Kinetic data estimation

Predicting the solvent or density dependence of rate constants by equation (A3.6.29) or equation (A3.6.31) requires the same ingredients as the calculation of TST rate constants plus an estimate of and a suitable model for the friction coefficient y and its density dependence. While in the framework of molecular dynamics simulations it may be worthwhile to numerically calculate friction coefficients from the average of the relevant time correlation fiinctions, for practical purposes in the analysis of kinetic data it is much more convenient and instructive to use experimentally detemiined macroscopic solvent parameters. 

Hofmann, Tndustrial process kinetics and parameter estimation , in ACS Advances in Chemlstiy, 109, 519-534 (1972) "Kinetic data analysis and parameter estimation , in de Lasa, ed.. Chemical Reactor De.sign and Technology, Martinus Nijhoff, 1986, pp. 69-105. 

Casado et al. have analyzed the error of estimating the initial rate from a tangent to the concentration-time curve at t = 0 and conclude that the error is unimportant if the extent of reaction is less than 5%. Chandler et al. ° fit the kinetic data to a polynomial in time to obtain initial rate estimates. 

The procedure, in analyzing kinetic data by numerical integration, is to postulate a reasonable kinetic scheme, write the differential rate equations, assume estimates for the rate constants, and then to carry out the integration for comparison of the calculated concentration-time curves with the experimental results. The parameters (rate constants) are adjusted to achieve an acceptable fit to the data. Carpen-(ej-48. pp. 76-81 some numerical calculations. Farrow and Edelson and Porter... 

That is, ipKa = pH at the point where Eq. (6-66) holds. Because the larger of the two constants is usually much greater than the smaller one, this often may be interpreted that pA o = pH when k = k J2 (see Fig. 6-10). Graphical methods for estimating K by using all of the kinetic data are considered later. 

The dissociation constant is most accurately estimated from kinetic data when all of the data points are used in the evaluation. There are several ways to do this. The Henderson-Hasselbalch equation... 

When estimates of k°, k, k", Ky, and K2 have been obtained, a calculated pH-rate curve is developed with Eq. (6-80). If the experimental points follow closely the calculated curve, it may be concluded that the data are consistent with the assumed rate equation. The constants may be considered adjustable parameters that are modified to achieve the best possible fit, and one approach is to use these initial parameter estimates in an iterative nonlinear regression program. The dissociation constants K and K2 derived from kinetic data should be in reasonable agreement with the dissociation constants obtained (under the same experimental conditions) by other means. 

The development of methods for the kinetic measurement of heterogeneous catalytic reactions has enabled workers to obtain rate data of a great number of reactions [for a review, see (1, )]. The use of a statistical treatment of kinetic data and of computers [cf. (3-7) ] renders it possible to estimate objectively the suitability of kinetic models as well as to determine relatively accurate values of the constants of rate equations. Nevertheless, even these improvements allow the interpretation of kinetic results from the point of view of reaction mechanisms only within certain limits ... 

Wilkinson s method for the estimation of the reaction order is illustrated for first-order (left) and second-order (right) kinetic data. The first-order reaction is the decomposition of diacetone alcohol (Table 2-3 and Fig. 2-4) data to about 50 percent reaction are displayed. The slope gives an approximate order of 1.2. The second-order data (Fig. 2-2) give a precise fit to Eq. (2-59) and an order of two exactly. 

Slightly removed from this in rigor is the use of a substituent to make a pure exchange into a net chemical reaction. No isotopic label is then needed. For example, the first reliable estimate of the rate constant for the exchange of ferrocenium ions and ferrocene was made on the basis of kinetic data for processes such as... 

The kinetic data fit a mechanism of successive reactions sequent to only one primary ion equally well, provided that the first step can yield 1.37 methyl radical/100 e.v. and is pressure dependent and that the succeeding pressure independent step yields methyl radicals with a lesser efficiency and leads to a pressure independent yield of 0.58 methyl radicals/100 e.v. If the first step is either Reaction 9a or Reaction 17b, one can once more use the rate constant ratios given earlier to estimate the yields of the possible primary precursor ions. Hence, either G-(C2H2+) = 1.9 ions/100 e.v., or G(C2H4+) = 1.52 ions/100 e.v. The... 

A new approach for obtaining kinetic data at short reaction times utilizing a static mixer coupled to the end of an extruder was introduced. This approach yielded kinetic data for an estimated 18.6 s reaction time and is potentially capable of much smaller times. 

Comparison of the kinetic data for 37 with those with the same enzyme and conduritol C fra 5-epoxide (27, see Table XI) reveals an estimated 50-fold higher reactivity of 37 if based on ki(max)/Ki. (This estimate takes account of the different temperatures employed, namely, 37° in Ref. 178 and 25 ° for the data in Table XI, re-evaluation of the data given in gave... 

The kinetic parameters estimated by the experimental data obtained frmn the honeycomb reactor along with the packed bed flow reactor as listed in Table 1 reveal that all the kinetic parameters estimated from both reactors are similar to each other. This indicates that the honeycomb reactor model developed in the present study can directly employ intrinsic kinetic parameters estimated from the kinetic study over the packed-bed flow reactor. It will significantly reduce the efibrt for predicting the performance of monolith and estimating the parameters for the design of the commercial SCR reactor along with the reaction kinetics. 

The reaction between Fe(IlI) and Sn(Il) in dilute perchloric acid in the presence of chloride ions is first-order in Fe(lll) concentration . The order is maintained when bromide or iodide is present. The kinetic data seem to point to a fourth-order dependence on chloride ion. A minimum of three Cl ions in the activated complex seems necessary for the reaction to proceed at a measurable rate. Bromide and iodide show third-order dependences. The reaction is retarded by Sn(II) (first-order dependence) due to removal of halide ions from solution by complex formation. Estimates are given for the formation constants of the monochloro and monobromo Sn(II) complexes. In terms of catalytic power 1 > Br > Cl and this is also the order of decreasing ease of oxidation of the halide ion by Fe(IlI). However, the state of complexing of Sn(ll)and Fe(III)is given by Cl > Br > I". Apparently, electrostatic effects are not effective in deciding the rate. For the case of chloride ions, the chief activated complex is likely to have the composition (FeSnC ). The kinetic data cannot resolve the way in which the Cl ions are distributed between Fe(IlI) and Sn(ll). 

Many kinetic data can be collected from ARC experiments the exothermic onset temperature, the rate of temperature rise, the rate of pressure rise, and the apparent activation energy. The basic data obtained are, however, thermodynamic properties the adiabatic temperature rise, the maximum pressure potential, the quantity of gaseous products generated, and the heat of reaction can be obtained in one run. The heat of reaction is estimated from ... 

Figure 2.40. Parameter estimation example using ESL to fit kinetic data to a model, smooth curve with squares is the fitted model and the irregular curve is the data.

Bellman, R., J. Jacquez, R. Kalaba, and S. Schwimmer, "Quasilinearization and the Estimation of Chemical rate Constants from Raw Kinetic Data", Math. Biosc. 7,71-76(1967). 

Figure 3.8. Kinetic data from molecular beam experiments with NO + CO mixtures on a Pd/MgO(100) model catalyst [70]. The upper panel displays raw steady-state C02 production rates from the conversion of Pco = PN0 = 3.75 x 10-8 mbar mixtures as a function of the sample temperature on three catalysts with different average particle size (2.8, 6.9, and 15.6 nm), while the bottom panel displays the effective steady-state NO consumption turnover rates estimated by accounting for the capture of molecules in the support. After this correction, which depends on particle size, the medium-sized particles appear to be the most active for the NO conversion. (Reproduced with permission from Elsevier, Copyright 2000).

The RHSE has the same limitation as the rotating disk that it cannot be used to study very fast electrochemical reactions. Since the evaluation of kinetic data with a RHSE requires a potential sweep to gradually change the reaction rate from the state of charge-transfer control to the state of mass transport control, the reaction rate constant thus determined can never exceed the rate of mass transfer to the electrode surface. An upper limit can be estimated by using Eq. (44). If one uses a typical Schmidt number of Sc 1000, a diffusivity D 10 5 cm/s, a nominal hemisphere radius a 0.3 cm, and a practically achievable rotational speed of 10000 rpm (Re 104), the mass transfer coefficient in laminar flow may be estimated to be ... 

The application of the calculated reaction enthalpy allows us to estimate the kinetic chain length (approximately 30) and other kinetic data (reaction rate, final conversion, inhibition time) of the crosslinking reaction. The reaction rate (dx/dt) of this process is a function of the light intensity, the exposure time, of the thiol content of the system (see Fig. 1) and also of the photoinitiator used. The final degree of conversion of the double bonds is generally high (80 - 100 %). 

Our data can be used to estimate the effective temperatures reached in each site through comparative rate thermometry, a technique developed for similar use in shock tube chemistry (32). Using the sonochemical kinetic data in combination with the activation parameters recently determined by high temperature gas phase laser pyrolysis (33), the effective temperature of each site can then be calculated (8),(34) the gas phase reaction zone effective temperature is 5200 650°K, and the liquid phase effective temperature is 1900°K. Using a simple thermal conduction model, the liquid reaction zone is estimated to be 200 nm thick and to have a lifetime of less than 2 usee, as shown in Figure 3. 

Chemical reactivity differences may be calculated if for the transition state of a rate-determining step of a reaction a structural model can be given which is describable by a force field with known constants. We give only two examples. Schleyer and coworkers were able to interpret quantitatively a multitude of carbonium-ion reactivities (63, 111) in this way. Adams and Kovacic studied the pyrolysis of 3-homoadamantylacetate (I) at 550 °C and considered as transition state models the two bridgehead olefins II and III (112). From kinetic data they estimated II to be about 2 kcal mole-1 more favourable than III. 

Up to now only limited kinetic data and thus rate models (and even mechanistic details) of aqueous phase operation are available. Thus, in many cases only estimates and experimentally found data are at the disposal for reaction engineers work (e.g.[25]). The state of the art of the hydroformylation of higher alkenes (>C -) comprises additions of supplementary solvents/diluents or extraction fluids, surface-active agents (detergents), intensity and mode of stirring ([22b], power of agitation (cf. Figure 5.5) operation in... 

To estimate costs for the liquid-liquid biphasic hydroformylation using ionic liquids, a process was designed for the production of 100,000 tons per year of nonanal. The use of ionic liquids in hydroformylation catalysis is a fairly new technology and exact kinetic data are scarce, thus the TOFs reported for the Rh-sulfoxantphos system [80] have been used to determine catalyst inventory and reactor dimensions. In a similar way the plant design for the SILP process for a production capacity of 100,000 tons per year of butanal has been derived based on preliminary literature results [68]. The process flow sheets for both process variations are shown in Figures 7.12 and 7.13. 

---