Chemical reaction rate coefficients

The global mean surface temperature is usually taken as 288 K, at which [M] = 2.55 x 1019 molecules cm 3. (If one chooses 298 K, which is the standard temperature at which chemical reaction rate coefficients are usually reported, then [M] = 2.46 x 1019 molecules cm 3.) In example calculations of chemical reaction rates, in which a value of [M] is needed at the Earth s surface, we will often simply use 2.5 x 1019 molecules cm-3 as the approximate value at 298 K. 

If diffusion and chemical reaction rate coefficients are high with respect to the flow of the bulk reactant gas supply (similar to the situation of a well-stirred reactor in which the contents are in thermodynamic equilibrium), so-called CVD diagrams or stability diagrams can be used to predict the process conditions necessary for... 

The chemical reaction rate coefficients contributing to the production terms in the... 

ABSTRACT. A description is given of calculations of chemical reaction rate coefficients at low temperatures (<100 K). Fast reactions relevant to interstellar chemistry are emphasized. Several comparisons with experimental data are made. The review concentrates on ion-molecule reactions, although neutral reactions are also briefly discussed. 

According to the above definitions, diffusion-controlled reactions are generally characterized by kdiff kchem- It should be noted though, that for reactions between highly mobile radical species, this condition is not always satisfied [19, 20]. In such cases, both the dififiision and chemical reaction rate coefficient contribute to the value of the observed rate coefficient. Noyes [19] and Rise [20] have reviewed several theoretical aspects of the calculation of diffusion-controlled reaction rates in solution. 

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

In evaluating their results they assumed the film theory, and, because the oxygen is sparingly soluble and the chemical reaction rate high, they also assumed that the liquid film is the controlling resistance. The results were calculated as a volumetric mass-transfer coefficient based, however, on the gas film. They found that the volumetric mass-transfer coefficient increased with power input and superficial gas velocity. Their results can be expressed as follows ... 

Chemical reaction rates, 14 607. See also Kinetic measurements Chemical reactions. See also Chemical processes Reaction entries with absorption, 2 47-48, 71-76 activated carbon for control of, 4 755 on adsorbents, 2 629-630, 650-651 atomic level of, 16 736 contexts of, 22 336 engine knock and, 22 390—391 heterogeneous, 22 331-332, 339 homogeneous, 22 339 independent and dependent, 22 336—337 mass-transfer coefficients with, 20 753-755... 

Relaxation times, MT ratios, and diffusion properties allow insight into the microstructure of various tissues. Determination of these parameters is possible by recording and analysing of a series of volume selective spectra, even for metabolites with relatively low concentrations in vivo. For recording series of spectra usually one parameter is changeable (e.g., inversion time TI for Ti measurements, echo time TE for T2 measurements, MT preparation for assessment of spin transfer and chemical reaction rates, or diffusion sensitizing gradients for assessment of apparent diffusion coefficients or even diffusion... 

Table 1-1 a Reaction rate coefficients for some chemical reactions in aqueous solutions... 

The CEB method can be extended to chemically reactive species by introducing decay factors into the mass balances for the chemical species. The decay factors can be evaluated from data for the composition of emissions and of the ambient aerosol. They can be related to first order reaction rate coefficients measured in the laboratory by means of an appropriate atmospheric model. 

Both the mass transfer kinetic parameters (diffusion in the phases, D, D j, surface renewal frequency, s) and chemical reaction rate constants (kg, kj) strongly influence enhancement of the absorption rate. The particle size, dp, the dispersed liquid holdup, e and the partition coefficient, H can also strongly alter the absorption rate [42-44,46,48]. Similarly, the distance of the first particle from the gas-liquid interface, 6q is an essential factor. Because the diffusion conditions are much better in the dispersed phase (larger solubility and, in most cases, larger diffusivity, as well) the absorption rate should increase with the decrease of the (5g value. 

Obviously, the importance of diffusion on slow chemical reaction rates is small. It is only when the diffusion rate coefficient 4irRD is comparable with or less than the activation-limited rate coefficient that the effect of diffuse process becomes apparent. Noyes [5] pointed out that the steady-state rate coefficient of eqn. (26) is k(°°) and this can be written as... 

The rotational relaxation times of these nitrocompounds have not been measured. Comparison with the studies of perylene by Klein and Haar [253] suggests that most of these nitrocompounds have rotational times 10—20 ps in cyclohexane. For rotational effects to modify chemical reaction rates, significant reaction must occur during 10ps. This requires that electron oxidant separations should be <(6 x 10-7x 10-11)J/2 2 nm. Admittedly, with the electron—dipole interaction, both the rotational relaxation and translational diffusion will be enhanced, but to approximately comparable degrees. If electrons and oxidant have to be separated by < 2 nm, this requires a concentration of > 0.1 mol dm-3 of the nitrocompound. With rate coefficients 5 x 1012 dm3 mol-1 s 1, this implies solvated electron decay times of a few picoseconds. Certainly, rotational effects could be important on chemical reaction rates, but extremely fast resolution would be required and only mode-locked lasers currently provide < 10 ps resolution. Alternatively, careful selection of a much more viscous solvent could enable reactions to show both translational and rotational diffusion sufficiently to allow the use of more conventional techniques. 

Of more concern are the comments by De Schepper et al. [528] and Resibois and De Leener [490]. They have discussed whether such a fourth-order derivative can have meaning. A mode-coupling theory and a kinetic theory of hard spheres both indicate that the Burnett coefficient diverges at tin. There seems little or no reason for the continued use of the Burnett equation in discussing chemical reaction rates in solution. Other effects are clearly more important and far more reasonable from a theoretical point of view. 

Electrode reactions may include elementary steps involving electron transfer, ion transfer, potential-independent or chemical steps, etc. Since electrochemical reactions are heterogeneous processes, the reaction rate coefficients have units of m s 1... 

If a first-order chemical reaction is occurring, the orifice outflow competes with reactant removal and can be treated as a parallel rate process. The total rate of disappearance of a reactant will be the sum of the reactive and flow contributions, with the overall rate coefficient given by k, + kp, where kx is the reaction rate coefficient ... 

The design of packed column reactors is very similar to the design of packed columns without reaction (Volume 2, Chapter 12). Usually plug flow is assumed for both gas and liquid phases. Because packed columns are used for fast chemical reactions, often the gas-side mass transfer resistance is significant and needs to be taken into account. The calculation starts on the liquid side of the gas-liquid interface where the chemical reaction rate constant is compounded with the liquid side mass transfer coefficient to give a reaction-enhanced liquid-film mass transfer... 

Complexity in multiphase processes arises predominantly from the coupling of chemical reaction rates to mass transfer rates. Only in special circumstances does the overall reaction rate bear a simple relationship to the limiting chemical reaction rate. Thus, for studies of the chemical reaction mechanism, for which true chemical rates are required allied to known reactant concentrations at the reaction site, the study technique must properly differentiate the mass transfer and chemical reaction components of the overall rate. The coupling can be influenced by several physical factors, and may differently affect the desired process and undesired competing processes. Process selectivities, which are determined by relative chemical reaction rates (see Chapter 2), can thenbe modulated by the physical characteristics of the reaction system. These physical characteristics can be equilibrium related, in particular to reactant and product solubilities or distribution coefficients, or maybe related to the mass transfer properties imposed on the reaction by the flow properties of the system. 

TABLE 5.1 Rate Coefficients for Film Diffusion, Particle Diffusion, and Chemical Reaction Rate Processes of K+ Adsorption under Static Conditions ... 

Abstract. In this chapter we discuss approaches to solving quantum dynamics in the condensed phase based on the quantum-classical Liouville method. Several representations of the quantum-classical Liouville equation (QCLE) of motion have been investigated and subsequently simulated. We discuss the benefits and limitations of these approaches. By making further approximations to the QCLE, we show that standard approaches to this problem, i.e., mean-field and surface-hopping methods, can be derived. The computation of transport coefficients, such as chemical rate constants, represent an important class of problems where the QCL method is applicable. We present a general quantum-classical expression for a time-dependent transport coefficient which incorporates the full system s initial quantum equilibrium structure. As an example of the formalism, the computation of a reaction rate coefficient for a simple reactive model is presented. These results are compared to illuminate the similarities and differences between various approaches discussed in this chapter. 

Turning our attention to surface phenomena rather than diffusion, we recognize that species will transit across the boundary layer and may be created or destroyed in this passage due to chemical reactions which will proceed at finite rates (homogeneous gas phase reactions). Upon impacting the surface, they may adsorb and then decompose, leaving a solid thin film. This will be a heterogeneous surface reaction which will have a characteristic chemical reaction rate. One way to describe this phenomena is in terms of a mass transfer" coefficient. The mass flux can be expressed in terms of this coefficient, as follows ... 

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