Computer pseudo-first-order rate

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). 

Fig. 14 Plots of observed pseudo-first-order rate constants for the methanolysis of increasing and equimolar [La3 + ] = [32, HPNPP] at 25 °C and pH 5.0 (iV,jV-dimethylaniline buffer, , right axis) or pH 6.7 (2,6-lutidine buffer, , left axis). Lines through the data computed from fits to a standard one-site binding model. Reproduced from ref. 81 with permission.

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. 

Fourthly, the starting point for lifetime estimations is often laboratorygenerated kinetic data for reaction of the compound of interest with OH radicals. The bimolecular rate constants measured in laboratory kinetic experiments need to be converted into a pseudo first order rate constant for loss of the compound, k . In principal this conversion is simple, i.e., the bimolecular rate constant merely has to be multiplied by the OH concentration ([OH]). In practice there are difficulties associated with the choice of an appropriate value of [OH], At present we cannot measure the global OH concentration field directly. The OH radical concentration varies widely with location, season, and meteorological conditions. To account for such variations requires use of sophisticated 3D computer models of the atmosphere. 

Least-squares plots of In [RHgX] vs. t by an IBM 1620 computer gave values for the pseudo-first-order rate constant k. Also, assuming a first-order rate dependence on ozone concentration, k was calculated via experimental saturation values for 03 in CHC13 at 0°C. The results of these calculations are shown in Table III. From Table III a few relative rate sequences can be formulated. These are listed below. 

To further examine the possible role of various processes in the consumption of methylchloroform, pseudo-first-order rate constants were approximately computed for the mixed layer of different oceanic regions (Table VII). 

If ah the first-order and pseudo-first-order rate constants, k A, k,B, ka, and k are of the same order of magnitude, the explicit solution is not possible and the computer is the simplest means to arrive at a solution (Fig. 3). 

All reactions were followed for three or four half-lives and gave good pseudo first-order plots of log(.4, — A o) vs, time, where At is the absorbance at time t and /loo is the absorbance after more than eight half-lives. A computer program which was adapted to the available CDC 3600 computer was used to calculate the least-squares-best slopes for the straight line plots of ln(/l, — /loo) vs. time and was used to obtain the pseudo first-order rate constants. The rate constants were calculated for the first, the first and second, and for the first, second and third half-lives in order to detect trends in the rate data. 

Direct-Computation Rate Methods Rate methods for analyzing kinetic data are based on the differential form of the rate law. The rate of a reaction at time f, (rate)f, is determined from the slope of a curve showing the change in concentration for a reactant or product as a function of time (Figure 13.5). For a reaction that is first-order, or pseudo-first-order in analyte, the rate at time f is given as... 

First-order and pseudo-first-order reactions are represented by the upper curve in Fig. 14-14. We note that for first-order reactions when the Hatta number is larger than about 3, the rate coefficient k can be computed by the formula... 

When a = b = 1 in (1.42) the overall reaction is second-order. Even a quite small excess of one reagent (here B) can be used and pseudo first-order conditions will still pertain. As the reaction proceeds, the ratio of concentration of the excess to that of the deficient reagent progressively increases so that towards the end of the reaction, pseudo first-order conditions certainly hold. Even if [B] is maintained in only a two-fold excess over [A], the error in the computed second-order rate constant is 2% for 60% conversion. ... 

PRZM was applied to a hypothetical situation of a pesticide In a Georgia agricultural environment. An overall, pseudo-first-order degradation rate coefficient of 0.001 day was used, along with a series of values. A cover crop of peanuts was assumed. The simulation was done for a 900 g/ha application to a class A soil (well drained) and a class D soil (poorly drained). Movement through the root zone was simulated using rainfall records. In the hypothetical 1-ha plot, 800 g and 550 g of the pesticide leached past 60 cm In the class A and D soils, respectively, when a Kj value of 0.06 was used 40 g and 5 g leached past 60 cm In the class A and D soils, respectively, when a Kj value of 1.5 was used. These computational results support the conclusion on Kj values stated at the end of this paper. 

Computed fits of experimental signals probed at different wavelengths allow for the careful investigation of ultrafast electronic pathways (Fig.2). The transient signal at 400 nm is assigned to a very short-lived CTTS state of aqueous hydroxyl ions (OH), . This excited state is instantaneously populated, typically in less than 50 fs and follows a pseudo first order dynamics with a frequency rate of 5 x 1012 s. Semi-quantum MD simulations emphasize that transient excited CTTS states play a crucial role in photoinduced electron transfers [4-6]. 

The formation of pyrazines fit a zero order reaction. Plotting concentrations of pyrazines formed versus time of reaction gave the better fit of the line, usually with a coefficient of determination (r2) of greater than 0.95. For a pseudo first order reaction, a curve rather than a line would be obtained. General least squares analysis of the data was used to compute rate constants (27). Two zero points were used for each regression. Duplicate samples were tested at the early sampling times vs. triplicate samples at later times. Each data point collected was treated separately in the regression analyses. 

Kinetic Studies. Although it was not possible to measure the ozonation rates for dialkylmercurials by the techniques described earlier, the alkylmercuric halides reacted slowly enough at 0°C that quite good rate plots were obtained. These plots, performed by an IBM 1620 computer and on concentration data obtained under pseudo-first-order reaction conditions, yielded the relative rate data listed in Table III. These data suggested the two general relative-rate sequences illustrated by sequences 16 and 17 (see p. 88). 

Figure 6< Computed eftects of sorption to bottom sediments on the pseudo-first-order system halfllves (log mass/flux) for a series of generic photoreactlve substrates, each having the same photolysis rate but differing octanol-water partition coefficients...

PHa + Oj- Products. The rate constants k were measured at 300 K by flash photolysis (FP) of PH3/O2/N2 mixtures (0.35 3.5 to 17 250 to 270 Torr) and PH3/O2 mixtures (0.35 1.5 Torr), above the upper and below the lower explosion limit, followed by absorption of radiation near 455 nm (from a pulsed dye laser) by PH2. k = (1.2 0.3)x10" at a total pressure of -270 Torr (i.e., above the upper explosion limit) was derived from the dependence of the effective rate constant k ff=d ln([PH2]o/[PH2])/dt on the O2 partial pressure, k = (0.8 0.2) x10" at 1.85 Torr (i.e., below the lower explosion limit) was obtained from a computer calculation of keff with known rate constants for PH3 + H PH2 + H2 (see p. 233) and 2PH2+M P2H4+M (see below). The agreement of both k values points to a pressure-independent reaction PH2 + 02 products. The step PH2 + 02 P02 + H2 is probably responsible for the observed rapid decay of PH2 [3, 4]. A later measurement of the removal of rotationally thermalized PH2 (X Bi, v = 0) in the presence of O2 by laser-induced fluorescence (LIF) under pseudo-first-order conditions gave k = 2.7x10 . The removal of vibrationally excited PH2 by O2 was also investigated [5]. 

The simultaneous absorption of two gases that react with the solvent at different rates has been studied by Ouwerkerk. The specific system which he selected for analysis was the selective absorption of HjS in the presence of CO2 into amine solutions. This operation is a feature of several commercially important gas purification processes. Bench scale experiments were conducted to collect the necessary pi sico-chemical data. An absorption rate equation was developed for H2S based on the assumption of instantaneous reaction. For CO2 it was found that the rate of absorption into diisopropanolamine (DIPA) solution at low CO2 partial pressures can best be correlated on the l is of a fast pseudo-first-order reaction. A computer program was developed which took into account the competition between H2S and CC>2 when absorbed simultaneously, and the computer predictions were verified by experiments in a pilot scale absorber. Finally, the methodology was employed successfully to design a large commercial plant absorber. 

The kinetics of the nitrenoid formation reaction were evaluated spectrally under pseudo first-order conditions. The rate of the reaction was independent of porphyrin concentration (over the range 10 to 100 pM) and directly dependent upon the TFAA concentration (over the range of 100- to 2000-fold excess). When trifluoracetic acid or acetic anhydride was substituted for TFAA, no reaction was observed. When the reaction was carried out in an excess of either cyclooctene or norbornylene, the apparent rate constant was slightly larger. This observation suggested that the formation of the nitrene is the rate determining step. An apparent rate constant of 14.0 x lO S" was computed from the spectral data at a... 

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