Maximum reaction rate

The exact composition of the liquid with respect to hydrogen cannot be guessed. Consequently, we can only estimate either transfer or reaction maximum rates and fluxes. From Eq. (12), the maximum mass transfer rate YI 1X (mol s ) is obtained when the reaction is so fast that the bulk concentration of dissolved hydrogen is zero (Ch,l= 0), as given in Eq. (18). 

A theory of KIE for multistep enzymatic reactions was developed by Cleland and Northrop (1999). It is obvious that when the barrier of the chemical reaction step is at least several kcal/mole above all others, the step is essentially step- limiting. The isotope in this step is fully expressed in the experimental ratio V/K, where V and K are the reaction maximum rate and Michaelis constant, respectively. If the chemical step does not have the highest barrier, the isotope effect can be partially or fully suppressed. For the mechanism ... 

Michaelis constant An experimentally determined parameter inversely indicative of the affinity of an enzyme for its substrate. For a constant enzyme concentration, the Michaelis constant is that substrate concentration at which the rate of reaction is half its maximum rate. In general, the Michaelis constant is equivalent to the dissociation constant of the enzyme-substrate complex. 

For the nitration of the very weak base, acetophenone, there is reasonable agreement between observed and calculated activation parameters, and there is no doubt that nitration of the free base occurs at acidities below that of maximum rate. In this case the equilibrium concentration of free base is much greater than in the examples just discussed and there is no question of reaction upon encounter. ... 

By protodetritiation of the thiazolium salt (152) and of 2 tritiothiamine (153) Kemp and O Brien (432) measured a kinetic isotope effect, of 2.7 for (152). They evaluated the rate of protonation of the corresponding yiides and found that the enzyme-mediated reaction of thiamine with pyruvate is at least 10 times faster than the maximum rate possible with 152. The scale of this rate ratio establishes the presence within the enzyme of a higher concentration of thiamine ylide than can be realized in water. Thus a major role of the enzyme might be to change the relative thermodynamic stabilities of thiamine and its ylide (432). 

Batch readers—optimum residence time for series and complex reactions, minimum cost, optimal operating temperature, and maximum rate of reaction... 

The Michaelis constant is equal to substrate concentration at which the rate of reaction is equal to one-half the maximum rate. The parameters and characterize the enzymatic reactions that are described by Michaelis-Menten kinetics. is dependent on total... 

Sulphur Trioxide (SO2 -I- O2) Linear reaction rates are observed due to phase boundary control by adsorption of the reactant, SO3. Maximum rates of reaction occur at a SO2/O2 ratio of 2 1 where the SO3 partial pressure is also at a maximum. With increasing 02 S02 ratio the kinetics change from linear to parabolic and ultimately, of course, approach the behaviour of the Ni/NiO system. At constant gas composition and pressure, the reaction also reaches a maximum with increasing temperature due to the decreasing SO3 partial pressure with increasing temperature, so that NiS04 formation is no longer possible and the reaction rate falls. 

Imine and enamine formation are slow at both high pH and low pH but reach a maximum rate at a weakly acidic pH around 4 to 5. For example, the profile of pH versus rate shown in Figure 19.9 for the reaction between acetone and hydroxylamine, NH2OH, indicates that the maximum reaction rate is obtained at pH 4.5. 

Fig. 1. Generalized a—time plot summarizing characteristic kinetic behaviour observed for isothermal decompositions of solids. There are wide variations in the relative significance of the various stages (distinguished by letter in the diagram). Some stages may be negligible or absent, many reactions of solids are deceleratory throughout. A, initial reaction (often deceleratory) B, induction period C, acceleratory period D, point of inflection at maximum rate (in some reactions there is an appreciable period of constant rate) E, deceleratory (or decay) period and F, completion of reaction.

The maximum rate of decomposition and associated values of a and T(=Tm) are noted. Early use of the method with first-order reactions [572] excited undue controversy since, in some cases, it was mistakenly concluded that the maximum reaction rate occurs at the peak temperature. For first-order reactions... 

Relationship between reaction order, n, and the value of a corresponding to maximum rate, a, during non-isothermal rate processes... 

A minor component, if truly minute, can be discounted as the reactive form. To continue with this example, were KCrQ very, very small, then the bimolecular rate constant would need to be impossibly large to compensate. The maximum rate constant of a bimolecular reaction is limited by the encounter frequency of the solutes. In water at 298 K, the limit is 1010 L mol-1 s"1, the diffusion-controlled limit. This value is derived in Section 9.2. For our immediate purposes, we note that one can discount any proposed bimolecular step with a rate constant that would exceed the diffusion-controlled limit. 

It was found that the maximum rate of polymerization occurred at (NRe)e 5000. This shift in (NRe) corresponds to the shift of the laminar turbulent transition in a helically coiled tube as reported by White ( ). Further, no plugging of this reactor, under any conditions of operation, was noticed. The reaction mechanism appears to be very close to the Smith-Ewart model, although conversions were not always a3 complete as expected. 

Mutations in bacteria and mammalian cells (including some that result in human disease) have supported these conclusions. Facilitated diffusion and active transport resemble a substrate-enzyme reaction except that no covalent interaction occurs. These points of resemblance are as follows (1) There is a specific binding site for the solute. (2) The carrier is saturable, so it has a maximum rate of transport (V Figure 41-11). (3) There is a binding constant (Al) ) for the solute, and... 

The rate of oxidation of mercury (I) by Ce(IV) is slow in any medium but 3.6 times faster ini M perchloric acid than in 1 M sulphuric acid, achieving a maximum in the former medium at 4 Af, and then decreasing . Sulphate ion retards the reaction the rate increase observed in HCIO4 solutions is ascribed to the formation of less complexed, more reactive species of Ce(IV). The kinetics of the reaction between Hg(I) perchlorate and Ce(IV) sulphate have been examined in 2.0 M perchloric acid at 50.0 °C, under which conditions the rate law... 

The reaction is very slow in acid solution, and has a maximum rate near pH 9. It is quite rapid, however, in the high pH region in which Stewart and Van der Linden found evidence for two reaction paths. At pH > 13 and at low reactant concentrations, the kinetics are... 

This is an example of a reversible reaction the standard electrode potential of the 2PS/PSSP + 2c couple is zero at pH 7. The oxidation kinetics are simple second-order and the presence of a radical intermediate (presumably PS-) was detected. Reaction occurs in the pH range 5 to 13 with a maximum rate at pH 6.2, and the activation energy above 22 °C is zero. The ionic strength dependence of 2 afforded a value for z Zg of 9 from the Bronsted relation... 

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