Rate constant apparent pressure dependence

The chemically activated molecules are fonned by reaction of with the appropriate fliiorinated alkene. In all these cases apparent non-RRKM behaviour was observed. As displayed in figure A3.12.11 the measured imimolecular rate constants are strongly dependent on pressure. The large rate constant at high pressure reflects an mitial excitation of only a fraction of the total number of vibrational modes, i.e. initially the molecule behaves smaller than its total size. However, as the pressure is decreased, there is time for IVR to compete with dissociation and energy is distributed between a larger fraction of the vibrational modes and the rate constant decreases. At low pressures each rate constant approaches the RRKM value. 

The chemically activated molecules are formed by reaction of CDj with the appropriate fluorinated alkene. In all these cases apparent non-RRKM behavior was observed. As displayed in figure 8.7, the measured unimoleeular rate constants are strongly dependent on pressure. However, at low pressures each rate constant approaches the RRKM value. 

The two isomers n-CsHy and FC3H7 are separated by a barrier of 37kcal/mol (measured with respect to n-CsH ) and they can easily interconvert at sufficiently high temperatures. Although in reality both radicals dissociate to propene + H and ethylene+ CH3 (see Fig. 8), we will ignore these channels here and focus exclusively on the isomerization part. The steady-state analysis with CARRA yields one apparent pressure-dependent rate constant, since the rate constant for the reverse reaction is determined by the equilibrium constant. The predictions with both versions (MSC and ME) for T = 1200 K and various pressures are shown in Fig. 9. The results are very similar and show the expected fall-off behavior. The MSC treatment—despite its simplicity—captures the pressure dependence well. 

The reaction rate increases almost linearly with pressure, and without H2 the reaction does come to a complete standstill. Thus, the two rate constants used in the above equations (kneo-men and kiso-neo in kg s m ) are apparent rate constants, which still depend on the H2 pressure. This can formally be described by the following equations ... 

The effect of pressure on chemical equilibria and rates of reactions can be described by the well-known equations resulting from the pressure dependence of the Gibbs enthalpy of reaction and activation, respectively, shown in Scheme 1. The volume of reaction (AV) corresponds to the difference between the partial molar volumes of reactants and products. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state (TS) with respect to the partial molar volumes of the reactants. Volumes of reaction can be determined in three ways (a) from the pressure dependence of the equilibrium constant (from the plot of In K vs p) (b) from the measurement of partial molar volumes of all reactants and products derived from the densities, d, of the solution of each individual component measured at various concentrations, c, and extrapolation of the apparent molar volume 4>... 

Pressure dependence analysis. Kofel and McMahon pointed out that if the apparent bimolecular association rate constant is measured as a function of pressure, k and can be obtained from the slope and intercept of the pressure plot, provided that k and k are independently known k is often taken equal to the Langevin or ADO orbiting rate constant k (the strong collision assmnption), and kf is either taken equal to k or is measured independently by high-pressure mass spectrometry. 

As for other organics in the atmosphere, the OH radical is a major oxidant for alkenes. Table 6.8 gives the rate constants for some OH-alkene reactions as well as their temperature dependence in Arrhenius form. Several points are noteworthy (1) the reactions are very fast, approaching 10-l() cm3 molecule-1 s-1 for the larger alkenes (2) the rate constants have a pressure dependence (3) the apparent Arrhenius activation energies are negative. ... 

The rate constants which have just been defined differ from the rate constants of an ordinary chemical reaction. They are constant only for the course of an exchange reaction with a single mixture of reacting gases, but they are dependent on pressure and assume different values if the initial pressures of the reactants are altered. The true kineties of an exchange reaction can be determined only by means of a series of experiments with different mixtures of the reactants because the course of a reaction with a single mixture follows the apparent first-order Equation (5). 

This is a fair approximation to most chain decompositions, i.e., that the apparent first-order rate constant is about 10 to 100 times the initiation rate. The general problem is to ascertain this process and then to try to decide if it is pressure dependent. 

We have demonstrated for the first time that we could apply the theory of generalized Thiele modulus to an enzymatic reaction both in n-hexane and SC CO2. The comparison between the two reaction media is not so clear in n-hexane the real reaction velocity is higher than that obtained in SC C02. Nevertheless, the Thiele modulus values indicates a limitation due to the internal mass transfer rate g 1. Thus we observed, in the hexane case, a diffusional control, while in SC C02 an intermediate rate between the reactional and diffusional rates was apparent. It therefore, seems that SC CO2 should be the solvent of choice in reactions catalyzed by immobilized enzymes, since it reduces problems with internal mass transfer. An other advantage is that the value of the inhibition constant is 43 mM in n-hexane and 120 mM in SC CO2 [14], so SC CO2 should be more convenient if we have to work with higher ethanol concentration. The economic feasibility of an industrial scale lipase catalyzed reaction on C02 may depend upon possible costs for high-pressure equipment. 

The pattern of kinetic behaviour is influenced by salt coating. Thus in uncoated vessels of porcelain or silica the reaction commences immediately, but the reaction rate increases before consumption of reactants causes it to decrease again. In potassium chloride coated vessels, on the other hand, there is no auto catalysis the rate apparently reaches its maximum value at the very start and remains constant for some time. There are also differences in the pressure dependences of the reaction rate in the two types of vessel, and in the reaction products which can be isolated. 

Like the pressure dependence, the temperature dependence is also often expressed in an empirical form, in which an apparent overall rate constant is used (like in Eqn. (3.44)). The observed (or apparent) activation energy can be expressed as ... 

The kinetics of the self-reaction of amidogen radicals, NH2 + NH2, has been studied extensively using different techniques and bath-gases.228 239 The apparent bimolecular rate constant was found to be strongly pressure dependent. The amidogen radicals can recombine or disproportionate ... 

The experiments of Pagsberg et al.25 were performed at bath-gas pressures (M = SF6) of 10 - 1000 mbar. A strong pressure dependence of the apparent bimolecular rate constants was found in this pressure range. 

Although most rate measurements have been made at sufficiently low conversion (low pressure) for Equation 3 to apply, it has been shown that the psuedo first order rate laws (Equations 4 and 5) are obeyed over wide ranges of pressure, if subsequent reactions do not interfere. Thus, Field et al. (24) found the disappearance of CH4+ in methane to obey first law kinetics over a pressure range of about 0.1 to 400 microns. However, in certain systems, reactions of apparently higher order do occur. Actually, these are the result of a succession of reactions which show dependence upon a higher power of the pressure. Rates of reactions of such high order do not yield satisfactory rate constants, but it has been possible to determine rate constants for reactions of 3rd order, and Field (20) and several others have made approximate measurements of the rate constants for such third order processes. As is the case with the second order processes, these reaction rates are relatively high. For... 

As in the case of unimolecular processes, it is certainly possible for a reaction to be neither second nor third order, and a more detailed model of the pressure dependence must be used. For example, the apparent rate constant can be expressed as a function of the air density (M) and the temperature T by the empirical Troe s relation (Troe, 1979)... 

Figures 41 (a) and (b) show the predicted and experimental rate coefficients at different temperatures as a function of N2 pressure. In these figures, the solid 1 ines represent the calculated results using the predicted AH°o = -15.8 kcal/mol the dotted and dashed lines represent the results using experimentally estimated AH°o = -14.8 [130] and -11.1 [131] kcal/mol, respectively the dash-dot-dotted line is the results based AH°o = -17.7 kcal/mol which is the upper-limit reported by Hayman and Cox [130]. Symbols are experimental results [130, 131, 141]. Apparently, the pressure-dependent rate constants are strongly sensitive to AH°o for the low-dissociation energy process our predicted values based on Affo = -15.8 kcal/mol are in good agreement with experimental data.

Figure 149. Temperature and humidity dependence of the tetrahydrate-to-monohydrate transition kinetics for 5-(4-oxo-phenoxy-4//-quinolizine-3-carboxamidc)-tctrazolatc. Here k refers to the apparent zero-order rate constant for the process (time unit h) and V = k/Ps, where P is water vapor pressure. (Reproduced from Ref. 613 with permission.)...

In eq. (7.29) the rate constants are apparent ones as they include also the hydrogen pressure dependence. Surface coverage can be expressed by eq. (7.30). 

Figure 5 shows the CO oxidation activity over Rh-Sn/Si02 catalysts which were reduced at different temperatures. The activity was evaluated with the apparent first order rate constant. The initial reaction rate for CO oxidation depended on partial pressure of O2 in first order over Rh and Rh-Sn/Si02 described previously [3]. The dashed line indicates the activity over Rh/Si02. The activity over the catalyst reduced at 573 K was identical to that over Rh/Si02 as shown in Fig. 5. 

---