Rate process

Rate processes are those in which one component of a feed stream is transferred from the feed phase into a second phase owing to a gradient in a physical property. Gradients in pressure or concentration are the most common. Other gradients include temperature, electric fields, and gravity. The limiting step upon which design is based is the rate of transfer of the particular component from the feed material to the second phase. For relative motion of the various chemical species (rate), the mathematical description relates the rate of transfer of a particular compo- 

A second example is the use of a mass-transfer coefficient to relate the flux across a fluid boundary layer (fluid region over which the solute concentration changes from the bulk phase value) to the concentration difference across the layer  

In choosing between these two models, one needs to consider the specific process. The use of mass-transfer coefficients represents a lumped, more global view of the many process parameters that contribute to the rate of transfer of a species from one phase to another, while diffusion coefficients are part of a more detailed model. The first gives a macroscopic view, while the latter gives a more microscopic view of a specific part of a process. For this reason, the second flux equahon is a more engineering representation of a system. In addihon, most separahon processes involve complicated flow patterns, limihng the use of Pick s Law. 

A few points become obvious. First, in each case, the concentrahon difference across the barrier changes with axial posihon x. So, the flux (or rate) will change with posihon. Second, for cocurrent flow, the concentrahon difference (the driving force for mass transfer) becomes very small as the flow moves axially away from the entrance x = 0). So, the separahon becomes less efficient as the barrier beco- 

To account for the variation in driving force, a log-mean driving force is used instead of a linear one  

Knowledge of the principles of kinetics (rate processes), analytical chemistry and therapeutics is essential in providing an effective concentration of a drug at the site of action.  

Pharmacokinetics and biopharmaceutics are the result of such a successful integration of the various disciplines mentioned above. 

The first such approach was made by Teorell (1937), when he published his paper on 

Please note that in every case, the use must he preceded by observations. 

Generally, the goal of biopharmaceutical studies is to develop a dosage form that will provide consistent bioavailability at a desirable rate. The importance of a consistent bioavailability can be very well appreciated if a drug has a narrow therapeutic range (e.g. dlgoxin) where small variations in blood concentrations may result in toxic or subtherapeutic concentrations. 

It is convenient initially to classify elementary reactions either as energy-transfer-limited or chemical reaction-rate-limited processes. In the former class, the observed rate corresponds to the rate of energy transfer to or from a species either by intermolecular collisions or by radiation, or intramolecular-ly due to energy transfer between different degrees of freedom of a species. All thermally activated unimolecular reactions become energy-transfer-limited at high temperatures and low pressures, because the reactant can receive the necessary activation energy only by intennolecular collisions. 

Chemical processes, in contrast, are processes that are not limited by rates of energy transfer. In thermal processes, chemical reactions occur under conditions in which the statistical distribution of molecular energies obey the Maxwell-Boltzmann form, i.e., the fraction of species that have an energy E or larger is proportional to e p(—E/RT). In other words, the rates of intermolecular collisions are rapid enough that all the species become thermalized with respect to the bulk gas mixture (Golden and Larson, 1984 Benson, 1976). 

The transition state theory (TST) developed by Eyring and co-workers has been shown to be extremely useful to describe both the qualitative and quantitative features of chemical processes in the gas and condensed phases (Eyring, 1935 Glasstone et ai, 1941). As we shall discuss below, TST also plays a central role in the determination of rate parameters by quantum mechanics. 

At present two major approaches exist for the implementation of the TST theory. In the first approach, partition functions are used to describe the chemical equilibrium between the reactant(s) and the transition state (Laidler, 1987 Moore and Pearson, 1981). The partition function for the transition 

State is modified to account for the reaction coordinate. This approach readily allows the rationalization of the various temperature coefficients observed the preexponential factors in experimental data (Moore and Pearson, 1981) however, this method provide no insights for the expected activation energies for the reactions. 

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A quantitative theory of rate processes has been developed on the assumption that the activated state has a characteristic enthalpy, entropy and free energy the concentration of activated molecules may thus be calculated using statistical mechanical methods. Whilst the theory gives a very plausible treatment of very many rate processes, it suffers from the difficulty of calculating the thermodynamic properties of the transition state. 

It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

S. Glasstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes, McGraw-Hill, New York, 1941. 

Kang H C and Weinberg W H 1994 Kinetic modeiing of surface rate processes Surf. Sol. 299-300 755... 

Giasstone S, Laidier K J and Eyring Fi 1941 The Theory of Rate Processes (New York McGraw-Fiiii)... 

Collins F C and Kimball G E 1949 Diffusion-controlled rate processes J. Colloid Sol. 4 425... 

Berezhkovskii A M and Zitzerman V Yu 1990 Activated rate processes in a multidimensional case Physica A 166 585-621... 

Berezhkovskii A M and Zitserman V Yu 1991 Activated rate processes in the multidimensional case. Consideration of recrossings in the multidimensional Kramers problem with anisotropic friction Chem. Phys. 157 141-55... 

Berezhkovskii A M and Zitserman V Yu 1992 Multidimensional activated rate processes with slowly relaxing mode Physica A 187 519-50... 

A3.8.4 QUANTUM ACTIVATED RATE PROCESSES AND SOLVENT EFFECTS... 

Nitzan A 1988 Activated rate processes in condensed phases the Kramers theory revisited Adv. Chem. Phys. 70 489 Onuchic J N and Wolynes P G 1988 Classical and quantum pictures of reaction dynamics in condensed matter resonances, dephasing and all that J. Phys. Chem. 92 6495... 

Singh S, Krishnan R and Robinson G W 1990 Theory of activated rate processes with space-dependent friction Chem. 

Straus J B and Voth G A 1992 Studies on the influence of nonlinearity in classical activated rate processes J. Chem. Phys. 96 5460... 

See, for example, Poliak E 1986 Theory of activated rate processes a new derivation of Kramers expression J. Chem. Phys. 85 865... 

Poliak E 1990 Variational transition state theory for activated rate processes J. Chem. Phys. 93 1116 Poliak E 1991 Variational transition state theory for reactions in condensed phases J. Phys. Chem. 95 533 Frishman A and Poliak E 1992 Canonical variational transition state theory for dissipative systems application to generalized Langevin equations J. Chem. Phys. 96 8877... 

Berezhkovskii A M, Poliak E and Zitserman V Y 1992 Activated rate processes generalization of the Kramers-Grote-Hynes and Langer theories J. Chem. Phys. 97 2422... 

Poliak E, Grabert H and Hanggi P 1989 Theory of activated rate processes for arbitrary frequency dependent friction solution of the turnover problem J. Chem. Phys. 91 4073... 

Cao J and Voth G A 1996 A unified framework for quantum activated rate processes I. General theory J. Chem. Phys. 105 6856... 

Levine R D 1969 Quantum Mechanics of Molecular Rate Processes (London Oxford University Press)... 

Gutowsky H S and Holm C H 1956 Rate processes and nuclear magnetic resonance spectra. II. Hindered internal rotation of amides J. Chem. Phys. 25 1228-34... 

Zwanzig R 1990 Rate processes with dynamical disorder 4cc. Chem. Res. 23 148-52... 

Many equilibrium and rate processes can be systematized when the influence of each substituent on the reactivity of substrates is assigned a characteristic constant cr and the reaction parameter p is known or can be calculated. The Hammett equation... 

The rate process for termination is hindered through the Trommsdorff effect. 

Adsorption Dynamics. An outline of approaches that have been taken to model mass-transfer rates in adsorbents has been given (see Adsorption). Detailed reviews of the extensive Hterature on the interrelated topics of modeling of mass-transfer rate processes in fixed-bed adsorbers, bed concentration profiles, and breakthrough curves include references 16 and 26. The related simple design concepts of WES, WUB, and LUB for constant-pattern adsorption are discussed later. 

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