Kinetic energy indirect determination

The temperature of a substance in a particular state of aggregation (solid, liquid, or gas) is a measure of the average kinetic energy possessed by the substance molecules. Since this energy cannot be measured directly, the temperature must be determined indirectly by measuring some physical property of the substance whose value depends on temperature in a known manner. Such properties and the temperature-measuring devices based on them include electrical resistance of a conductor (resistance thermometer), voltage at the junction of two dissimilar metals (thermocouple), spectra of emitted radiation (pyrometer), and volume of a fixed mass of fluid (thermometer). 

The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed for orienting molecules prior to collision (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) bmte force orientation of polar molecules in extremely strong electric fields. Several chemical reactions have been studied with one of the reagents oriented prior to collision. ... 

An indirect method has been used to determine relative rate constants for the excitation step in peroxyoxalate CL from the imidazole (IM-H)-catalyzed reaction of bis(2,4,6-trichlorophenyl) oxalate (TCPO) with hydrogen peroxide in the presence of various ACTs18. In this case, the HEI is formed in slow reaction steps and its interaction with the ACT is not observed kinetically. However, application of the steady-state approximation to the reduced kinetic scheme for this transformation (Scheme 6) leads to a linear relationship of 1/S vs. 1/[ACT] (equation 5) and to the ratio of the chemiluminescence parameters /ic vrAi), which is a direct measure of the rate constant of the excitation step. Therefore, this method allows for the determination of relative rate constants for the excitation step in a complex reaction system, where this step cannot be observed directly by kinetic measurements18. The singlet quantum yield at infinite activator concentrations ( °), where all high-energy intermediates formed interact with the activator, is also obtained from this relationship (equation 5). 

The kinetic restraints that are placed on the crystallization of polymers make it difficult, if not impossible to directly determine their equilibrium melting temperatures. The directly observed melting temperatures are primarily a reflection of the structure and morphology of the actual crystalline systems. The primary factors involved are the crystallite thickness, the interfacial free energy, and the influence, if any, of the noncrystalline region. There are, however, indirect methods by which to estimate the value of T. One of these is a theoretical method. The others are based on extrapolative procedures. To properly use the T values that are tabulated, and to understand their limitations, the basic assumption involved and the problems in execution need to be recognized. 

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