Kinetic excess

In the example shown in Figure 7.5, a 25% molar excess of B has been added (M = 1.25). The function of this excess is to increase the reaction rate when CA becomes small. It is often called the kinetic excess, because it increases the reaction rate at high conversion (Equation 7.7). 

Surface heterogeneity may merely be a reflection of different types of chemisorption and chemisorption sites, as in the examples of Figs. XVIII-9 and XVIII-10. The presence of various crystal planes, as in powders, leads to heterogeneous adsorption behavior the effect may vary with particle size, as in the case of O2 on Pd [107]. Heterogeneity may be deliberate many catalysts consist of combinations of active surfaces, such as bimetallic alloys. In this last case, the surface properties may be intermediate between those of the pure metals (but one component may be in surface excess as with any solution) or they may be distinctly different. In this last case, one speaks of various effects ensemble, dilution, ligand, and kinetic (see Ref. 108 for details). 

Atom abstraction occurs when a dissociation reaction occurs on a surface in which one of the dissociation products sticks to the surface, while another is emitted. If the chemisorption reaction is particularly exothennic, the excess energy generated by chemical bond fomiation can be chaimelled into the kinetic energy of the desorbed dissociation fragment. An example of atom abstraction involves the reaction of molecular halogens with Si surfaces [27, 28]. In this case, one halogen atom chemisorbs while the other atom is ejected from the surface. 

There is one special class of reaction systems in which a simplification occurs. If collisional energy redistribution of some reactant occurs by collisions with an excess of heat bath atoms or molecules that are considered kinetically structureless, and if fiirthennore the reaction is either unimolecular or occurs again with a reaction partner M having an excess concentration, dien one will have generalized first-order kinetics for populations Pj of the energy levels of the reactant, i.e. with... 

In chemical kinetics, it is often important to know the proportion of particles with a velocity that exceeds a selected velocity v. According to collision theories of chemical kinetics, particles with a speed in excess of v are energetic enough to react and those with a speed less than v are not. The probability of finding a particle with a speed from 0 to v is the integral of the distribution function over that interval... 

In the kinetic runs always a large excess of catalyst was used. Under these conditions IQ does not influence the apparent rate of the Diels-Alder reaction. Kinetic studies by UV-vis spectroscopy require a low concentration of the dienophile( 10" M). The use of only a catalytic amount of Lewis-acid will seriously hamper complexation of the dienophile because of the very low concentrations of both reaction partners under these conditions. The contributions of and to the observed apparent rate constant have been determined by measuring k pp and Ka separately. ... 

Since for the kinetic measurements a large excess of catalyst is used, the concentration of free catalyst [M" ]/ essentially equals the total concentration of catalyst. Moreover, since ko k jt and under the conditions of the measurements the concentration of free 2.4 is small, the contribution of the uncatalysed reaction can be neglected and equation 7 simplifies to ... 

Kinetic measurements were performed employii UV-vis spectroscopy (Perkin Elmer "K2, X5 or 12 spectrophotometer) using quartz cuvettes of 1 cm pathlength at 25 0.1 C. Second-order rate constants of the reaction of methyl vinyl ketone (4.8) with cyclopentadiene (4.6) were determined from the pseudo-first-order rate constants obtained by followirg the absorption of 4.6 at 253-260 nm in the presence of an excess of 4.8. Typical concentrations were [4.8] = 18 mM and [4.6] = 0.1 mM. In order to ensure rapid dissolution of 4.6, this compound was added from a stock solution of 5.0 )j1 in 2.00 g of 1-propanol. In order to prevent evaporation of the extremely volatile 4.6, the cuvettes were filled almost completely and sealed carefully. The water used for the experiments with MeReOj was degassed by purging with argon for 0.5 hours prior to the measurements. All rate constants were reproducible to within 3%. 

The kinetics of nitration of benzene in solutions at c. 20 °C in carbon tetrachloride have been investigated. In the presence of an excess of benzene (c. 2-4 mol 1 ) the rate was kinetically of the first order in the concentration of benzoyl nitrate. The rate of reaction was depressed by the addition of benzoic anhydride, provided that some benzoic acid was present. This result suggested that benzoyl nitrate itself was not responsible for the nitration, but generated dinitrogen pentoxide... 

The ketone is added to a large excess of a strong base at low temperature, usually LDA in THF at -78 °C. The more acidic and less sterically hindered proton is removed in a kineti-cally controlled reaction. The equilibrium with a thermodynamically more stable enolate (generally the one which is more stabilized by substituents) is only reached very slowly (H.O. House, 1977), and the kinetic enolates may be trapped and isolated as silyl enol ethers (J.K. Rasmussen, 1977 H.O. House, 1969). If, on the other hand, a weak acid is added to the solution, e.g. an excess of the non-ionized ketone or a non-nucleophilic alcohol such as cert-butanol, then the tautomeric enolate is preferentially formed (stabilized mostly by hyperconjugation effects). The rate of approach to equilibrium is particularly slow with lithium as the counterion and much faster with potassium or sodium. 

The integrated form of the rate law for equation 13.4, however, is still too complicated to be analytically useful. We can simplify the kinetics, however, by carefully adjusting the reaction conditions. For example, pseudo-first-order kinetics can be achieved by using a large excess of R (i.e. [R]o >> [A]o), such that its concentration remains essentially constant. Under these conditions... 

The concentration of nitromethane, CH3NO2, can be determined from the kinetics of its decomposition in basic solution. In the presence of excess base the reaction is pseudo-first-order in nitromethane. For a standard solution of 0.0100 M nitromethane, the concentration of nitromethane after 2.00 s was found to be 4.24 X 10 M. When a sample containing an unknown amount of nitromethane was analyzed, the concentration remaining after 2.00 s was found to be 5.35 X 10 M. What is the initial concentration of nitromethane in the sample ... 

When D and H3O+ are present in excess, the kinetics of the reaction are pseudo-first-order in H2O2, and can be used to determine the concentration of H2O2 by following the production of I2 with time. In one analysis the absorbance of the solution was measured after 240 s at 348 nm (where Beer s law holds for I2). When a set of standard solutions of H2O2 was analyzed, the following results were obtained... 

In (a), an ion and a gas atom approach each other with a total kinetic energy of KE, + KEj. After collision (b), the atom and ion follow new trajectories. If the sum of KE, + KEj is equal to KE3 + KE4, the collision is elastic. In an inelastic collision (b), the sums of kinetic energies are not equal, and the difference appears as an excess of internal energy in the ion and gas molecule. If the collision gas is atomic, there can be no rotational and no vibrational energy in the atom, but there is a possibility of electronic excitation. Since most collision gases are helium or argon, almost all of the excess of internal energy appears in the ion. 

Af higher frequencies fhe excess energy of fhe photons is converted info kinetic energy of fhe phofoelectrons... 

Ek-El,. This energy is then used up in ejecting an Auger electron from the Lu orbital, any excess energy being converted into kinetic energy of the electron. 

Figure 9.50(a) illustrates the ionization process in a UPS experiment. In this type of experiment the incident radiation always has much more energy than is necessary to ionize the molecule M into either the zero-point level or a vibrationally excited level of M. The excess energy is then removed as kinetic energy of the photoelectron. 

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