Pressure dependence first-order rate constant

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

Calculation of kinetic parameters - In the experiments carried out in the single autoclave the H2 pressure was not maintained and the consumption of H2 controlled the conversion of AcOBu, which could be described by pseudo-first order rate constant. In the activity tests performed in SPR16 the conversion of AcOBu increased linearly up to ca. 50 % with reaction time. Initial reaction rates were calculated from AcOBu conversion vs. reaction time dependence, the initial concentration of substrate and the amount of catalyst or the amount of promoters in 1 g of catalyst. 

As pointed out before kuni is a pseudo first order rate constant. Since kuni/[M] is independent of [M], kuni/[M] is a second order rate constant at low pressure. It is significant and important for consideration of isotope effects that this second order rate constant for unimolecular reactions depends only on the energy levels of reactant molecules A and excited molecules A, and on the minimum energy Eo required for reaction. It does not depend on the energy levels of the transition state. There will be further discussion of this point in the following section. 

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. 

The ratio -ln[yp(r)]/T = 1 describes first-order decay that is unaffected by mass transport. When yp is calculated by Eq. 6 the ratio will not equal 1, and will express the deviation between the case of the measured first-order rate constant with flow and diffusion and the ideal case of no flow and diffusion. Figure 6 shows a plot of -ln[yp(r)]/T vs. z for the case when reaction zone at t = 0. The parameters are those from an investigation of the reaction flash photolysis of CF2ClBr in the presence of 02 and NO, where the reaction of CF2C102 radicals with N02 was studied [41]. For reference, rd = 0.1024 corresponds to a total pressure of 1 torr. Figure 6 clearly shows that at low pressures the deviation from exponential decay occurs at shorter times, z = kt, than at higher pressures. This is due to the pressure dependence of the diffusion coefficient. 

Methane is slightly soluble in HF-SbF5 even at atmospheric pressure (0.005 M), which facilitates direct kinetic studies by NMR. Thus the transition states for methane activation in this medium have been studied experimentally by Ahlberg et al.49 The first-order rate constants [Eqs. (5.9) and (5.10)], determined experimentally on the basis of2H -decoupled 600-MHz 1H NMR time-dependent spectra (Figure 5.2), are on the order of 3.2 x 10 1 s 1 at —20°C and show a secondary kinetic isotope effect (SKIE) of 1 0 02. 

At high pressures the observed first order rate constant is strictly independent of pressure, but if experiments are carried out at low or intermediate pressures then the first order rate constant depends on pressure, and the reaction moves from strict first order kinetics at high pressures to second order at low pressures. At pressures intermediate between these two limits, the reaction shows complex kinetics with no simple order. This requires explanation, see below and Problem 4.17. 

Kinetic measurements of the binding of NO to the porphyrin species were carried out in excess [NO] 3> [porphyrin], as a function of varying [NO], pH, temperature, and pressure. The first-order rate constants showed a linear dependence on [NO], allowing the determination of the kon and k,)tl values at pH 3 of 9.6 x 10 dm3/(mol s) and 51 s 1, respectively, in good agreement with values determined from earlier flash photolysis studies.327 Kinetics measurements over a range of pH permitted the... 

The specific rate constants of interest to the ECD and NIMS are dissociative and nondissociative electron attachment, electron detachment, unimolecular anion dissociation, and electron and ion recombination. The reactions that have been studied most frequently are electron attachment and electron and ion recombination. To measure recombination coefficients, the electron concentration is measured as a function of time. The values are dependent on the nature of the positive and negative ions and most important on the total pressure in the system. Thus far few experiments have been carried out under the conditions of the NIMS and ECD. However, the values obtained under other conditions suggest that there is a limit to the bimolecular rate constant, just as there is a limit to the value of the rate constant for electron attachment. The bimolecular rate constants for recombination are generally large, on the order of 10 7 to 10-6 cc/molecule-s or 1014 to 1015 1/mole-s at about 1 atm pressure. Since the pseudo-first-order rate constants are approximately 100 to 1,000 s 1, the positive-ion concentrations in the ECD and NIMS are about 109 ions/cc. 

The detailed kinetics and energetics of the reactions in the rf-ion trap can be understood by considering that the total pressure inside the ion trap is on the order of 1 Pa, which means that the experiment is operating in the kinetic low-pressure regime. Therefore, a Lindemann-t3rpe mechanism has to be considered for each reaction step, and the reaction rates depend on the buffer gas pressure [187, 188]. As a consequence, the obtained pseudo first order rate constant k contains the termolecular rate constant as well as the concentrations of the helium buffer gas and of the reactants in the case of the adsorption reaction of the first CO molecule (1.1) ... 

Two-body ion-ion recombinations have rate constants in the same general range, although few have been studied in detail, none with precise analysis of reactants and products. Some three-body ion-ion recombinations have recently been studied by Mahan and co-workers (4, 21) who found effective termolecular rate constants in the range 4 X 10"26 to 3 X 10"25 cm.6 molecule 2 sec. 1 for NO+ + N02" + M near 300°K. With an approximate T 5/2 dependence, and at a total pressure of 1 torr, such processes would have effective first-order rate constants of ion removal in the 10 to 100 sec."1 range, too slow to be of importance. 

The contributions from these terms frequently cannot be separated with the result that only the composite term k is known. One example for which the separation of these terms was possible, concerns the complex-formation reaction of aqua-cobalamin (vitamin Bn). Here the usually inert Co(III) center is labilized by the corrin ring, which induces a dissociative substitution mode. From the non-linear dependence of the observed pseudo-first-order rate constant on the entering ligand concentration for the reaction shown in Eq. (1.5), the precursor formation constant and rate-determining interchange constant can be determined, as can their pressure dependences. 

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. 

To interpret the dependence on pressure of the first-order rate constant for the isomerization of cyclopropane in the vapour phase. 

Figure 2.10 Pressure dependence of the first-order rate constant for cyclo-propane isomerization. [After H.O. Pritchard, R.G. Sowden, and A.F. Trotman-Dickenson, Proc. Roy. Soc. (London), A217, 563, with permission of The Royal Society, (1953).]...

For isomerization of small hydrocarbons (fewer than five carbons), the observed rate constants are generally independent of total pressure at pressure greater than about 1 atm. However, at lower pressures the first-order rate constants fall ofiF and are dependent on pressure. Importantly, the smaller the molecule the higher the pressure at which the fall off behavior occurs. 

With respect to the practical considerations of gas flow and vacuum requirements, the PHPMS experiment might, upon cursory consideration, appear to be easily extended into the VHP region. That is, several MS-based analysis techniques routinely use ion source pressures of 1 atm. However, when an attempt to increase the pressure within a PHPMS ion source is made, the factors that do become problematic are those related to the subtle principles on which the method is based. Most importantly, the PHPMS method requires that the fundamental mode of diffusion be quickly established within the ion source after each e-beam pulse, so that all ions are transported to the walls in accordance with a simple first-order rate law while the IM reactions of interest are occurring. This ensures that a constant relationship exists between the ion density in the cell and the detected ion signal. The rates of the IM reactions can then be quantitatively determined from the observed time dependencies of the reactant ion signal because the contribution of diffusion to the time dependencies are well known and easily accounted for. 

Very little work has been reported on the gas-phase pyrolysis of acid halides and two excellent reviews are available4,185. Acetyl chloride was decomposed in a static system at 242-491 °C186. The reversible reaction (equation 97) occurs at 242-350 °C, where the equilibrium lies to the left. The equilibrium constant, Kp, was found to be invariable with initial pressure, and temperature-dependent according to the van t Hoff equation 8.314 In Kp (-100.3 2.0) 103/T + (132.9 3.2). Addition of HC1 reduced the extent of the reaction but did not alter the value of Kp. However, at 270-329 °C the reaction is found to be homogeneous, molecular, and to obey a first-order rate law. The rate coefficients were given by... 

The combination rate constant ks, is known , so that the v and b measurements lead to a value of k. Lin and Back carried out such measiurements over a range of temperatures and pressures. They found a considerable pressure-dependence of the first-order rate coeflBcient for the ethyl radical decomposition. In the temperature range 823 to 893 °K and the pressure range 200 to 600 torr the rate is in fact approximately proportional to [C2Hg]. At higher pressures the rate of (3) becomes independent of the ethane concentration, and the first-order rate coefficient can then be represented by... 

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