Kinetic Half Life Time

The kinetic stability of 17 increases on deprotonation. The half-life times of 17 and its anion N 19 have been estimated [104] from the observed [105, 106] and computed free energy to be only 10 min and 2.2 days, respectively. The high kinetic stability of the anion 19 can be understood in terms of enhanced pentgon stability and aromaticity. The deprotonation raises the energy of lone pair orbitals and promotes cyclic delocalization of o- and rr-electrons. 

Bobrowski and Das33 studied the transient absorption phenomena observed in pulse radiolysis of several retinyl polyenes at submillimolar concentrations in acetone, n -hexane and 1,2-dichloroethane under conditions favourable for radical cation formation. The polyene radical cations are unreactive toward oxygen and are characterized by intense absorption with maxima at 575-635 nm. The peak of the absorption band was found to be almost independent of the functional group (aldehyde, alcohol, Schiff base ester, carboxylic acid). In acetone, the cations decay predominantly by first-order kinetics with half life times of 4-11 ps. The bimolecular rate constant for quenching of the radical cations by water, triethylamine and bromide ion in acetone are in the ranges (0.8-2) x 105, (0.3-2) x 108 and (3 — 5) x 1010 M 1 s 1, respectively. 

The data for the insertion rate of CO into a palladium-methyl bond for dppp as the ligand has been studied with considerably more precision by Brookhart and co-workers [24], The kinetics were studied in the temperature range between 191 and 210 K for a reaction similar to that of Figure 12.6, i.e. the starting material was the CO adduct of the methylpalladium(dppp)+BArF complex. A AG of 62 kJ.mol"1 was observed and since AS was close to zero, a half-life time of 10 s is calculated for the CO-adduct at 235 K, much shorter than the value for dppe given above (150 s). 

Bianchini has reported that the migratory insertion reactions of [Pd(R)(CO)(P-P)]+ complexes (R = Me, Et) are reversible and follow first-order kinetics irrespective of the chelating diphosphine (P-P = dppp, dppe, meso-dppb, rac-dppb, meso-bdpp, rac-bdpp) [5e, f]. The free energies of activation for these reactions were calculated from the half-life times (tj 2) obtained by P( H HP NMR spectroscopy as all the rates of conversion of the methyl carbonyl complexes were independent of the CO pressure. Therefore, the AG values associated with the migratory insertion of the methyl carbonyl complexes could be straightforwardly calculated from the values using the equation AG = RT(ln k -ln kT/h) with = In First-order... 

The rate of decomposition of initiators usually follows first-order kinetics and is dependent on the solvent present and the temperature of polymerization. The rate is usually expressed as a half-life time (h/2), where ti/2 = In 2/A d = 0.693/fcd- The rate constant ( d) changes with temperature in accordance with the Arrhenius equation as shown below ... 

It is convenient at this juncture to introduce a concept that, in electro analytical chemistry, sometimes is referred to as the reaction order approach. Consider first the half-life-time, t1/2> which in conventional homogeneous kinetics refers to the time for the conversion of half of the substrate into product(s). From basic kinetics, it is well known that t /2 is independent of the substrate concentration for a reaction that follows a first-order rate law and that 1/t j2 is proportional to the initial concentration of the substrate for a reaction that follows a second-order rate law. Similarly, in electro analytical chemistry it is convenient to introduce a parameter that reflects a certain constant conversion of the primary electrode intermediate. In DPSCA, it is customary to use ti/2 (or to.s), which is the value of (f required to keep the value of Ri equal to 0.5. The reaction orders (see Equation 6.30) are then given by Equations 6.35 and 6.36, where Ra/b = a + b, and Rx = x (in reversal techniques such as DPSCA, in which O and R are in equilibrium at the electrode surface, it is not possible to separate the... 

In contrast to the (E)-isomer, (Z)-alkenyl(phenyl)-A3-iodane 41 is labile and decomposes with a half-life time of 20 min to terminal alkynes in chloroform solution at room temperature [64]. Stereo electronically preferable reductive anti / -elimination accounts for this facile decomposition. In fact, the kinetic results for E2-type dehydrohalogenation of vinyl halides show that the relative rates of elimination decrease in the order anti /3->syn / - a-elimination [65]. Similar anti -elimination of vinyl-A3-iodane was proposed in the oxidation of methoxyallene with (diacetoxyiodo)benzene 4 to 3-acetoxy-3-methoxypropyne [66]. 

The time (hours, days or years) required for the chemical concentration in a medium to be reduced by half. If the elimination rate involves transport and transformation processes that follow first order kinetics, the half-life time is related to the total elimination rate constant k by 0.693 /k. 

Note Kinetics of the inhibition of photosystem II electron flow in these macrophytes by 50 pg/L linuron and the subsequent recovery of inhibition by washing with uncontaminated well water are expressed as half-life times (f1/2). 

We compared the l3C NMR spectra of the subtilisin complexes of [M]SSI and [M]SSI. Rather surprisingly, the NMR spectrum taken within two hours after the preparation of [M]SSI -subtilisin BPN complex was absolutely identical to that of [M]SSI-subtilisin BPN. A period of two hours was necessary to obtain the 13C NMR spectrum of the [M]SSI -subtilisin complex with a sufficient signal-to-noise ratio. This included the time after the modified inhibitor was brought in contact with subtilisin BPN. There were no extra signgals detected other than those observed for the [M]SSI-subtilisin complex, indicating that the cleaved scissile bond in [M]SSI can be rapidly restored in the complex. Since time-resolution of 13C NMR spectroscopy is rather limited by its inherent insensitivity, we are not able to tell exactly how fast this process is. Tonomura et al., however, have recently found by a stopped flow technique an unknown kinetic process having a half-life time of two seconds for the SSI -subtilisin system. Obviously this process should be the restoration process of the cleaved scissile bond of SSI in the complex. Therefore, the hydrolyzed scissile bond could in fact be restored within several seconds (private communication). 

Isomerization can be induced by light in both directions or by heat in the Z — E direction. The reverse thermal reaction is not observed at normal temperatures. Any one of the elementary reactions can be missing. Z-azobenzene in solution has a thermal Z E activation enthalpy AH 96 kJ moT and a half life time of 2 to 3 days at room temperature. Thus, the thermal reaction is irrelevant for the photoisomerization at usual irradiation intensities (for comparison Z-stilbene has Eg 180 kJ moT is liquid, and is kinetically stable). On the other hand, one of the photoreactions may not be active (e.g., when an irradiation wavelength is selected where one form does not absorb or when the quantum yield is too small). Inspection of Figure I.IB shows that E- and Z-azobenzene have virtually no spectral region without overlapping absorption. 

Decomposition of organic peroxides to free radicals follows first order kinetics. Half life (t ) is defined as the time required for half of the organic peroxide to decompose at a certain temperature. Half-life is an important parameter in... 

Generation and reactivity of a CrIV aqua complex (believed to be [CrO(OH2)5]2+) in acidic aqueous solutions has been investigated.231-235 Typical pathways for the formation and decay of CrIvaq. (which has a half-life time of 20s at pH 1 and 25 °C) are summarized in Scheme 6.231-2 5 Kinetic studies of the reactions of CrIvaq. are complicated by ... 

The kinetic constant k of this rearrangement can be extracted from the variation of the cathodic current versus time and its average value is 0.007 0.003 s In other words, the half-life time of tetracoordinated Cu(II) rotaxane is 120 50 s. 

Oscilloscope traces obtained from a 10 3M Ph2C-0 solution are displayed in Fig. 7.4. In catalyst-free solution, the 550-nm absorption of the ketyl decays as expected according to a second-order rate law. The rate constant obtained from the kinetic analysis if 8.5 x 10sM-1s 1 in agreement with published literature values. At the low laser intensity applied, this decay is barely visible on the 10-/is/division time scale in Fig. 7.4 a. Addition of catalyst, 8 mg of Pt/100 ml of solution as determined by atomic absorption spectroscopy, sharply enhances the absorption decay. This process follows approximately first-order kinetics, the half-life time being 40 /is. The decay is attributed to the reaction... 

Dewar pyridine, 2-azabicyclo[2.2.0]hexa-2,5-diene (218), thermally reverted to pyridine at room temperature with a half-life time of 2.5 minutes (Ea = 16 kcal/mol).255 Far more stable were 2-azabicyclo-[2.2.0]hex-5-en-3-ones (225).265-267 The kinetics of the thermal (2 + 2)-cycloreversion of 225 (R = Me) in the temperature range of 130° to 160° have been reported (A//J = 33.2 kcal mol-1 ASt = + 2.7 cal mol-1 deg-1).266 An interesting difference in rate was observed between 225 (R = H) and its methyl homolog 225 (R = Me). At 130° the former reverted ten times as rapidly to 2-pyridone as the latter did to 1-methyl-2-pyridone this difference has been related to the intermediacy of the lactim tautomer of 225 (R = H) in the former reaction. Dewar benzene oxide, 2,3-epoxybicyclo[2.2.0]hex-5-ene (266), isomerized to an equilibrium mixture of benzene oxide/oxepin at 115° with a half-life time of 18 minutes.270 The relatively high thermal stability of such strained bicyclic heterocycles has been attributed to the fact that the symmetry-allowed conrotatory process would give rise to an unfavored cis.trans heterocyclic diene.265... 

The values of E and A are used to calculate the other kinetic parameters such as specific rate constant (reaction constant) k and half life time with the help of equations 3-7 and 3-8 ... 

The considerable differences in the coefficients of the Arrhenius equation (Table 4-37) lead to different half-life times at identical temperatures. In Fig. 4-33 the plots of half-life time as a function of temperature (1 000/T) of the samples with maximum, minimum, and average values of the kinetic coefficients are shown ... 

The plot of log half-life time of the cracking reaction versus the inverse Kelvin temperature (1 000/7) once more shows straight lines (Fig. 4-34). The slope of the line is determined by the value of the activation energy. The half-life times of the samples possessing the maximum and minimum values of the kinetic coefficients, as well as the average values were plotted. 

The onset temperature, and the temperature and kinetic data of the first oxidation peak maximum are the criteria which define the practical behavior of bitumens in its applications. Calculation of the reaction rate constants and of the half-life time using the Arrhenius coefficients gives values, which may be reproduced by other methods, although the oxidation does not obey the first order reaction law. The plot of the log versus the inverse Kelvin temperature (1 000/T) is shown in Fig. 4-78. Corresponding graphs for the other peaks show the increase in the half-life times. However, they are only of theoretical interest and do not have any relevance to practical behavior in production and manufacturing. Fig. 4-78 and Table 4-102 show that oxidation commences at temperatures... 

Knowledge of the kinetics of the oxidation reaction permits extrapolation of the resulting half life time to lower temperatures, producing information about the oxidation stability at manufacturing temperatures and the application of the bitumens. This only gives a rough estimate of the behavior on the actual road surface, since there are additional... 

The kinetics of LTO have been published [4-93 to 4-96], but only one of them [4-96] deals with the relation of the coefficients of the Arrhenius equation to the system pressure between 1 and 63 bar. Whilst the activation energies between 63 and 65 kJ/Mol are not related to the pressure, a clear correlation has been found for the frequency factor, with log A = 6.18 min at 1 bar pressure and log A = 8.08 min at 63 bar. The half-life times ty2 at 200, 250, and 300 °C calculated using those coefficients are given in Fig. 4-158. 

As expected the asphaltenes possess the highest oxidation stability in the LTO range, which is manifested by the high values of the activation energy, the frequency factor, and thereupon of the half life time. The low values for the kinetic coefficients and log A for n-hexacontane do not noticably affect the half life times. In contrast to the values for Athabasca bitumen (Fig. 4-158), the real systems tested display higher values for their half hfe times, by approximate half a power of ten. 

---