Decay process, first-order chemical

We consider only the relatively simple case of a first order chemical decay process. This is consistent with the way laboratory data for PAH reactions are reported (10). 

The chemical species balance method can be extended to first-order chemical decay processes as follows ... 

Many important natural processes ranging from nuclear decay to uni-molecular chemical reactions are first order, or can be approximated as first order, which means that these processes depend only on the concentration to the first power of the transforming species itself. A cellular automaton model for such a system takes on an especially simple form, since rules for the movements of the ingredients are unnecessary and only transition rules for the interconverting species need to be specified. We have recently described such a general cellular automaton model for first-order kinetics and tested its ability to simulate a number of classic first-order phenomena.70... 

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 ... 

Such a chemical reaction, in which molecules are not colliding with other atoms or molecules, is called a first-order reaction because the rate at which chemical concentration changes at any instant in time is proportional to the concentration raised to the first power. Certain chemical processes, such as radioactive decay, are described by first-order kinetics. In the absence of any other sources of the chemical, first-order kinetics may lead to exponential decay or first-order decay of the chemical concentration (i.e., the concentration of the parent compound decreases exponentially with time) ... 

Radioactive decay processes involve the emission of a particle and/or photon (a gamma ray) from the nucleus of an atom. (See Chemical Connection 5.3.8.1 Radioactive Decay—A First-Order Reaction). Alpha decay is the ejection of an alpha particle from the nucleus of the atom (Equation 5.3.8.1) and produces a daughter nucleus that has two fewer protons and a decrease of four mass units. The velocity of the alpha particle accounts for the energy range of 4-6 MeV shown in Table 5.3.8.1. While alpha radiation can cause damage to tissues, it can only do so if the source is ingested or inhaled because the energy of alpha emitters is usually very weak and can readily be stopped by a sheet of paper. 

For any given radionuclide, the rate of decay is a first-order process that is constant, regardless of the radioactive atoms present and is characteristic for each radionuclide. The process of decay is a series of random events temperature, pressure, or chemical combinations do not effect the rate of decay. While it may not be possible to predict exactly which atom is going to undergo transformation at any given time, it is possible to predict, on average, the fraction of the radioactive atoms that will transform during any interval of time. 

Decay of adsorbed chemical, modeled as a first-order process. 

To extend the transport equation (22-4) to other processes affecting the spatial distribution of a chemical we introduce a zero-order production rate, J [M L"3T" ], and a first-order decay rate (specific reaction rate kT [T1]) ... 

The 1,5-, 1,6-, 1,7-, 1,8-, 2,6-, and 2,7-naphthyridines have been electro-chemically reduced to afford radicals that decay by a slow shift of hydrogen from nitrogen to carbon.143 The resulting radicals dimerize readily. In acid media the first reduction step produces a radical-cation that is relatively stable in the 1,7- and 2,6-naphthyridines, whereas in 2,7-naphthyridine, the species is stable for a few minutes only. All of these radical-cations undergo a hydrogen shift from nitrogen to carbon to form unstable radicals that react with original cation radicals to form dimers. The process is an acid- or base-catalyzed first-order reaction.144... 

If you recall, back in Chapter 5 we discussed half-life in the context of the decay of radioactive nuclei. In that chapter, we defined the half-life as the amount of time it took for one half of the original sample of radioactive nuclei to decay. Because the rate of decay only depends on the amount of the radioactive sample, it is considered a first-order process. Using the same logic, we can apply the concept of half-life to first-order chemical reactions as well. In this new context, the half-life is the amount of time required for the concentration of a reactant to decrease by one-half. The half-life equation from Chapter 5 can be used to determine the half-life of a reactant ... 

But, enough of this dalliance in other fields, let s get back to Ostwald and the order of a reaction. We ve illustrated a first-order decay process, but if we were talking about a chemical reaction, rather than radioactive decay, we would use concentration in moles per liter (mol I/1) rather than using the number of molecules or moles of a material in our differential equation. This is usually indicated by putting square brackets around the symbol for the reacting group, where k is now called the rate constant (Equation 4-3). 

A more remarkable elongation of the CS lifetime was attained by complex formation of yttrium triflate [Y(OTf)3] with the CS state in photoinduced ET of a ferrocene-anthraquinone (Ec AQ) dyad (53). Photoexcitation of the AQ moiety in Ec AQ in deaerated PhCN with femtosecond (150 fs width) laser light results in appearance of the absorption bands 420 and 600 run at 500 fs, as shown in Eig. 14(a) (53). The absorption bands 420 and 600 nm, which are assigned to AQ by comparison with the absorption spectrum of AQ produced by the chemical reduction of AQ with naphthalene radical anion (53). The decay process obeys first-order kinetics with the lifetime of 12 ps [Eig. um. 

In the expressions for the gas exchange coefficient employed previously, it is evident that the air-water gas exchange flux density is proportional to the difference between a chemical concentration in the water (Cw) and the corresponding equilibrium concentration (Cw H) in air. Consequently, the difference between actual and equilibrium concentration in the water tends to decay exponentially, as expected for any first-order process. In many situations, exponential decay may provide a useful model of a volatile chemical concentration in a surface water. A classic example is degassing of a dissolved gas from a stream if the gas is present at concentration C0 upstream, atmospheric concentration of the gas is negligible, and flow is steady and uniform along the stream, then the gas concentration in the stream is given by... 

The conceptual approach is particularly effective when solving problems that have half-lives that are whole number values. For more complex problems, we need to use some ideas borrowed from chemical kinetics. Radioactive decay can be described as a first order processes, which means it can be described with the following equation ... 

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