Zero conversion rate constant

The zero-conversion rate constant (k0) is correlated with feed properties. The dominant parameter is the average feed carbon number. Feed hydrogen content and i/n paraffin content also play an important role. These parameters are embodied in Equation 15 (29), where bs are positive numbers. 

Figure 5 shows predicted zero-conversion rate constants for C5 through C8 n-paraffins. Also shown are fc-values extrapolated from low conversion literature data (15,31-35). The correlation is seen to be in good agreement with literature data. The temperature dependence is well captured by the constant activation energy of 55,000 cal/g-mol. Figure 6... 

The first-order rate coefficient, k, of this pseudo-elementary process is assumed to vary with temperature according to an Arrhenius law. Model parameters are the stoichiometric coefficients v/ and the Arrhenius parameters of the rate coefficient, k. The estimation of the decomposition rate coefficient, k, requires a knowledge of the feed conversion, which is not directly measurable due to the complexity of analyzing both reactants and reaction products. Thus, a supplementary empirical relationship is needed to relate the feed conversion (conversion of A) to some experimentally accessible variable (Ross and Shu have chosen the yield of C3 and lighter hydrocarbons). It is observed that the rate coefficient, k, is not constant and decreases with increasing conversion. Furthermore, the zero-conversion rate coefficient depends on feed specifications (such as average carbon number, hydrogen content, isoparaffin/normal-paraffin ratio). Stoichiometric coefficients are also correlated with conversion. Of course, it is necessary to write supplementary empirical relationships to account for these effects. 

Figure 7 shows the formose reaction-rate as a function of molarity of calcium hydroxide in the product. One line, independent of the concentration of formaldehyde in the reactor, fits data at intermediate conversion-levels this line passes through the origin. In a study of the selfaddition of formaldehyde catalyzed by magnesium oxide, Schmalfusz and Kalle observed similar behavior, almost independent of concentrations of formaldehyde and first-order in magnesium oxide that had not been consumed in the Cannizzaro reaction. A zero-order rate-constant... 

Eig. 2. Efficiency to a primary intermediate as % of maximum (zero conversion) efficiency x axis is feed conversion. Parameters are oxidation rate-constant ratios ( 2 / i) for primary intermediate vs feed and reactor type A, plug-flow or batch B, back-mixed. 

This equation (eq. 5) is commonly known as the Mayo equation.1" The equation is applicable at low (zero) conversion and is invalidated if the rate constants are chain length dependent. 

The rate constants associated with the conversion of the pyrrolo[ 1,2-c/Jindole hydroquinone to its quinone methide were fit to the rate law equation (7.1), see Fig. 7.17 for rate data and the fit. The solid line in Fig. 7.17 was generated with Eq. 7.1 where k0 = 0.09min-1 and k 1.5 x 105M min The mechanism consistent with the pH-rate profile is the spontaneous elimination of acetate (kf) process) and the proton assisted elimination of acetate (kx process) from the electron-rich hydroquinone. The k0 process is independent of pH and exhibits a zero slope while the kx process exhibits a — 1 slope consistent with acid catalysis. 

As shown in Figure 3, solubilization roughly conforms to first-order kinetics, where rate = k[unconverted coal]. Rate constants of 3 x 10 and 1 x 10 min l are found for 250° and 275°C respectively, with nearly total conversion in less than 30 minutes at the higher temperature. Although negligible reaction takes place with heatup to 250°C (so-called "zero time), considerable reaction occurs in the few minutes of heatup between 250° and 275°C. During this period, solubility rises 20%, incorporation approaches its maximum extent, and the H/C ratio drops to 0.75. 

Why are the activation energies of the reactions of nitroxyl radicals with O—H bonds lower than those in their reactions with C—H bonds As in the case of the reaction of R02 with quinones, the difference in E values occurs as a result of the different triplet repulsions in TS [23]. When a TS of the O H O type is formed (the AmO + H02 reaction), the triplet repulsion is close to zero because the O—O bond in the labile compound AmOOH is very weak. Conversely, the triplet repulsion in the reaction of AmO with the C—H bond is fairly great, due to the high dissociation energy of the AmO—R bond. This accounts for the difference between the activation energies and between the rate constants for the reactions considered above. Thus, the possibility of the realization of a cyclic chain termination mechanism in the reactions of nitroxyl radicals with peroxyl radicals, incorporating O—H groups, is caused by the weak triplet repulsion in the TS of such disproportionation reactions... 

If a reaction that must be investigated follows a reaction sequence as in Scheme 10.1, and if the reaction order for the substrate equals unity, it means that (with reference to Eq. (4 b)), the observed rate constant (k0bs) is a complex term. Without further information, a conclusion about the single constants k2 and fCM is not possible. Conversely, from the limiting case of a zero-order reaction, the Michaelis constant cannot be determined for the substrate. For particular questions such as the reliable comparison of activity of various catalytic systems, however, both parameters are necessary. If they are not known, the comparison of catalyst activities for given experimental conditions can produce totally false results. This problem is described in more detail for an example of asymmetric hydrogenation (see below). 

This paper is about a reinterpretation of the cationic polymerizations of hydrocarbons (HC) and of alkyl vinyl ethers (VE) by ionizing radiations in bulk and in solution. It is shown first that for both classes of monomer, M, in bulk ([M] = niB) the propagation is unimolecular and not bimolecular as was believed previously. This view is in accord with the fact that for many systems the conversion, Y, depends rectilinearly on the reaction time up to high Y. The growth reaction is an isomerization of a 7t-complex, P +M, between the growing cation PB+ and the double bond of M. Therefore the polymerizations are of zero order with respect to m, with first-order rate constant k p]. The previously reported second-order rate constants kp+ are related to these by the equation... 

Reaction temperature can also affect the order of a reaction. It is generally agreed that the rate constant for the conversion (or desorption) of the surface-oxygen complex has a higher activation energy than the rate constant for the formation of the complex. Therefore, a reaction which is zero order at low temperatures and a given pressure can become first order at the same pressure and a sufficiently high temperature. 

Scheme 4.1 Enantioselective kinetic resolution of a racemate. = rate constants for the individual enantiomers of the substrate, E = enantiomeric ratio, i.e., the ratio between the specificity constants kat/Km for the fast and slow reacting enantiomer. If a racemate is used as substrate, then these concentrations are equal at the start (i.e. zero conversion), and hence E = kR/ks.

We should first recall the stationary-state behaviour for this case. If the reaction rate constant for the catalyst decay step is large compared with that for the autocatalytic step, so that k2 > iV, the system can only ever have one stationary state. This state corresponds to no net conversion of A to B, so ass = 1. For slower decay rates, k2 < Vs non-zero stationary states exist over a range of residence times t 9 < ires < t+s in the form of an isola. The extents of conversion along the branches of the isola are given by... 

These discussions provide an explanation for the fact that fluorescence emission is normally observed from the zero vibrational level of the first excited state of a molecule (Kasha s rule). The photochemical behaviour of polyatomic molecules is almost always decided by the chemical properties of their first excited state. Azulenes and substituted azulenes are some important exceptions to this rule observed so far. The fluorescence from azulene originates from S2 state and is the mirror image of S2 S0 transition in absorption. It appears that in this molecule, S1 - S0 absorption energy is lost in a time less than the fluorescence lifetime, whereas certain restrictions are imposed for S2 -> S0 nonradiative transitions. In azulene, the energy gap AE, between S2 and St is large compared with that between S2 and S0. The small value of AE facilitates radiationless conversion from 5, but that from S2 cannot compete with fluorescence emission. Recently, more sensitive measurement techniques such as picosecond flash fluorimetry have led to the observation of S - - S0 fluorescence also. The emission is extremely weak. Higher energy states of some other molecules have been observed to emit very weak fluorescence. The effect is controlled by the relative rate constants of the photophysical processes. 

Several approaches are available to determine a rate-constant ratio for intermolecular reactions. (1) The most general method is much like that used to determine rate constants with a single nucleophile. However, by employing a pair of nucleophiles, the concentration of the alkylating agent need not be known. Equation (17) is used to calculate a rate-constant ratio. Both small and large conversions of reactant to product are conveniently handled by the equation it is written in a form to be used when a reactant concentration, [Het], is determined as well as when a product concentration, [MeHet], is obtained. The zero subscript designates an initial concentration. 

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