Decay rate pseudo first-order

Analysis of density of the parent band revealed that the decay followed pseudo-first-order kinetics. The pseudo-first-order rate constant was proportional to (the... 

Figure 3 is the result of pulse radiolysis experiment about the reaction of hydrated electron with polymer chains(0 or 30 mM carboxymethyl chitosan solution with 0.3 M terf-butanol under Ar saturation), and shows the decay of the absorbance as a function of time. This absorbance was measured at wavelength 720 nm, which is the absorption peak of hydrated electron. As seen in Figure 3, the absorbance increases immediately after the irradiation, and attenuates afterwards. This means that hydrated electron is generated immediately after irradiation and diminishes gradually by some reactions of hydrated electron. Compared the absorbance decay of polymer solution with the decay of solution without polymer, the decay of polymer solution is faster than without polymer, so it is obvious that hydrated electron reacts with polymer chains. The decay curve can be fitted by pseudo first-order decay. The pseudo first-order decay is shown by equation (8). From estimating the slope of the pseudo first-order decay rate of the absorbance at 720 nm against polymer concentration, the rate constant of the reaction of hydrated electron with polymer chains can be calculated Figure 4). The rate constants of the reaction of hydrated electron with CM-chitin and CM-chitosan was determined as l.lxlO7 and MxlO M V1]. These values are almost the same with the value of carboxymethyl cellulose(2< ).

In addition to comparing overall quenching rate constants, it is also possible to recover the values of the quencher association and dissociation rate constants from quenching experiments. The same model that was employed for fluorescent probes can be employed. This model considered that the probe was immobile. The general solution to this model is given by Eq. (8), which has four parameters defined by the rate constants for the processes described in Fig. 1. However, the experimental results showed that the triplet state decayed by pseudo-first-order kinetics, suggesting that once the quenchers enter the supramolecular system, quenching occurred with an efficiency of unity. Under these conditions, Eq. (5) can be applied. In addition, if the condition that [H] holds, Eq. (5) can be reduced to... 

The conditions chosen make the reaction appear to be first-order overall, although the reaction is really not first-order overall, unlessjy and happen to be 2ero. If a simple exponential is actually observed over a reasonable extent (at least 90—95%) of decay the assumptions are considered vaUdated and is obtained with good precision. The pseudo-first-order rate constant is related to the k in the originally postulated rate law by... 

The intermediate diphenylhydroxymethyl radical has been detected after generation by flash photolysis. Photolysis of benzophenone in benzene solution containing potential hydrogen donors results in the formation of two intermediates that are detectable, and their rates of decay have been measured. One intermediate is the PhjCOH radical. It disappears by combination with another radical in a second-order process. A much shorter-lived species disappears with first-order kinetics in the presence of excess amounts of various hydrogen donors. The pseudo-first-order rate constants vary with the structure of the donor with 2,2-diphenylethanol, for example, k = 2 x 10 s . The rate is much less with poorer hydrogen-atom donors. The rapidly reacting intermediate is the triplet excited state of benzophenone. 

Using the pseudo-first-order equation A obsd = 0 + co2 [COiKwhere kcoi is the second-order rate constant for the reaction of carbene with CO2 and ko is the rate of carbene decay in the absence of CO2), solution-phase values of kcoi for phenylchlorocarbenes 9 and 12, and diphenylcarbenes 14 and 15 in dichloromethane were estimated (Table 4.1). (The concentration of CO2 in saturated dichloromethane solution at 25°C and 1 atm is 196mmol/L. ) The trend of these estimated second-order order rate constants agrees with that observed in low-temperature matrices by Sander and co-workers. ... 

IR kinetic measurements on Cr(CO)5(N2) were a particular technological triumph (99) because not only were the strong vc—o bands observed but also the very weak (2240 cm J) and natural abundance vnCo bands were detected. The compound Cr(CO)5(N2) decayed at 25°C with a pseudo-first order rate constant of 1.7 second-1. Thus, Cr(CO)5(H2) and Cr(CO)5(N2) have similar thermal stabilities, and it has been one of the great surprises of the Miilheim work (96-99) to find how long-lived unstable molecules can be. 

Fig. 5 shows the time dependence of the solid-state ion exchange process. The process has pseudo first order kinetics in the investigated conversion range for both (i) the distribution and crystallinity loss of the CdCl2 salt and (ii) the formation of new Cd,H-Y phase. The rate constant obtained for the decay of... 

For CO, the decay rate was measured in sc Ar for five different CO concentrations between ca. 7 x 1019 molecule cm-3 and 2x 102° molecule cm-3 (42). These concentrations correspond to add[CO] values of 1.6 x 109 to 4.4 x 109s 1, respectively - again larger than k13, but not much so. Applying the full Eq. (1) to the five concentration values gives predicted pseudo-first-order decay rate constants varying almost linearly from 3.3xl06s 1 to... 

Net addition of CO to 3Fe(CO)3(H2) to form Fe(CO)4(H)2 was observed upon photolysis of Fe(CO)s in sc Ar in the presence of H2 (24). The intermediate species 3Fe(CO)3(H2) is involved as a minor product of the photolysis, and was proposed to arise from addition of H2 to Fe(CO)3 or Fe(C0)3Ar (24). Experimentally, this species was shown to decay in the presence of excess CO with a pseudo-first-order rate constant 0bs — 4.1( + 0.3) x 107s-1. The mechanism for this spin-forbidden process was however unclear from experiment alone, and computation was used to explore the various possibilities (24). 

The cyclohexadienyl radicals decay by second-order kinetics, as proven by the absorption decay, with almost diffusion-controlled rate (2k = 2.8 x 109 M 1 s 1). The cyclohexyl radicals 3 and 4 decay both in pseudo-first-order bimolecular reaction with the 1,4-cyclohexadiene to give the cyclohexadienyl radical 5 and cyclohexene (or its hydroxy derivative) (equation 15) and in a second order bimolecular reaction of two radicals. The cyclohexene (or its hydroxy derivative) can be formed also in a reaction of radical 3 or... 

Rate measurements are straightforward if the carbenes can be monitored directly. As a rule, the decay of carbene absorption is (pseudo) first-order, due to rearrangement and/or reaction with the solvent. In the presence of a quencher, the decay is accelerated (Eq. 1), and the rate constant kq is obtained from a plot of k0bs versus [Q], Curved plots were often observed with proton donors (HX) as quenchers, particularly for high concentrations of weakly acidic alcohols. Although these effects have been attributed to oligomerization of the alcohols,91 the interpretation of curved plots remains a matter of dispute.76 Therefore, the rate constants reported in Tables 2-4 are taken from linear (regions of) obs-HX plots, or refer to a specified concentration of HX. 

Spectroscopically invisible carbenes can be monitored by the ylide method .92 Here, the carbene reacts with a nucleophile Y to form a strongly absorbing and long-lived ylide, competitively with all other routes of decay. Although pyridine (Py) stands out as the most popular probe, nitriles and thiones have also been used. In the presence of an additional quencher, the observed pseudo-first-order rate constant for ylide formation is given by Eq. 2.92,93 A plot of obs vs. [Q] at constant [Y ] will provide kq. With Q = HX, complications can arise from protonation of Y and/or the derived ylides. The available data indicate that alcohols are compatible with the pyridine-ylide probe technique. 

In the 1988-1999 period, almost all absolute kinetic studies of carbenic reactions employed LFP with UV detection. Carbenes that contain a UV chromophore (e.g., PhCCl) are easily observed, and their decay kinetics during reaction can be readily followed by LFP.11 However, alkyl, alkylhalo, and alkylacyloxycarbenes are generally transparent in the most useful UV region. To follow their kinetics, Jackson et al. made use of the ylide method, 12 in which the laser-generated carbene (2) is competitively captured by (e.g.) pyridine, forming a chromophoric ylide (3, cf. Scheme 1). The observed pseudo first order rate constants (kobs) for the growth of ylide 3 at various concentrations of pyridine are monitored by UV spectroscopy, and obey Eq. 1. 

Most importantly, the direct reaction of anisole cation radical with N02 (64) is established by the pseudo-first-order kinetics observed for the disappearance of AN+- in the presence of added N02 (see Fig. 16A). The magnitude of the second-order rate constant of k2 = 1.5x109m i s evaluated in this way is thus consistent with the spectral decay of the freely diffusing aromatic cation radical (AN+<) in Fig. 15. 

Fig. 16 (A) Typical decay of anisole cation radical in the presence of added NO-, showing the fit to first-order kinetics (smooth curve). (AN+- generated from the 355-nm irradiation of 0.2 m anisole and 0.3 m MeOPyNOF in acetonitrile.) (B) Plot of the pseudo-first-order rate constant against the concentration of added N02. (C) Similar to (B), but with added pyridine or 2.6-lutidine.

Fast spectroscopy was also used to probe the reactivity of PBN +. The 266 nm laser excitation of peroxydisulfate ion in aqueous solution at room temperature gives the powerful oxidant SOr, which oxidizes PBN in an exergonic reaction (by about 0.8 eV, see Tables 1 and 5) with k = 3 X 109 dm3 mol-1 s 1. The pseudo-first-order rate constant for the decay of PBN + by reaction with water to give HO-PBN" was 2 x 106 s 1, a relatively slow reaction (k = 3.6 x 104 dm3 mol-1 s-1 at ambient temperature). 

Figure 1. Competition kinetics for the Ru(NH2)62y reduction of Co([14 aneNk)-(0H,)0 Reactions at 25°C, pH 2, and n = 0.1(NaClO,). Individual pseudo-first-order rate constants were determined from the exponential (to four half-lives) decay of Co([14]aneN,)(OH2)022 absorbance at 360 nm. Reactions were performed by mixing a solution containing Ru(NH2)62 and Co([14]aneNh)(OHt) -(1 X I 3 M) with a solution saturated in 02(1.2 X 10 3 in an Aminco stopped-...

The rate of Sc -promoted photoinduced electron transfer from Ceo to CI4Q determined from the decay rate of the absorbance due to Ceo at 740 nm (inset of Fig. 11) obeys pseudo-first-order kinetics and the pseudo-first-order rate constant increases linearly with increasing the p-chloranil concentration [CI4Q] [135]. From the slope of the linear correlation, the second-order rate constant of electron transfer ( et) in Scheme 15 was obtained. The A et value increases linearly with increasing the Sc + concentration. This indicates that CUQ produced in the photoinduced electron transfer forms a 1 1 complex with Sc + (Scheme 15) [78]. When CI4Q is replaced by p-benzoquinone (Q), the value for electron transfer from Ceo to Q increases with an increase in [Sc " ] to exhibit a first-order dependence on [Sc ] at low concentrations, changing to a second-order dependence at high concentrations, as shown in Fig. 13 (open circles) [135]. Such a mixture of first-order and second-order dependence on [Sc ] was also observed in electron transfer from CoTPP (TPP = tetraphenylporphyrin dianion) to Q... 

Pseudo-first-order rate constants for carbonylation of [MeIr(CO)2l3]" were obtained from the exponential decay of its high frequency y(CO) band. In PhCl, the reaction rate was found to be independent of CO pressure above a threshold of ca. 3.5 bar. Variable temperature kinetic data (80-122 °C) gave activation parameters AH 152 (+6) kj mol and AS 82 (+17) J mol K The acceleration on addition of methanol is dramatic (e. g. by an estimated factor of 10 at 33 °C for 1% MeOH) and the activation parameters (AH 33 ( 2) kJ mol" and AS -197 (+8) J mol" K at 25% MeOH) are very different. Added iodide salts cause substantial inhibition and the results are interpreted in terms of the mechanism shown in Scheme 3.6 where the alcohol aids dissociation of iodide from [MeIr(CO)2l3] . This enables coordination of CO to give the tricarbonyl, [MeIr(CO)3l2] which undergoes more facile methyl migration (see below). The behavior of the model reaction closely resembles the kinetics of the catalytic carbonylation system. Similar promotion by methanol has also been observed by HP IR for carbonylation of [MeIr(CO)2Cl3] [99]. In the same study it was reported that [MeIr(CO)2Cl3]" reductively eliminates MeCl ca. 30 times slower than elimination of Mel from [MeIr(CO)2l3] (at 93-132 °C in PhCl). 

It was found that the rate of the protonation step depended on both the acidity of the alcohol and the nature of the substituent on the nitrile ylide. After protonation, the azaallyl cation 370 might have been expected to react rapidly with the aUcoxy anion but, instead, it was found that it decayed according to pseudo-first-order kinetics via reaction with an alcohol molecule at a rate which depended on the alcohol pKs- The overall mechanism proposed (212) is shown in the scheme. 

When oxygen is removed from a reaction solution of tetrakis-(dimethylamino)ethylene (TMAE), the chemiluminescence decays slowly enough to permit rate studies. The decay rate constant is pseudo-first-order and depends upon TMAE and 1-octanol concentrations. The kinetics of decay fit the mechanism proposed earlier for the steady-state reaction. The elementary rate constant for the dimerization of TMAE with TMAE2+ is obtained. This dimerization catalyzes the decomposition of the autoxidation intermediate. 

That is, A decays exponentially with time determined by (kl7[B]0), as if it were a first-order reaction. Thus under these so-called pseudo-first-order conditions, a plot of ln[A] against time for a given value of [B]0 should be linear with a slope equal to ( — I7[B]0). These plots are carried out for a series of concentrations of [B](l and the values of the corresponding decays determined. Finally, the absolute rate constant of interest, kl7, is the slope of a plot of the absolute values of these decay rates against the corresponding values of [B] . Some examples are discussed below. 

FIGURE 5.10 Plots of ozone pseudo-first-order decay rate constant as a function of the o-cresol concentration using U.S. EPA protocol for determining 03 rate constants (adapted from Pitts et al., 1981). 

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