Observed Rate Behavior

P-Hydride transfer either directly to the transition metal 

Both P-hydride transfers result in polypropene molecules with one vinylidene and one n-propyl end group. The two transfers are zero- and first-order, respectively, in monomer. P-Hydride transfer yields vinyl end groups in ethylene polymerization. 

Hydrolytic workup of the polymer cleaves the aluminium-polymer bond to yield an isopropyl end group. 

Chain transfer to an active hydrogen compound such as molecular hydrogen  

Chain transfer to molecular hydrogen not only affects polymer molecular weight, but unlike other transfer agents, also affects polymerization rate. Hydrogen often decreases the rate of ethylene polymerization, but increases the rate of propene polymerization [Chadwick, 

---

Molecularities, defined only for single elementary steps, state the number of reactant molecules involved. The reaction order with respect to a participant is the exponent of the concentration of that species in the (possibly empirical) power-law rate equation. The overall reaction order is the sum of all such exponents. The rank of a product is an empirical quantity derived from observed rate behavior and indicating whether that species is formed directly from reactants or indirectly from intermediates. 

This rate equation is of the same algebraic form as eqn 8.5, but with different physical significance of the coefficient k. Ibis is another example of the fact that an observed rate behavior can usually be explained in several different ways. 

Kei et al. [22] have used Langmuir-type adsorption to explain the observed rate behavior both during the initial stage (build-up period) and in the stationary state of the polymerization of propylene with TiCls-AlEta which exhibits a decay-type behavior (curve A in Fig. 9.9) (see Problem 9.8). Similarly the observed rate behavior in the build-up period of the acceleration-type curve (curve B in Fig. 9.9) can be explained. 

The rate law in Equation 15.18 quantitatively accounts for the observed rate behavior for the hydrogenation of cydohexene. Since the migratory insertion reaction k is the slowest step in the catalytic cycle, under conditions of constant H, pressure, high olefin concentrations (> 1 M), and no added phosphine, the rate reaches a limiting value determined by the rate of the migratory insertion step. 

Each mechanism predicts a rate behavior that can be compared with the experimental rate law. If the prediction differs from the experimental observation, the mechanism is incorrect. 

The two proposed mechanisms for this reaction predict different rate laws. Whereas Mechanism I predicts that the rate is proportional to NO2 concentration. Mechanism II predicts that the rate is proportional to the square of NO2 concentration. Experiments agree with the prediction of Mechanism II, so Mechanism II is consistent with the experimental behavior of the NO2 decomposition reaction. Mechanism I predicts rate behavior contrary to what is observed experimentally, so Mechanism I cannot be correct. 

Another point that one has to observe from analysis of Figure 10, is that despite the different precursor atmospheres, and consequently different N precursor partial pressures in the deposition, there is a coincidence of the deposition rate behavior upon nitrogen content (for mixtures other than C2H-N2). This points to a strong dependence of growth kinetics with nitrogen content. 

Similar complex data has been reported by Haowen et al. [109] for Ni-Sn-P films, again using citrate as a complexant, and by Aoki and Takano [110] for the influence of citrate concentration on the composition W in Ni-W-P alloys. In a study of the deposition of films containing up to 30 at% Sn, Osaka and coworkers [111] observed simpler behavior, evidently due to the more selective complexation of Ni2+ by citrate as a function of citrate concentration, they reported a rapid decrease in alloy deposition rate, an increase in Sn content in the deposit, and a slow decline in P content of the deposits. 

During conventional polymerizations of both HEMA and DEGDMA, complications resulting from diffusion limitations to termination and propagation are observed. Features such as autoacceleration, autodeceleration and incomplete conversion of double bonds characterize the rate behavior of these polymerizations. As TED is added to the reacting system, the carbon-DTC radical termination reaction is introduced. Diffusion limitations to carbon-DTC radical combination are lower than those to carbon-carbon radical termination as the DTC radical is smaller and much more mobile than a typical polymeric carbon radical. As a result, the cross-... 

Autocatalysis is a special type of molecular catalysis in which one of the products of reaction acts as a catalyst for the reaction. As a consequence, the concentration of this product appears in the observed rate law with a positive exponent if a catalyst in the usual sense, or with a negative exponent if an inhibitor. A characteristic of an autocat-alytic reaction is that the rate increases initially as the concentration of catalytic product increases, but eventually goes through a maximum and decreases as reactant is used up. The initial behavior may be described as abnormal kinetics, and has important consequences for reactor selection for such reactions. 

Fig. 9. A comparison of the results computed from Eq. (12) for transitional burning (indicated by O) with the observed burning rate behavior for silica-alumina catalyst (solid curve).

---