Reaction rate constants activation volume

Supercritical solvents can be used to adjust reaction rate constants (k) by as much as two orders of magnitude by small changes in the system pressure. Activation volumes (slopes of In k vs P) as low as —6000 cm3/mol were observed for a homogeneous reaction (97). Pressure effects can also be pronounced on reversible reactions (17). In one example the equilibrium constant was increased from two- to sixfold by increasing the solvent pressure. The choice of supercritical solvent can also dramatically affect an equilibrium constant. An obvious advantage of using supercritical fluid solvents as a media for chemical reactions is the adjustability of the reaction kinetics and equilibria owing to solvent effects. 

The enthalpies of solution and apparent molar volumes in various solvents have been determined for methyltriphenylphosphonium iodide (10) rate constants, activation enthalpies, activation volumes and reaction enthalpies were also determined for its synthesis from triphenylphosphine and methyl iodide156. (Equation 3). 

After in the foregoing chapter thermodynamic properties at high pressure were considered, in this chapter other fundamental problems, namely the influence of pressure on the kinetic of chemical reactions and on transport properties, is discussed. For this purpose first the molecular theory of the reaction rate constant is considered. The key parameter is the activation volume Av which describes the influence of the pressure on the rate constant. The evaluation of Av from measurement of reaction rates is therefor outlined in detail together with theoretical prediction. Typical value of the activation volume of different single reactions, like unimolecular dissociation, Diels-Alder-, rearrangement-, polymerization- and Menshutkin-reactions but also on complex homogeneous and heterogeneous catalytic reactions are presented and discussed. 

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

The carbon support used was a Norit activated carbon (RX3 extra) having a surface area of 1190 m2.g 1 and a pore volume of 1.0 cm3.g . The Co/C catalyst (4.1 wt% Co) was prepared by pore volume impregnation with an aqueous solution of cobalt nitrate (Merck p.a.) followed by drying in air at 383 K (16 h). The promoted catalyst (1.5 wt% Co, 7.7 wt% Mo) was prepared in a special way to ensure a maximum amount of the Co-Mo-S phase (11). Mossbauer spectroscopy of this promoted catalyst clearly showed that only the Co-Mo-S phase was present after sulfiding (11) and furthermore that this Co-Mo-S is probably a Co-Mo-S type II phase, meaning a minor influence of active phase-support interaction (11,12). The catalytic activity of the sulfided catalysts was determined by a thiophene HDS measurement at 673 K and atmospheric pressure, as described elsewhere (10). The thiophene HDS reaction rate constant kHDg per mol Co present (approximated as a first order reaction) was found to be 17 10 s 1 for Co/C and 61 10 3s 1 for Co-Mo/C. 

Not only the internal pressure of a solvent can affect chemical reactions (see Section 5.4.2 [231, 232]), but also the application of external pressure can exert large effects on reaction rates and equilibrium constants [239, 429-433, 747-750]. According to Le Chatelier s principle of least restraint, the rate of a reaction should be increased by an increase in external pressure if the volume of the activated complex is less than the sum of the volumes of the reactant molecules, whereas the rate of reaction should be decreased by an increase in external pressure if the reverse is true. The fundamental equation for the effect of external pressure on a reaction rate constant k was deduced by Evans and Polanyi on the basis of transition-state theory [434] ... 

For the second reaction step, the observed rate constant of this reaction (kobsi) was independent of the hydrogen peroxide concentration. As described above, the temperature dependence of kobsi was used to construct a linear Eyring plot from which AH and A5 were obtained. The volume of activation was derived from the slope of the hnear plot of In kobsi versus pressure at 25 °C in the pressure range 10 -170 MPa. The reported volumes of activation can be used to construct a volume profile for the overall reaction. The positive activation volume, AV = -F6.8 0.4cm mol, suggests a dissociative interchange Id) mechanism for the hgand substitution reaction on [Fe(edta)OH] with hydrogen peroxide. 

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 use of SCB as media for diemical reactions has increased during the past few years, as discussed in the next sectioiL The large partial molar volumes of solutes near the critical point result in unusualty large volumes of activation and large variations of certain reaction rate constants and selectivities with pressure. The following section on rate processes desolbes relatively novel crystallization processes that have commercial promise and transport properties in SCFs. The last two sections disr a variety of food, pharmaceutical, and environmental applications and provide an in-depth treatment of the design of commercial plants. 

Temperature dependence of environmentally important reaction rate constants. (A) CO2 reaction with H2O or OH in seawater. The data are plotted so that the sfope of the line is the Arrhenius activation energy, divided by the gas constant, R (8.315 J mor deg ) (Johnson, 1982). (B) HS oxidation (Millero et a/., 1987a). (C) Fe(ll) oxidation in seawater (Millero et o/., 1987b). (D) The dissolution rate constants for opal as a function of temperature. The values plotted here are normalized to a constant area volume ratio, A /V = I0cm . The high dissolution rate constants (circles) are for acid-cleaned siliceous sediments (Hurd, 1972) the squares are data for peroxide and acid-washed plankton (Lawson et a/., 1978) and the other results (triangles) are for two untreated single species of diatom (Kamatani, 1982). 

Another measure of the associative or dissociative nature of reactions is the activation volume (AV ). The following equation shows the approximate relationship between the rate constant (kp or kobs) and the applied pressure. 

In a related study, the volume of reaction, the volume of activation for diffusion (A F ff), and the volume of activation obtained from the standard electrode reaction rate constant at various pressures, have been determined for the dec-amethylferrocene (DmFc+/0) system, in several non-aqueous solvents.238 The deca-methylated ferrocene couple, rather than the unmethylated couple, was chosen. This... 

Apart from the direct conformational changes in enzymes, which may occur at very high pressures, pressure affects enzymatic reaction rates in SCFs in two ways. First, the reaction rate constant changes with pressure according to transition stage theory and standard thermodynamics. Theoretically, one can predict the effect of pressure on reaction rate if the reaction mechanism, the activation volumes and the compressibility factors are known. Second, the reaction rates may change with the density of SCFs because physical parameters, such... 

Photoreactions of [Ru(bipy)3]Cl2 and of [Ru(phen)3]Cl2 in acetonitrile proceed more slowly as pressure increases. The activation volumes increase dramatically with temperature, from +12 and +9 cm mol respectively at 288 K to +22 and +27 at 333 K. These increases are ascribed to a key role for chloride ion pairs in these dissociatively activated reactions. Rate constants for base-catalyzed isomerization of the y to the p form of [Ru(azpy)2Cl2], azpy = (22), are not linear in hydroxide concentration, prompting speculation on the detailed role of hydroxide in this conversion.Rate constants for replacement of coordinated water in cis- and tra 5-[Ru(LL)2X(OH2)]" by acetonitrile span a range of nearly 2 X 10" times. Several factors have to be invoked to explain the observed trend in the effects of ligand X on the ease of replacement of the aqua-ligand. " The... 

In (5.37), r stands for the volumetric reaction rate, Ci represents the concentration of acid groups per unit volume of catalyst, and a, is the liquid-phase activity of component i. The temperature dependence of the reaction rate constant k can be expressed by the Arrhenius equation. All kinetic and thermodynamic parameters can be found elsewhere [7]. 

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