Catalysis frequency factor

Case 3 will be of special interest in this paper. It is encountered in all the examples listed above for Equations (1) and (2). Especially in heterogeneous catalysis it shows what has been called the compensation effect (C.E.). This term indicates that an increase in the enthalpy of activation AH frequently has not the expected result of a considerable decrease in the rate constant, because there occurs a simultaneous increase in the entropy of activation AS or of the frequency factor A, which compensates partly or entirely for the change in the exponent (AH /Er, or AE/ET). 

The catalyzed pathway for a reaction might have a faster rate than the uncatalyzed pathway either because of a larger frequency factor A or a smaller activation energy Ea in the Arrhenius equation. Usually, however, catalysts function by making available a reaction pathway with a lower activation energy (Figure 12.17). In the decomposition of hydrogen peroxide, for example, catalysis by I-lowers Ea for the overall reaction by 19 kj/mol. 

Table 10.2 presents the kinetic information for the main reactions, in which the frequency factors have been calculated from turnover-frequency (TOF) data [8, 9]. This term, borrowed from enzymatic catalysis, quantifies the specific activity of a catalytic center. By definition, TOF gives the number of molecular reactions or catalytic cycles occurring at a center per unit of time. For a heterogeneous catalyst the number of active centers can be found by means of sorption methods. Let us consider that the active sites are due to a metal atom. By definition [15] we have ... 

This is a correlation which has been frequently reported in the literature. While there exists undoubtedly many instrinsic relationships between activation energies and frequency factors in catalysis, some of the observations of this type may be traceable to the effect of diffusion parameters. 

AT any biochemical processes involve very rapid reactions and transient intermediates. Frequently the rapidity of the reaction causes major technical difficulties in ascertaining the details of the events occurring in the process. One approach to overcome this inherent problem is to utilize the fact that most chemical reactions are temperature dependent. This relationship is quantitatively described by the Arrhenius equation, k = Ae E /RT, where k represents the rate constant, A is a constant (the frequency factor), and Ea is the energy of activation. Consequently, by initiating the reaction at a sufficiently low temperature, interconversion of the intermediates may be effectively stopped and they may be accumulated and stabilized individually. Although the focus of this article is on the application of this low-temperature approach to the study of enzyme catalysis, that is, cryoenzymology, the technique is potentially of much wider biological application (1, 2,3). 

One way it may be possible to increase the frequency factor alone is by inducing the sites to form in patches on the total surface. This would make site density beneficially high within the patches without an increase in the total number of sites per unit of catalyst, as measured by some kind of test, such as adsorption. Theoretical studies of adsorption have considered both uniform and patch-wise site distributions in physical adsorption. The consequences of this dichotomy need to be understood as they relate to catalysis. 

Van t Hoff, as well as some other scientists, studied the increase in rate constants with increasing temperature. An earlier equation was modified by the Swedish chemist Svante Arrhenius to the form noted below. The Arrhenius equation is more than a semi-empirical equation to account for the usual doubling or tripling of reaction rate for every 18°F (10°C) increase. The E denotes the energy needed to induce reaction and A represents a frequency factor related to the probability of reaction. These parameters would be better understood during the 1930s with the development of transition-state theory. Wilhelm Ostwald s contributions to kinetics were many and included the application of thermodynamics to kinetics and mechanism as well as the explanation of catalysis. This magnificent triumvirate of physical chemists would all win Nobel Prizes in chemistry van t Hoff (1901) Arrhenius (1903) Ostwald (1909). 

The preexponential or the frequency factor A is catalyst dependent, that is, it varies with the extent of surface and has the same units as the rate constant k. On the basis of the collision theory, it can be estimated that the frequency factor of a unimo-lecular heterogeneous reaction is smaller than that of its homogeneous counterpart by a factor of 10. It follows that, for efficient catalysis, the activation energy ,4 of the catalyzed reaction should be at least 80 kj/mol lower than that of the uncatalyzed one at 298 K. At higher reaction temperatures, the difference in must also be higher in order to keep the advan-... 

Ultrasound denotes sound waves with a frequency of more than 20 kHz. In the field of two-phase catalysis ultrasound can be used to create stable emulsions and extremely large liquid-liquid phase boundaries. Special dipping oscillators provide a source of ultrasound in autoclaves. When the reaction mixture is exposed to ultrasonic vibration under stirring [29], the conversion rate of 1-hexene hydrofor-mylation is increased by a factor of 2 under standard conditions. 

It was recognized early in the history of heterogeneous catalysis that, in many instances, only a relatively small proportion of the surface was catalytically active. The pre-exponential rate factor was seen to be very small in relation to likely collision frequencies of molecules adsorbed on the surface, taking into account steric requirements, while poisoning (inhibition of the catalysed reaction) could result from surprisingly low levels of specific impurities (see below). Hence the term active sites was coined to describe those localities on the surface which would induce the desired chemical reaction. 

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