Experimental rate constant calculation

The recipe (5.58) is even more sensitive to the high-frequency dependence of kjj than similar criterion (5.53), which was used before averaging over kinetic energy of collisions E. It is a much better test for validity of microscopic rate constant calculation than the line width s j-dependence, which was checked in Fig. 5.6. Comparison of experimental and theoretical data on ZR for the Ar-N2 system presented in [191] is shown in Fig. 5.7. The maximum value Zr = 22 corresponding to point 3 at 300 K is determined from the rate constants obtained in [220],... 

Pulsed source techniques have been used to study thermal energy ion-molecule reactions. For most of the proton and H atom transfer reactions studied k thermal) /k 10.5 volts /cm.) is approximately unity in apparent agreement with predictions from the simple ion-induced dipole model. However, the rate constants calculated on this basis are considerably higher than the experimental rate constants indicating reaction channels other than the atom transfer process. Thus, in some cases at least, the relationship of k thermal) to k 10.5 volts/cm.) may be determined by the variation of the relative importance of the atom transfer process with ion energy rather than by the interaction potential between the ion and the neutral. For most of the condensation ion-molecule reactions studied k thermal) is considerably greater than k 10.5 volts/cm.). 

In Table III we compare for several reactions the experimental rate constants with rate constants calculated on the basis of ion-induced dipole interactions only from the relation (4) ... 

For the remaining systems ion-permanent dipole interactions should be negligible. In these systems the experimental rate constants are considerably lower than the calculated values, and this undoubtedly reflects the fact that other reaction channels are available to the collision complex. It might be noted that many of the reactions are of the type ... 

The reaction rate constant for each elementary reaction in the mechanism must be specified, usually in Arrhenius form. Experimental rate constants are available for many of the elementary reactions, and clearly these are the most desirable. However, often such experimental rate constants will be lacking for the majority of the reactions. Standard techniques have been developed for estimating these rate constants.A fundamental input for these estimation techniques is information on the thermochemistry and geometry of reactant, product, and transition-state species. Such thermochemical information is often obtainable from electronic structure calculations, such as those discussed above. 

SOLUTION. Kinetic parameters are estimated by using the least squares technique, by minimizing the function defined as squared residuals between calculated and experimental rate constants ... 

We note at this point that the nonadiabatic-transition state method used here (6,19,77) is not expected to be able to give quantitative agreement with experimental rate constants. There are too many factors that are treated approximately (or not at all) in this theory for such performance to be possible. One of the key difficulties is that calculated rate constants are very sensitive to the accuracy of the potential energy surface at room temperature, an error of lkcalmol-1 on the relative energy of the MECP relative to reactants will equate, roughly speaking, to an error by a factor of five on the calculated rate constant. Even though we... 

This reaction is endothermic, its enthalpy is AH=DR K 327.6 kJ mol-1. The experimental rate constants of these reactions are collected in Table 3.10 and those calculated by the IPM method [168] in Table 3.11. 

Bun ton et al., 1981b). Estimation of the extent of micellar binding becomes a non-problem if the organic iori is very hydrophobic, because then it is completely micellar bound under essentially all conditions (Martinek et al., 1977). Perhaps for this reason, there are many examples of good fits between experimental rate constant-surfactant profiles and those calculated using (5), (6) or equivalent expressions. 

Although we cannot clearly determine the reaction order from Figure 3.9, we can gain some insight from a residual plot, which depicts the difference between the predicted and experimental values of cA using the rate constants calculated from the regression analysis. Figure 3.10 shows a random distribution of residuals for a second-order reaction, but a nonrandom distribution of residuals for a first-order reaction (consistent overprediction of concentration for the first five datapoints). Consequently, based upon this analysis, it is apparent that the reaction is second-order rather than first-order, and the reaction rate constant is 0.050. Furthermore, the sum of squared residuals is much smaller for second-order kinetics than for first-order kinetics (1.28 X 10-4 versus 5.39 xl0 4). 

One of the innovations in this work was that the author calculated wherever necessary and possible the original experimental rate-constants, and this enabled him to see kinetic irregularities that had been unrecognised or at least had not been reported by the original workers and in many cases these eventually provided new insights by which the validity of their claims could be assessed. 

From the data provided by the systematic experimental study at standardized conditions the free energy of activation (AG exp.) was calculated from the experimental rate constant and compared to calculated AG values. Two different basis sets have been employed in the DFT calculations the split valence double- (DZ) basis set 6-31G(d) with a triple- (TZ) [44, 45] valence basis set for manganese (we will refer to this combination as basis set I (BS1)) and the triple- basis set 6-311+G(d,p), which will be denoted basis set n (BS2). The BSl-results for transition states and intermediates are shown in Table 5, a comparison of the free activation energies is shown in Figure 8 [46],... 

The reaction of OH with HFCs has attracted interest. The temperature dependence of the fast initial H abstraction by HO in HFCs has been calculated using ab initio methods. Rate constants calculated using HF and MP2(G-31G(d)) were found to be substantially greater than those determined experimentally. In other work investigating reactions of OH with HFCs, rate constants for its reactions with HFC-245cb (MeCFaCFs) and other fluoroalkenes have been determined. ... 

Another common approach consists of the comparison between the experimental rate constants and theoretical values calculated by the procedure developed by Marcus (1956), Marcus and Sutin (1985) as well as Hush (1958). This classical procedure is used widely. Premsingh et al. (2004) gave the relevant references and described a detailed procedure to analyze the ion-radical reaction between anilines and chromium (V) complexes of azomethyne derivatives. Lepage et al. (2003) studied transformation of para-substituted thioanisoles to corresponding methylarylsulfoxides... 

The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed for orienting molecules prior to collision (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) bmte force orientation of polar molecules in extremely strong electric fields. Several chemical reactions have been studied with one of the reagents oriented prior to collision. ... 

It is apparent from Table II that variations in the experimental rate constants (k) are essentially controlled by the Henry s law constant, in agreement with the two-film theory prediction. A plot of kys. H for the five pesticides gave an intercept of 5.4 x 10 hr, a slope of 6.9 x 10 mol/(hr atm m" ), and a correlation coefficient of 0.969. Thus, it seems that Henry s law values could be used to predict relative volatilization rates of the pesticides, and an absolute volatilization rate for one pesticide can be calculated if the volatilization rate is known for another and Henry s law constants are known for both ... 

Equation 10 does not provide an adequate representation of the data. First, the rate constants calculated using this equation for experiments carried out at a pH greater than 10 are 15-20% smaller than the experimentally determined values. A second, and perhaps more compelling point is that Equation 10 does not correctly predict the dependence of rate upon Ns concentration in the more alkaline solutions. In qualitative terms what is observed is that the points in a plot of k vs. (N3-) approach linearity as the alkalinity of the solution is increased. A plot of the data in Table II obtained at pH 10.1 exhibits much less curvature than that presented in Figure 1. In a similar plot of the data in Table III obtained at a hydroxide ion concentration of 9 x 10r3M there is no detectable deviation from linearity. 

Experimental rate constants (kH,) for the breakdown of 2-alkyl-2-hydroxy-1,3-dioxolans and calculated rate constant (kH.) for the breakdown of methyl hemiorthoacetates... 

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