Reaction rate as a function of temperature

The activation enthalpies and entropies are in principle dependent on temperature (eq. 12.22)), but only weakly so. For a limited temperature range they may be treated as constants. Obtaining these quantities experimentally is possible by measuring the reaction rate as a function of temperature, and plotting ln(k/T) against T" (eq. 12.24). 

FIGURE 2.11. Reaction Rate as a Function of Temperature (Arrhenius Equation)... 

Arrhenius plots permit the determination of activation energies (Ea) associated with a particular pathway of degradation that allows one to estimate reaction rates as a function of temperature. Such information, if demonstrated to accurately model... 

Figure 4-6 Interface reaction rate as a function of temperature, pressure, and composition. The vertical dashed line indicates the equilibrium condition (growth rate is zero), (a) Diopside growth and melting in its own melt as a function of temperature with the following parameters Te= 1664K at 0.1 MPa, A5m-c = 82.76J mol K , E/R —30000 K, 4 = 12.8 ms K, and AV c l. l x 10 m /mol. The dots are experimental data on diopside melting (Kuo and Kirkpatrick, 1985). (b) Diopside growth and melting in its own melt as a function of pressure at 1810 K (Tg = 1810 K at 1 GPa from the equilibrium temperature at 0.1 MPa and the Clapeyron slope for diopside). (c) Calcite growth and dissolution rate in water at 25 °C as a function of Ca " and CO concentrations.

Figure 4-6 Interface reaction rate as a function of temperature, ...

This equation was used to calculate the reaction rates as a function of temperature and rongalite/Ni(II) concentration ratio, and Table 11.6 shows the results for a ratio of 1.5/0.5. The data in this table confirm the previous conclusion that a temperature of about 333 K should be used in order to have an economical and technologically acceptable reaction rate for the reduction of Ni(II) by rongalite and to avoid the large influence of autoinhibition by formaldehyde, an unfavourable effect that increases with temperature. 

With these data it is possible to calculate the reaction rate as a function of temperature and conversion. This is at the basis of modeling using the simplified Benito-Perez model consisting of two balances ... 

The behavior of the reaction rate as a function of temperature dispels any notion that the reaction is simple. Figure 3 shows that there is a maximum in the first-order rate constant-temperature curve at approximately 80 °C. At such a low temperature, the rate-temperature maximum cannot be explained by depolymerization, nor can it be explained by deactivation of the catalyst as a result of more rapid polymer accumulation on the catalyst at higher temperatures since the maximum is obtained for initial rates measured as a function of temperature. Theoretical considerations predict that a maximum in the rate-temperature curve may be expected from the Langmuir-Hinshelwood model for polymerization on solid surfaces but not from the Rideal model (5). The rate of reaction for the Langmuir-Hinshelwood model is given by ... 

To predict nutrient deterioration, knowledge of the reaction rate as a function of temperature of storage or processing is needed. The kinetics of ascorbic acid destruction have been examined most extensively in model systems, with particular attention being given to intermediate moisture foods (17, 71,78,79). Most of the data available for vitamin C losses in actual food systems are insuflBcient to calculate the kinetic parameters needed to predict losses during heat treatment or storage. 

The F + H2 - FH + FI reaction has received considerable attention from theory as it is an excellent system for the calibration of methods there is experimental data for the reaction rate as a function of temperature, information on product vibrational energy distribution, and the reaction thresholds are known for both H2 and In Table IX, several... 

The influence of capillary condensation upon catalyst effectiveness factor has been assessed both by approximate calculations and by pore network simulations. It was found that catalyst effectiveness could be affected by the presence of capillary condensation, depending on the ratio of reaction rates in the gas and liquid phases. The effectiveness factor under conditions of capillary condensation is sensitive to operating conditions of the reactor, such as pressure, and to properties of the catalyst pore structure like pore-size distribution and connectivity. Once the catalyst pellet contains some pores filled with liquid, the kinetics of the process become dependent upon the phase equilibria of the system. This can lead to multiple steady states in the reaction rate as a function of temperature or pressure, because the current state of the catalyst pellet depends on the history of temperature and pressure profiles to which it has been subjected. 

Temperature also affects the rate of chemical reactions. An increase in temperature generally results in an increased rate of reaction. This can be understood by noting that most reactions, viewed from the molecular perspective, require some energy input to get them started. Increasing the temperature creates more energetic molecular collisions, and the rate increases. Experimental studies of reaction rates as a function of temperature provide the data needed to measure the activation energy. 

The available experimental systems for potentiometric measmements, as well as for measmements of the electrochemical reaction rates as a function of temperature are represented here. 

In the earlier chapters, we presented the reaction rates as a function of temperature and the concentration of the species involved. In this chapter, we will elaborate on the theories behind the concentration dependencies, temperature dependencies, and how the overall reaction mechanisms are proposed and elucidated. In such a context, it is reasonable to start from... 

The feedback effect of heat evolution on the rate of exothermic reactions may cause thermal runaway. This is a major issue in the operation of industrial reactors, as the loss of control of a chemical reactor constitutes a serious hazard everybody has in mind the SEVESO accident or those which occured recently in the Swiss industry. Thermal instability is due to the irreducible coupling between heat accumulation and the quasi-exponential increase of reaction rate as a function of temperature accounted for by Arrhenius equation. This problem can be studied by the methods of non linear dynamics. Here again, characteristic times make it possible to establish simple criteria which give at least an order of magnitude for dangerous and safe ranges of operation. 

Reaction rates, as a function of temperature, for different heating rates were obtained by differentiation of the weight loss curves and are displayed in Fig. 2.12. The two-stage reaction encountered during slow activation can now be recognized... 

At the present time, it is not possible in general to obtain the free energy of activation from numerical data tabulated in the literature. The enthalpy of activation is obtained experimentally by measuring the reaction rate as a function of temperature (by a plot of Log k/T as a function of (1/T)), and Arrhenius energy of activation by a plot of log k as a function of (1/T). The two plots should be linear with slopes equal to... 

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