Rate constants back reaction

For di- and trimethoxy carbocations, for which rate constants for reaction of the cations with water have been measured by McClelland and Steen-ken,4 133 rate constants for the back reactions of the hemiorthoester and hemiorthocarbonate were assigned in the same way as for the hemiacetals from the corresponding methyl or ethyl ethers.134 136 Estimates of pAiR for representative methoxy and dimethoxy carbocations are shown in the first two rows of structures at the bottom of the page. 

Species in parentheses may be adsorbed or in the aqueous phase. In the treatment in the text, kT] refers to the rate constant for reaction (Tl), KT2, kT2 and k-T2 and refer to the equilibrium constant and rate constants for the forward and back reactions respectively of the process described by reactions (T2a/T2b). The equilibrium and rate constants for reactions (T3) to (T15) are defined in a similar manner. 

The rate constant of reaction of Compound I with H2O2 is much higher than that with alcohols [207]. No free radicals are formed in the typical cycle of CAT. Organic peroxides, such as peroxyacetic acid, can substitute for hydrogen peroxide by slowly forming Compound I however, they do not reduce CAT back to the resting state. 

Several important points should be stressed in discussing the data of Fig. 8.4. First, we note that with this colloidal catalyst it is possible to intercept the back reaction very efficiently at surprisingly low Pt-concentration. The rate constant for reaction (7.17) is calculated to be k = 2 x 109M-1s 1 if the analytical Pt concentration is used (10-4M). However, this gives certainly only a lower limit as Pt is present in aggregated and not... 

The exponential fiinction of the matrix can be evaluated tln-ough the power series expansion of exp(). c is the coliinm vector whose elements are the concentrations c.. The matrix elements of the rate coefficient matrix K are the first-order rate constants W.. The system is called closed if all reactions and back reactions are included. Then K is of rank N- 1 with positive eigenvalues, of which exactly one is zero. It corresponds to the equilibrium state, witii concentrations r detennined by the principle of microscopic reversibility ... 

For QPh-x, the decay of SPV- was faster than that for the APh-x-SPV system, and obeyed first-order kinetics [76]. The addition of NaCl (0.2 M) caused the decay profile to change i.e. the back ET was considerably slowed and the decay kinetics changed from first-order to second-order, with a reaction rate constant of kb = 1.8 x 109 M-1 s-1. These findings suggest the impossibility of escape of... 

The respective rate constants (25 °C, p. = 0.5 M) are k = 2.7x 109 L mol-1 s 1 and 52 = 2.8 X 107 L mol1 s-1. Other things happen next they, too, are of considerable chemical interest. The first thing to consider is the process sometimes referred to as the back reaction. In these two cases the back reactions are... 

It is of substantial interest to note that, c.s the temperature of the reaction mixture is increased to —33-5°, ion 19 is converted quantitatively back to 18. At that temperature the first-order rate constant for the reversion has been calculated to be 8-0 x 10 sec , which corresponds to a free enthalpy barrier AG ) of 17-4 kcal/mol. 

These results assume that all the rate constants are different. Special forms apply when some of the k values are identical, but the qualitative behavior of the solution remains the same. Figure 2.2 illustrates this behavior for the case of bo = Co = do = 0. The concentrations of B and C start at zero, increase to max-imums, and then decline back to zero. Typically, component B or C is the desired product whereas the others are undesired. If, say, B is desired, the batch reaction time can be picked to maximize its concentration. Setting dbjdt = Q and bo =Q gives... 

At equilibrium, the reaction rates (not the rate constants) of the forward and back reactions are equal. 

The magnitude of the values of 1/t indicates that the original assumption that radiationless decay of the triplet back to the ground state is unimportant in these reactions is correct since the triplet states of aliphatic ketones commonly have rate constants for radiationless decay from the triplet state on the order of 105 sec-1 (t = 10 5 sec).(8>... 

Based on high performance liquid chromatography (HPLC) studies regarding the equilibration of isomeric fractions of P-carotene isomers at 45°C, a model consisting of two reversible concurrent isomerization reactions was developed by Pesek et al. 1990. Under dark storage conditions at 45°C, a P-carotene solution reached an equilibrium after 4-6 days yielding approximately 66% aW-trans-, 8% of 9-cis-, and 25% of 13-d.s-P-carotene. The observed rate constant (k) for the formation of the 13-d.v- isomer was faster than that of the 9-d.s-p-carotene isomer, and the back rate constants toward the all -trans- isomer were intrinsically faster as compared to the formation of d,v-isomcrs of P-carotene (Chart 12.1). 

Note All other pairs and back reactions have rate constants <1 x 109 M s 1. 

The intermediate reaction complexes (after formation with rate constant, fc,), can undergo unimolecular dissociation ( , ) back to the original reactants, collisional stabilization (ks) via a third body, and intermolecular reaction (kT) to form stable products HC0j(H20)m with the concomitant displacement of water molecules. The experimentally measured rate constant, kexp, can be related to the rate constants of the elementary steps by the following equation, through the use of a steady-state approximation on 0H (H20)nC02 ... 

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