Rate laws orders

A more active zinc catalyst has been developed containing a /3-diketiminate ancillary ligand.823 Complex (272) converts 200 equivalents rac-LA. in less than 20 min at room temperature to highly heterotactic PLA (the probability of a racemic junction between monomer units, PR = 0.90 at 25 °C and 0.94 at 0°C) of narrow polydispersity (Mn = 37,900, Mn calc = 28,800, Mw/Mn= 1.10). Kinetic studies reveal that the zinc initiators display a fractional rate law order (1.56 0.06). In accord with the observation that kR/ss > kR/RR (or ks/RR > ks/ss), the polymerization of L-LA proceeds significantly slower than rac-LA (kapp L-LA = 0.031 min-1 kapp rac-LA = 0.22 min-1).824... 

Rate Law. Orders of reaction with respect to the concentrations of 1, BPH2, lied and OAc" (investigation of general-base catalysis) and ionic strength (p) were established... 

Reaction rate constants k. in all reviewed equations are numerically equal to the rate itself at C. = 1. For this reason its dimension directly depends on the rate laws order and is quoted in s -(mole-m )i where V is reaction order. Correlation of the reactant content vs. different order reaction rate is represented in Figure 1.10. 

However, there are now many observations that show a higher rate law order dependence on monomer concentration (up to 2) for ethene [2, 25-27], propene [2, 28-39], styrene [40], and diene [41] using heterogeneous ZN catalysts as well as homogeneous and supported metallocene systems of different kinds. 

Reaction order n. The exponent on a concentration term in a simple rate law (order with respect to one component) or the sum of all such exponents (overall order). 

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase. 

Table A3.4.2 Rate laws, reaction order, and rate constants.

Neither (A3.4.15) nor (A3.4.17) is of the fonn (A3,4,10) and thus neither reaction order nor a unique rate codficient can be defined. Indeed, the number of possible rate laws that are not of the fonu of (A3.4.10) greatly exceeds those cases following (A3.4.10). However, certain particularly simple reactions necessarily follow a law of type of (A3.4.10). They are particularly important from a mechanistic point of view and are discussed in the next section. 

Excited O2 molecules are fomied by UV light absorption. Monomolecular reactions (e.g., c = [Oi]) show a first-order rate law ... 

Experimentally, one finds the same first-order rate law as for monomolecular reactions, but with an effective rate constant /rthat now depends on [M],... 

Case 1. The particles are statistically distributed around the ring. Then, the number of escaping particles will be proportional both to the time interval (opening time) dt and to the total number of particles in the container. The result is a first-order rate law. 

Case 2. The particles rotate in small packets ( coherently or in phase ). Obviously, the first-order rate law no longer holds. In chapter B2.1 we shall see that this simple consideration has found a deeper meaning in some of the most recent kinetic investigations [21]. 

The second-order rate law for bimolecular reactions is empirically well confinned. Figure A3.4.3 shows the example of methyl radical recombination (equation (A3.4.36)) in a graphical representation following equation (A3.4.38) [22, 23 and 24]. For this example the bimolecular rate constant is... 

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj. 

Empirically, one indeed finds a third-order rate law... 

However, the postulated trimolecular mechanism is highly questionable. The third-order rate law would also be consistent with mechanisms arising from consecutive bimolecular elementary reactions, such as... 

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

The Lindemaim mechanism for thennally activated imimolecular reactions is a simple example of a particular class of compound reaction mechanisms. They are mechanisms whose constituent reactions individually follow first-order rate laws [11, 20, 36, 48, 49, 50, 51, 52, 53, 54, 55 and 56] ... 

The Landolt reaction (iodate + reductant) is prototypical of an autocatalytic clock reaction. During the induction period, the absence of the feedback species (Irere iodide ion, assumed to have virtually zero initial concentration and fomred from the reactant iodate only via very slow initiation steps) causes the reaction mixture to become kinetically frozen . There is reaction, but the intemiediate species evolve on concentration scales many orders of magnitude less than those of the reactant. The induction period depends on the initial concentrations of the major reactants in a maimer predicted by integrating the overall rate cubic autocatalytic rate law, given in section A3.14.1.1. 

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 ... 

The paradigmatical binding reaction (equation (C2.l4.22)) is generally analysed as a second order forward reaction and a first order backward reaction, leading to the following rate law ... 

The rates of nitration of mesitylene-a-sulphonate anion (iii) and iso-durene-a -sulphonate anion (iv) in mixtures of aqueous nitric and perchloric acid followed a zeroth-order rate law. Although the rate of exchange of oxygen could not be measured because of the presence of perchloric acid, these results again show that, under conditions most amenable to its existence and involvement, the nitric acidium ion is ineffective in nitration. 

A simple kinetic order for the nitration of aromatic compounds was first established by Martinsen for nitration in sulphuric acid (Martin-sen also first observed the occurrence of a maximum in the rate of nitration, occurrii for nitration in sulphuric acid of 89-90 % concentration). The rate of nitration of nitrobenzene was found to obey a second-order rate law, first order in the concentration of the aromatic and of nitric acid. The same law certainly holds (and in many cases was explicitly demonstrated) for the compounds listed in table 2.3. 

Chloroanisole and p-nitrophenol, the nitrations of which are susceptible to positive catalysis by nitrous acid, but from which the products are not prone to the oxidation which leads to autocatalysis, were the subjects of a more detailed investigation. With high concentrations of nitric acid and low concentrations of nitrous acid in acetic acid, jp-chloroanisole underwent nitration according to a zeroth-order rate law. The rate was repressed by the addition of a small concentration of nitrous acid according to the usual law rate = AQ(n-a[HN02]atoioh) -The nitration of p-nitrophenol under comparable conditions did not accord to a simple kinetic law, but nitrous acid was shown to anticatalyse the reaction. 

First-order nitrations. The kinetics of nitrations in solutions of acetyl nitrate in acetic anhydride were first investigated by Wibaut. He obtained evidence for a second-order rate law, but this was subsequently disproved. A more detailed study was made using benzene, toluene, chloro- and bromo-benzene. The rate of nitration of benzene was found to be of the first order in the concentration of aromatic and third order in the concentration of acetyl nitrate the latter conclusion disagrees with later work (see below). Nitration in solutions containing similar concentrations of acetyl nitrate in acetic acid was too slow to measure, but was accelerated slightly by the addition of more acetic anhydride. Similar solutions in carbon tetrachloride nitrated benzene too quickly, and the concentration of acetyl nitrate had to be reduced from 0-7 to o-i mol 1 to permit the observation of a rate similar to that which the more concentrated solution yields in acetic anhydride. 

The effects of added species. The rate of nitration of benzene, according to a rate law kinetically of the first order in the concentration of aromatic, was reduced by sodium nitrate, a concentration of io mol 1 of the latter retarding nitration by a factor of about Lithium nitrate... 

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