Pseudo-coefficient rate

This difference is exemplified by the variation of the pseudo first order rate coefficients (Rate = k [Substrate]) for the deamination and denitrosation of N-n-butyl -nitroso acetamide at 25 C with [HpSO ] shown in Figure 1 Denitrosation becomes the domin- ant pathway above 5M H SO. (9) but the crossover acidity i lower (ca.0 5M. H SO ) ror N-nitroso-2-pyrrolidone (10) ... 

For Eq. (3.10) and Eq. (3.12) the bimolecular rate constants can be replaced with pseudo unimolecular rate constants within the limits of either fractional electron capture or constant positive ion concentration. All the above reactions take place on a time scale that is fast relative to the time required for transport through the detector. Under steady state conditions the electron capture coefficient K (see Eq. 3.7) is given by... 

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj. 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

First-order and pseudo-first-order reactions are represented by the upper curve in Fig. 14-14. We note that for first-order reactions when the Hatta number is larger than about 3, the rate coefficient k can be computed by the formula... 

Throughout this section the hydronium ion and hydroxide ion concentrations appear in rate equations. For convenience these are written [H ] and [OH ]. Usually, of course, these quantities have been estimated from a measured pH, so they are conventional activities rather than concentrations. However, our present concern is with the formal analysis of rate equations, and we can conveniently assume that activity coefficients are unity or are at least constant. The basic experimental information is k, the pseudo-first-order rate constant, as a function of pH. Within a senes of such measurements the ionic strength should be held constant. If the pH is maintained constant with a buffer, k should be measured at more than one buffer concentration (but at constant pH) to see if the buffer affects the rate. If such a dependence is observed, the rate constant should be measured at several buffer concentrations and extrapolated to zero buffer to give the correct k for that pH. 

The concentration of monomers in the aqueous phase is usually very low. This means that there is a greater chance that the initiator-derived radicals (I ) will undergo side reactions. Processes such as radical-radical reaction involving the initiator-derived and oligomeric species, primary radical termination, and transfer to initiator can be much more significant than in bulk, solution, or suspension polymerization and initiator efficiencies in emulsion polymerization are often very low. Initiation kinetics in emulsion polymerization are defined in terms of the entry coefficient (p) - a pseudo-first order rate coefficient for particle entry. 

Abbreviations k = pseudo-first order rate constant R2 = correlation coefficient r° = initial reaction rate in mmole/gcataiystxh r0Pi and r°Re = reaction rate related to the amount of Pt and Re, respectively C = conversion of AcOBu at t=24 h selectivity to BuOH was above 90 % a2 g catalyst was used. 

The rate of photolytic transformations in aquatic systems also depends on the intensity and spectral distribution of light in the medium (24). Light intensity decreases exponentially with depth. This fact, known as the Beer-Lambert law, can be stated mathematically as d(Eo)/dZ = -K(Eo), where Eo = photon scalar irradiance (photons/cm2/sec), Z = depth (m), and K = diffuse attenuation coefficient for irradiance (/m). The product of light intensity, chemical absorptivity, and reaction quantum yield, when integrated across the solar spectrum, yields a pseudo-first-order photochemical transformation rate constant. 

The ions or cluster ions are thermalized by collisions with an inert carrier gas (usually helium), although often argon or even nitrogen is employed. Neutral reactant gas is added through a reactant gas inlet at an appropriate location downstream in the flow tube, and allowed to react with the injected ions. Rate coefficients, k, are determined by establishing pseudo-first-order reaction conditions in which the reactant ion concentration is small compared to the reactant neutral concentration. Bimolecular rate coefficients, k, are obtained from the slope of the natural logarithm of the measured signal intensity, /, of the reactant ion versus the flow rate (2b of reactant gas 45,48-50... 

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) ... 

A reagent in solution can enhance a mass transfer coefficient in comparison with that of purely physical absorption. The data of Tables 8.1 and 8.2 have been cited. One of the simpler cases that can be analyzed mathematically is that of a pseudo-first order reaction that goes to completion in a liquid film, problem P8.02.01. It appears that the enhancement depends on the specific rate of reaction, the diffusivity, the concentration of the reagent and physical mass transfer coefficient (MTC). These quantities occur in a group called the Hatta number,... 

Bertole et al.u reported experiments on an unsupported Re-promoted cobalt catalyst. The experiments were done in a SSITKA setup, at 210 °C and pressures in the range 3-16.5 bar, using a 4 mm i.d. fixed bed reactor. The partial pressures of H2, CO and H20 in the feed were varied, and the deactivation, effect on activity, selectivity and intrinsic activity (SSITKA) were studied. The direct observation of the kinetic effect of the water on the activity was difficult due to deactivation. However, the authors discuss kinetic effects of water after correcting for deactivation. The results are summarized in Table 1, the table showing the ratio between the results obtained with added water in the feed divided by the same result in a dry experiment. The column headings refer to the actual experiments compared. It is evident that adding water leads to an increase in the overall rate constant kco. The authors also report the intrinsic pseudo first order rate-coefficient kc, where the overall rate of CO conversion rco = kc 6C and 0C is the coverage of active... 

Fluorescence quenching studies in micellar systems provide quantitative information not only on the aggregation number but also on counterion binding and on the effect of additives on the micellization process. The solubilizing process (partition coefficients between the aqueous phase and the micellar pseudo-phase, entry and exit rates of solutes) can also be characterized by fluorescence quenching. 

Table 23.1 HMF formation kinetics in isothermal heating as a function of treatment temperature, first order reaction pseudo rate constant and regression coefficients...

PhC properties most investigated by scientists to date are their water solubility (s, mg/mL), volatility (correlated to the Henry constant H) (pg m atr/pg m wastewater), biodegradability (correlated to pseudo-first-order degradation constant bioi L gSS d ), acid dissociation constant K, distribution and sorption (through the sludge-water distribution coefficient K, expressed in L gSS or the octanol-water partition coefficient Kg ). The main focus has been to find any correlations between these parameters and to determine PhC removal rates during the different treatment steps. Thus, different properties have been quantified for many compounds, and software, such as EPl Suite 4.00 [54], consenting their estimation, is available. 

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