First-order decomposition constant

I. Natural Radiocarbon—For Samples Collected Prior to 1950, or Assumed to Contain No Bomb Radiocarbon. For samples not complicated by the presence of bomb 14C, the ratio of 14C/12C measured in a sample represents the rate of decomposition relative to the rate of radiodecay of 14C. This treatment is most useful for very old C found in soils. For a homogeneous carbon-containing reservoir, i, with input rate Iu first-order decomposition constant kh and carbon content C the change in stock over time (balance of inputs and outputs) is... 

Table B2.5.5. The photochemical decomposition of methyl radicals (UV excitation at 216 nm). ris tire wavenumber linewidth of the methyl radical absorption and /ris the effective first-order decay constant [54].

The first-order rate constant for the decomposition of a certain drug at 25°C is 0.215 month1. 

By way of example, consider the first-order decomposition of 4-hydroxy-4-methyl-2-pentanone ( diacetone alcohol ) in a reaction that is catalyzed by hydroxide ions, carried out at constant [OH-] 6... 

Self-Tfst 13.9A Calculate (a) the number of half-lives and (b) the time required for the concentration of N20 to fall to one-eighth of its initial value in a first-order decomposition at 1000. K. Consult Table 13.1 for the rate constant. 

Influence of OH concentration on the reaction rate constant. From the dependence of the observed first order rate constant on the sodium hydroxide concentration, shown in Table 3, it can be established that equation (2) holds, where ko represents the contribution due to the unimolecular decomposition process and koH is the contribution due to the base-catalysed process in alkaline medium. 

Sensitivity to step size was thought to be likely due to an unnecessary simplification in the original development of the model. The simplification was to consider initiator concentration constant over a small time increment. When instead the initiator was allowed to vary according to the usual first order decomposition path an analytical solution for the variation of polymer concentration could still readily be obtained and was as follows ... 

From the results of experiment 2.1, we confirmed decomposition reaction is pseudo first-order, and calculated pseudo first-order decomposition rate constants. Then fixnn relationship between each first-order reaction rate constant and sodium hydroxide concentration, we confirmed that the reaction is expressed by second-order with expression first-orders for both of sodium hydroxide and fenitrothion. 

The complex has been separated by ion exchange and characterised by direct analysis . The complex has a distinctive absorption spectrum (Fig. 11), quite unlike that of Np(V) and Cr(III). The rate coefficient for the first-order decomposition of the complex is 2.32 x 10 sec at 25 °C in 1.0 M HCIO. Sullivan has obtained a value for the equilibrium constant of the complex, K = [Np(V) Cr(III)]/[Np(V)][Cr(III)], of 2.62 + 0.48 at 25 °C by spectrophotometric experiments. The associated thermodynamic functions are AH = —3.3 kcal. mole" and AS = —9.0 cal.deg . mole . The rates of decay and aquation of the complex, measured at 992 m/t, were investigated in detail. The same complex is formed when Np(VI) is reduced by Cr(II), and it is concluded that the latter reaction proceeds through both inner- and outer-sphere paths. It is noteworthy that the substitution-inert Rh(lII), like Cr(III), forms a complex with Np(V) °. This bright-yellow Np(V) Rh(III) dimer has been separated by ion-exchange... 

These procedures were further extended to tris(acetylacetonato)technetium(III) [24]. In an acetonitrile solution of Tc(acac)3, the absorbances at the characteristic absorption maxima at 348,375,505 and 535 nm decreased with time, while an increase in the absorbance at 272 nm corresponded to an increase of free acetylacetone liberated during the substitution reaction. The final absorption spectra of the reaction mixture exhibited absorption maxima at 271,325 and 387 nm. The first order rate constant k for decomposition was found to be k = (8.86 + 0.08) x 10 4s 1at [H+] = 2.0 M at 30°C. 

The apparent activation energy for the thermal decomposition of phenyl benzyl ether was calculated to be 50 kcal/mole, since the first order rate constants were 1.39x10 at 320°C, 5.19xl0"4 at 340°C and 9.52x10" S at 350°C, respectively. 

The useful thing about the Lineweaver-Burk transform (or double reciprocal) is that the y intercept is related to the first-order rate constant for decomposition of the ES complex to E + P (7ccat or Vmax) and is equal to the rate observed with all of the enzyme in the ES complex. The slope, in contrast, is equal to the velocity when the predominant form of the enzyme is the free enzyme, E (free meaning unencumbered rather than cheap). 

The formation of radicals from hydrogen peroxide in cyclohexanol was measured by the free radical acceptor method [60] the effective rate constant of initiation was found to be equal to ki = 9.0 x 106 exp(—90.3/RT) s 1. For the first-order decomposition of H2O2 in an alcohol medium, the following reactions were discussed. 

Rate constants for the first-order decomposition of nitrogen pentoxide (N2O5) at various temperatures are as follows (Alberty and Silbey, 1992, p. 635) ... 

The three rate constants for Eq. (98) correspond to the acid-catalyzed, the acid-independent and the hydrolytic paths of the dimer-monomer equilibrium, respectively, and were evaluated independently (107). The results clearly demonstrate that the complexity of the kinetic processes is due to the interplay of the hydrolytic and the complex-formation steps and is not a consequence of electron transfer reactions. In fact, the first-order decomposition of the FeS03 complex is the only redox step which contributes to the overall kinetic profiles, because subsequent reactions with the sulfite ion radical and other intermediates are considerably faster. The presence of dioxygen did not affect the kinetic traces when a large excess of the metal ion is present, confirming that either the formation of the SO5 radical (Eq. (91)) is suppressed by reaction (101), or the reactions of Fe(II) with SO and HSO5 are preferred over those of HSO3 as was predicted by Warneck and Ziajka (86). Recently, first-order formation of iron(II) was confirmed in this system (108), which supports the first possibility cited, though the other alternative can also be feasible under certain circumstances. 

Hydrogen peroxide, H202, decomposes by first-order decomposition and has a rate constant of 0.015/min at 200°C. Starting with a 0.500 M solution of H202, calculate ... 

Let s apply the preceding two paragraphs to an example problem. The first-order decomposition of gaseous dinitrogen pentoxide, N205, to nitrogen dioxide, NO2, and oxygen, 02, has a rate constant of 4.9 X 10 4 s 2 at a certain temperature. Calculate the half-life of this reaction. 

Consider the first order decomposition of a substance A to products. At constant temperature, what is the half-life of the substance ... 

Cyclopropane, CaHe, has a three-membered hydrocarbon ring structure. It undergoes rearrangement to propene. At 1000°C, the first-order rate constant for the decomposition of cyclopropane is 9.2 s- ... 

O O A first-order decomposition reaction has a rate constant of 2.34 X 10 year . What is the half-life of the reaction Express your answer in years and in seconds. 

A kinetic study has been carried out in order to elucidate the mechanism by which the cr-complex becomes dehydrogenated to the alkyl heteroaromatic derivative for the alkylation of quinoline by decanoyl peroxide in acetic acid. The decomposition rates in the presence of increasing amounts of quinoline were determined. At low quinoline concentrations the kinetic course is shown in Fig. 1. The first-order rate constants were calculated from the initial slopes of the graphs and refer to reaction with a quinoline molecule still possessing free 2- and 4-positions. At high quinoline concentration a great increase of reaction rate occurs and both the kinetic course and the composition of the products are simplified. The decomposition rate is first order in peroxide and the nonyl radicals are almost completely trapped by quinoline. The proportion of the nonyl radicals which dimerize to octadecane falls rapidly with increase in quinoline concentration. The decomposition rate in nonprotonated quinoline is much lower than that observed in quinoline in acetic acid. 

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... 

The reactions obeyed pseudo-first-order kinetics consistent with a rapid reversible protonation of the substrate, S, at the ester carbonyl followed by a rate-determining decomposition to acetic acid and nitrenium ion according to Scheme 19. In accordance with equation 13, the pseudo-first-order rate constant, k, was shown to be proportional to acid concentration and inversely proportional to the activity of the water/acetonitrile solvent . 

Consider the following first order decompositions with rate constants as shown... 

Baranski and Lu [209] have carried out, applying microelectrodes, voltammetric studies on ammonium amalgam in propylene carbonate solutions at room temperatures. The sweep rates up to 80 V s were appropriate for the analysis of the formation kinetics of this compound. Experimental and numerical simulation results have shown that ammonium amalgam was formed via fast charge-transfer process and its first-order decomposition was characterized by the rate constant of about 0.6 s . Diffusion coefficient of NH4 radical in mercury was estimated to be about 1.8 X 10 cm s k The formal potential of NH4+ (aq)/NH4(Hg) couple was determined as—1.723 V (SHE). 

Johnston et al. (1986), for example, examined kinetic data from laboratory studies reported in the literature and estimated a first-order rate constant at 1 atm pressure at room temperature of (3 + 2) X 10 3 s , corresponding to a lifetime for NO, with respect to decomposition of about 6 min. Subsequent attempts by Davidson et al. (1990) to measure this decomposition directly were complicated by a contribution from a wall-catalyzed decomposition of NO,. However, they suggest that their data support this conclusion weakly, with their data being not inconsistent with the rate constant suggested earlier by Johnston et al. (1986). 

Apparent first-order rate constants for peroxynitrite decomposition in various buffers versus pH. When peroxynitrite is fully protonated at acidic pH, the decomposition rate is constant. The breakpoint in the curve identifies the pK, of peroxynitrite since a larger fraction present as an anion slows the rate of decomposition. In 50 mM potassium phosphate, the apparent pK, is at 6.8 and is not affected by temperatute (Koppenol, 1993). The rate of decomposition is not affected hy DMSO, mannitol, or ethanol. As shown in Fig. 28, many buffers can slightly accelerate the decomposition of peroxynitrite and the rate of decomposition reaches a maximum at high buffer concentrations. When these maximal rates are plotted as a function of pH, peroxynitrite exhibits a second pK, of approximately 8.0. 

The rate constant for the first-order decomposition of N205 has the value of 4.8 x lO 4 s 1...What will be the pressure, initially 500 Tore, after (a) 10 s... ( )... 

This is a fair approximation to most chain decompositions, i.e., that the apparent first-order rate constant is about 10 to 100 times the initiation rate. The general problem is to ascertain this process and then to try to decide if it is pressure dependent. 

With cobalt as catalyst the plot of log [peracetic acid] vs. time was linear for each cobalt acetate concentration. The first-order rate constants obtained at different cobalt concentrations (k2 ) were plotted as a function of total cobalt (Cot) concentration, and the plot indicates a first-order dependence on total cobalt as shown in Figure 3. The experimental rate law for the cobalt-catalyzed decomposition is thus ... 

The kinetics of the noncatalytic reaction were studied by the method of Bawn and Williamson (4). They found 3.3-3.7 moles/liter for the equilibrium constant for the formation of the intermediate acetaldehyde monoperacetate (AMP) and a first-order rate constant for the decomposition of this intermediate to acetic acid of 0.015 min."1 at 25°C. We found difficulty in reproducing our results probably caused mainly by the high values of the blanks in the iodometric methods used. However, as an average of four determinations we obtained 0.03 min."1 at 30°C. 

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