Constant rate conversion

The overall rate constant for conversion of the E S complex to products E + P is called the turnover number because it represents the number of substrate molecules the enzyme turns over into product per unit time. A value of about 103 per second is typical. 

Figure 9.1 Predicted evolution of molecular weight (arbitrary units) with monomer conversion for a conventional radical polymerization with a constant rate of initiation (---------------) and a living polymerization (--).

In order to estimate the dependence of the termination rate constant on conversion, molecular weight and temperature, the following is assumed k- becomes diffusion controlled when the diffusion coefficient for a polymer radical Dp becomes less than or equal to a critical diffusion coefficient D ... 

The LDPE reactor is sometimes termed heat transfer limited in conversion. While this is true, the molecular weight (or melt index)—conversion relationship is not since this work shows that a selected initiator can allow conversion improvements to be made under adiabatic conditions for a specified molecular weight. The actual limitation to conversion is the decomposition temperature of the ethylene and given that temperature as a maximum limitation, an initiator (not necessarily commercial or even known with present initiator technology) can be found which will allow any product to be made at the rate dictated by this temperature. Conceptually, this is a constant (maximum) conversion reactor, runnirg at constant operating conditions where the product produced dictates the initiator to be used. 

Feed concentration Active zone concentration Deadzone concentration Effluent concentration Ideal tank concentration Total flow rate Fractional by-pass flow By-pass flow rate Dead volume fraction Deadzone exchange flow Rate constant Fractional conversion Fractional deadzone flow... 

For the aminolysis of TV-acylimidazoles in dry tetrahydrofuran a bimolecular reaction is suggested. The rate constant for conversion of AT-acetylimidazole with an ammonia-saturated solution in tetrahydrofuran at 25 °C was found to be 0.01 min-1, with t1/2 = 69.3 min.[3]... 

Raney-nickel catalysts - The effect of NH3 and base modifier on the activity and selectivity of RNi-C catalyst is shown in Table 1. The addition of NH3 significantly decreased the pseudo first-order rate constants, the conversion of RCN and the selectivity to R2NH. Upon increasing the reaction time (t) on... 

In our previous indole oxidation experiments, H202 has been added continuously with a flow rate of 10 pmol min 1 to a buffered indole solution in a batch reactor. In this case a constant maximum conversion at pH values between 3.0 and 8.0 was observed, whereas the indole conversion of the tandem system is limited by the H202 formation rate. At pH... 

The turnover number, or kCM (pronounced kay kat ), is another way of expressing Vmax. It s Vmax divided by the total concentration of enzyme (Vmax/E,). The kcat is a specific activity in which the amount of enzyme is expressed in micromoles rather than milligrams. The actual units of kcat are micromoles of product per minute per micromole of enzyme. Frequently, the micromoles cancel (even though they re not exactly the same), to give you units of reciprocal minutes (min-1). Notice that this has the same units as a first-order rate constant (see later, or see Chap. 24). The kcat is the first-order rate constant for conversion of the enzyme-substrate complex to product. For a very simple mechanism, such as the one shown earlier, kcat would be equal to k3. For more complex... 

Table 5. First-Order Rate Constants for Conversion of Monofunctional Adducts of c/s-[Pt(NH3)2(-G-)(H20)] into Bifunctional Adducts in Various Oligonucleotides...

This behavior can be shown graphically by constructing the rD-7 -/A relation from equation 5.3-16, in which kp kr, and Keq depend on T. This is a surface in three-dimensional space, but Figure 5.2 shows the relation in two-dimensional contour form, both for an exothermic reaction and an endothermic reaction, with /A as a function of T and ( rA) (as a parameter). The full line in each case represents equilibrium conversion. Two constant-rate ( -rA) contours are shown in each case (note the direction of increase in (- rA) in each case). As expected, each rate contour exhibits a maximum for the exothermic case, but not for the endothermic case. 

In Section 5.3 for reversible reactions, it is shown that the rate of an exothermic, reversible reaction goes through a maximum with respect to T at constant fractional conversion /, but decreases with respect to increasing / at constant T. (These canchisians apply whether the reaction is catalytic or noncatalytic.) Both features are illustrated graphically in Figure 21.4 for the oxidation of SO, based on the rate law of Eklund (1956) ... 

Scheme 1 illustrates the design of an experiment that could be used to determine the rate constant for H-atom abstraction from a group 14 hydride. Radical A- reacts with the hydride to give product A-H. In competition with this reaction, radical A- gives radical B- in a unimolecular or bimolecular reaction with a known rate constant, and product radical B- also reacts with the hydride, giving B-H. The rate constant for reaction of A- with the metal hydride can be determined from the product distribution, the known rate constant for conversion of A- to B-, and the concentrations... 

According to Equation 9 polymers with close to theoretical molecular weight distributions could be prepared even at very high conversions provided [M] and [I] remain constant throughout the polymerization. This condition can be fulfilled by continuously adding a mixed monomer/inifer feed at a sufficiently low constant rate to a coinitiator charge, making certain that the rate of monomer/inifer addition and that of monomer/inifer consumption are equal over the course of the polymerization. 

Conversely, since peaks are superimposed on a ramped baseline, the peaks obtained during differential pulse voltammetry are not square since the plateau of the peak increases at the constant rate of d /df that the baseline follows. 

At a constant pace (i.e. constant power output) and dierefore constant rate of ATP utilisation, the rate of glycogen breakdown decreases with time. This is due to the increase in blood supply to die muscle (vasodilation) which increases oxygen supply so that ATP generation from complete oxidation of glycogen, rather than conversion of glycogen to lactic acid, becomes increasingly more important. 

We win next develop expressions for X,(t) and the residence time Ts for complete reaction of the sohd in terms of parameters of systems for (hfiferent approximations of rate parameters. In a continuous reactor sohd particles are fed into reactor at a constant rate, and each transforms as a function of the time it has been in the reactor. Therefore, we would have to use the probabihty distribution function to compute the average conversion,... 

The effects of several reaction variables on the activity and selectivity of the iodide-promoted catalyst in nonreactive solvents have been studied (190-191). These reactions have been generally performed with relatively low conversion under conditions where constant rates to the primary products are observed secondary reactions are usually minor. Increases in... 

Closely related to the problem of the structure of the effective rate constant is the above-mentioned problem of the compensation mechanism. Without a knowledge of this mechanism, it would be impossible to understand why in such a complicated epoxyamine system one can frequently observe relatively simple kinetic principles, viz., a weak dependence of the effective rate constant on conversion, simple dependences of the initial rate on reagent concentrations, a linear dependence of the total heat release on conversion and almost equal values of the heat release and enthalpy of the epoxy ring opening. The latter two aspects have been discussed above, whereas the first two problems can be understood, say, from a consideration of a noncatalytic reaction. 

Temperature Effect. The rate of hydroperoxide conversion depends on the reaction temperature. It is slow at temperatures below 90°C. but increases rapidly with increasing temperature. However, the epoxide yield at constant hydroperoxide conversion tends to decrease at temperatures greater than optimum (Table III). 

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