Magnitude of Individual Rate Constants

The above explanation of autoacceleration phenomena is supported by the manifold increase in the initial polymerization rate for methyl methacrylate which may be brought about by the addition of poly-(methyl methacrylate) or other polymers to the monomer.It finds further support in the suppression, or virtual elimination, of autoacceleration which has been observed when the molecular weight of the polymer is reduced by incorporating a chain transfer agent (see Sec. 2f), such as butyl mercaptan, with the monomer.Not only are the much shorter radical chains intrinsically more mobile, but the lower molecular weight of the polymer formed results in a viscosity at a given conversion which is lower by as much as several orders of magnitude. Both factors facilitate diffusion of the active centers and, hence, tend to eliminate the autoacceleration. Final and conclusive proof of the correctness of this explanation comes from measurements of the absolute values of individual rate constants (see p. 160), which show that the termination constant does indeed decrease a hundredfold or more in the autoacceleration phase of the polymerization, whereas kp remains constant within experimental error. 

A quantitative expression developed by Albery and Knowles to describe the effectiveness of a catalyst in accelerating a chemical reaction. The function, which depends on magnitude of the rate constants describing individual steps in the reaction, reaches a limiting value of unity when the reaction rate is controlled by diffusion. For the interconversion of dihydroxacetone phosphate and glyceraldehyde 3-phosphate, the efficiency function equals 2.5 x 10 for a simple carboxylate catalyst in a nonenzymic process and 0.6 for the enzyme-catalyzed process. Albery and Knowles suggest that evolution has produced a nearly perfect catalyst in the form of triose-phosphate isomerase. See Reaction Coordinate Diagram... 

Changes in pH also affect the magnitude of individual rate expressions. Wollast (28) found for K-feldspar a progressive decrease in the parabolic rate constant for silica with increases in pH over the range 4-10 at 25 C. In investigating magnesium silicate dissolution at 25 C, Luce and others ( ) found a slight... 

Obviously, the relative magnitudes of the rate constants for the two LHD reactions and of that for the cross-coupling of the two different radical anions will affect the efficiency of MHC production. Even for equal concentrations of the two radical anions, the three individual rate constants must be similar to result in the statistical distribution of MHC and LHD products. 

Parameter estimation, that is the extraction of individual rate constants, was accomplished by a command ESTIMATE. Here the rate constants are varied until the best fit between the observed and calculated values are obtained. With the rate constants in this system covering five orders of magnitude in range, and somewhat limited amount of concentration data, it was often necessary to change the rate constants after the ESTIMATE procedure. This is done interactively through repeated use of SET, START, and PLOT commands. One such plot is shown in Figure 2. The lines in Figure 2 represent the calculated values, whereas the points represent the observed values. Arrhenius parameters for individual reactions are then calculated from the rate constants at three temperatures. These constants are then used in the REACTOR model. 

Many organic reactions consist of a series of steps involving several intermediates. The overall rate expression then depends on the relative magnitude of the rate constants for the individual steps. The relationship between a kinetic expression and a reaction mechanism can be appreciated by considering the several individual steps that constitute the overall reaction mechanism. The expression for the rate of any single step in a reaction mechanism contains a term for the concentration for each reacting species. Thus, for the reaction sequence ... 

It is apparent from Equation 2.5 that the overall rate constant for hydrolysis, k yd, depends on pH and the magnitude of the rate constants for the individual processes. Plots of log khyd versus pH are very useful for determining the contribution of the acid, neutral, and base terms for hydrolysis of a compound of interest at a specific pH. Figure 2.1 illustrates the log k[,yd versus pH plot for several chemicals of interest. These data demonstrate that the relationship between hydrolysis kinetics and pH is dependent on the nature of the hydrolyzable functional group. For example, over typical environmental pH values (4 to 8), the neutral hydrolysis rate term for ethylene oxide and methyl chloride will dominate. Only below pH 4 will the acid-catalyzed rate term for ethylene oxide contribute to the overall hydrolysis rate term. Likewise, base-catalyzed hydrolysis of ethylene oxide and methyl chloride will not... 

A number of procedures have been used to separate rate constants in enzyme mechanisms. We shall mention only briefly (a) rapid mixing techniques that can separate and measure almost all individual rate constants, (b) studies with alternative substrates that can provide information about the relative magnitude of some rate constants, and (c) work with alternative nucleophiles that can help to... 

Suppose that the reaction between A and B to give the intermediate is very fast and very favorable. If we have more B than A to start with, all the A is converted instantly into the intermediate. If we re following P, what we observe is the formation of P from the intermediate with the rate constant k2. If we increase the amount of B, the rate of P formation won t increase as long as there is enough B around to rapidly convert all the A to the intermediate. In this situation, the velocity of P formation is independent of how much B is present. The reaction is zero-order with respect to the concentration of B. This is a special case. Not all reactions that go by this simple mechanism are zero-order in B. It depends on the relative magnitudes of the individual rate constants. At a saturating concentration of substrate, many enzyme-catalyzed reactions are zero-order in substrate concentration however, they are still first-order in enzyme concentration (see Chap. 8). 

Since the structural factors and the solvent can affect the individual rate constants in ways which may differ in magnitude and sign, comparison of the experimental rate constants for various systems cannot always be straightforward. 

The value of 0 is a function of the magnitude of the individual rate constants for the formation of the surface complex and its conversion to a desorbable product and the pressure of the reacting gas. If the product of the rate constant for the formation of the surface-oxygen complex and the pressure of the reacting gas is large compared with the rate constant for... 

Other workers 67, 85-89) have determined over-all activation energies for the carbon-carbon dioxide reaction, but the values have been affected to some extent by mass-transport control. Workers 6, 39, 40, 41) have also determined activation energies for the individual rate constants in Equation (5) but do not agree on their magnitude. The values of activation energy reported for rate constant i vary from 26.5 41) to 61.5 kcal./ mole 40). 

It is important to realize that a steady state treatment on a mechanism does not necessarily generate a rate expression in which all the individual rate constants appear. If, as in the H2/Br2 reaction above, all the rate constants do appear in the rate expression, then it may be possible to determine the magnitudes of all the rate constants from a steady state analysis. But if they do not all appear, then the steady state treatment can only allow determination of those rate constants which do appear in the rate expression, and alternative ways will have to be found to give an independent determination of the remaining rate constants. 

---