, 261-264 Concentration-dependent antagonism, 99 Concentration-response curve, 13 Confidence intervals, 228-229 Conformations, 13-14 Constitutive activity of receptors description of, 49—51 receptor density and, 56 Schild analysis, 108-111 Context-dependent biological effect, 188 Correction factors, 211-213, 223 Correlational research, 231 CP320626, 128... 

We have noted previously that the forward and reverse rates are equal at equilibrium. It seems, then, that one could use this equality to deduce the form of the rate law for the reverse reactions (by which is meant the concentration dependences), seeing that the form of the equilibrium constant is defined by the condition for thermodynamic equilibrium. By and large, this method works, but it is not rigorously correct, since the coefficients in the equilibrium condition are only relative, whereas those in the rate law are absolute.19 Thus, if we have this net reaction and rate law for the forward direction,... 

Before scattering intensity measurements can be converted to molecular weights, the two corrections previously discussed—the dissymmetry correction for intraparticle interference and the extrapolation to zero concentration—must be introduced, or established to be negligible. The relationships given in the preceding sections unfortunately account rigorously for either only in the absence of the other. The theory of the concentration dependence of the scattered intensity applies to the turbidity corrected for dissymmetry, and the treatment of dissymmetry is strictly valid only at zero concentration (where interference of radiation scattered by different polymer molecules vanishes). 

In practice, however, the situation is more complicated since some of the triplets may be excited to higher triplet levels (7 -> Tx) by the same wavelengths of light used to determine AOD. This results in a [A ]r less than the actual concentration depending upon the magnitude of the triplet molar absorptivity et. If et is known, a correction for Tx -> TX absorption can be made<63) ... 

Theoretical rate of modification of an introduced cysteine using four different concentrations of MTS (10 xM, 20 ulM, 30 ii.M, and 60 ulM, ). The pseudo first-order rate constants (kfl are 0.1285, 0.2445,0.4849, and 0.7564, respectively. When corrected for the concentration-dependence of MTS modification, the second-order rate constants (k2) are 12,900, 12,275 12,122 and 12,606 M s respectively. Although all k2 values are similar, the early phase of modification (<20 s) is less well described when higher concentrations (>20 xM) of the reagents are applied (see inset). Based on these data, we would use 10 xM for control experiments and protection assays... 

The second-order rate constant can then be determined by dividing the pseudo first-order rate (ki) by the molar concentration of the MTS reagent apphed. This value corrects for the concentration-dependence of the effect and permits comparisons about the nature of the environment within the series of mutations. 

The H-NMR spectra of FCC feeds were recorded on a Bruker DRX 400 MHz NMR spectrometer. The concentration of the samples of 5 wt% in CDCI3 was recommended by Molina, Navarro Uribe, and Murgich [2] to avoid concentration dependence of the chemical shift. A 30° pulse sequence was applied, with 4.089 s acquisition time, 2 s pulse delay [2], 8012.8 Hz spectral width, and 64 scans. Hexamethyldisiloxane (HMDSO) was used as a reference. NMR processing was realized using MestReNova software. The phase and baseline of the resulting spectra were manually adjusted and corrected. The spectra were integrated six times and average values were taken for the purpose of calculations. The spectra were divided... 

The apparent dispersion coefficient in Equation 10.8 describes the zone spreading observed in linear chromatography. This phenomenon is mainly governed by axial dispersion in the mobile phase and by nonequilibrium effects (i.e., the consequence of a finite rate of mass transfer kinetics). The band spreading observed in preparative chromatography is far more extensive than it is in linear chromatography. It is predominantly caused by the consequences of the nonlinear thermodynamics, i.e., the concentration dependence of the velocity associated to each concentration. When the mass transfer kinetics is fast, the influence of the apparent axial dispersion is small or moderate and results in a mere correction to the band profile predicted by thermodynamics alone. 

Administration of sotalol is associated with dose- and concentration-dependent slowing of the heart rate and prolongation of the PR interval. The QRS duration is not affected with plasma concentrations within the therapeutic range. The corrected QT interval is prolonged as a result of the increase in the ERP of ventricular myocardium. 

The yield determined in a certain type of experiment usually strongly depends on the assumptions made about the formation mechanism. In the older literature, the excited molecules were often assumed to be produced solely in neutral excitations [127,139-143] and energy-transfer experiments with Stern-Volmer-type extrapolation (linear concentration dependence) were used to derive G(5 i). For instance, by sensitization of benzene fiuorescence, Baxendale and Mayer established G(5 i) = 0.3 for cyclohexane [141]. Later Busi [140] corrected this value to G(5 i) = 0.51 on the basis that in the transfer, in addition to the fiuorescing benzene state S, the S2 and S3 states also form and the 82- 81 and 83 81 conversion efficiencies are smaller than 1. Johnson and Lipsky [144] reported an efficiency factor of 0.26 0.02 per encounter for sensitization of benzene fluorescence via energy transfer from cyclohexane. Using this efficiency factor the corrected yield is G(5 i) = 1.15. Based on energy-transfer measurements Beck and Thomas estimated G(5 i) = 1 for cyclohexane [145]. Relatively small G(5 i) values were determined in energy-transfer experiments for some other alkanes as well -hexane 1.4, -heptane 1.1 [140], cyclopentane 0.07 [142] and 0.12 [140], cyclooctane 0.07 [142] and 1.46 [140], methylcyclohexane 0.95, cifi-decalin 0.26 [140], and cis/trans-decalin mixture 0.15 [142]. 

The concentration dependence of sedimentation causes an additional reshaping of the boundary, called boundary sharpening. The faster moving material is at a higher concentration than the slower material, with the result that the boundary is progressively sharpened as the concentration increases that is, it shifts to the left. The dependence of sedimentation constant on concentration and on the concentration of other molecules around the sedimenting molecule, which causes the above effects, are too difficult to measure. In some systems with spherical macromolecules, approximate corrections have been made (5). The extrapolation of s to zero polymer concentration should eliminate the major part of these effects. 

Initially, all the hydrocarbon is adsorbed on the core and none is observed at the outlet. Once the core is saturated, hydrocarbon breakthrough is observed. Example breakthrough curves for two temperatures are shown in Fig. 27. The amount of hydrocarbon adsorbed is given by the area above the breakthrough curve (after correction for the residence time of the reactor). By conducting experiments with different hydrocarbon concentrations and at different temperatures, the temperature and concentration dependency of the amount stored can be determined and hence isotherms generated. 

The heats of solution of lithium perchlorate in aqueous acetonitrile were measured at concentrations between 0.01 and 0.1m. The concentration dependence was small compared with the experimental scatter of about 0.1-0.2 kcal mole-1. AHs values are given in Table II. The heats of solution in anhydrous acetonitrile were corrected to infinite dilution using measured heats of dilution (6), and the corrected values were averaged. The heats of dilution were measured for lithium perchlorate in the mixed solvent containing 90% MeCN. 

We have described several properties of aqueous solutions, some of which appear anomalous. It is now appropriate to discuss briefly what bearing these observations have on the degree and nature of involvement of the water structure in ion hydration. Specifically, are the observed concentration-dependent anomalies determined by the nature of the hydrated structures or are they manifestations of structural changes, induced by the ions, in the pure solvent The information which we have discussed also bears on the question of which model of hydration is most likely to be correct—the Frank-Wen (48) model or that of Samoilov (115). Some anomalies are amazingly abrupt. Vaslows occur over rather narrow concentration ranges, and those observed by Zagorets, Ermakov and Grunau are even sharper. Sharp transitions could be ex-... 

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