Half-life first-order

Field studies on the transformation of endrin in the atmosphere were not located in the available literature. Photochemical isomerization of endrin, primarily to the pentacyclic ketone commonly called delta ketoendrin or endrin ketone, was observed after exposure of thin layers of solid endrin on glass to sunlight (Burton and Pollard 1974). Minor amounts of endrin aldehyde were also formed in this reaction. Results of seasonal studies indicated that this isomerization would proceed with a half-life (first-order kinetics) of 5-9 days in intense summer sunlight, with complete conversion to the pentacyclic ketone in 15-19 days. Knoevenagel and Himmelreich (1976) reported that photodegradation of solid endrin in the laboratory... 

Example I6-5 Half-Life First-Order Reaction... 

I See the Saunders Interactive General Chemistry CD-ROM, Screen 15.8, Half-Life First-Order Reactions. 

Functional groups in both alcohols and ethers are generally resistant to hydrolysis (Harris 1990). Therefore, hydrolysis of 2-butoxyethanol, which contains both alcohol and ether functional groups, is not expected. The estimated hydrolysis half-life (first order kinetics) for 2-butoxyethanol acetate of >1,000 days (ASTER 1995a) indicates that the hydrolysis of 2-butoxyethanol acetate in water is also not expected. 2-Butoxyethanol does not absorb light of wavelength >290 nm (Silverstein and Bassler 1963). Therefore, photolysis of this compound by absorption of sunlight is not important. Aerobic... 

Half-life (first order, radioactive decay)... 

V = V max [S]// m- A reaction of higher order is called pseudo-first-order if all but one of the reactants are high in concentration and do not change appreciably in concentration over the time course of the reaction. In such cases, these concentrations can be treated as constants. See Order of Reaction Half-Life Second-Order Reaction Zero-Order Reaction Molecularity Michaelis-Menten Equation Chemical Kinetics... 

Second half-life > first half-life, confirming the second order behaviour. 

Here, as in all first rate kinetics, a plot of the natural logarithm of the count rate vs. the time results in a straight line whose slope is proportional to the rate constant and whose intercept is In N. Another reaction rate characteristic, called the half-life, t. is the time required for the initial reactant concentration to be reduced to one half. For first order reactions, the t, independent of concentration, = 0.693/k. 

In addition to the initial reaction between nitric acid and acetic anhydride, subsequent changes lead to the quantitative formation of tetranitromethane in an equimolar mixture of nitric acid and acetic anhydride this reaction was half completed in 1-2 days. An investigation of the kinetics of this reaction showed it to have an induction period of 2-3 h for the solutions examined ([acetyl nitrate] = 0-7 mol 1 ), after which the rate adopted a form approximately of the first order with a half-life of about a day, close to that observed in the preparative experiment mentioned. In confirmation of this, recent workers have found the half-life of a solution at 25 °C of 0-05 mol 1 of nitric acid to be about 2 days. ... 

II [Anisole] = 2 x lo mol i" first-order reactions. For the experiment using pure nitric acid the half-life was about i min, but for that using fuming nitric acid reaction was complete in < 30 s. 

Expts. 16, //. Pure nitric acid was used. In expt. 16 the reaction was of the first order in the concentration of the aromatic, and of half-life 1-1-5 minutes (similar to that of toluene under the same conditions). In expt. 17 the sodium nitrate slowed the reaction (half-life c. 60 min). About 2 % of an acetoxylated product was formed (table 5-4). 

An important characteristic property of a radioactive isotope is its half-life, fj/2, which is the amount of time required for half of the radioactive atoms to disintegrate. For first-order kinetics the half-life is independent of concentration and is given as... 

Because the decomposition is first order, the rate of free-radical formation can be controlled by regulating the temperature equations relating half-life to temperature are provided in Table 7. These decomposition rates ate essentially independent of the solvent (73). 

First order decomposition was established for dimethyldiazirine (215) and ethylmethyl-diazirine (216). The activation energy is 139 kJ moF for (215) the half life at 100 °C is 97 h. On decomposition of (216) the products formed and their respective yields are as indicated. The products correspond qualitatively and quantitatively with the results of thermal decomposition of 2-diazobutane formed in situ in aprotic solvents. Analogous comparisons of decomposition products of diethyldiazirine, isopropylmethyldiazirine, n-butyl- and t-butyl-diazirine agree equally well 66TL1733). 

The unit of the veloeity eonstant k is see Many reaetions follow first order kineties or pseudo-first order kineties over eertain ranges of experimental eonditions. Examples are the eraeking of butane, many pyrolysis reaetions, the deeomposition of nitrogen pentoxide (NjOj), and the radioaetive disintegration of unstable nuelei. Instead of the veloeity eonstant, a quantity referred to as the half-life iyj is often used. The half-life is the time required for the eoneentration of the reaetant to drop to one-half of its initial value. Substitution of the appropriate numerieal values into Equation 3-33 gives... 

Equation 3-39 shows that in the first order reaetions, the half-life is independent of the eoneentration of the reaetant. This basis ean be used to test whether a reaetion obeys first order kineties by measuring half-lives of the reaetion at various initial eoneentrations of the reaetant. 

The half-life method requires data from several experiments, eaeh at different initial eoneentration. The method shows that the fraetional eonversion in a given time rises with inereased eoneentration for orders greater than one, drops with inereased eoneentration for orders less than one, and is independent of the initial eoneentration for reaetions of first order. This also applies to the reaetion A -i- B —> produets when... 

In addition to the elimination rate constant, the half-life (T/i) another important parameter that characterizes the time-course of chemical compounds in the body. The elimination half-life (t-1/2) is the time to reduce the concentration of a chemical in plasma to half of its original level. The relationship of half-life to the elimination rate constant is ti/2 = 0.693/ki,i and, therefore, the half-life of a chemical compound can be determined after the determination of k j from the slope of the line. The half-life can also be determined through visual inspection from the log C versus time plot (Fig. 5.40). For compounds that are eliminated through first-order kinetics, the time required for the plasma concentration to be decreased by one half is constant. It is impottant to understand that the half-life of chemicals that are eliminated by first-order kinetics is independent of dose. ... 

The half-life tvi is defined to be the time required for the reactant concentration to decay to one-half its initial value. To find tvi for a first-order reaction we use Eq. (2-6) with the substitutions Ca = c°/2 and t = finding... 

Figure 2-1 is a plot of Eq. (2-10) from n = 0 to = 4. Note that equal time irrcrements result in equal fractional decreases in reactant concentration thus in the first half-life decreases from 1.0 to 0.50 in the second half-life it decreases from 0.50 to 0.25 in the third half-life, from 0.25 to 0.125 and so on. This behavior is implicit in the earlier observation that a first-order half-life is independent of concentration. 

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