Difference between the volumes of activation

There are two different basic approaches in the control of selectivity in chemical transformations. In a kinetically controlled reaction the difference between the volumes of activation leading to the isomers must be considered, whereas in a thermodynamically controlled reaction the difference in the volumes of reaction is important. 

Swaddle has determined the partial molar volumes and reexamined the effects of pressure on the water exchange of [M(NH3)5(H20)] (M = Co, Rh, Ir and Cr). The partial molar volume of the transition state, (AF ) was defined to be the difference between the volume of activation and the partial molar volume of the ground state (AF = AF — AF°). While earlier studies showed that the volume of activation (AF ) did vary as the central metal changed, the partial molar volume of the transition state (AF ) is quite insensitive to the nature of the central metal (Table 27). Swaddle concludes that contrary to intuition.. . the transition states of a series of aqua exchange reactions must resemble one another surprisingly closely, regardless of detailed mechanism . ... 

In the original transition state theory, the activation volume is defined as the difference between the volume of the activated state VXJ and the volumes of the initial reactants, VA and VB,... 

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 quantity Vm, given by Eq. 7.26, is the difference between the volume of the system in an activated state and a well state. This volume difference is generally termed the activation volume for migration and is a positive quantity because of the atomic squeezing and resulting expansion of the system that occurs in the activated state. The activation volume can be measured experimentally by measuring the pressure dependence of the jump frequency, T. Find an expression for the pressure dependence of F and describe how it can be used to determine Vm. 

Characteristic of such dienes, a-keto-p,7-unsaturated esters such as (3 see also Table 3 and Table 5) exhibit good thermal reactivity toward simple vinyl ethers in [4 + 2] cycloaddition reactions that proceed with exclusive regiocontrol predominately through an erulo transition state. The endo selectivity increases as the reaction temperature is decreased and both the reaction rate and the endo selectivity increase as the reaction pressure is increased (Figure 3, Table 3). The substantial increase in the diastereoselectivity of the pressure-promoted [4 + 2] cycloaddition reaction of (3) with a cis 1,2-disub-stituted dienophile has been attributed to the additional differences in the volume of activation between the reaction paths leading to the endo and exo diastereomers due to the additional cis C-2 dienophile sub-... 

The effect of pressure on chemical equilibria and rates of reactions can be described by the well-known equations resulting from the pressure dependence of the Gibbs enthalpy of reaction and activation, respectively, shown in Scheme 1. The volume of reaction (AV) corresponds to the difference between the partial molar volumes of reactants and products. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state (TS) with respect to the partial molar volumes of the reactants. Volumes of reaction can be determined in three ways (a) from the pressure dependence of the equilibrium constant (from the plot of In K vs p) (b) from the measurement of partial molar volumes of all reactants and products derived from the densities, d, of the solution of each individual component measured at various concentrations, c, and extrapolation of the apparent molar volume 4>... 

The volume of activation, AV is defined as the difference between the partial molar volumes of the transition state and the reactants. It is related to the pressure variation of the rate constant by Eq. (4) ... 

The kinetic effect on (1/72—1/7)) is proportional to (Amagnetic field as shown in Fig. 7.23. From the temperature and pressure dependence, the kinetic parameters presented in Table 7.13 were obtained. The two activation parameters, namely the entropy and the volumes of activation, are negative and also are of the same magnitude for all the lanthanide ions. These activation parameters imply a common water exchange mechanism for all the lanthanides studied and possibly an associative activation path of exchange. The activation volume, AV of —6.0 cm3 mol-1 probably reflects the difference between a large negative contribution due to the transfer of a water molecule electrostricted in the second coordination sphere to the first coordination sphere and a positive contribution due to the difference in partial molar volumes of N + 1 coordinated transition state and N coordinated aquo lanthanide ion. It should be noted that the latter difference (in partial molar volumes of Fn(H20)w+i and Fn(H20)jv is due to the increase in Fn-O bond distance (Fig. 7.16). 

Excluded volume The difference between the shapes of a compound that binds to, for example, an enzyme and one that does not. Some of the volume areas in a model of the inactive compound, with van der Waals radii around atoms, will not fit in the active site of the enzyme. These areas should be avoided when designing new inhibitors. 

To generate an expression for the effect of pressure upon equilibria and extend it to reaction rates, this early work consisted of drawing an analogy with the effect of temperature on reaction rates embodied in the Arrhenius equation of the late 19th century.2 In the more coherent understanding since the development of transition state theory (TST),3 6 the difference between the partial molar volumes of the transition state and the reactant state is defined as the volume of activation, A V, for the forward reaction. A corresponding term A Vf applies for the reverse reaction. Throughout this contribution A V will be used and is assumed to refer to the forward reaction unless an equilibrium is under discussion. Thus ... 

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