Second-order reaction rotation

A series of tests of a second order reaction were made in a rotating basket CSTR with several sizes of catalyst pellets. All runs were made with the same residence time and with inlet C0 = 4. Effluent concentrations were measured. Beyond R = 0.1 cm, there were no differences in conversion. 

One form of "binding" that can occur between two reactants is simple proximity, a major tenet of the spatial temporal vision of catalysis. When a second order reaction ocairs in solution, two reactants must collide in the rate-determining step. This causes a loss in translational degrees of freedom in the reactants, thereby increasing the Gibbs free energy at the transition state due to the increased order of the system (look back at Section 2.1.2 to review this idea). The translational and rotational entropies of a freely moving molecule in solution are both around 30 entropy units (eu). 

Basak J, Penar J, Sykut K (1987/1988) Digital simulation for determining rate constants in diffusion layer titration on the rotating ring disc electrode. Part II. Second order reactions. Ann Univ Mariae Curie - SModowska, Sectio AA XLII/XLIII 43-49... 

Reaction of 3 with Ph3C+PF6" resulted in the formation of methylidene complex [(n-C5H5)Re(N0)(PPh3)(CH2)]+ PF6 (8) in 88-100% spectroscopic yields, as shown in Figure 11. Although 8 decomposes in solution slowly at -10 °C and rapidly at 25 °C (She decomposition is second order in 8), it can be isolated as an off-white powder (pure by H NMR) when the reaction is worked up at -23 °C. The methylidene H and 13C NMR chemical shifts are similar to those observed previously for carbene complexes [28]. However, the multiplicity of the H NMR spectrum indicates the two methylidene protons to be non-equivalent (Figure 11). Since no coalescence is.observed below the decomposition point of 8, a lower limit of AG >15 kcal/mol can be set for the rotational barrier about the rhenium-methylidene bond. 

Quantitative measurements of simple and enzyme-catalyzed reaction rates were under way by the 1850s. In that year Wilhelmy derived first order equations for acid-catalyzed hydrolysis of sucrose which he could follow by the inversion of rotation of plane polarized light. Berthellot (1862) derived second-order equations for the rates of ester formation and, shortly after, Harcourt observed that rates of reaction doubled for each 10 °C rise in temperature. Guldberg and Waage (1864-67) demonstrated that the equilibrium of the reaction was affected by the concentration ) of the reacting substance(s). By 1877 Arrhenius had derived the definition of the equilbrium constant for a reaction from the rate constants of the forward and backward reactions. Ostwald in 1884 showed that sucrose and ester hydrolyses were affected by H+ concentration (pH). 

A second-order phase transition is one in which the enthalpy and first derivatives are continuous, but the second derivatives are discontinuous. The Cp versus T curve is often shaped like the Greek letter X. Hence, these transitions are also called -transitions (Figure 2-15b Thompson and Perkins, 1981). The structure change is minor in second-order phase transitions, such as the rotation of bonds and order-disorder of some ions. Examples include melt to glass transition, X-transition in fayalite, and magnetic transitions. Second-order phase transitions often do not require nucleation and are rapid. On some characteristics, these transitions may be viewed as a homogeneous reaction or many simultaneous homogeneous reactions. 

The second-order rate constants for the hydroxide-ion catalysed breakdown of compounds [124] and [126] (Table 19) are very much less than those for the breakdown of hemiorthoesters (cf. Tables 13-15) presumably as a result of the difficulty of expelling a nitrogen anion. Nevertheless both compounds break down more rapidly than rotation about the C—N bond of the amide product, since in both reactions rotational isomers of the products have been detected in non-equilibrium proportions by nmr spectroscopy, and their subsequent equilibration has been followed (Capon el al., 1981a Tee et al., 1982). With [126] the rate constants for breakdown into both rotational isomers were measured, although their structures were uncertain. 

The homogeneous reaction may be of first or second order in the latter case, X is a non-electroactive species. Both these cases have been studied at the rotating ring—disc electrode and the first-order case at a double channel electrode. 

Depending on the relative gains and losses in internal rotation, the intramolecular reaction is favored entropically by up to 190 J/deg/mol (45 cal/deg/mol) or 55 to 59 kJ/mol (13 to 14 kcal/mol) at 25°C. Substituting 190 J/deg/mol (45 cal/deg/mol) into the exp (ASVR) term of equation 2.7 gives a factor of 6 X 109. Taking into account the difference in molecularity between the second-order and first-order reactions, this may be considered as the maximum effective concentration of a neighboring group, i.e., 6 X 109 M. In other words, for B in equation 2.22 to react with the same first-order rate constant as A B in equation 2.23, the concentration of A would have to be 6 X 109 M. 

There may be a contrast between the effects of various types of ionization. With a heavy particle such as an alpha particle or a proton the specific ionization is very high, that is, many ions are formed per unit path length. Thus ion-ion, ion-radical, and radical-radical reactions may be very important because concentrations of these intermediates are high. With particles of lower mass, such as photoelectrons, the specific ionization is much lower and the chance of second order effects much less. Thus the effect of specific ionization bears some resemblance to that obtained with rotating sectors and pulse radiolysis. 

Experimental data from nucleophilic substitution reactions on substrates that have optical activity (the ability to rotate plane-polarized light) shows that two general mechanisms exist for these types of reactions. The first type is called an S 2 mechanism. This mechanism follows second-order kinetics (the reaction rate depends on the concentrations of two reactants), and its intermediate contains both the substrate and the nucleophile and is therefore bimolecular. The terminology S 2 stands for substitution nucleophilic bimolecular. ... 

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