Rate laws half-life

If the decomposition reaction follows the general rate law, the activation energy, heat of decomposition, rate constant and half-life for any given temperature can be obtained on a few milligrams using the ASTM method. Hazard indicators include heats of decomposition in excess of 0.3 kcal/g, short half-lives, low activation energies and low exotherm onset temperatures, especially if heat of decomposition is considerable. 

Another way to describe reaction rates is by half-life, t/, the amount of time it takes for the reactant concentration to drop to one half of its original value. When the reaction follows a first-order rate law, rate = -krxn[reactant], ti is given by ... 

Wilkinson s method allows the evaluation of the reaction order from data taken during the first half-life. This, as we saw, was not possible from treatment by the integrated rate law. Note, however, that relatively small errors in [A] can lead to a larger error in E at small conversions.17... 

Second-order kinetics, (a) Derive expressions for the half-time and lifetime of A if the rate law for its disappearance is v = fc[A]2 (b) calculate t]/i and t for the data presented in Section 2.2 (c) calculate the second half-life, t /i(2), i.e., the time elapsed between 50 percent and 75 percent completion, for the same reaction (d) compare fj/2(l) and fi/>(2), and contrast this result with that from first-order kinetics. 

STRATEGY The level of mercury(II) in the urine can be predicted by using the integrated first-order rate law, Eq. 5b. To use this equation, we need the rate constant. Therefore, start by calculating the rate constant from the half-life (Eq. 7) and substitute the result into Eq. 5b. 

A radioactive isotope X with a half-life of 27.4 d decays into another radioactive isotope Y with a half-life of 18.7 d, which decays into the stable isotope Z. Set up and solve the rate laws for the amounts of the three nuclides as a function of time, and plot your results as a graph. 

The Henry s law constant value of 2.Ox 10 atm-m /mol at 20°C suggests that trichloroethylene partitions rapidly to the atmosphere from surface water. The major route of removal of trichloroethylene from water is volatilization (EPA 1985c). Laboratory studies have demonstrated that trichloroethylene volatilizes rapidly from water (Chodola et al. 1989 Dilling 1977 Okouchi 1986 Roberts and Dandliker 1983). Dilling et al. (1975) reported the experimental half-life with respect to volatilization of 1 mg/L trichloroethylene from water to be an average of 21 minutes at approximately 25 °C in an open container. Although volatilization is rapid, actual volatilization rates are dependent upon temperature, water movement and depth, associated air movement, and other factors. A mathematical model based on Pick s diffusion law has been developed to describe trichloroethylene volatilization from quiescent water, and the rate constant was found to be inversely proportional to the square of the water depth (Peng et al. 1994). 

The experimental rate-law [10) is valid over a wide range of conditions. From Equations (10) and (5) it follows that the half-life tV2, of the polymerisation is given by... 

Utterly Confused About Rate Law and Half-Life (t1/2)... 

Based on its very small calculated Henry s law constant of 4.0xl07-5.4xl0"7 atm-m3/mol (see Table 3-2) and its strong adsorption to sediment particles, endrin would be expected to partition very little from water into air (Thomas 1990). The half-life for volatilization of endrin from a model river 1 meter deep, flowing 1 meter per second, with a wind speed of 3 meters per second, was estimated to be 9.6 days whereas, a half-life of greater than 4 years has been estimated for volatilization of endrin from a model pond (Howard 1991). Adsorption of endrin to sediment may reduce the rate of volatilization from water. 

The transport of disulfoton from water to air can occur due to volatilization. Compounds with a Henry s law constant (H) of <10 atm-m /mol volatilize slowly from water (Thomas 1990). Therefore, disulfoton, with an H value of 2.17x10" atm-m /mol (Domine et al. 1992), will volatilize slowly from water. The rate of volatilization increases as the water temperature and ambient air flow rate increases and decreases as the rate of adsorption on sediment and suspended solids increases (Dragan and Carpov 1987). The estimated gas- exchange half-life for disulfoton volatilization from the Rhine River at an average depth of 5 meters at 11 °C was 900 days (Wanner et al. ] 989). The estimated volatilization half-life of an aqueous suspension of microcapsules containing disulfoton at 20 °C with still air was >90 days (Dragan and Carpov 1987). 

In the meantime, E. Rutherford (NLC 1908 ) studied the radioactivity discovered by Becquerel and the Curies. He determined that the emanations of radioactive materials include alpha particles (or rays) which are positively charged helium atoms, beta particles (or rays) which are negatively charged electrons, and gamma rays which are similar to x-rays. He also studied the radioactive decay process and deduced the first order rate law for the disappearance of a radioactive atom, characterized by the half-life, the time in which 50% of a given radioactive species disappears, and which is independent of the concentration of that species. 

The half-life of any first-order reaction is always a constant, and it depends on k. In other words, any first-order reaction (that is, any reaction with a rate law equation in the form Rate = k[A]) has a half-life that is independent of the initial concentration of the reactant, A. The half-life of any first-order reaction can be calculated using the following equation. 

Where does the equation for half-life come from Each rate law has an associated integrated rate law. (A calculus teacher may be able to show you howto arrive at the integrated rate law.) For first-order reactions, the integrated rate law is... 

In this section, you learned how to relate the rate of a chemical reaction to the concentrations of the reactants using the rate law. You classified reactions based on their reaction order. You determined the rate law equation from empirical data. Then you learned about the half-life of a first-order reaction. As you worked through sections 6.1 and 6.2, you may have wondered why factors such as concentration and temperature affect the rates of chemical reactions. In the following section, you will learn about some theories that have been developed to explain the effects of these factors. 

Surface Water. The volatilization half-life of naphthalene from surface water (1 m deep, water velocity 0.5 m/sec, wind velocity 22.5 m/sec) using experimentally determined Henry s law constants is estimated to be 16 h (Southworth, 1979). The reported half-lives of naphthalene in an oil-contaminated estuarine stream, clean estuarine stream, coastal waters, and in the Gulf stream are 7, 24, 63, and 1,700 d, respectively (Lee, 1977). Mackay and Wolkoff (1973) estimated an evaporation half-life of 2.9 h from a surface water body that is 25 °C and 1 m deep. In a laboratory experiment, the average volatilization half-life of naphthalene in a stirred water vessel (outer dimensions 22 x 10 x 21 cm) at 23 °C and an air flow rate of 0.20 m/sec is 380 min. The half-life was independent of wind velocity or humidity but very dependent upon temperature (Klopffer et al., 1982). 

Hamelink, J.L., Simon, P.B., and Silberhorn, E.M. Henry s law constant, volatilization rate, and aquatic half-life of octamethylcyclotetrasiloxane, Environ. Sci. Technol, 30(6) 1946-1952, 1996. 

Rate constant, rate law, concentration profile, experimental measurement, integrated rate laws, linear plots, half-lifes Theory of the rate constant (activation energy, orientation factor, collision frequency factor, Transition State Theory)... 

To relate the reaction s half-life to the rate constant, let s begin with the integrated rate law ... 

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