Direct rate constant

In this case, the direct rate constants of H-abstraction could be determined... 

Values of for chloride ions have been determined by combining a rate constant for solvolysis ksoiv (for reactions for which the ionization step is ratedetermining) with a rate constant for the reverse reaction corresponding to recombination of cation and nucleophile. The latter constant may be found (a) by generating the cation by photolysis and measuring directly rate constants for reactions with nucleophiles or (b) from common ion rate depression of the solvolysis reaction coupled with diffusion-controlled trapping by a competing nucleophile used as a clock. 

An interesting observation is that in the presence of a large excess of Br, the reaction of AcO- with 15, Ar = An, is of a second order (71). This result is a rare example of an SN2(C+) route where the cation-anion recombination is rate-determining in a solvolysis reaction, and in principle, such a process could be used for obtaining directly rate constants for capture of vinyl cations. 

The sequence is closed. It is a simple one in the sense that each elementary step is first-order with respect to an active center in both directions. Rate constants for the Jth step are ki from left to right and from right to left. It is convenient to use the notation a< = A<(A,) and a < = The a s are... 

According to equation (2.98) if there is a strong inequality between direct rate constants k (addition of individual activated molecules to aggregates) and inverse rate constants q (molecules split-off from aggregates) q kM, i.e. the reverse process stops, and the modifieation of generating funetion F(z,t) has two oharaeteristie stages. 

Note that the sums are restricted to the portion of the frill S matrix that describes reaction (or the specific reactive process that is of interest). It is clear from this definition that the CRP is a highly averaged property where there is no infomiation about individual quantum states, so it is of interest to develop methods that detemiine this probability directly from the Scln-ddinger equation rather than indirectly from the scattering matrix. In this section we first show how the CRP is related to the physically measurable rate constant, and then we discuss some rigorous and approximate methods for directly detennining the CRP. Much of this discussion is adapted from Miller and coworkers [44, 45]. 

An important development in the quantum theory of scattering in the last 20 years has been the development of exact expressions which directly detennine either thennal rate constant lc(T) from the... 

In deriving the RRKM rate constant in section A3.12.3.1. it is assumed that the rate at which reactant molecules cross the transition state, in the direction of products, is the same rate at which the reactants fonn products. Thus, if any of the trajectories which cross the transition state in the product direction return to the reactant phase space, i.e. recross the transition state, the actual unimolecular rate constant will be smaller than that predicted by RRKM theory. This one-way crossing of the transition state, witii no recrossmg, is a fiindamental assumption of transition state theory [21]. Because it is incorporated in RRKM theory, this theory is also known as microcanonical transition state theory. 

VER in liquid O 2 is far too slow to be studied directly by nonequilibrium simulations. The force-correlation function, equation (C3.5.2), was computed from an equilibrium simulation of rigid O2. The VER rate constant given in equation (C3.5.3) is proportional to the Fourier transfonn of the force-correlation function at the Oj frequency. Fiowever, there are two significant practical difficulties. First, the Fourier transfonn, denoted [Pg.3041]

Studies by the group directed by Mayoral have been limited to Diels-Alder reactions of type A. When water was not included, the rate constants correlate with the solvent hydrogen-bond-donating capacity Upon inclusion of water the solvophobidty parameter, Sp, contributed significantly in... 

The catalytic effect on unimolecular reactions can be attributed exclusively to the local medium effect. For more complicated bimolecular or higher-order reactions, the rate of the reaction is affected by an additional parameter the local concentration of the reacting species in or at the micelle. Also for higher-order reactions the pseudophase model is usually adopted (Figure 5.2). However, in these systems the dependence of the rate on the concentration of surfactant does not allow direct estimation of all of the rate constants and partition coefficients involved. Generally independent assessment of at least one of the partition coefficients is required before the other relevant parameters can be accessed. 

When the dienophile does not bind to the micelle, reaction will take place exclusively in the aqueous phase so that the second-order rate constant of the reaction in the this phase (k,) is directly related to the ratio of the observed pseudo-first-order rate constant and the concentration of diene that is left in this phase. 

The results in table 2.6 show that the rates of reaction of compounds such as phenol and i-napthol are equal to the encounter rate. This observation is noteworthy because it shows that despite their potentially very high reactivity these compounds do not draw into reaction other electrophiles, and the nitronium ion remains solely effective. These particular instances illustrate an important general principle if by increasing the reactivity of the aromatic reactant in a substitution reaction, a plateau in rate constant for the reaction is achieved which can be identified as the rate constant for encounter of the reacting species, and if further structural modifications of the aromatic in the direction of further increasing its potential reactivity ultimately raise the rate constant above this plateau, then the incursion of a new electrophile must be admitted. 

A similar circumstance is detectable for nitrations in organic solvents, and has been established for sulpholan, nitromethane, 7-5 % aqueous sulpholan, and 15 % aqueous nitromethane. Nitrations in the two organic solvents are, in some instances, zeroth order in the concentration of the aromatic compound (table 3.2). In these circumstances comparisons with benzene can only be made by the competitive method. In the aqueous organic solvents the reactions are first order in the concentration of the aromatic ( 3.2.3) and comparisons could be made either competitively or by directly measuring the second-order rate constants. Data are given in table 3.6, and compared there with data for nitration in perchloric and sulphuric acids (see table 2.6). Nitration at the encounter rate has been demonstrated in carbon tetrachloride, but less fully explored. ... 

A plot against Hammett s cr-constants of the logarithms of the rate constants for the solvolysis of a series of Mz-substituted dimethylphenylcarbinyl chlorides, in which compounds direct resonance interaction with the substituent is not possible, yielded a reasonably straight line and gave a value for the reaction constant (p) of — 4 54. Using this value of the reaction constant, and with the data for the rates of solvolysis, a new set of substituent parameters (cr+) was defined. The procedure described above for the definition of cr+, was adopted for... 

The Restart checkbox can be used in conjunction with the explicit editing of a HIN file to assign completely user-specified initial velocities. This may be useful in classical trajectory analysis of chemical reactions where the initial velocities and directions of the reactants are varied to statistically determine the probability of reaction occurring, or not, in the process of calculating a rate constant. 

Curve-Fitting Methods In the direct-computation methods discussed earlier, the analyte s concentration is determined by solving the appropriate rate equation at one or two discrete times. The relationship between the analyte s concentration and the measured response is a function of the rate constant, which must be measured in a separate experiment. This may be accomplished using a single external standard (as in Example 13.2) or with a calibration curve (as in Example 13.4). 

Km for an enzymatic reaction are of significant interest in the study of cellular chemistry. From equation 13.19 we see that Vmax provides a means for determining the rate constant 2- For enzymes that follow the mechanism shown in reaction 13.15, 2 is equivalent to the enzyme s turnover number, kcat- The turnover number is the maximum number of substrate molecules converted to product by a single active site on the enzyme, per unit time. Thus, the turnover number provides a direct indication of the catalytic efficiency of an enzyme s active site. The Michaelis constant, Km, is significant because it provides an estimate of the substrate s intracellular concentration. 

This experiment describes the use of FIA for determining the stoichiometry of the Fe +-o-phenanthroline complex using the method of continuous variations and the mole-ratio method. Directions are also provided for determining the stoichiometry of the oxidation of ascorbic acid by dichromate and for determining the rate constant for the reaction at different pH levels and different concentration ratios of the reactants. 

In the presence of 6-iodo-l-phenyl-l-hexyne, the current increases in the cathodic (negative potential going) direction because the hexyne catalyticaHy regenerates the nickel(II) complex. The absence of the nickel(I) complex precludes an anodic wave upon reversal of the sweep direction there is nothing to reduce. If the catalytic process were slow enough it would be possible to recover the anodic wave by increasing the sweep rate to a value so fast that the reduced species (the nickel(I) complex) would be reoxidized before it could react with the hexyne. A quantitative treatment of the data, collected at several sweep rates, could then be used to calculate the rate constant for the catalytic reaction at the electrode surface. Such rate constants may be substantially different from those measured in the bulk of the solution. The chemical and electrochemical reactions involved are... 

In laser-impulse experiments with chlorophenyldiazirine the carbene could be observed by UV spectroscopy. On addition of defined amounts of alkene the rate of cyclopropanation was measured directly. The rate constants with various alkenes were (lO moF s ) 1-hexene, 1.3 ( )-2-pentene, 34 2-methyl-2-butene, 77 2,3-dimethyl-2-butene, 130 (80JA7576>. 

Given the foregoing assumptions, it is a simple matter to construct an expression for the transition state theory rate constant as the probability of (1) reaching the transition state dividing surface and (2) having a momenrnm along the reaction coordinate directed from reactant to product. Stated another way, is the equilibrium flux of reactant states across... 

Note that only Er, which is actually the sum of the reorganization energies for all degrees of freedom, enters into the high-temperature rate constant formula (2.62). At low temperature, however, in order to preserve E, one has to fit an additional parameter co, which has no direct physical sense for a real multiphonon problem. 

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