Volume of activation calculation

From the data listed in Table 6 the van der Waals volume of the Diels-Alder reac-tion13,25,52,65 can be calculated to be with AVw = — 11.2 cm3 mol 1 only roughly one-quarter of the experimentally accessible volume of reaction (AV = —41.7 cm3 mol-1) (Scheme 3). Consequently, a significant part of the observed A V results from the higher packing of the cyclic product (compared to the acyclic reactants) rather than from the changes in bonding. The difference between the van der Waals volume of activation calculated for the pericyclic and stepwise reaction is small (5AV y = —1.7 cm3 mol-1) and is inconsistent with the experimental data listed in Tables 4 and 5. In order to explain... 

SCHEME 18. van der Waals volume of activation AV and volume of activation calculated for degenerate Cope rearrangement of 1,5-hexadiene... 

The effect of pressure on the hydrolysis of ethyleneiminium, 2> ethylethyleneiminium, and 2,2-dimethyleHiyleneiminium ions has been measured at 1 and 550 b at 21°0 (Earley et td., 1958). The volumes of activation calculated from the results are 1 8, —2 5, and —4 4 cm mole respectively and the authors could draw no conclusions from this. In fact, the simple conclusion is that the ethyleneiminium ion, which has a volume of activation of 1-8 cm mole S hydrolyzes uni-molecularly, and the 2,2-dimethylethyleneiminium ion hydrolyzes at least partly bimolecularly. This conclusion is not easy to reconcile with other evidence and, since each volume of activation is apparently based on only two rate constants, these measurements would be worth repeating. 

This form assumes that the effect of pressure on the molar volume of the solvent, which accelerates reactions of order > 1 by increasing the concentrations when they are expressed on the molar scale, has been allowed for. This effect is usually small, ignored but in the most precise work. Equation (7-41) shows that In k will vary linearly with pressure. We shall refer to this graph as the pressure profile. The value of A V is easily calculated from its slope. The values of A V may be nearly zero, positive, or negative. In the first case, the reaction rate shows little if any pressure dependence in the second and third, the applied hydrostatic pressure will cause k to decrease or increase, respectively. A positive value of the volume of activation means that the molar volume of the transition state is larger than the combined molar volume of the reactant(s), and vice versa. 

Volume of activation. The rate constant for the base hydrolysis of C1C(CH3)2C=CH in 80 20 ethanol-water varies with pressure at 25 °C as shown.27 Calculate AT. ... 

Volume of activation. The following values were obtained for the rate of exchange of r/ms-Co(en)2(H280)2+ and solvent at 308 K.28 Calculate AT. What is the implication of that value for the mechanism ... 

Since experimental mechanistic investigations measure activation volumes, Rotzinger proposed to use in calculations, the currently well-accepted quantum chemical descriptor difference of sums ofr(M-O) , A Sr, for the volume of activation, AV (160). As the structures are all similar (Table I) this descriptor is in all four cases identical. 

Fig. 4. Interpretation of volumes of activation (in cm3 mol-1) for water exchange on aqueous M(H20)g+ in terms of contributions from bond-making and -breaking (a) summary of volumes of activation for metal aqua ions (b) calculated curves for Al(III), Ga(III), and In(III) with use of the Connolly volumes in Table IV.

Volume changes, by vitreous silica, 22 438 Volume flux, of droplets, 23 187 Volume fraction, in filtration, 11 328 Volume fraction calculation, in equivalent box model, 20 345—346 Volume mean diameter, 23 186 Volume of activation, 13 407-408... 

What would you think about measuring volumes of activation for such systems and then trying to compare them with such calculations ... 

In order to determine the volume of activation, first the rate constant, k, is calculated from the measured reaction rate, r, and the concentration, Ca, through eqn. 3.2-19. The exponent n can be obtained from experiments at different concentrations. The value of k is then plotted on a logarithmic scale versus the pressure, and Av (10 6 cm3/mol) is evaluated from the slope, a, of the resulting straight line (Fig. 3.2-2). For this purpose a, (MPa ), is multiplied by the gas constant, R (8.314 J mol 1 K 1), and the temperature, T(K). 

Gas studies are well covered with extensive explanation and interpretation of experimental data, such as steady state calculations, all illustrated by frequent use of worked examples. Solution kinetics are similarly explained, and plenty of practice is given in dealing with the effects of the solvent and non-ideality. Students are given plenty of practice, via worked problems, in handling various types of mechanism found in solution, and in interpreting ionic strength dependences and enthalpies, entropies and volumes of activation. 

The kinetics of the reactions of cyt ciwn with [Co(bpy)3]2 + /3+ and [Co (phen)3]2 + /3+ have also been investigated at ambient and elevated pressures and in the forward and reverse directions leading to the calculation of the reaction volume from the respective volumes of activation.283 Furthermore, the reaction volume was independently obtained from equilibrium high-pressure spectrophotometry, from density measurements of components, and from pressure-dependent electrochemistry measurements and in all cases the value of the reaction volume was identical within... 

Clearly, a difficulty in calculation of volumes of activation is addressing correctly the calculation of the partial molar volumes of both the activated complex and the reactant... 

Olivier JP. Improving the models used for calculating the size distribution of micropore volume of activated carbons from adsorption data. Carbon, 1998 36(10) 1469-1472. 

Standard thermodynamic operations (Prigogine and Defay, 1954) on the Gibbs function, AG, yield expressions for related thermodynamic activation parameters. Thus the dependence of k on T can be used to calculate the enthalpy of activation, A, for processes at constant pressure or the thermodynamic energy of activation, A, for processes at constant volume, which in turn lead to the related entropies of activation, ASp and AS respectively. The dependence of k on pressure can be used to calculate the volume of activation, AV which is related to AHp by eqn (5) where a is the thermal... 

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