Arrhenius model

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

The temperature profiles of the rate constants for reaction (7-10) are shown for the Arrhenius model (a) and for transition state theory (b). Panels (c) and (d) present the corresponding data for reaction (7-11). Data are from Refs. 1 and 2 see Table 7-1. 

Arrhenius model, 156, 159-160 Association equilibria, 145-148 Autocatalysis (see Product-catalyzed reactions)... 

If isotope effects arise solely from the difference between isotopic zero-point energy differentials in the reactant state and transition state, with no role of excited vibrational states, then - A5p) = 0 on the Eyring model and Ah = Ad on the Arrhenius model. Thus ... 

Hopf bifurcation analysis with Arrhenius model birth and growth of oscillations... 

Table 2.6 presents constants for Carreau-WLF (amorphous) and Carreau-Arrhenius models (semi-crystalline) for various common thermoplastics. In addition to the temperature shift, Menges, Wortberg and Michaeli [50] measured a pressure dependence of the viscosity and proposed the following model, which includes both temperature and pressure viscosity shifts ... 

Table 11.2 Carreau and Arrhenius model constants for the Coupled Heat Transfer Flow Problem...

Using exposure to higher temperature to accelerate bond degradation has been studied in detail by Gillespie and coworkers during the last 10 years. Most recently (48), effect of dry heat was compared to earlier work with wet heat. They concluded that the Arrhenius model does describe the degradation of the bonds,... 

VFT behavior is obtained by equating z = T/(T — Tv ft) and noting that increment of chemical potential Ap — Vft [65], Fitting the VFT model to the experimental results of iH in the paraelectric phase gives Tv ft = 228 and Ap 0.02 eV. Identifying the temperature at which xB deviates from the Arrhenius model with the onset of cooperativity yields a minimum cluster size given by... 

Let us discuss a system that consists of a number of particles where their relaxation is provided by the reorientations (a jump or another type of transition) of particles between two local equilibrium states. In the spirit of the Arrhenius model (26), the first requirement for the relaxation is that the particles have enough energy to overcome the potential barrier Ea between the states of local equilibrium for the elementary constituents of the system under consideration. Thus,... 

The progressive increase in the starting product formation rate observed with increasing the temperature up to 80 °C and the successive decrease beyond this value confirmed the occurrence of reversible biocatalyst inactivation. The Arrhenius model was used for estimating the apparent activation enthalpies of the acetylation of geraniol (AH = 35kJ/mol) and the reversible inactivation of the biocatalyst (AHf = 150kJ/mol) [15]. The thermodynamic data were compared with those of ethanol acetylation (Table 6.3). 

Table 6.3 Apparent thermodynamic parameters of geraniol and ethanol acetylations by lyophilized cells of A. oryzae MIM estimated by the Arrhenius model under different conditions, with reference temperature 50°C.

In this chapter we will always represent an acid as simply dissociating. This does not mean we are using the Arrhenius model for acids. Since water does not affect the equilibrium position, we leave it out of the acid dissociation reaction for simplicity. 

Figure 2-14 Applicability of the Arrhenius Model to the Apparent Viscosity versus Temperature Data on a Concentrated Orange Juice Serum Sample (Vitali and Rao, 1984b) is Shown.

The Arrhenius equation did not describe very well the influence of temperature on viscosity data of concentrated apple and grape juices in the range 60-68 °Brix (Rao et al., 1984, 1986). From non-linear regression analysis, it was determined that the empirical Fulcher equation (see Ferry, 1980 p. 289, Soesanto and Williams, 1981) described the viscosity versus temperature data on those juice samples better than the Arrhenius model (Rao et al., 1986) ... 

Because of the availability of reliable TR data from 65 to 95°C during gelatiniza-tion (Equations 8.42 and 8.43), as well as of both the experimental heat penetration data and computer simulation based temperatures, it was considered safe to assume the temperature profile described by Equation 8.43 from 95 to 121°C. Comparison of the numerically calculated temperatures with the experimental profiles to be discussed strongly support the assumption of an Arrhenius model (Equation 8.41) for the magnitudes of ja fiom 95 to 121°C. 

The rate constant (/ ,) was expressed in terms of the results of the computer simulations, for which a non-adiabatic transition-state theory (TST) model was used. Since the experimental results were analyzed in terms of a phenomenological Arrhenius model [158], we relate experiment (left-hand side) and theory (right-hand side) in terms of the following two equations. For the weakly temperature-dependent prefactor we have ... 

E(j is the activation energy of the deactivation rate and may be determined from an Arrhenius plot for a(T), as shown in Fig. 5. In addition to the a(T) values for the three laboratory runs in Fig. 3, Fig. 5 also contains the a(T) value for Run E-3. Although the data do not fit an Arrhenius model particularly well, the activation energy derived from this figure is about 20 kcal/mole. This value is consistent with the known range of activation energies for sintering, and shows that the rate of catalyst deactivation increases rapidly with temperature. 

Although the existence of "polyamorphism is debatable, heterogeneity is inherent in an amorphous system (29-31). Amorphous. systems, in addition to exhibiting cooperative primary or a-relaxations and non-cooperative secondary or p-relaxations, may reveal multiple secondary relaxations (32). These different relaxation processes are likely to have different temperature dependences, e.g., a-relaxations are generally described by the VTF or WLF models whereas the Johari-Gold,stein relaxations are usually de.scribed by Arrhenius model (27). 

The Arrhenius model of acids and bases If pure water itself is neutral, how does an aqueous solution become acidic or basic The first person to answer this question was the Swedish chemist Svante Arrhenius, who in 1883 proposed what is now called the Arrhenius model of acids and bases. The Arrhenius model states that an acid is a substance that contains hydrogen and ionizes to produce hydrogen ions in aqueous solution. A base is a substance that contains a hydroxide group and dissociates to produce a hydroxide ion in aqueous solution. Some household acids and bases are shown in Figure 19-3. 

As an example of the Arrhenius model of acids and bases, consider what happens when hydrogen chloride gas dissolves in water. HCl molecules ionize to form H+ ions, which make the solution acidic. 

Although the Arrhenius model is useful in explaining many acidic and basic solutions, it has some shortcomings. For example, ammonia (NH3) does not contain a hydroxide group, yet ammonia produces hydroxide ions in solution and is a well known base. Clearly, a model that includes all bases is needed. 

Compare what you have learned about the Arrhenius model and the Br0nsted-Lowry model of acids and bases. It should be clear to you that all substances classified as acids and bases by the Arrhenius model are classified as acids and bases by the Br0nsted-Lowry model. In addition, some substances not classified as bases by the Arrhenius model are classified as bases by the Br0nsted-Lowry model. 

Analyzing and Concluding Is it possible that an acid according to the Arrhenius model is not a Br0nsted-Lowry acid Is it possible that an acid according to the Brpnsted-Lowry model is not an Arrhenius acid Explain and give examples. 

Arrhenius model (p. 597) A model of acids and bases states that an acid is a substance that contains hydrogen and ionizes to produce hydrogen ions in aqueous solution and a base is a substance that contains a hydroxide group and dissociates to produce a hydroxide ion in aqueous solution. 

Arrhenius model/modelo de Arrhenius (pag. 597) Modelo de acidos y bases establece que un acido es una sustancia que contiene hidrogeno y se ioniza para producir iones hidrogeno en solucion acuosa y una base es una sustancia que contiene un grupo hidroxido y se disocia para producir un ion hidro-xido en solucion acuosa. 

The Arrhenius theory of acid-base behavior satisfactorily explained reactions of protonic acids with metal hydroxides (hydroxy bases). It was a significant contribution to chemical thought and theory in the latter part of the nineteenth century. The Arrhenius model of acids and bases, although limited in scope, led to the development of more general theories of acid-base behavior. They will be considered in later sections. 

---