Pseudo-first-order disappearance rate

Chemical. Although no products were identified, p-chloronitrobenzene (1.5 x 10 M) was reduced by iron metal (33.3 g/L acid washed 18-20 mesh) in a carbonate buffer (1.5 x 10 M) at pH 5.9 and 15 °C. Based on the pseudo-first-order disappearance rate of 0.0336/min, the half-life was 20.6 min (Agrawal and Tratnyek, 1996). 

Figure 5. The pseudo-first-order disappearance rate constants for ground-state CtO are plotted as a function of 02 pressure for two pressures of C3Ot. The results fall on a straight line and the slope gives a second-order disappearance rate constant for C20 reacting with 02 of 3.30 0.12 X 10 13 cm3 moleculesec 1 (9), 10 mtorr Cs02 (+), 5 mtorr C302. K" — 3.30 0.12 X 10 13 cm3 sec 1.

The kinetics of the Amadori-compound formation from D-glucose and l-lysine, as well as melanoidin formation, has been examined. The so-called Amadori compounds are formed at an exponential rate, while showing pseudo-first-order disappearance of L-lysine in the presence of... 

Flooding and Pseudo-First-Order Conditions For an example, consider a reaction that is independent of product concentrations and has three reagents. If a large excess of [BJ and [CJ are used, and the disappearance of a lesser amount of A is measured, such flooding of the system with all components butM permits the rate law to be integrated with the assumption that all concentrations are constant except A. Consequentiy, simple expressions are derived for the time variation of A. Under flooding conditions and using equation 8, if x happens to be 1, the time-dependent concentration... 

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. 

Thus, we may write the pseudo first-order rate constant for disappearance of CD4 as n(CH5 iD -+) = 4.40 X 10 4 sec.-1 Appropriate rate equations are... 

Figure 3. Plot of the pseudo first order rate for reaction of Fe(C0)3 with CO. The rate of disappearance of Fe(C0)3 at 1954 cm l ( ) and the rate of appearance of Fe(C0)4 at 1984 cm ( ) are plotted against pressure of added CO. (Reproduced with permission from reference 8. Copyright 1986 American Institute of Physics.)...

Activation rate constants (k) in ATRP/ATRA are typically determined from model studies in which copper complex is reacted with alkyl halide in the presence of radical trapping agents such as TEMPO [127,128,129], Rates are determined by monitoring the rate of disappearance of alkyl halide in the presence of large excess of the activator (Cu X/L) and TEMPO. Under such pseudo-first order conditions, the activation rate constant can be calculated ln([RX]0/[RX]() vs.t plots (slope =-k) Cu C/... 

Fig. 20 A plot of the observed pseudo-first-order rate constants (kobs) for the methanolysis of HPNPP (4 x 10 5moldm ) as a function of [35 2Zn(II)] in the presence of 1 equivalent of added CH30 per complex giving jpH = 9.5, T = 25 + 0.1 °C. Dotted line is presented as a visual aid directed through all actual data collected at 280 nm ( ) or 320 nm (O) which are the wavelengths for disappearance of HPNPP and appearance of /j-nitrophenol solid line is a linear fit of the data corrected for inhibition by triflate counterions at 280 nm ( ) or 320 nm ( ). Reproduced with permission from ref. 95.

Samples 1-4 correspond to VPO treated in steam for 92, 312h, in N2 and activated base catalysts, respectively, k, are pseudo-first-order rate constants for the disappearance of butane. The constants are measured in a microreactor on a larger amount ( 1 g) of catalyst at 633 K. k (intrinsic) are based on the BET surface area. 

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. 

Various rate constants which enter into the expression for k i, Equation 14.14, have now been discussed. kunj as defined in Equation 14.13 has the appearance of a first order rate constant for the disappearance of A molecules but it is actually only a pseudo first order rate constant since it explicitly depends on the concentration of M, the species involved in the activation and deactivation of A molecules. In the limit of high concentration, [M] oo, kuni reduces to an apparent first order process, lim (kuni j oo) = ka(E)(8ki(E)/k2)[A] = kt(Apparent)[A], while at low concentration the reduction is to an apparent second order process, lim(kunij[M]->.o) = 8k (E)[A][M] = k2 (Apparent) [A] [M],... 

In the first type of study, pseudo first-order kinetics were observed in both the sediment and aqueous phases from t=0 through two half-lives in overall chlorpyrifos disappearance (total time -8 days). For these studies, computer calculations using the model illustrated in equations 7 were again used to calculate values for kj, k and kg, assuming a value of k equal to the pseudo first-order rate constant in distilled water buffered to the same pH. Values were also calculated for Obfi assuming kg 0 (equation 10) for comparison to the experimental kg values. The results of these calculations are shown in Table VII. 

Studies of the disappearance of the octyl ester at pH 9.8 in sediment/water systems aged 3 days prior to pH adjustment are summarized in Figure 8. For the systems with p=0.013 and 0.005 (fractions sorbed =. 978 and. 945) the rate is pseudo first order, but the rate constant is 10 times smaller than the aqueous value (1.6x10 min ) at this pH. As was suggested for chlorpyrifos, this k value may be characteristic of the actual value of k. At p=0.001, (fraction sorbed = 0.78), the disappearance kinetics is not first order, but shows rapid disappearance of the aqueous ester, followed by disappearance of the sorbed ester at a rate similar to the studies with higher sediment to water ratios. 

As described in the previous section the presence of inhibitors at high enough concentrations ensures the kinetic isolation of the initiation step which becomes the rate determining step in a pseudo first order reaction, the rate of PH2 disappearance... 

Metathesis activity. A quantitative comparison of metathesis activities was made in the gas phase homometathesis of propylene. The reaction kinetics are readily monitored since all olefins (propylene, ethylene, cis- and fra/3s-2-butylenes) are present in a single phase. Metathesis of 30 Torr propylene was monitored in a batch reactor thermostatted at 0 °C, in the presence of 10 mg catalyst. The disappearance of propylene over perrhenate/silica-alumina (0.83 wt% Re) activated with SnMe4 is shown in Figure 2a. The propylene-time profile is pseudo-first-order, with kob (1.11 + 0.04) X 10" slightly lower rate constant, (0.67 constants are linearly dependent on Re loading. Figure 3. The slope yields the second-order rate constant k = (13.2 + 0.2) s (g Re) at 0°C. 

A variety of concave pyridines 3 (Table 1) and open-chain analogues have been tested in the addition of ethanol to diphenylketene (59a). Pseudo-first-order rate constants in dichloromethane have been determined photometrically at 25 °C by recording the disappearance of the ketene absorption [47]. In comparison to the uncatalyzed addition of ethanol to the ketene 59a, accelerations of 3 to 25(X) were found under the reaction conditions chosen. Two factors determine the effectiveness of a catalyst basicity and sterical shielding. Using a Bronsted plot, these two influences could be separated from one another. Figure 4 shows a Bronsted plot for some selected concave pyridines 3 and pyridine itself (50). 

The potentially greater toxicity of peroxynitrite can be readily visualized by comparing the mean diffusion distances that various nitrogen and oxygen-centered species may traverse in one lifetime. The definition of lifetime (t) is the time required for 67% of the initial concentration to decompose, and is readily calculated as the reciprocal of the pseudo-first-order rate constant for the disappearance of the species in question. Distances were calculated from the following equation, which is readily derived from the Fick s laws of diffusion (Nobel, 1983 Pryor, 1992). 

The next set of experiments was run in the presence of <5mM Mn2+, which reduces Craq02+ to the unreactive Cr2+. In 02 -saturated solutions, the kinetic traces became exponential, and the dependence on [MeOH] disappeared as expected on the basis of the large rate constant for the Mn2+/Craq02+ reaction (105—106 M-1 s-1) (58) which took over as the sole pathway for the removal of Craq02 +. The plot of the pseudo-first order rate constant against the concentration of under such conditions is linear with a slope of 0.28 M-1 s-1. 

Pseudo First Order Rate Constant, kobs, for the Disappearance of Quadricyclane at Various pH Values in Aqueous Solution (Data from Hill et al., 1997). 

Jafvert and Wolfe (1987) studied the rate of disappearance of a series of halogenated ethanes in an anaerobic sediment-water slurry. They found the following initial pseudo-first-order rate constants, kobs, for the various compounds ... 

The kinetics of the carbon disulfide elimination reaction were studied using PMR and visible spectroscopy (16). This spontaneous reaction was found to be first order in the M(RSXant)2 complexes (M = Ni, R = Et, r-Bu, Bz M = Pd, R =/ -Bu), both in the disappearance of the starting material and in the formation of the mercaptide-bridged species in CHC13 and THF. The pseudo-first-order kinetics observed in CS2 are attributed to an equilibrium between the M(RSXant)2 complexes and this solvent. Rate constants for the reaction are of the order of 10 3 to 10"1 min"1 depending on solvent, temperature, alkyl... 

---