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** First-order reaction rate coefficient for **

** First-order reactions reaction **

** Rate coefficient pseudo first-order **

The term (t) times the second-order rate coefficient, k, is the pseudo-first-order rate coefficient for reaction. In the equation above, v(t) occurs on both sides, so taking Laplace transforms shows that [Pg.275]

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 [Pg.1367]

Because the conditions for the reaction are the same as in Example 4.6, the pseudo first-order rate constant k will again be 16.8 s 1, and the effective diffusivity of hydrogen in the liquid filled pores of the catalyst Dt will be 0.11 x 10 8 m2/s. Also because the transfer coefficients kt and ks depend mainly on the physical properties of the system, the same values, namely, ki = 1.23 x 10"3 m/s and ks = 0.54 x 10-3 m/s, will be used even though the hydrodynamics of the three-phase fluidised-bed will be different and the particle size is larger. [Pg.241]

In this equation the reaction is taken to be pseudo first-order with respect to A (as is the case for hydrogen in the reaction with thiophene) with an effectiveness factor r). The factor er appearing in this equation converts the basis of the reaction rate constant from unit volume of particles to unit volume of bed in order to be consistent with the basis used for the volumetric mass transfer coefficients. [Pg.244]

A kinetic analyses of the data was performed by noting the pseudo-first order loss of substrate together with selectivity. This enabled a pseudo-first order kinetic description of the two pathways to be obtained. Table 1 lists the lifetimes of 2-butanone and 2-butanol production for the various experiments. Here the lifetimes refers to the inverse of the pseudo-first order reaction rate coefficients. [Pg.216]

Direct, time-resolved investigation of radical-radical and atom-radical rate coefficients present more experimental difficulty than radical-molecule reactions, for both species of interest must be generated simultaneously and their time dependence must be accurately followed. Furthermore, in contrast with radical-molecule reactions studied by pseudo-first-order kinetics, where relative radical concentrations combined with straightforward measurement of the molecule concentration suffice, the concentration of one radical (when it is in excess), or both radicals, must be known. The FPTRMS method is readily adaptable to these reactions when species concentrations are suitably calibrated. [Pg.44]

The chemical method used to estimate the interfacial area is based on the theory of the enhancement factor for gas absorption accompanied with a chemical reaction. It is clear from Equations 6.22 to 6.24 that, in the range where y> 5, the gas absorption rate per unit area of gas-liquid interface becomes independent of the liquid phase mass transfer coefficient kL, and is given by Equation 6.24. Such criteria can be met in the case of absorption with an approximately pseudo first-order reaction with respect to the concentration of the absorbed gas component. Reactions that could be used for the chemical method include, for example, C02 absorption in aqueous NaOH solution, and the air oxidation of Na2S03 solution with a cupric ion or cobaltous ion catalyst (this is described in the following section). [Pg.108]

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. [Pg.29]

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. [Pg.64]

Numerous experimental combinations of process conditions (SS or US), hydrogenation gas (H2 or D2), and solvent (H2O or D2O) have been explored. A summary of combinations we have chosen for study is presented in Table 2. In this table it is seen that the experiments are labeled B1-B7 for 3B20L and P1-P6 for 14PD30L. The second column lists the experimental conditions, whereas the third column lists the initial system concentration based on 100 mM of substrate and the amount of catalyst used. The penultimate column lists the final (extent of reaction > 95%) selectivity to ketone (2-butanone or 3-pentanone) and the final column lists the pseudo-first order substrate loss rate coefficient. The dataset contained in Table 2 enables numerous conclusions to be made regarding the reaction systems. The differences in initial concentrations (e.g., 67 versus 100 M/g-cat.) arise from the chosen convenience of having similar activities and therefore comparable reaction times. [Pg.219]

** First-order reaction rate coefficient for **

** First-order reactions reaction **

** Rate coefficient pseudo first-order **

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