Volume of the activated complex

The effect of external pressure on the rates of liquid phase reactions is normally quite small and, unless one goes to pressures of several hundred atmospheres, the effect is difficult to observe. In terms of the transition state approach to reactions in solution, the equilibrium existing between reactants and activated complexes may be analyzed in terms of Le Chatelier s principle or other theorems of moderation. The concentration of activated complex species (and hence the reaction rate) will be increased by an increase in hydrostatic pressure if the volume of the activated complex is less than the sum of the volumes of the reactant molecules. The rate of reaction will be decreased by an increase in external pressure if the volume of the activated complex molecules is greater than the sum of the volumes of the reactant molecules. For a decrease in external pressure, the opposite would be true. In most cases the rates of liquid phase reactions are enhanced by increased pressure, but there are also many cases where the converse situation prevails. 

The experimental activation volume is unambiguously determined from the slope of In kvs.p but its interpretation is not necessarily that of the original definition, the difference between the volumes of the activated complex and the reactants. In most cases the activation volume is a linear combination of volume changes in steps 1 and 2. In other cases one may have linear combinations of 3 and 4 volume contributions to AV. This will be treated in detail in the next section. 

The sign of the volume of activation, Av, determines whether the rate constant, k, increases or decreases with the pressure. The value of Av is positive when the volume of the activated complex is larger than the volume of the initial reactants. Thus the rate constant, k, decreases when the pressure is increased. When the volume reduces in the transition state, Av 1 is negative and k will increase with increasing pressure (Table 3.2-2). 

A Vf = the partial molar volume of the activated complex minus the partial molar volume of the reactant(s), and... 

Activation volume — As in case of homogeneous chemical reactions, also the rate of heterogeneous electron transfer reactions at electrode interfaces can depend on pressure. The activation volume AVZ involved in electrochemical reactions can be determined by studying the pressure dependence of the heterogeneous -> standard rate constant ks AVa = -RT j (p is the molar - gas constant, T absolute temperature, and P the pressure inside the electrochemical cell). If AI4 is smaller than zero, i.e., when the volume of the activated complex is smaller than the volume of the reactant molecule, an increase of pressure will enhance the reaction rate and the opposite holds true when A14 is larger than zero. Refs. [i] Swaddle TW, Tregloan PA (1999) Coord Chem Rev 187 255 [ii] Dolidze TD, Khoshtariya DE, Waldeck DH, Macyk J, van Eldik R (2003) JPhys Chem B 107 7172... 

V volume of the activated complex Vs volume of the free educts k reaction rate constant... 

AV means the volume difference of the activated complex and of the educts which are the substrates and the free enzyme. A difference in the volumes of the activated complex and of the educts leads to an increase or decrease of the reaction rate depending upon a positive or negative volume change. According to Chen the enantioselectivity is defined as... 

Intuitively, one would expect that the volume of the reactants, the volume of the activated complex, and the corresponding activation volume, as well as the internal... 

Fig. 5-9 shows that there is also a very rough, inverse correlation between g k/k(f) and 8l for the dissociation of the dimer of the triphenylmethyl radical [167]. It can be safely assumed that in this unimolecular reaction the molar volume of the activated complex is greater than the molar volume of the reactant, since a bond breaking must occur to some extent on activation. 

Effect of Pressure on Reaction Rate Constant Pressure can have a direct impact on the reaction rate through its effect on the reaction rate constant. The pressure dependence of the reaction rate constant and unusual partial molar behavior of a solute in a SCF can result in enhancement of the reaction rate in the critical region of the mixture (136). According to the transition state theory (172, 173), pressure enhances the rate of a reaction if the activation volume (difference in the partial molar volumes of the activated complex and the reactants) is negative, whereas the reaction is hindered by pressure if the activation volume is positive. 

The molar volumes of the reactants, V, V, are presumably known. The ds are known for many substances or can be calculated from known quantities (Hildebrand and Scott, 1962 Marcus, 1985). The molar volume of the activated complex is not usually known may be obtained through the effect of pressure on the reaction rate (see earlier. Section 1.10). Finally, may be obtained from the best fit of data for the rate constant of the reaction in a variety of solvents to Equation 2.14. 

It is the most direct equation which can be used to calculate a volume of activation from rate-coefficient data in a supercritical fluid. It gives an activation volume which is the difference between the partial molar volume of the activated complex and those of the reagents and includes both intrinsic and solvent effects. The term in pressure, or the corresponding term for concentration-based rate data, are absent for a unimolecular reaction and are sometimes ignored by investigators in systems of different molecularity. 

For the cleavage of one bond, the volume of the activated complex is larger than that of the initial molecule and, hence, an increase in pressure retards this decomposition (see below). The opposite situation is observed for the concerted decomposition of two bonds. 

In the liquid phase, both the initial molecule and activated complex exist in the field of molecular forces of surrounding molecules, and these forces exert a pressure of (1 - 5)-10 Pa on each particle. This internal pressure in liquid has an effect on molecule decomposition. For the homolytic decomposition of one bond, the volume of the activated complex is somewhat greater than that of the initial molecule AV - V= AP, AP = 10 cmVmol for the decomposition of benzoyl peroxide. On going from the gas to liquid with an internal pressure of 2-10 Pa, Alogk = -0.30, i.e.., =... 

Equation (2.6.1) shows that the reaction rate constant will increase with increasing pressure if A V is negative (A V < 0), which means that the volume of the activated complex is smaller than the sum of molar volumes of reactants. This will happen in an associative mechanism. On the other hand, the transition state of a dissociative mechanism will have weakened (longer) bonds, and consequently A V > 0. 

The activation volume of degradation reactions which can occur at high temperatures should be positive because bond cleavage increases the volume of the activated complex more than the formation of double bonds from single bonds decreases it. 

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