Rate constant time dependence

It is once again the non-Markovian equation in a sense that the relaxation rates are time-dependent. They become constant for the times which are long enough to extend the integration over t to 00. This leads... 

Every reaction has its own characteristic rate constant that depends on the intrinsic speed of that particular reaction. For example, the value of k in the rate law for NO2 decomposition is different from the value of k for the reaction of O3 with NO. Rate constants are independent of concentration and time, but as we discuss in Section 15-1. rate constants are sensitive to temperature. 

The extraction system which was measured by the HSS method for the first time was the extraction kinetics of Ni(II) and Zn(II) with -alkyl substituted dithizone (HL) [14]. The observed extraction rate constants linearly depended on both concentrations of the metal ion [M j and the dissociated form of the ligand [L j. This seemed to suggest that the rate determining reaction was the aqueous phase complexation which formed a 1 1 complex. However, the observed extraction rate constant k was not decreased with the distribution constant Kj of the ligands as expected from the aqueous phase mechanism. 

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... 

Here, one does not desire variation of the flow rate, as this may affect the performance of this and further microfluidic elements downstream. The individual flow rates are time dependent owing to their interrelationship the sum is a constant over time. 

The selectivity of a productive reaction refers to the relative amounts of P, P at the time of observation. The ratio of the amounts of P and P which are formed is the ratio of the corresponding rate constants, if the stereoselective is a pair of corresponding reactions53. If, however, the productive stereoselective reaction is a more complex kinetic scheme, then the ratio of the amounts of any two stereoisomeric products, P and P , which depends on time and pairs of the appropriate kinetic constants, has a positive lower bound and a finite upper bound. Both of these bounds are the ratios of two rate constants54. However, since the free enthalpy difference of stereoisomeric transition states is due to different non-bonded interaction and does not, as a rule, exceed 3 kcal/mole, and since the rate constant ratio depends on the free enthalpy difference, this ratio has a rather low upper bound. Accordingly, the stereoselectivity of productive reactions is generally low (50—90% relative yield of the preferred product in most cases). 

At a constant dissolution rate, the time dependence of the ApBq layer thickness is seen to be similar that shown in Fig. 2.7b (line 1). After a certain period of time, the thickness of the layer reaches the value xmax and then it grows no longer because the stationary state is established when an increase in the layer thickness is just equal to a decrease due to its dis-solution in the liquid phase. The process of an asymptotic approach of the thickness of the ApBq layer with passing time to its maximum value possible under given dissolution conditions is described by equation (5.25). 

Regardless of the order of the reactions, the rate of reaction has the units of concentration/time (i.e., mole/L sec). The units of the rate constant are dependent on the overall order of the reaction ... 

Figure 29. Simulated para selectivity y°ut at the reactor outlet as a function of the isomerization rate constant k. Dependence on the modified residence time m jq (ceb = const.).

Clearance reflects the volume of fluid cleared per time, whereas the rate of drug elimination from the body, as described by the elimination rate constant k, depends on both clearance and volume of distribution. A related parameter, the elimination half-life, which is the time it takes for the concentration to fall to half, also depends on both clearance and volume of distribution. These relationships are summarised in Panel 5.1. Changes in clearance or volume of distribution that lead to an increase in elimination half-life will prolong the time it takes for a drug to be eliminated from the body, which may allow the dosage interval to be increased, e.g. from 12 hours to 24 hours. 

This may be concentration and drug dependent. t = Increase = decrease — = no effect, k, = absorption rate constant = time AUC = area under the plasma drug concentration time curve. for peak drug concentration in plasma ... 

Examination of equation (4.17) shows that the second-order rate constant is dependent on the units used to express concentration the units of k2 are concentration" time"b For reactions in which both concentration terms refer to the same reactant we may write... 

In a full-scale SCR unit two or three layers of honeycomb elements are used. In these layers several elements are placed for ex situ testing at regular time intervals [129]. Testing these samples in bench-scale equipment produces overall rate constants which depend on the location in the SCR reactor. Moreover, information is obtained when catalyst layers have to be exchanged. 

Reaction kinetics represented by the general form of Equation 1 have been employed in a number of quantitative chemical models of natural systems. Under ideal conditions, the four parameters, total mass transfer, kinetic rate constants, time, and the reactive surface area can be determined independently, permitting the unique definition of the model. In most cases, at least one of the variables, most often surface area, is treated as a dependent term. This nonuniqueness arises when the reactive surface area of a natural system cannot be estimated, or because such estimates made either from geometric or BET measurements do not produce reasonable fits to the other parameters. Most often the calculated total mass transfer significantly exceeds the observed transfer based on measured aqueous concentrations. 

At first glance, Eq. (15) appears too complex to allow measurement of individual reaction rate constants. However, as we illustrate with this example, it is possible to extract estimates of all four rate constants from an analysis of the concentration dependence of the observed rates. The time dependence of reaction of serine with pyridoxal phosphate at the /3-site of tryptophan synthase provides a good example of two-step reaction kinetics because of the unique optical... 

Conclusion (a) Photochemical steps of reaction include many thermal degradation processes, which do not need to be considered in the rate law, if the Bodenstein hypothesis is valid, (b) The mechanism has to be reduced as far as possible to avoid linear dependencies, (c) Thermal and photochemical reactions can be treated in principle by the same formalism. Rate constants times concentrations have to be substituted by the product of the partial photochemical quantum yield times the amount of light absorbed, which contains the concentration of the reactant which starts the photoreaction. 

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