Rate constant apparent concentration dependence

A closer examination was made of the mechanism of deprotonation of HMB radical cation in acetonitrile. Tables 7 and 8 show the effect of substrate concentration and temperature, respectively, on the apparent rate constants for the deprotonation of the radical cations of HM B and HMB-dig measured by DCV (Parker, 1981b). Although data for both substrates gave a very good fit to theoretical data for the disproportionation mechanism, the observed rate constants were concentration dependent. This indicates that Raib is greater than 1 and less than 2 suggesting a complex mechanism. The com-... 

Thus far the discussion has involved mainly constant infusion experiments rather than LC/MS. In the latter case, flow rate is generally varied via the diameter of the HPLC column or by post-column splitting of the effluent before transport to the ESI sprayer. In the case of conventional ESI sources and mobile phase flow rates, the apparent concentration dependent response will apply... 

Why are we so ignorant about the magnitude of propagation rate constants Apparent rate constants kA are dependent on the total Nd-concentration (cNd), the fraction of active Nd (ejffNd), the functionality of Nd (fNd) and the propagation rate constant kp ... 

FIGURE 3.6 Compartmental analysis for different terms of volume of distribution. (Adapted from Kwon, Y., Handbook of Essential Pharmacokinetics, Pharmacodynamics and Drug Metabolism for Industrial Scientists, Kluwer Academic/Plenum Publishers, New York, 2001. With permission.) (a) Schematic diagram of two-compartment model for compound disposition. Compound is administrated and eliminated from central compartment (compartment 1) and distributes between central compartment and peripheral compartment (compartment 2). Vj and V2 are the apparent volumes of the central and peripheral compartments, respectively. kI0 is the elimination rate constant, and k12 and k21 are the intercompartmental distribution rate constants, (b) Concentration versus time profiles of plasma (—) and peripheral tissue (—) for two-compartmental disposition after IV bolus injection. C0 is the extrapolated concentration at time zero, used for estimation of V, The time of distributional equilibrium is fss. Ydss is a volume distribution value at fss only. Vj, is the volume of distribution value at and after postdistribution equilibrium, which is influenced by relative rates of distribution and elimination, (c) Time-dependent volume of distribution for the corresponding two-compart-mental disposition. Vt is the starting distribution space and has the smallest value. Volume of distribution increases to Vdss at t,s. Volume of distribution further increases with time to Vp at and after postdistribution equilibrium. Vp is influenced by relative rates of distribution and elimination and is not a pure term for volume of distribution. 

For the pharmacokinetics of rhG-CSF in humans, it has been reported that the absorption and clearance of rhG-CSF follow first-order kinetics without any apparent concentration dependence [114], When rhG-CSF was administered by 24-h constant i.v. infusion at a dose level of 20pg/kg, the mean serum concentration achieved 48ng/mL. Constant i.v. infusion for 11 to 20 days produced steady-state serum concentrations over the infusion period. Subcutaneous administration of rhG-CSF at doses of 3.45 and 11.5pg/kg resulted in peak serum concentrations of 4 and 49ng/mL, respectively. The mean value of volume of distribution was 150mL/kg. The elimination half-life was 3.5h after either i.v. routes or s.c. routes, with a clearance rate of 0.5-0.7 mL/min/kg. The administration of a daily dose for 14 consecutive days did not affect the half-life. 

Modeling of the two paths to fit phosphate concentration data by solving the rate equations in an optimization of the rate constants reveals that depending on the initial guess, two different, but apparently valid, results may be achieved. Figure 3 is the response surface of the optimization plotted as a function of the rate constants kz and k. The response F k) is defined as... 

In conclusion, we can postulate that the apparent rate constant is potential-dependent. This effect is not simply due to the potential dependence of the surface concentration. The local electrochemical driving force is the total applied potential difference. However, no experimental studies have been able to... 

If certain species are present in large excess, their concentration stays approximately constant during the course of a reaction. In this case the dependence of the reaction rate on the concentration of these species can be included in an effective rate constant The dependence on the concentrations of the remaining species then defines the apparent order of the reaction. Take for example equation (A3,4.10) with e. The... 

Figure 5.3 shows the dependence of the apparent second-order rate constants (koi "/[5.2]i) on the concentration of surfactant for the Diels-Alder reactions of 5.If and 5.1 g with 5.2. The results of the analysis in terms of the pseudophase model are shown in the inset in Figure 5.3 and in the first two... 

Rate Equations with Concentration-Independent Mass Transfer Coefficients. Except for equimolar counterdiffusion, the mass transfer coefficients appHcable to the various situations apparently depend on concentration through thej/g and factors. Instead of the classical rate equations 4 and 5, containing variable mass transfer coefficients, the rate of mass transfer can be expressed in terms of the constant coefficients for equimolar counterdiffusion using the relationships... 

The isomerization of A to B yielded kinetic data that conformed to a first-order rate law. but the apparent first-order rate constant depended on the initial concentration of A. The authors propose competing unimolecular and bimolecular processes, and they show that the system reduces to a first-order expression when the equilibrium constant K is unity that is,... 

Data given in Tables 1-6 clearly show a significant dependence of P2 and p4 on amine concentration, that is, at least one of the apparent rate constants kj contains a concentration factor. Thus, according to the mathematical considerations outlined in the Analysis of Data Paragraph, both p2, P4 exponents and the derived variables -(P2 + p)4> P2 P4 ind Z (see Eqns. 8-12) are the combinations of the apparent rate constants (kj). To characterize these dependences, derived variables -(p2+p)4, P2 P4 and Z (Eqns. 8,11 and 12) were correlated with the amine concentration using a non-linear regression program to find the best fit. Computation resulted in a linear dependence for -(p2 + p)4 and Z, that is... 

The ET reaction between aqueous oxidants and decamethylferrocene (DMFc), in both DCE and NB, has been studied over a wide range of conditions and shown to be a complex process [86]. The apparent potential-dependence of the ET rate constant was contrary to Butler-Volmer theory, when the interfacial potential drop at the ITIES was adjusted via the CIO4 concentration in the aqueous phase. The highest reaction rate was observed with the smallest concentration of CIO4 in the aqueous phase, which corresponded to the lowest driving force for the oxidation process. In contrast, the ET rate increased with driving force when this was adjusted via the redox potential of the aqueous oxidant. Moreover, a Butler-Volmer trend was found when TBA was used as the potential-determining ion, with an a value of 0.38 [86]. 

This is a linear equation, and we can thus expect kobs to track linearly with inhibitor concentration for an inhibitor conforming to the mechanism of scheme B. As illustrated in Figure 6.4, a replot of kobs as a function of [/] will yield a straight line with slope equal to k3 and y-intercept equal to k4. It should be noted that in such an experiment the measured value of k3 is an apparent value as this association rate constant may be affected by the concentration of substrate used in the experiment, depending on the inhibition modality of the compound (vide infra). Hence the apparent value of Ki (Kfw) for an inhibitor of this type can be calculated from the ratio of... 

Electrocatalysis employing Co complexes as catalysts may have the complex in solution, adsorbed onto the electrode surface, or covalently bound to the electrode surface. This is exemplified with some selected examples. Cobalt(I) coordinatively unsaturated complexes of 2,2 -dipyridine promote the electrochemical oxidation of organic halides, the apparent rate constant showing a first order dependence on substrate concentration.1398,1399 Catalytic reduction of dioxygen has been observed on a glassy carbon electrode to which a cobalt(III) macrocycle tetraamine complex has been adsorbed.1400,1401... 

The apparent rate constant kapp depends on the concentration of hydroxide ion as is shown in Fig. 1. The absorption maxima of TcCl2(acac) 2 in chloroform appear at 281,314(sh), 340(sh), 382 and 420 nm. On the other hand, the spectrum of the aqueous phase exhibits absorption maxima at 292,350 and 540 nm. The absorbances at 350 and 540 nm increase with time, but decrease after reaching maxima. This suggests that the chemical species which is formed by the back-extraction of TcCl2(acac)2 decomposes with time. In order to clarify the behavior of chloride ion liberated from the complex, an electrochemical method was introduced for the homogeneous system. In acetonitrile, no detectable change in the spectrum of TcCl2(acac)2 was observed. On the addition of an aqueous solution of hydroxide, however, the brown solution immediately turned red-violet, and exhibited absorption maxima at 292,350 and 540 nm. The red-violet... 

Fig. 1, Dependence of the apparent decomposition rate constant of TcCl2(acac) 2 on the concentration of hydroxide at 25 °Ca. The solid line was calculated by Eq. (13)...

The next difficulty in comparing the predictions of Eq. (1) with experiment is that experimental values are reported in terms of either second-order rate constants for the gas-phase experiments or pseudo-first-order rate constants for the solution experiments. According to Eq. (1), neither pure reaction order is correct nor should the apparent rate constant depend on the concentration or... 

As mentioned earlier, ascorbate and ubihydroquinone regenerate a-tocopherol contained in a LDL particle and by this may enhance its antioxidant activity. Stocker and his coworkers [123] suggest that this role of ubihydroquinone is especially important. However, it is questionable because ubihydroquinone content in LDL is very small and only 50% to 60% of LDL particles contain a molecule of ubihydroquinone. Moreover, there is another apparently much more effective co-antioxidant of a-tocopherol in LDL particles, namely, nitric oxide [125], It has been already mentioned that nitric oxide exhibits both antioxidant and prooxidant effects depending on the 02 /NO ratio [42]. It is important that NO concentrates up to 25-fold in lipid membranes and LDL compartments due to the high lipid partition coefficient, charge neutrality, and small molecular radius [126,127]. Because of this, the value of 02 /N0 ratio should be very small, and the antioxidant effect of NO must exceed the prooxidant effect of peroxynitrite. As the rate constants for the recombination reaction of NO with peroxyl radicals are close to diffusion limit (about 109 1 mol 1 s 1 [125]), NO will inhibit both Reactions (7) and (8) and by that spare a-tocopherol in LDL oxidation. 

Various rate constants which enter into the expression for k i, Equation 14.14, have now been discussed. kunj as defined in Equation 14.13 has the appearance of a first order rate constant for the disappearance of A molecules but it is actually only a pseudo first order rate constant since it explicitly depends on the concentration of M, the species involved in the activation and deactivation of A molecules. In the limit of high concentration, [M] oo, kuni reduces to an apparent first order process, lim (kuni j oo) = ka(E)(8ki(E)/k2)[A] = kt(Apparent)[A], while at low concentration the reduction is to an apparent second order process, lim(kunij[M]->.o) = 8k (E)[A][M] = k2 (Apparent) [A] [M],... 

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