Volume change on activation

Some experimental criteria are mainly concerned with a distinction between unimolecular and bimolecular mechanisms in acid—base catalysis. One of the most straightforward criteria is based on the determination of the volume change on activation, AV, from the pressure dependence of the rate coefficient, according to the equation 

This method has been applied to various acid catalyzed reactions by Whalley and co-workers [31—45]. 

For rate-determining proton transfer (mechanism A-SK2), the determined AV value directly refers to the slow step. For the mechanisms with pre-equilibrium proton transfer, A1 and A2, the experimental AV is the sum of the volume changes of the two steps 

Aj j V concerns the volume change in the formation of the transition state from the intermediate SH+ in the slow step of the reaction. 

Values expected for At V° are estimated on the following basis. For reactions of the type 

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Volume changes on activation for some acid catalyzed reactions in water... 

Volume changes on activation and mechanisms of some acid catalyzed and uncatalyzed reactions... 

A discussion of the cardiac cycle requires the correlation of pressure changes ventricular volume changes valve activity and heart sounds. In this section, the focus will be on the left side of the heart (see Table 13.3). Identical events occur simultaneously on the right side of the heart however, the pressures are lower. 

The acid-catalyzed ring openings of ethylenimine and 2-ethyl-ethylenimine have also been characterized as A-2 reactions (Earley et al., 1958). The entropies of activation are —9-4 and —10.0 e.u., respectively. However, AS for the reaction of 2,2-dimethylethylenimine is —1.9 e.u., suggesting incursion of the unimolecular mechanism, a conclusion which is supported on other grounds (Earley et al., 1958). The volume changes of activation have also been measured (Earley et al., 1958). These results, if interpreted in terms of Whalley s (1959) criterion, would indicate the A-l mechanism for ethylenimine and the A-2 for the ethyl and dimethyl derivatives, a conclusion which seems unacceptable. 

Van Laar activity coefficient equations. The van Laar activity coefficient model is based on the assumption that — 0 and = 0. Therefore,. In other words, the model allows for heat of mixing but does not allow for volume change on mixing. Van Laar used the van der Waals EOS to calculate and then Eq. (1.144) can be used to obtain the activity coefficients. The predicted activity coefficients for a binary system are... 

Scatchard Hlldebrand regular-solution activity coefficients. Hildebrand (1929) defined a regular solution as the mixture in which components mix with no excess entropy provided there is no volume change on mixing. Scatchard in an independent work arrived at the same conclusion. The definition of regular solutions (Hildebrand and Scott, 1950) is in line with van Laar s assumption that the excess entropy and the excess volume of mixing are negligible. Scatchard and Hildebrand used an approach different from van Laar s to calculate G. They defined parameter C as... 

In this equation the total molar amounts, Wk rather than concentrations are used. This is valid because the process is first order and necessary in a near-critical fluid because the volume change on reaction could be substantial. However, it is more convenient to use mole fractions, Xk and (as can be easily shown by differentiation) if s is the total number of product molecules formed from the activated complex. 

The character of carbonaceous material s influence on performance of asymmetric EC systems (carbon - NiOx) is more complicated than that of carbon-carbon system. It is determined by the higher operating potential of NiOx electrode, due to which oxidation and volume changes in electrode active mass upon charge-discharge processes are taking place as the reaction of transformation of Ni(OH)2 into NiOOH is occurring. 

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