Pseudo-first order rate law

The experiments were perfonued in a static reaction cell in a large excess of N2 (2-200 bar). An UV laser pulse (193 mu, 20 ns) started the reaction by the photodissociation of N2O to fonu O atoms in the presence of NO. The reaction was monitored via the NO2 absorption at 405 mu using a Hg-Xe high-pressure arc lamp, together with direct time-dependent detection. With a 20-200-fold excess of NO, the fonuation of NO2 followed a pseudo-first-order rate law ... 

It may be noted that the pseudo-first-order rate law for an Sn2 reaction in the presence of a large excess of Y [Eq. (10.2)] is the same as that for an ordinary SnI reaction [Eq. (10.3)]. It is thus not possible to tell these cases apart by simple kinetic... 

There are about 10 functional groups per nm2 (cf. Chapter 2.1). That corresponds to 1019 groups or Sj = 1.7 10 5 mol groups per m2. A representative weathering rate (Table 5.3) is 103 - 10 4 mol m-2 y1. Converting this in a pseudo first order rate law... 

In this case, the new rate law has the form of a first-order rate law and is classified as a pseudo first-order rate law. 

All data obtained on the rate of reaction of [Ni(NiL2)2]Cl2 with alkyl halides— i.e., methyl iodide, benzyl bromide, benzyl chloride, p-nitrobenzyl chloride, p-chlorobenzyl chloride, ethyl bromide, ethyl iodide, n-propyl bromide, and n-propyl iodide—conform closely to a pseudo-first-order rate law. Almost all experiments were carried out in the presence of an excess of alkyl halide. Since methanol solutions of the alkylated complexes have only negligible absorption at 495 m//, rates were obtained by graphs of log A0—A vs. time. The graphs are linear over the entire time interval, which corresponds to more than two half lives in most cases, passing through the origin at zero time. The rate is essentially the same whether measured by the spectrophotometric or conductivity method. 

Under excess of the second reactant (in automobile exhaust gas typically H20, C02 and for lean-burn engines exhaust specifically also 02), the effectiveness factor calculation can be simplified by approximating the reaction rate Rj by a pseudo-first-order rate law with respect to the component using new rate constant kiefj (evaluated from the original rate law)... 

It may be noted that the pseudo-first-order rate law for an Sn2 reaction in the presence of a large excess of Y [Eq. (2)) is the same as that for an ordinary SnI reaction [Eq. (3)]. It is thus not possible to tell these cases apart by simple kinetic measurements. However, we can often distinguish between them by the common-ion effect mentioned above. Addition of a common ion will not markedly affect the rate of an Sn2 reaction beyond the effect caused by other ions. Unfortunately, as we have seen, not all SnI reactions show the common-ion effect, and this test fails for f-butyl and similar cases. 

The hydration of an aldehyde RCHO can be expressed with two (pseudo-first-order rate laws consisting of an elimination (minus sign) and a production (plus sign) term ... 

Consider a compound that is transformed by two different reactions exhibiting very different activation energies E3 (reaction 1) = 50 kJ mol-1 and Ea (reaction 2) = 100 kJ-mol-1. Assume that both reactions can be described by a pseudo-first-order rate law, and that at 25°C, they are equally important that is, equal amounts of the two different transformation products are formed. What is the product distribution that you would expect at (i) 5°C and (ii) 40°C ... 

Assuming a (pseudo-)first-order rate law, kh can be determined from a least squares fit of ln([DNPA]t / [DNPA]0) versus time (see also Figure below) ... 

Now we have an easy way of describing the indirect photolysis of a pollutant by a pseudo-first-order rate law, provided that the compound considered does not significantly affect [Ox]°, and that we are able to measure or estimate [Ox]°. The nearsurface rate of loss of the pollutant is then given by ... 

We were hopeful when toluene solutions of the [MCl(COT)2]2 complexes (M = Rh and Ir), in the presence of PCy3 at 25°C under 1 atm C02 (phosphine dimer = 4) absorbed 1 mol C02 per metal atom. The rhodium solution, for example, changed gradually from yellow to red and, in the constant pressure apparatus used, the measured gas uptake analyzed excellently for the pseudo-first-order rate law k[Rh], with k = 9.3 x 10"4s 1. However, such C02 uptake was observed in only five experiments twenty others revealed no reactivity whatsoever The reasons for the irreproducibility have not been traced water content and visible light are not problems. The systems certainly are complicated by the blank dehydrogenation reactions (vide supra). 

In many cases, the concentration of the environmental oxidant or reductant is effectively constant over the time frame of interest, so Equation (21) can be simplified to a pseudo-first-order rate law... 

Fig. 4A. Experimental tests of the rate laws in lk. 4.61 for VO2 adsorbed on S - A120, (left, data from H. Wehrli and W. Stiimm") and Mn2 adsorbed on gocthite or Icpidocrocilc (right, data from S. II. K. Davies and. 1.. 1. Morgan 2). I.inear plots indicate conformity to a pseudo-first order rate law.

A preliminary value for the rate of water vapor removal in the closed tomb was calculated from these peaks by fitting the first five or six points of the slow decays to a pseudo-first-order rate law. The rate constant was approximately 5 X 10 3 min1. From these data, it is possible to estimate quantitatively the effects of human entry on the atmospheric water vapor... 

Danesi P and Reichley-Yinger L. Origin and significance of the deviations from a pseudo first order rate law in the coupled transport of metal species through supported Uquid membranes. J Mem Sci, 1986 29 195-211. 

The expected half-lives on the order of 1 day for microbial catalysis and 1 year for the surface-controlled process can now be compared with the average oxidation rate in Lake Sempach, which is given in Table II. The average oxidation rate of 0.77 mmol/m2 per day within a 5-m layer of deep water in Lake Sempach corresponds to a rate of RIIX = 0.15 pM/day. This value and a pseudo-first-order rate law with the average concentration of dissolved >In(II)]av = 0.3 aM... 

The pseudo-first-order rate law for excess dissolved oxygen can then be given as the sum of the three parallel oxidation pathways ... 

The oxygenation kinetics of Cu(I) in different electrolyte solutions has been measured by Sharma and Millero (1988). Contrary to Fe(II) and V(IV), the rates were found to be independent of [H + ] in the range 5.3 < PH < 8.6. The chloride ion, however, exerts a strong inhibitory effect. Millero (1985) interpreted the observations with a similar pseudo-first-order rate law as in the case of ferrous iron. In presence of excess oxygen the rate is given as... 

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