Chemical reactions coefficients

Chemical reaction coefficient, 25 281,283, 290 combinations of, 25 293t effect on critical value of mass transfer Peclet number, 25 284t Chemical reaction engineering (CRE), 22 330... 

Since the principle of conservation of masses applies to chemical reactions, coefficients must often be used in writing chemical reactions so that the number of atoms of products is equal to the number of atoms of reactants, An example is the reaction of two moles of hydrogen with one mole of oxygen to form ru n moles of water... 

The rate of interphase mass transfer is affected by the physical and chemical characteristics of the system and the mechanical features of the equipment. The former include viscosities and densities of the phases, interfacial surface properties, diffusion coefficients, and chemical reaction coefficients. The latter include, for example, the type and diameter of the impeller, vessel geometry, the flow rate of each phase, and the rotational speed of the impeller. 

Quantitative results in Table 30-1 reveal that one achieves maximum conversion of reactants to products in ideal (i.e., 30%) and non-ideal (i.e., 25%) packed catalytic tubular reactors when the mass transfer Peclet number is approximately 6 for second-order irreversible chemical kinetics with an interpeUet porosity of 50%. Specific values for PeMT and the corresponding maximum conversion are sensitive to the simple mass transfer Peclet number and the chemical reaction coefficient, where the latter is defined by the product of the effectiveness factor, the interpeUet Damkohler number, and the catalyst filling factor. For example, when Pesimpie is 50 and the chemical reaction coefficient is 5 for second-order irreversible chemical kinetics, the critical value of PeMT [i e., (Re Sc)criacai] is approximately 30, whereas maximum conversion is obtained when PeMT is only 6. Hence, one concludes that the ideal simulations in Table 30-1 with a 0,... 

TABLE 30-2 Combinations of Pesimpie, Pcmt, and the Chemical Reaction Coefficient That Yield Maximum Conversion of Reactants to Products in Non-Ideal Packed Catalytic Tiibular Reactors ... 

Another, purely experimental possibility to obtain a better estimate of the friction coefficient for rotational motion in chemical reactions consists of measuring rotational relaxation times of reactants and calculating it according to equation (A3,6,35) as y. =... 

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. 

Instead of concentrating on the diffiisioii limit of reaction rates in liquid solution, it can be histnictive to consider die dependence of bimolecular rate coefficients of elementary chemical reactions on pressure over a wide solvent density range covering gas and liquid phase alike. Particularly amenable to such studies are atom recombination reactions whose rate coefficients can be easily hivestigated over a wide range of physical conditions from the dilute-gas phase to compressed liquid solution [3, 4]. 

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

Stoichiometric relationships and calculations are important in many quantitative analyses. The stoichiometry between the reactants and products of a chemical reaction is given by the coefficients of a balanced chemical reaction. When it is inconvenient to balance reactions, conservation principles can be used to establish the stoichiometric relationships. 

Rates determined by monitoring different species in a chemical reaction need not have the same value. The rate R in equation A5.2 and the rate R in equation A5.3 will have the same value only if the stoichiometric coefficients of A and C in reaction A5.1 are the same. In general, the relationship between the rates R and R is... 

Mass-Transfer Coefficients with Chemical Reaction. Chemical reaction can occur ia any of the five regions shown ia Figure 3, ie, the bulk of each phase, the film ia each phase adjacent to the iaterface, and at the iaterface itself. Irreversible homogeneous reaction between the consolute component C and a reactant D ia phase B can be described as... 

The Rheometric Scientific RDA II dynamic analy2er is designed for characteri2ation of polymer melts and soHds in the form of rectangular bars. It makes computer-controUed measurements of dynamic shear viscosity, elastic modulus, loss modulus, tan 5, and linear thermal expansion coefficient over a temperature range of ambient to 600°C (—150°C optional) at frequencies 10 -500 rad/s. It is particularly useful for the characteri2ation of materials that experience considerable changes in properties because of thermal transitions or chemical reactions. 

Another parameter of relevance to some device appHcations is the absorption characteristics of the films. Because the k quantum is no longer vaUd for amorphous semiconductors, i -Si H exhibits a direct band gap (- 1.70 eV) in contrast to the indirect band gap nature in crystalline Si. Therefore, i -Si H possesses a high absorption coefficient such that to fully absorb the visible portion of the sun s spectmm only 1 p.m is required in comparison with >100 fim for crystalline Si Further improvements in the material are expected to result from a better understanding of the relationship between the processing conditions and the specific chemical reactions taking place in the plasma and at the surfaces which promote film growth. 

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. 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

Penetration theoiy often is used in analyzing absorption with chemical reaction because it makes no assumption about the depths of penetration of the various reacting species, and it gives a more accurate result when the diffusion coefficients of the reacting species are not equal. When the reaction process is veiy complex, however, penetration theoiy is more difficult to use than film theory, and the latter method normally is preferred. 

The gas-phase rate coefficient fcc is not affecded by the fact that a chemic reaction is taking place in the liquid phase. If the liquid-phase chemical reaction is extremely fast and irreversible, the rate of absorption may be governed completely by the resistance to diffusion in the gas phase. In this case the absorption rate may be estimated by knowing only the gas-phase rate coefficient fcc of else the height of one gas-phase transfer unit Hq =... 

The liquid-phase rate coefficient is strongly affected by fast chemical reactions and generally increases with increasing reac tion rate. Indeed, the condition for zero hquid-phase resistance m/k-d) imphes that either the equilibrium back pressure is negligible, or that... 

It is important to understand that when chemical reactions are involved, this definition of Cl is based ou the driving force defined as the difference between the couceutratiou of un reacted solute gas at the interface and in the bulk of the liquid. A coefficient based ou the total of both uureacted and reached gas could have values. smaller than the physical-absorption mass-transfer coefficient /c . 

Extrapolation of KgO data for absorption and stripping to conditions other than those for which the origin measurements were made can be extremely risky, especially in systems involving chemical reactions in the liquid phase. One therefore would be wise to restrict the use of overall volumetric mass-transfer-coefficient data to conditions not too far removed from those employed in the actual tests. The most reh-able data for this purpose would be those obtained from an operating commercial unit of similar design. 

In turbulent flow, axial mixing is usually described in terms of turbulent diffusion or dispersion coefficients, from which cumulative residence time distribution functions can be computed. Davies (Turbulence Phenomena, Academic, New York, 1972, p. 93), gives Di = l.OlvRe for the longitudinal dispersion coefficient. Levenspiel (Chemical Reaction Engineering, 2d ed., Wiley, New York, 1972, pp. 253-278) discusses the relations among various residence time distribution functions, and the relation between dispersion coefficient and residence time distribution. 

Traditional Design Method The traditionally employed conventional procedure for designing packed-tower gas-absorption systems involving chemical reactions makes use of overall volumetric mass-transfer coefficients as defined by the equation... 

In 1966, in a paper that now is considered a classic, Danckwerts and Gillham [Tmns. Inst. Chem. Eng., 44, T42 (1966)] showed that data taken in a small stirred-ceU laboratoiy apparatus could be used in the design of a packed-tower absorber when chemical reactions are involved. They showed that if the packed-tower mass-transfer coefficient in the absence of reaction (/cf) can be reproduced in the laboratory unit, then the rate of absorption in the l oratoiy apparatus will respond to chemical reactions in the same way as in the packed column even though the means of agitating the hquid in the two systems might be quite different. 

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