Temperature-dependent activation

An implicit assumption of the foregoing treatment is that A// remains independent of temperature over the range investigated. This is very nearly correct in general, and is particularly the case given that studies of reactions in solution are usually conducted over a temperature interval of only some 30-50°. In certain circumstances the temperature profiles show curvature outside the experimental error. Such cases have, or appear to have, temperature-dependent activation enthalpies. Here we explore one of the reasons for that another is given in Section 7.3. 

Figure 23. Schematic representation of generalized isokinetic behavior with temperature-dependent activation parameters.

The temperature-dependent fluctuation rates a>i2 of the EFG, which result from this simultaneous fit, were interpreted in terms of low-temperature tunneling plus a temperature-dependent activation of the terminal O-atom from position 1 to 2 and vice versa, described by the expression... 

Intrinsic kinetic data can only be measured provided that the overall reaction rate is not limited by mass transport. Only then reahstic parameters can be calculated concerning the influence of catalyst and substrate concentrations (reaction order) as well as the temperature dependency (activation... 

The presence of cross-linked phosphates may be recognized by their ready hydrolysis, which leads to a rapid drop in the viscosity of the solution and a parallel decrease in its pH. Aqueous solutions of all cross-linked phosphates are hydrolyzed after twenty hours. In contrast to the hydrolysis of normal P—O—P bonds in meta- and polyphosphates, that of the cross-linking sites is practically independent of concentration, pH, ionic strength and the nature and concentration of added salts. It does, however, follow a first-order law, as for normal P—O—P bonds, and is strongly temperature dependent. Activation energies of 18.9 and 15.4 kcal/mole have been... 

Jortner, J., 1976, Temperature dependent activation energy for electron transfer between biological molecules J. Chem. Phys. 64 486034867. 

The entire data set, p E, T), can be summarized by the intercept, p 0, T), and slope, S T), as functions of temperature. A typical temperature dependence of T) is illustrated in Figure 31. While the data may be described qualitatively as activated , p exponential in T, the dependence is actually somewhat stronger, p exponential in T as if there were a temperature-dependent activation energy. Whenever the data permit one to judge between and T, an exponential dependence on is usually the better description. This dependence can be characterized by its T — 00 limit, //q (a hypothetical mobility at infinite temperature), and a slope (where To may be viewed as a characteristic temperature) (Eq. (5)). 

Hops from deep sites to nearby, higher-energy sites contribute to the activation energy for transport. At lower and lower temperature, that contribution increases because a carrier spends most of its time in deeper and deeper sites. The apparent temperature-dependent activation energy mentioned in conjunction with Eq. (5) is easily understood on this basis. (Of course, any reorganization energy for the electron transfer process may also contribute to the temperature dependence.)... 

Almost all the known heat capacities of activation refer to reactions in solution. While most of the information has been obtained relatively recently, it is noteworthy that temperature-dependent activation energies, indicating a significant value for AO, were already reported for a number of reactions in the 1930 s when recalculation of previous data also provided a few further examples (see Moelwyn-Hughes, 1947a ... 

Two separate sets of workers have reported a positive AG ( 60 cal deg. ) for the acid-catalysed isomerisation of N-chloroacetanilide (Earned and Selz, 1922 Percival and La Mer, 1936) the earlier study represents the first report of temperature-dependent activation parameters which can still be accepted today. There is now much evidence (see Ingold, 1953f) that the protonated anilide is in equilibrium with the initial reactants and that the rate-determining step involves one or more of reactions (33)-(35) ... 

Depending on the nature of the class, the instructor may wish to spend more time with the basics, such as the mass balance concept, chemical equilibria, and simple transport scenarios more advanced material, such as transient well dynamics, superposition, temperature dependencies, activity coefficients, redox energetics, and Monod kinetics, can be skipped. Similarly, by omitting Chapter 4, an instructor can use the text for a water-only course. In the case of a more advanced class, the instructor is encouraged to expand on the material suggested additions include more rigorous derivation of the transport equations, discussions of chemical reaction mechanisms, introduction of quantitative models for atmospheric chemical transformations, use of computer software for more complex groundwater transport simulations, and inclusion of case studies and additional exercises. References are provided... 

For materials showing WLF-like behavior, such a plot yields a curved line and thus a temperature-dependent activation energy. 

Sprague, J., Harrison, C., Rowbotham, D.J., Smart, D., and Lambert, D.G. (2001) Temperature-dependent activation of recombinant rat vanilloid VRl receptors expressed in HEK293 cells by capsaicin and anandamide, Eur. J. Pharmacol, 423 121-5. 

Solution The solution will be easier to follow by first examining the Txy graph in Figure 13-5. Temperature affects mutual solubility and the shape of the liquid-liquid phase boundary. Since we have temperature-dependent activity coefficients, it possible compute the liquid-liquid boundary as a function of temperature. This calculation will be performed up to the bubble temperature. Above the bubble temperature the calculation will be done by solving the bubble T problem. 

Enzymatic activity is pH and temperature dependent activity curves are given for each particular enzyme preparation, which describe the initial reaction rate on a specific substrate as a function of pH and temperature. The optimum pH value can be very different for the different enzymes. It ranges from 1-2 (pepsin) to 10 and more for alkaline micro-... 

Several chemical marker compounds formed at sterilizing temperatures from precursor compounds inherently present in the foods have been reported (Kim and Taub, 1993 Kim et al, 1994). In order to apply these chemical markers to real processing conditions, where lethality accumulates under nonisothermal conditions, accurate informations about the reaction rate constants and their temperature dependence (activation energy or Z-value) are needed. The variability of the precursor concentration within the particulates and among different particulates also needs to be considered carefully. 

The mechanism for the modification of the kinetic parameters under the influence of the dietary lipids will be easily understood by describing the studies performed with the acetylcholinesterase from rat erythrocytes. The allosteric behavior (Hill plots) and temperature-dependent activity (Arrhenius plots) of the enzyme from rats fed a fat-free diet will be discussed in detail in the first part of this presentation. 

A very distintive characteristic of the regulatory phenomenon already described is that the observed changes of the kinetic parameters require the integrity of the membrane, which means that the modification of the fatty acid composition change the behavior of the enzyme when membrane lipids are structuraly organized. This work shows that complementary information could be obtained from the studies of allosteric behavior and temperature-dependent activity... 

More generally, it can be seen that eqn (1.6) can be used to obtain an expression for a temperature-dependent activation energy (and imply a temperature-dependent pre-exponential factor), usually written as ... 

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