Intrinsic chemical rate constant

It is the ratio of the measured rate constant to the intrinsic chemical rate constant. 

After these qualitative considerations we will go on and study chemical reactions in solution in more detail and determine the effective rate constant in terms of fundamental properties such as a diffusion constant D and the intrinsic bimolecular rate constant ks. 

Intrinsic Kinetics. Chemisorption may be regarded as a chemical reaction between the sorbate and the soHd surface, and, as such, it is an activated process for which the rate constant (/ ) follows the familiar Arrhenius rate law ... 

In the former case, the rate is independent of the diffusion coefficient and is determined by the intrinsic chemical kinetics in the latter case, the rate is independent of the rate constant k and depends on the diffusion coefficient the reaction is then diffusion controlled. This is a different kind of mass transport influence than that characteristic of a reactant from a gas to ahquid phase. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

Bench scale experiments. The reactors used in these experiments are usually designed to operate at constant temperature, under conditions that minimize heat and mass transfer limitations on reaction rates. This facilitates an accurate evaluation of the intrinsic chemical effects. 

In a similar fashion, it is easily shown that the apparent activation energy of the reaction may differ appreciably from the intrinsic activation energy of the chemical reaction. The apparent rate constant is equal to the product of the effectiveness factor and the true rate constant and, in the limit of low effectiveness factors, it can be said that... 

Using the various simplifications above, we have arrived at a model for reaction 11.9 in which only one step, the chemical conversion occurring at the active site of the enzyme characterized by the rate constant k3, exhibits the kinetic isotope effect Hk3. From Equations 11.29 and 11.30, however, it is apparent that the observed isotope effects, HV and H(V/K), are not directly equal to this kinetic isotope effect, Hk3, which is called the intrinsic kinetic isotope effect. The complexity of the reaction may cause part or all of Hk3 to be masked by an amount depending on the ratios k3/ks and k3/k2. The first ratio, k3/k3, compares the intrinsic rate to the rate of product dissociation, and is called the ratio of catalysis, r(=k3/ks). The second, k3/k2, compares the intrinsic rate to the rate of the substrate dissociation and is called forward commitment to catalysis, Cf(=k3/k2), or in short, commitment. The term partitioning factor is sometimes used in the literature for this ratio of rate constants. 

The intrinsic inertness of the peptide bond is demonstrated by a study of the chemical hydrolysis of N-benzoyl-Gly-Phe (hippurylphenylalanine, 6.37) [67], a reference substrate for carboxypeptidase A (EC 3.4.17.1). In pH 9 borate buffer at 25°, the first-order rate constant for hydrolysis of the peptide bond ( chem) was 1-3 x 10-10 s-1, corresponding to a tm value of 168 y. This is a very slow reaction indeed, confirming the intrinsic stability of the peptide bond. Because the analytical method used was based on monitoring the released phenylalanine, no information is available on the competitive hydrolysis of the amide bond to liberate benzoic acid. 

Intrinsic barriers define the intrinsic velocity by which an ET (or any other reaction) proceeds. Although they are tailored to the particular acceptor considered, chemical intuition suggests that if the main reaction site is kept constant, e.g. the S—S bond, the intrinsic ET rate should be some function of the substituents at the atoms of concern. Let us consider first the data... 

Marcus5 8 taught us that the most appropriate and useful kinetic measure of chemical reactivity is the intrinsic barrier (AG ) rather than the actual barrier (AG ), or the intrinsic rate constant (kQ) rather than the actual rate constant (k) of a reaction. These terms refer to the barrier (rate constant) in the absence of a thermodynamic driving force (AG° = 0) and can either be determined by interpolation or extrapolation of kinetic data or by applying the Marcus equation.5 8 For example, for solution phase proton transfers from a carbon acid activated by a ji-acceptor (Y) to a buffer base, Equation (1), k0 may be determined from Br A ns ted-type plots of logki or... 

The overall (effective) reaction rate of a bimolecular reaction is, in general, determined by both the diffusion rate and the chemical reaction rate. A steady-state limit for the effective reaction rate is approached at long times and the rate constant takes a simple form. When the chemical reaction is very fast, the overall rate is determined by the diffusion rate, which is proportional to the diffusion constant. In the opposite limit where the chemical reaction is very slow, the overall rate is equal to the intrinsic rate of the chemical reaction. 

In the activation-controlled limit where ks C k d, the rate constant is seen to be ks, that is, the reaction rate is determined by the intrinsic rate constant alone. The majority of chemical reactions in liquid solution are activation controlled. 

Some of this theoretical thinking may be utilized in reactor analysis and design. Illustrations of gas-liquid reactors are shown in Fig. 19-26. Unfortunately, some of the parameter values required to undertake a rigorous analysis often are not available. As discussed in Sec. 7, the intrinsic rate constant kc for a liquid-phase reaction without the complications of diffusional resistances may be estimated from properly designed laboratory experiments. Gas- and liquid-phase holdups may be estimated from correlations or measured. The interfacial area per unit reactor volume a may be estimated from correlations or measurements that utilize techniques of transmission or reflection of light, though these are limited to small diameters. The combined volumetric mass-transfer coefficient kLa, can be also directly measured in reactive or nonreactive systems (see, e.g., Char-pentier, Advances in Chemical Engineering, vol. 11, Academic Press, 1981, pp. 2-135). Mass-transfer coefficients, interfacial areas, and liquid holdup typical for various gas-liquid reactors are provided in Tables 19-10 and 19-11. 

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