First-order decay process

Half-life estimates of approximately 28 days for thiophanate-methyl indicate a very slow decay compared to methiocarb with an estimate of half-life of about 11 days. The application of a model based on a first-order decay process resulted in fairly high R2 and significant fit. The results suggest that both pesticides are relatively stable compared to other compounds under similar environmental conditions (Brouwer et al., 1994). With respect to the objectives of the study and the proposed model, it can be stated that the results confirm the assumption of a linear relationship between application rate (for both application techniques) and the increase of dislodgeable foliar residue. This relationship holds for modeling purposes. The contribution of the crop density or total crop surface area to the process of interception cannot be quantified with the results of the present study. Because the interception factor ranges from about 0.35 to 0.9 (Willis and McDowell, 1987), the... 

The time (symbolized by t) needed for a concentration of a molecular entity to decrease, in a first-order decay process to e of its initial value. In this case, the lifetime (sometimes called mean lifetime) is equal to the reciprocal of the sum of rate constants for all concurrent first-order decompositions. If the process is not first-order, the term apparent lifetime should be used, and the initial concentration of the molecular entity should be provided. The terms lifetime and half-life should not be confused. See Half-Life Fluorescence... 

When the autocatalyst is not indefinitely stable, but instead undergoes further reaction such as the first-order decay process... 

In most cases the de-activation caused by temperature or other single environmental factors, is a first-order decay process. 

The two random numbers, denoted r and r2, are randomly sampled from a uniform distribution over the interval [0,1], The time T, as dictated by any first-order decay process, is exponentially distributed ... 

This rate equation describes a first-order decay process, characterized by a rate constant 2W, which may be defined as Rt or 1/Tj.The quantity n0fiB0/kT is the value of n at equilibrium or eq. With this notation, Eq. 2.28 becomes... 

The emission intensity is proportional to I so that, from the integrated rate equation for these first-order decay processes, the fluorescence intensity will decrease according to the relation... 

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). 

Radioactive decay can be described as a first-order process. Thus, for any first-order decay process, the amount of material present declines in an exponential fashion with time. This is easy to see by integrating Equation (1.5.3) to give ... 

Under environmental conditions low steady-state concentrations are likely to favor first-order decay processes. If one of the substituents is OH, 0, or NR2 (e.g., CH3CHOH, C02, CH2N(CH3)2 (i.e., a heteroatom with a nonbonding or antibonding electron pair), the peroxy radical is unstable and decays within a few milliseconds to yield the corresponding aldehyde, ketone, acid, or imine and a superoxide radical (OJ ) ... 

The cascade decay of CH on silica gel has also been reported by Joppien and Willard (19) over the temperature range of 77 K to room temperature. The decay rate was resolved into multiple first and second order processes. The activation energies for the 3 first order decay processes were 3, 5 and 6 kcal/mol respectively. 

The half-time (ti/2) for the 1st species desorbing is between 6.5 and 7.5 hours. While it is not possible accurately to determine ti/2 for the second species from the graph, it may be calculated from the relation for a first order decay process... 

Solute transport with biodegradation modelled as a first-order decay process (simple, lumped-parameter approach),... 

BIOCHLOR (Aziz et al., 2000) is a screening model that simulates remediation by natural attenuation of dissolved solvents in groundwater. The software, programmed in the Microsoft Excel spreadsheet environment and based on the Domenico analytical solute transport model, has the ability to simulate 1-D advection, 3-D dispersion, linear adsorption, and biotransformation via reductive dechlorination (the dominant biotransformation process at most chlorinated solvent sites). Dissolved solvent degradation is assumed to follow a sequential first order decay process. 

Solute transport with biotransformation modelled as a sequential first-order decay process with 2 different reaction zones (i.e., each zone has a different set of rate coefficient values). 

The release of clay particles from the pore wall is approximated as a first order decay process and the rate at which particles leave the suspension to plug the pores is assumed to be directly proportional to the particle concentration in the suspension. The resulting equations are solved in conjunction with a semi-empirical relationship relating the local permeability and the amount of clay particles captured to determine the overall permeability of the sandstone core as a function of time. Model predictions are in agreement with experimental observations. 

Release rate equation The process of release of clay particles is assumed to be a first order decay process and can be written mathematically as... 

In a collection of N identical nuclei, the number of nuclei decaying in a short time interval is proportional to the number of nuclei, which defines a first-order decay process (Section 14.2). We have... 

Polymeric organolithium compounds exhibit limited stability in ether solvents analogous to alkyllithium compounds. Living carbanionic pol5mers react with ether solvents such as THF in a pseudo-first-order decay process and the rate decreases in the order Li > Na > K. For example, a 10 M solution of poly(styryl)lithium in THF at 25° C exhibited a rate of decay of a few percent per minute, but poly(styryl)cesium was found to be exceptionally stable (78). Metalation and decomposition reactions can also occur in the presence of amines such as TMEDA. 

Analyze and Plan We are given the half-life for cobalt-60 and asked to calculate the amoimt of cobalt-60 remaining from an initial 1.000-mg sample after a 15.9-54T period. To do this we utilize the constant half-life characteristic of a first-order decay process. Solve A period of 15.9 yi is three half-lives for cobalt-60. At the end of one half-Ufe 0.500 mg of cobalt-60 remains, 0.250 mg at the end of two half-lives, and 0.125 mg at the end of three half-Uves. 

Glycine is oxidized by Co to give CO2, NH3, and HjCO. The reaction proceeds by way of a Co -glycine complex with a stability constant of 1.25 1 mol- which can hydrolyse with a hydrolysis constant of 2.6 mol 1 . Both unhydrolysed and hydrolysed species undergo first-order decay processes with rate constants 1.33 x 1Q- S- and 5.13 X 1Q- s- respectively at 29.5 °C (7= 5.06 mol - ). 

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