Disappearance rate

The type of catalyst influences the rate and reaction mechanism. Reactions catalyzed with both monovalent and divalent metal hydroxides, KOH, NaOH, LiOH and Ba(OH)2, Ca(OH)2, and Mg(OH)2, showed that both valence and ionic radius of hydrated cations affect the formation rate and final concentrations of various reaction intermediates and products.61 For the same valence, a linear relationship was observed between the formaldehyde disappearance rate and ionic radius of hydrated cations where larger cation radii gave rise to higher rate constants. In addition, irrespective of the ionic radii, divalent cations lead to faster formaldehyde disappearance rates titan monovalent cations. For the proposed mechanism where an intermediate chelate participates in the reaction (Fig. 7.30), an increase in positive charge density in smaller cations was suggested to improve the stability of the chelate complex and, therefore, decrease the rate of the reaction. The radii and valence also affect the formation and disappearance of various hydrox-ymethylated phenolic compounds which dictate the composition of final products. 

Consequently, the observed disappearance rate of S will be given by ... 

Another method is to measure the disappearance rate of the excited parent molecules, that is, the intensity changes of the disk-like images at various delay times (therefore, at various photolysis laser positions) along the molecular beam. This is very useful when the dissociation rate is slow and the method described above cannot be applied. This measurement requires a small molecular beam velocity distribution and a large variable distance between the crossing points of the pump and probe laser beams with the molecular beam. The small velocity distribution can be obtained through adiabatic expansion, and the available distances between the pump and probe laser beams depend on the design of the chamber. For variable distances from 0 to 10 cm in our system and AV/V = 10% molecular beam velocity distribution, dissociation rates as slow as 3 x 103 s 1 under collisionless condition can be measured. 

Requiring that the disappearance rate from the donor be equal to the appearance rate in the receiver, it follows that... 

Because VD and Vfi were taken to be unequal for the general case, the disappearance rate constant (a(3) is not equal to the appearance rate constant (a P )- However, the rate constants become identical when the volumes of the compartments are also identical. 

The conditions for Eqs. (72) and (73) are that the disappearance rate must be equal to the appearance rate and there is insignificant binding and metabolism by the cell. These assumptions are satisfied by the steroids with the exception of testosterone and progesterone. Hence, Pe values of testosterone and progesterone based on appearance kinetics will be underestimated unless the enzyme system is saturated. 

Let us now interrelate the fluxes in a variety of meaningful ways. All fluxes have units of moles per square centimeter per second. The conservation of mass is satisfied by the requirement that the disappearance rate of drug from the solution is equal to the sum of fluxes of drug and metabolite emerging from the cell ... 

The efflux of drug, J x=m, is related to the disappearance rate in the donor by Eq. (104). Consequently, (C) is a function of time and approaches zero upon depletion of drug in the donor with time. 

Using the relationships of the disappearance rate from the donor and efflux into the receiver (sink) given in Eqs. (96), (102), and (104) and the initial condition of CR = 0 at t = 0, the time-dependent change in drug concentration in the receiver is... 

In the initial stage the amount of fines consumed per unit charge weight depends only on the total number of drum revolutions, independent of the rotational speed (12, M6). The disappearance rate per unit charge weight and per drum revolution of the fines varies directly with seed density, the... 

The first term on the right-hand side of Equation (2) describes the formation rate of k-flocs, and the second term is the disappearance rate. In the present study the flow was turbulent, and an effective shear rate was calculated as (e/v) / (19), where e is the energy dissipation, W/kg, and v is the kinematic viscosity, m /s. Equation (2) was also extended to include a collision efficiency factor, a, defined as... 

Portmann and co-workers then studied the kinetic pathways in man for hydroxynalidixic acid, the active primary metabolite.(26) The rate constants for glucuronide formation, oxidation to the dicarboxylic acid and excretion of hydroxynalidixic acid were calculated. Essentially total absorption of hydroxynalidixic acid was found in every case. Good agreement between experimental and theoretical plasma levels, based on the first order rate approximations used for the model, was found. Again, the disappearance rate constant, kdoi was found to be very similar for each subject, although the individual excretion and metabolic rate constants varied widely. The disappearance rate constant, k was defined as the sum of the excretion rate constant, kg j and the metabolic rate constants to the glucuronide and dicarboxylic acid, kM-j and kgj, respectively. 

All the surface recombination processes, including back reaction, can be incorporated in a heavy kinetic model [22]. The predicted, and experimentally observed, effect of the back reactions is the presence of a maximum in the donor disappearance rate as a function of its concentration [22], Surface passivation with fluoride also showed a marked effect on back electron transfer processes, suppressing them by the greater distance of reactive species from the surface. The suppression of back reaction has been verified experimentally in the degradation of phenol over an illuminated Ti02/F catalyst [27]. 

For each differential value, the carbon disappearance must equal o times the oxygen consumed. The molar carbon disappearance rate is given by dy, where Wc is the weight fraction of carbon on the... 

Estimation of Trifluralin Disappearance Rate. The trifluralin disappearance rate can be estimated by regression analysis in two ways, either by using the five individual sample means obtained... 

We consider a particular case, for which the replication and disappearance rate coefficients and the diffusion coefficients are the same for all species and depend only on the total population density p (n) = Du = D. We also... 

Chemical. Although no products were identified, p-chloronitrobenzene (1.5 x 10 M) was reduced by iron metal (33.3 g/L acid washed 18-20 mesh) in a carbonate buffer (1.5 x 10 M) at pH 5.9 and 15 °C. Based on the pseudo-first-order disappearance rate of 0.0336/min, the half-life was 20.6 min (Agrawal and Tratnyek, 1996). 

In anoxic hypolimnion samples collected from Lower Mystic Lake, MA, hexachloroethane was abiotically transformed into tetrachloroethylene via reductive elimination and to pentachloro-ethane via hydrogenolysis. Tetrachloroethylene accounted for 70% of hexachloroethane in unaltered lake water and 62% in filter-sterilized water after 10 d. Trichloroethylene and pent-achloroethane accounted for <1 and 2% in unaltered lake water and filter-sterilized water, respectively. Disappearance rate constants for hexachloroethane were 0.33/d for unaltered water and 0.26/d for filter-sterilized water. At least 80% of the hexachloroethane disappearance in unaltered water was abiotic in origin due to the reactions with naturally occurring aqueous polysulfides, H2S and (Miller et al, 1998a). 

In addition to the environmental pH and type of hydrolysis, contaminant hydrolysis in sediments is controlled by the properties of the contaminant molecule and the sediment constituents. In a natural sediment, it is difficult to determine if hydrolysis is a biologically mediated or an abiotic reaction. A simple test consists of measuring the contaminant disappearance rate in the sediment and in distilled water, with a pH adjusted to that of the sediment. If the two disappearance rates are similar, the process can be assumed to be abiotic, while if the rate is greater in the sediment system, the hydrolysis is biologically mediated. 

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