Theoretical rate constant

Then, using the assumption that the reaction rate is proportional to the concentration of the activated complex together with the empirical expression for the rate, the observed rate constant can be expressed in terms of the theoretical rate constant k3°... 

Theoretical rate constants are found to agree within 20% of the experimental value. Further refinements of this theory (Su et al., 1978). including conservation of angular momentum, bring the calculated rate constants within experimental error (Su and Bowers, 1979). 

Fig. 11.25 Experimental and theoretical rate constant for associative ionization of Nan + Na 3s atoms at T = 1000 K plotted against effective principal quantum number. Results for 17 < n < 27 (ref. 99) are scaled to absolute results obtained by Boulmer etal. for 5 < n s 15 (ref. 100). Experimental data ns levels ( ) np levels ( ) 2 2 levels (O). Theoretical...

Figure 9 shows the temperature dependence of the recovered kinetic rate coefficients for the formation (k bimolecular) and dissociation (k unimolecular) of pyrene excimers in supercritical CO2 at a reduced density of 1.17. Also, shown is the bimolecular rate coefficient expected based on a simple diffusion-controlled argument (11). The value for the theoretical rate constant was obtained through use of the Smoluchowski equation (26). As previously mentioned, the viscosities utilized in the equation were calculated using the Lucas and Reichenberg formulations (16). From these experiments we obtain two key results. First, the reverse rate, k, is very temperature sensitive and increases with temperature. Second, the forward rate, kDM, 1S diffusion controlled. Further discussion will be deferred until further experiments are performed nearer the critical point where we will investigate the rate parameters as a function of density. 

The k on the left-hand side of the equation is the theoretical rate constant. 

Table II shows the k and k values obtained. The table shows theoretical rate constants for diffusion-controlled association...

Table III shows the effects of charge density and the diameter of the anionic particles on the forward rate constants (k ) of the association with MATA-2. The charge density on the latex surface clearly affects the k values, which supports the importance of the electrostatic interaction on the association of oppositely charged latex particles. The claim, that the observed rate constant and the theoretical rate constant calculated for neutral particles (by equations (l)-(4)) agreed, would not be physically sound.

Matching of phenomenological and theoretical rate constant models... 

Experimental and Theoretical Rate Constants for Some Ion-Molecule Reactions"... 

This equation is an example of a rate equation and, more explicitly, it is the theoretical rate equation for the elementary reaction described by Equation 4.1. The quantity theory is the theoretical rate constant for the elementary reaction it has a value that is independent of the concentrations of reactants A and B. 

The theoretical rate constant for Reaction 4.1, although called a constant , does depend on temperature. Increasing the temperature increases, in most circumstances, the magnitude of A theory So carrying out a reaction at a higher temperature, but with the same initial concentrations of A and B, will be expected to result in an increase in the rate of reaction. This behaviour can be understood in a qualitative way in terms of a simple collision model. 

According to the simple collision model, the fraction of collisions with a kinetic energy sufficient to overcome the energy barrier to reaction increases with increasing temperature. This behaviour largely accounts for the temperature dependence of the theoretical rate constant. 

Although this system was somewhat idealized, relative to the hiPP, it is still a multicomponent system, due to the broad molecular weight distribution of the HDPE. Using some approximations (described in Reference 29), the theoretical rate constant for Ostwald ripening was calculated from Equation 12.4 and was OR = 3.6 X 10 cm s . The experimentally determined rate constant (K in Equation 12.3) was = 4.8 x 10 cm s. The agreement between the experimentally measured and the theoretically calculated rate constants is quite good. The ratio of these two rate constants is =1.3. This was taken as an indication... 

Table 12.4 Parameters for Calculation of Theoretical Rate Constants for Coarsening by Ostwald Ripening (Evaporation/Condensation) and Coalescence for HDPE (Fraction)/HPB Blend .

Theoretically, Nitzamov et al. [6] studied the rate constants and energy partitioning for the OH -I- HBr reaction via quasi-classical trajectories. Liu and coworkers [9] predicted that the OH -I- HBr reaction has a small barrier (<1.0 kcal/mol, from CCSD(T)/6-31 H-G(2df,2p) singlepoint energies), and their theoretical rate constants are comparable with the experimental results [4, 11-14]. 

The calculation of theoretical rate constants for gas-phase chemical reactions involved in atmospheric chemistry is a subject of great interest. Theoretical kinetic methodologies utilize the quantum chemical characterization of the stationary points along the PES of a reaction to calculate the rate constants and product distributions. These methods allow for the elucidation of rate constants over the temperature and pressure range in the atmosphere. Various theoretical methods are available for rate constant calculations. Here, we focus on transition state theory (TST) and its variants to calculate the reaction rate constants. 

Table 6.4 Rate constants for electronic-energy transfer (a) Short-range transfer ( 3 f> Ud). D A D - - A. Values of 3 are experimental rate constants for electronic-energy transfer, at various temperatures close to 298 K room temperamre (r.t.) may be taken as 292 K. The theoretical rate constant for transfer at every encounter is kD=4RT jt]. Many of the values of kp are calculated from the viscosity r] at 298 K, so where the rates were measured at r.t. the values of 3/ 0 in the table will be slightly below the true values. For the singlet-singlet reactions at 301 K, however, ko has been calculated for this temperature...

A key point in transition-state theory is to calculate a theoretical rate constant k for the bimolecular elementary process. In terms of transition-state theory, the bimolecular elementary process given as... 

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