Hydrolysis rate equation

Table 2 Structural effects on base hydrolysis rates (equation 7)...

There is also a term in the hydrolysis rate equation which is independent of the acidity, but first-order in [BF4 ] for which... 

The experimental and mathematical models were divided into two hierarchical steps, as seen in Fig. 5. First, hydrolysis experiments were conducted, and the hydrolysis time profile was matched to hydrolysis rate equations. A separate hydrolysis-only model was used to match the hydrolysis data to Michaelis-Menten based kinetics and to solve for unknown parameters. Second, SSF experiments were conducted using identical enzyme loading, and these datasets were matched to a complete SSF model. The SSF model incorporated the hydrolysis parameters from the first step and was used to solve for the unknown fermentation parameters using Monod-based kinetics. 

This mechanism leads to the rate equation (eq. 3) for hydrolysis and to an analogous expression for the esterification (13) ... 

FIG. 7-2 Linear analysis of catalytic rate equations, a), (h) Sucrose hydrolysis with an enzyme, r = 1curve-fitted with a fourth-degree polynomial and differentiated for r — (—dC/dt). Integrated equation,... 

An instance of autocatalysis is the hydrolysis of methyl acetate, which is catalyzed by product acetic acid, A C. The rate equation may be... 

It is otherwise for complex reactions, for which the rate equation may or may not be simply related to the overall stoichiometric reaction. For example, the rate equation for the alkaline hydrolysis of ethyl acetate, which is a complex reaction (see Section 1.2),... 

In deciding whether to write an elementary reaction as either a reversible or an irreversible reaction, we take the practical view that if the reverse reaction is negligibly slow on the exp>erimental time scale, the reaction is essentially irreversible. Consider the alkaline hydrolysis of an ester, for which the rate equation is... 

If a pH-rate curve does not exhibit an inflection, then very probably the substrate does not undergo an ionization in this pH range. The kinds of substrates that often lead to such simple curves are nonionizable compounds subject to hydrolysis, such as esters and amides. Reactions other than hydrolysis may be characterized by similar behavior if catalyzed by H or OH . The general rate equation is... 

This compound undergoes hydrolysis of the amide group intramolecularly catalyzed by the neighboring carboxylic acid group. The rate equation, in the pH range 1—... 

Analogous, but slightly different, is the treatment of the acid-base equilibria and the basic hydrolysis rates of the phthalimids (19). In both of these cases, the two paths to the reaction site are equivalent, hence pi and po of Eq. (3) are equal, and the equation reduces to ... 

The global rate of the process is r = rj + r2. Of all the authors who studied the whole reaction only Fang et al.15 took into account the changes in dielectric constant and in viscosity and the contribution of hydrolysis. Flory s results fit very well with the relation obtained by integration of the rate equation. However, this relation contains parameters of which apparently only 3 are determined experimentally independent of the kinetic study. The other parameters are adjusted in order to obtain a straight line. Such a method obviously makes the linearization easier. 

An irreversible, elementary reaction must have Equation (1.20) as its rate expression. A complex reaction may have an empirical rate equation with the form of Equation (1.20) and with integral values for n and w, without being elementary. The classic example of this statement is a second-order reaction where one of the reactants is present in great excess. Consider the slow hydrolysis of an organic compound in water. A rate expression of the form... 

Then again, if the hydrolysis in aqueous solution of the alkyl halide, RHal, is found to follow the rate equation,... 

Thus for hydrolysis in 50% aqueous acetone, a mixed second and first order rate equation is observed for phenylchloromethane (benzyl chloride, 10)—moving over almost completely to the SV1 mode in water alone. Diphenylchloromethane (11) is found to follow a first order rate equation, with a very large increase in total rate, while with triphenylchloromethane (trityl chloride, 12) the ionisation is so pronounced that the compound exhibits electrical conductivity when dissolved in liquid S02. The main reason for the greater promotion of ionisation—with consequent earlier changeover to the SW1 pathway in this series—is the considerable stabilisation of the carbocation, by delocalisation of its positive charge, that is now possible ... 

This is like the A1 mechanism except that the protonated substrate SH +, instead of reacting alone, reacts with something else in the rate-determining step, a nucleophile or a base, written as Nu in equation (41). A typical example of this very common mechanism is ester hydrolysis, say of the methyl esters in equation (42), where SH+ reacts with two water molecules in the slow step,29 giving the neutral tetrahedral intermediate [5] directly. Reasonably enough, the rate equations obtainable are very similar to those for the A1 mechanism, with the addition of an extra aNu term, see equation (43) ... 

In the case where the anaerobic processes take place under conditions where consumption of Ss by the sulfate-reducing biomass and the fermenting biomass must be considered, Equation (7.10) expresses the total anaerobic hydrolysis rate. This equation is based on the assumption that methane formation in sewers without sediment normally can be neglected (Section 3.2.2). 

The hydrolysis of ethyl acetate (B) with an alkaline hydroxide (A] non-aqueous solutions is believed to have the third order rate equation... 

Furthermore, although the rates of addition and loss may differ at each end (i.e., the transition states for the individual association-dissociation reactions may depend on the polarity of protomer-polymer interactions), the initial state (protomer + MT ) and the final state (MT +i) are independent of the pathway for protomer addition. This result is true because addition or loss of a protomer at either end leads to structurally indistinguishable polymers. Thus, the energetics of the reactions at each end are the same, and Ki equals for the case of no nucleotide hydrolysis accompanying assembly. We may then reexpress the rate equations for protomer addition or loss to the two ends in the following manner ... 

Wegner also treated the case wherein assembly is coupled to nucleotide hydrolysis. Here, we consider a slight modification of his model to deal with the microtubule process. Normally, the concentration of GTP is maintained by use of a GTP-regenerating system (MacNeal et ai, 1977), and the system at the steady-state plateau of assembly can be described as in Scheme II. Under these conditions, the assembly-disassembly reactions are no longer reversible, and the primed rate constants are used to emphasize that we are dealing with a different case. The rate equations for the two ends are now given as ... 

Variations in pH induce acid-base mediated hydrolysis. For base-catalyzed hydrolysis, for example, the rate equation for an organic contaminant is... 

Samples were prepared and analyzed as reported previously (18). Because of slow concentration decreases with time, low volatilization rates relative to hydrolysis rates in some cases, and small artificial losses of pesticide due to repeated water sampling, the most accurate method of determining volatilization rate constants was to divide the average pesticide concentration for that day into the average volatilization rate over the same period (Equation 1). Rate constants for the seven days were averaged. The entire experiment was performed in triplicate. 

Generalized Rate Equations. This last reaction is typical of a large class of reactions which may proceed simultaneously by several parallel paths. The rate can be expressed as the sum of several contributions from the uncatalyzed and catalyzed paths. The overall rate for the hydrolysis of an amino acid ester in the presence of a metal salt may be expressed as... 

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