Volumes of activation

The effect of pressure on Rp and Xn, like that of temperature, manifests itself by changes in the three rate constants—initiation, propagation, and termination. The quantitative effect of P (at constant temperature) on a rate constant is given by 

A V+ corresponds to the volume of the transition state being smaller than that of the reactants the result is that increased pressure leads to an increase in the reaction rate constant. A AW of —10 cm3 mol-1 corresponds to 1.5- and 60-fold increases in rate constant at 100 and 1000 MPa, respectively, at 25°C. The increases are 2.2- and 3500-fold if A0 is —20 cm3 mol-1. Positive values of A0 correspond to a decrease in the reaction rate constant with increasing pressure as the volume of the transition state is larger than that of the reactants. 

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In the thennodynamic fomiiilation of TST the pressure dependence of the reaction rate coefficient defines a volume of activation [24, 25 and 26]... 

The intrinsic volume of activation was estimated to correspond to the molar volume difference between cyclohexene and cyclohexane, adding the molar volume difference between ethane and ethene to account for... 

Apart from the thoroughly studied aqueous Diels-Alder reaction, a limited number of other transformations have been reported to benefit considerably from the use of water. These include the aldol condensation , the benzoin condensation , the Baylis-Hillman reaction (tertiary-amine catalysed coupling of aldehydes with acrylic acid derivatives) and pericyclic reactions like the 1,3-dipolar cycloaddition and the Qaisen rearrangement (see below). These reactions have one thing in common a negative volume of activation. This observation has tempted many authors to propose hydrophobic effects as primary cause of ftie observed rate enhancements. 

The observation that in the activated complex the reaction centre has lost its hydrophobic character, can have important consequences. The retro Diels-Alder reaction, for instance, will also benefit from the breakdown of the hydrophobic hydration shell during the activation process. The initial state of this reaction has a nonpolar character. Due to the principle of microscopic reversibility, the activated complex of the retro Diels-Alder reaction is identical to that of the bimoleciilar Diels-Alder reaction which means this complex has a negligible nonpolar character near the reaction centre. O nsequently, also in the activation process of the retro Diels-Alder reaction a significant breakdown of hydrophobic hydration takes placed Note that for this process the volume of activation is small, which implies that the number of water molecules involved in hydration of the reacting system does not change significantly in the activation process. 

We conclude that the beneficial effects of water are not necessarily limited to reactions that are characterised by a negative volume of activation. We infer that, apart from the retro Diels-Alder reaction also other reactions, in which no significant reduction or perhaps even an increase of solvent accessible surface area takes place, can be accelerated by water. A reduction of the nonpolar nature during the activation process is a prerequisite in these cases. 

Discernible associative character is operative for divalent 3t5 ions through manganese and the trivalent ions through iron, as is evident from the volumes of activation in Table 4. However, deprotonation of a water molecule enhances the reaction rates by utilising a conjugate base 7T- donation dissociative pathway. As can be seen from Table 4, there is a change in sign of the volume of activation AH. Four-coordinate square-planar molecules also show associative behavior in their reactions. 

A key parameter in the design of the fuel vapor control system is the volume of activated carbon required to meet the emission standards for the various regulatory tests. In the case of the three-day diurnal test sequence, the emission limits are 0.05 grams of HC per mile during the run loss portion of the test (maximum emission -0.85 grams), and a maximum release of 2.0 grams for the sum of the hot soak period and any one of the three 24-hour periods making up the diurnal test sequence. 

Recently, Suzuki and Taniguchi93 hydrolyzed n-butylacetate, ethylacetate, and methylacetate with HPSt and 41 (PVA B) (partially-o-benzalsulfonated polyvinylalcohol). The volume of activation, A P+, was obtained from the pressure dependence of reaction rates [ F + = -kT(d Ink/dP)]. The A + increased with increasing hydro-phobidty of the substrate. 

The volumes of activation for some additions of anionic nucleophiles to arenediazonium ions were determined by Isaacs et al. (1987) and are listed in Table 6-1. All but one are negative, although one expects — and knows from various other reactions between cations and anions — that ion combination reactions should have positive volumes of activation by reason of solvent relaxation as charges become neutralized. The authors present various interpretations, one of which seems to be plausible, namely that a C — N—N bond-bending deformation of the diazonium ion occurs before the transition state of the addition is reached (Scheme 6-2). This bondbending is expected to bring about a decrease in resonance interaction in the arenediazonium ion and hence a charge concentration on Np and an increase in solvation. 

Table 6-1. Volumes of activation for reactions of arenediazonium ions with nucleophiles (Isaacs et al., 1987).

Differentiation between inner- and outer-sphere complexes may be possible on the basis of determination of activation volumes of dediazoniations catalyzed by various metal complexes, similar to the differentiation between heterolytic and homolytic dediazoniations in DMSO made by Kuokkanen, 1989 (see Sec. 8.7). If outer-sphere complexes are involved in a dediazoniation, larger (positive) volumes of activation are expected than those for the comparable reactions with inner-sphere complexes. Such investigations have not been made, however, so far as we are aware. 

Vesicular films 284 Volume of activation in additions to diazonium ions 108... 

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 ... 

Volumes of activation for fast reactions are determined from the effects of high pressure on rate constants, as presented in Chapter 7. Several versions of stopped-flow instruments suitable for high-pressure experiments have been described.7-10... 

The value of is the difference in partial molal volume between the transition state and the initial state, but it can be approximated by the molar volume. Increasing pressure decreases the value of AV and if A V is negative the reaction rate is accelerated. This equation is not strictly obeyed above lOkbar. If the transition state of a reaction involves bond formation, concentration of charge, or ionization, a negative volume of activation often results. Cleavage of a bond, dispersal of charge, neutralization of the transition state and diffusion control lead to a positive volume of activation. Reactions for which rate enhancement is expected at high pressure include ... 

Still another method measures volumes of activation. These are negative for E2 and positive for ElcB mechanisms. Measurement of the activation volume therefore provides a continuous scale for deciding just where a reaction lies on the spectmm. 

Reductions of various Co(ni) complexes by Fe(II) have been studied under high pressures . The motivation for performing such experiments resides in the possibility that the volume of activation (AF ), like the entropy of activation, might be a criterion for distinguishing between inner- and outer-sphere reactions. For reactions of the type... 

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