Pseudo-order reaction, definition

In order to exemplify the potential of micro-channel reactors for thermal control, consider the oxidation of citraconic anhydride, which, for a specific catalyst material, has a pseudo-homogeneous reaction rate of 1.62 s at a temperature of 300 °C, corresponding to a reaction time-scale of 0.61 s. In a micro channel of 300 pm diameter filled with a mixture composed of N2/02/anhydride (79.9 20 0.1), the characteristic time-scale for heat exchange is 1.4 lO" s. In spite of an adiabatic temperature rise of 60 K related to such a reaction, the temperature increases by less than 0.5 K in the micro channel. Examples such as this show that micro reactors allow one to define temperature conditions very precisely due to fast removal and, in the case of endothermic reactions, addition of heat. On the one hand, this results in an increase in process safety, as discussed above. On the other hand, it allows a better definition of reaction conditions than with macroscopic equipment, thus allowing for a higher selectivity in chemical processes. 

In transition metal-catalyzed domino reactions, more than one catalyst is often employed. In Tietze s definition and the classification of domino reactions, no distinction has been made between transformations where only one or more transition metal catalyst is used for the different steps, provided that they take place in a chronologically distinct order. Poli and coworkers [13] differentiated between these processes by calling them pure-domino reactions (which consisted of a single catalytic cycle driven by a single catalytic system) or pseudo-domino reactions . The latter type was subdivided into ... 

Note that, unlike in the definition of effectiveness factor for catalytic reactions (Chapter 7) where the normalizing rate was the rate of reaction, here the normalizing rate is the rate of mass transfer. Thus the reaction is considered the intruder (albeit benevolent or enhancing), whereas for catalytic reactions, diffusion was the intruder (often, but not always, retarding). For a pseudo-mth-order reaction, one can write... 

Kapp, and the on- and off-rate constants of Qg are given in eqs. (1) ano (2) by their definitions under the three appropriate assumptions (i) under our experimental conditions the binding of Qg to the vacant site is a pseudo-first order reaction to the first approximation, (ii) the ratio of the amplitude of the fast decay component over that of the slow decay component in the decay kinetics following an actinic flash, is equal to the ratio of the fraction of the Qg-bound reaction centers over that of the Qg-unbound reaction centers in the dark, and (iii) the dissociation constant of Qg in the dark is equal to that following an actinic flash. 

Another condition for regime 2 is that the amount of A that reacts in the film before reaching the bulk be negligible. For the very slow and slow reactions, the kinetic term resides along with the differential equation describing the transport of the species in the film, such that the definition of Hatta modulus is necessary as was derived in Chapter 6 for a pseudo-first-order reaction. In Chapter 6, we defined the Hatta modulus as... 

This expression is similar to that which will be deduced in the next chapter for the yields of products of parallel first-order (or pseudo-first-order) reactions, such as reactions (3.XIV)-(3.XVI). From the definition of experimental molecular fluorescence lifetimes Tq = l/( f + the previous equation reduces to... 

Kinetic theory indicates that equation (32) should apply to this mechanism. Since the extent of protonation as well as the rate constant will vary with the acidity, the sum of protonated and unprotonated substrate concentrations, (Cs + Csh+), must be used. The observed reaction rate will be pseudo-first-order, rate constant k, since the acid medium is in vast excess compared to the substrate. The medium-independent rate constant is k(), and the activity coefficient of the transition state, /, has to be included to allow equation of concentrations and activities.145 We can use the antilogarithmic definition of h0 in equation (33) and the definition of Ksh+ in equation (34) ... 

Thus we see that the pseudo-steady-state approximation gives orders of the reaction as the thermodynamic equilibrium approximation, the only difference being the definition of the rate constant... 

For a pulse-type NMR experiment, the assumption has a straightforward interpretation, since the pulse applied at the moment zero breaks down the dynamic history of the spin system involved. The reasoning presented here, which leads to the equation of motion in the form of equation (72), bears some resemblance to Kaplan and Fraenkel s approach to the quantum-mechanical description of continuous-wave NMR. (39) The crucial point in our treatment is the introduction of the probabilities izUa which are expressed in terms of pseudo-first-order rate constants. This makes possible a definition of the mean density matrix pf of a molecule at the moment of its creation, even for complicated multi-reaction systems. The definition of the pf matrix makes unnecessary the distinction between intra- and inter-molecular spin exchange which has so far been employed in the literature. 

The reactions of DPAt and radical cations of other aromatic hydrocarbons with pyridine and substituted pyridines are among the most intensively studied electrode reactions of positive ions. The first definitive study of the mechanism of the reaction employed the rotating disk electrode (Manning et al 1969). Data were found to fit ECE working curves (Fig. 21) for the reactions of DPA7 with 4-cyanopyridine, 4-acetoxypyridine, pyridine and 4-methylpyridine. Pseudo first order rate constants of about 3, 10, 30, 300... 

The alkaline hydrolysis of phthalate diesters has been fit to the Taft-Pavelich equation (Eq. 9). Dimethyl phthalate (DMP) hydrolyzes to phthalic acid (PA) in two steps DMP + H20->MMP + CH30H and MMP + H20- PA + CH30H. The first step is about 12 times faster than the second, and nearly all the diester is converted to the monoester before product PA is formed. Other diesters are assumed to behave similarly. An LFER was obtained from rate measurements on five phthalate esters (Wolfe et al., 1980b). The reaction constants, p and S, were determined by multiple regression analysis of the measured rate constants and reported values of cr and Es for the alkyl substituents. The fitted intercept compares favorably with the measured rate constant (log kOH = — 1.16 0.02) for the dimethyl ester (for which a and s = 0 by definition). Calculated half-lives under pseudo-first-order conditions (pH 8.0, 30°C) range from about 4 months for DMP to over 100 years for di-2-ethylhexyl phthalate. 

Additional work soon discredited this postulate. The 386 nm transient could not be detected in other solvents. No transient was detected upon LFP of 10 in benzene or hexafluorobenzene. In cyclohexane, a transient with X = 367 nm was formed 144 ns after the laser pulse. Only in nitrile solvents were transient absorption bands observed near 400 nm. The definitive experiment was performed by Linda Fladel who demonstrated that the pseudo-first order rate constant of formation of the 386 nm absorbing transient was linearly dependent on the concentration of acetonitrile. This proved that the transient is formed by reaction of an invisible species which reacts with acetonitrile. The observable transient was ylide 12 formed by capture of 11. The same transient was formed by LFP of azirine 13. 

The radius of the neck varies with time so that the reactivities defined classically by relations [7.3], [7.7] or [7.9] become, even in pseudo-steady state mode, functions of the geometry at the time t and thus functions of the time. Therefore, it is necessary to re-examine the definitions in order to integrate otdy the geometry in the space function. For that, we will take again the two cases of reactions or diffusions as rate-determining steps. 

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