Reaction rate first-order

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

When a unimolecular reaction occurs with an initial product partial pressure of the reactant A, to yield an amount of die product, jc, the first-order reaction rate equation reads... 

Some workers in this field have used Eyring s equation, relating first-order reaction rates to the activation energy d(7, whereas others have used the Arrhenius parameter E. The re.sults obtained are quite consistent with each other (ef. ref. 33) in all the substituted compounds listed above, AG is about 14 keal/mole (for the 4,7-dibromo compound an E value of 6 + 2 keal/mole has been reported, but this appears to be erroneous ). A correlation of E values with size of substituents in the 4- and 7-positions has been suggested. A/S values (derived from the Arrhenius preexponential factor) are... 

Despite the utmost importance of physical limitations such as solubility and mixing efficiency of the two phases, an apparent first-order reaction rate relative to the olefin monomer was determined experimentally. It has also been observed that an increase of the nickel concentration in the ionic phase results in an increase in the olefin conversion. 

Westerterp et al. reported the first-order reaction rate constant with respect to oxygen concentration in a solution at 30°C containing 100 g of sodium sulfite per liter. The catalyst concentration was 0.001 g-mole/liter. They found that k is 37,000 sec 1 for the CoS04 catalyst and 9800 sec"1 for CuS04 catalyst. For the same sodium sulfite concentration but with copper sulfate concentration greater than 0.005 g-mole/liter, the reaction rate constant as a function of temperature is approximated by ... 

A comparative study [651] of the relative stabilities of various forms of U03 by DTA methods lists the temperatures of onset of reaction in the sequence a < e < amorphous < 0 < U02.9 < S < 7 (673, 733, 773, 803, 853, 863 and 903 K, respectively). Themal stabilities, as measured by the first-order reaction rate coefficient, magnitudes of E or enthalpies of reaction, increased with increasing structural symmetry. 

The kinetics of resole cure reactions monitored via FTIR suggest that a diffusion mechanism dominates below 140°C. The cure above 140°C exhibits a homogeneous first-order reaction rate. The activation energy of the cure reaction was -"-49.6 kJ/mole.66... 

A pure gas is absorbed into a liquid with which it reacts. The concentration in the liquid is sufficiently low for the mass transfer to be governed by Pick s law and the reaction is first order with respect to the solute gas. It may be assumed that the film theory may be applied to the liquid and that the concentration of solute gas falls from the saturation value to zero across the film. Obtain an expression for the mass transfer rate across the gas-liquid interface in terms of the molecular diffusivity, 1), the first order reaction rate constant k. the film thickness L and the concentration Cas of solute in a saturated solution. The reaction is initially carried our at 293 K. By what factor will the mass transfer rate across the interface change, if the temperature is raised to 313 K7... 

Fig. 2 shows the plot of ln[(CEcVCEc] vs. time during first 2 h. Quite good straight lines were obtained, and the pseudo first-order reaction rate constants for 120,130 and 140 °C were 0.002421, 0.002481 and 0.002545 h, respectively. From the Arrhenius plot of the first order reaction rate constants, one can estimate the activation energy as 41.5 kJ/mol. 

The overall reaction between CO2 and GMA was assumed to consist of two elementary reactions such as a reversible reaction of GMA and catalyst to form an intermediate and an irreversible reaction of this intermediate and carbon dioxide to form five-membered cyclic carbonate. Absorption data for CO2 in the solution at 101.3 N/m were interpreted to obtain pseudo-first-order reaction rate constant, which was used to obtain the elementary reaction rate constants. The effects of the solubility parameter of solvent on lc2/k and IC3 were explained using the solvent polarity. 

Similar results have been obtained for exothermic first-order reaction rate functions and Langmuir reaction rate functions for 5=2. 

From the results of experiment 2.1, we confirmed decomposition reaction is pseudo first-order, and calculated pseudo first-order decomposition rate constants. Then fixnn relationship between each first-order reaction rate constant and sodium hydroxide concentration, we confirmed that the reaction is expressed by second-order with expression first-orders for both of sodium hydroxide and fenitrothion. 

Component concentration First-order reaction rate constant Time... 

This value represents the upper limit of a first order reaction rate constant, k, which may be determined by the RHSE. This limit is approximately one order of magnitude smaller that of a rotating electrode. One way to extend the upper limit is to combine the RHSE with an AC electrochemical technique, such as the AC impedance and faradaic rectification metods. Since the AC current distribution is uniform on a RHSE, accurate kinetic data may be obtained for the fast electrochemical reactions with a RHSE. 

Da Second Damkohler number K l2 ID K = first-order reaction rate constant l = characteristic length D = diffusion coefficient... 

It is convenient to write the first-order reaction rate expression as... 

In case of Fischer-Tropsch synthesis, we have to consider that the first-order reaction rate constant is related to the concentration in the gas phase (e.g., ce2), and that the diffusive flux in the liquid-filled pores is related to the concentration in the liquid (ce21). Thus, instead of Equation 12.10, we have to use... 

No evidence of ruthenium metal formation was found in catalytic reactions until temperatures above about 265°C (at 340 atm) were reached. The presence of Ru metal in such runs could be easily characterized by its visual appearance on glass liners and by the formation of hydrocarbon products (J/1J) The actual catalyst involved in methyl and glycol acetate formation is therefore almost certainly a soluble ruthenium species. In addition, the observation of predominantly a mononuclear complex under reaction conditions in combination with a first-order reaction rate dependence on ruthenium concentration (e.g., see reactions 1 and 3 in Table I) strongly suggests that the catalytically active species is mononuclear. 

For first-order reactions rate = kX —> -dX/dt = kX Integrating from X0 to X gives... 

When C is sufficiently small, Equation (12.19) can be simplified to a first-order reaction rate equation. 

The yield (y) of a biomass production process is defined as the moles of biomass formed per mole of substrate consumed. Aerobic conditions are more conducive to higher biomass formation (and therefore also to biofilm formation) than anaerobic conditions. Empirically, under aerobic conditions, a yield of 0.05 - 0.6mol biomass/mol carbon can be obtained, while under anaerobic conditions the attainable yield falls to 0.04 -0.083mol. The reaction kinetics of biodegradation processes can be approximated by the first-order reaction rate constant k as follows ... 

Resins (19) ( 30 mg each) reacted with 5% TFA in DCM. Droplet of suspension was taken at various time intervals for single bead FTIR (Fig. 12.15) and kinetics analysis (Fig. 12.16). The data was also fitted to a first order reaction rate equation and rate constants were determined to be 4.8x10 (5% TFA). Cleavage of carbamides (18), (20), (21), ureas (22-25), amides (26-29), and sulfonamides (30-33) were studied in the same way. 

Fig. 12.17 Kinetic comparison of TFA cleavage reactions of all 16 resin-bound compounds (18-33). The kinetics of cleavage reaction was analyzed as in Figures 12.15 and 12.16. The curves represent the best fit and are displayed for each reaction. The first order reaction rate constants (s ) determined for these reactions are resins (18) (1%), 1.2x10 (19) (5%), 4.8x10 (20) (0.5%), 6.5x10 (21) (1%),...

De Visscher et al. (1996) investigated the sonolysis of benzene and other monocyclic aromatic compounds in aqueous solution by 520 kHz ultrasonic waves. The experiments were performed in a 200-mL glass reactor equipped with a cooling Jacket maintained at 25 °C. At initial benzene concentrations of 3.38 and 0.45 mM, the first-order reaction rates were 0.00171 and 0.02308/min, respectively. 

Peijnenburg et al. (1992) investigated the photodegradation of a variety of substituted aromatic halides using a Rayonet RPR-208 photoreactor equipped with 8 RUL 3,000-A lamps (250-350 nm). The reaction of 1,3-dichlorobenzene (initial concentration 10 M) was conducted in distilled water and maintained at 20 °C. Though no products were identified, the investigators reported photohydrolysis was the dominant transformation process. The measured pseudo-first-order reaction rate constant and corresponding half-life were 0.008/min and 92.3 min., respectively. 

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