Spontaneous processes rates

Second law of thermodynamics A basic law of nature, one form of which states that all spontaneous processes occur with an increase in entropy, 457 Second order reaction A reaction whose rate depends on the second power of reactant concentration, 289,317q gas-phase, 300t... 

Let us consider the typical mechanisms of spontaneous processes that decrease /. The direction and driving force of such mechanisms are determined by the laws of equilibrium thermodynamics, and the rate is proportional to diffusion in gases, viscosity in liquids, and transfer of atoms, vacancies, and other defects in solids. 

On the other hand, abzymes are generally able to accelerate reactions by at most 107 times the rate of the spontaneous process. It has to be said that scientists at large are looking for a major step forward in antibody catalysis to achieve rate accelerations up to 109 that would establish abzymes as a feature of synthetically useful biotransformations. At the same time, it is essential to demonstrate that product inhibition is not an obstacle to the scaled-up use of abzymes. 

Figures 2.13(a) and 2.13(b) illustrate the basis of a semiconductor diode laser. The laser action is produced by electronic transitions between the conduction and the valence bands at the p-n junction of a diode. When an electric current is sent in the forward direction through a p-n semiconductor diode, the electrons and holes can recombine within the p-n junction and may emit the recombination energy as electromagnetic radiation. Above a certain threshold current, the radiation field in the junction becomes sufficiently intense to make the stimulated emission rate exceed the spontaneous processes.

Equilibria and rates should be clearly distinguished. Equilibrium is the end point of any spontaneous process, whether chemical or physical, in which the driving forces (potentials) for changes are balanced and there is no further tendency to... 

Emission bands from the 42Z, B2n, C2n, and D2X states have been observed and decay rates of fluorescence have been measured extensively [Callear et al. (167-171, 174, 175)]. Various spontaneous processes of electronically excited NO are given in Table V-5. These states are quenched to a different degree by various gases. Quenching half pressures, p1/2, in torr defined as P112 — where is the quenching rate constant in sec-1 torr-1... 

It is clear that, by changing the experimental conditions and/or detection wavelength, limiting values can be found for all of the quantities mentioned above from measurements of the fluorescence decay time. The effects of collisional and spontaneous processes can be separated by conventional Stem—Volmer analysis [36]. The concentration, [M], of quenching molecules is varied and the reciprocal of the observed lifetime is plotted against the concentration of M. The quenching rate coefficient is thus obtained from the slope and the intercept gives the rate coefficient for the spontaneous relaxation processes, which is usually the natural lifetime of the excited state. In cases where the experiment cannot be carried out under collision-free conditions, this is the only way to measure the natural lifetime from observation of the fluorescence decay. 

All nuclear transformations proceed spontaneously at rates that are not altered by ordinary chemical or physical processes. For any population of unstable atoms, the rate of nuclear transformation or radioactive decay is first order that is, proportional to the number, N, of decomposing nuclei present ... 

In addition to absorption and stimulated emission, a third process, spontaneous emission, is required in the theory of radiation. In this process, an excited species may lose energy in the absence of a radiation field to reach a lower energy state. Spontaneous emission is a random process, and the rate of loss of excited species by spontaneous emission (from a statistically large number of excited species) is kinetically first-order. A first-order rate constant may therefore be used to describe the intensity of spontaneous emission this constant is the Einstein A factor, Ami, which corresponds for the spontaneous process to the second-order B constant of the induced processes. The rate of spontaneous emission is equal to Aminm, and intensities of spontaneous emission can be used to calculate nm if Am is known. Most of the emission phenomena with which we are concerned in photochemistry—fluorescence, phosphorescence, and chemiluminescence—are spontaneous, and the descriptive adjective will be dropped henceforth. Where emission is stimulated, the fact will be stated. 

In other words, as expected, at a spontaneous evolution of the system at fixed p and T, its Gibbs potential decreases, dG < 0. Thus, the rate of entropy pro duction and energy dissipation in an open system at constant temperature and pressure is proportional to the rate of decreasing its Gibbs potential due to occurrence of irreversible spontaneous processes inside the system. 

Inequalities (3.2) and (3.3) are generalizations of the principle of the minimal entropy production rate in the course of spontaneous evolution of its system to the stationary state. They are independent of any assump tions on the nature of interrelations of fluxes and forces under the condi tions of the local equilibrium. Expression (3.2), due to its very general nature, is referred to as the Qlansdorf-Prigogine universal criterion of evolution. The criterion implies that in any nonequilibrium system with the fixed boundary conditions, the spontaneous processes lead to a decrease in the rate of changes of the entropy production rate induced by spontaneous variations in thermodynamic forces due to processes inside the system (i.e., due to the changes in internal variables). The equals sign in expres sion (3.2) refers to the stationary state. 

A process is said to be spontaneous if it occurs without outside intervention. Spontaneous processes may be fast or slow. As we will see in this chapter, thermodynamics can tell us the direction in which a process will occur but can say nothing about the speed (rate) of the process. As we will explore in detail in Chapter 15, the rate of a reaction depends on many factors, including temperature and concentration. In describing a chemical reaction, the discipline of chemical kinetics (the study of reaction rates) focuses on the pathway between reactants and products in contrast, thermodynamics considers only the initial and final states and does not require knowledge of the pathway between the reactants and products (see Fig. 10.2). 

Forbidden pure rotational transitions of H3, following the selection rules Ak = +3, occur in the wide region from millimetre wave to mid-infrared.These transitions are caused by centrifugal distortions of the symmetric structure. No laboratory observation of them has been reported so far. These transitions are much weaker than the usual dipole-allowed rotational transitions in polar molecules, and their spontaneous emission rates range from ca. 10" s" to ca. 10" s". Nevertheless, such weak transitions may be observable in low-density regions just like the Hj quadrupole transitions. Also, the spontaneous emission lifetimes are short compared with the collisional time in low-density areas, making the forbidden rotational transitions important processes for cooling the rotational temperature of Hj. ... 

The outcome of a spontaneous process depends on the rate of the process. If it is slow, considerable time may be required before the results are seen. 

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