Activation volumes, temperature

Fig. 6.5. Yield strengths from flexural tests are plotted against strain rates at the surface of the samples. Tests were performed on polymers A, B, and E test temperature 23 °C. The slope of the three lines correspond to similar activation volumes v = 2 0.1 nm3...

The solvent may be an important parameter for reactions carried out in solution, since the value of activation volume is often dependent on the solvent. A limitation may be due to the effect of pressure on the freezing temperature of... 

E = activation energy R = ideal gas constant T = absolute temperature P = pressure AV = activation volume k" = frequency factor... 

Jenner investigated the kinetic pressure effect on some specific Michael and Henry reactions and found that the observed activation volumes of the Michael reaction between nitromethane and methyl vinyl ketone are largely dependent on the magnitude of the electrostriction effect, which is highest in the lanthanide-catalyzed reaction and lowest in the base-catalyzed version. In the latter case, the reverse reaction is insensitive to pressure.52 Recently, Kobayashi and co-workers reported a highly efficient Lewis-acid-catalyzed asymmetric Michael addition in water.53 A variety of unsaturated carbonyl derivatives gave selective Michael additions with a-nitrocycloalkanones in water, at room temperature without any added catalyst or in a very dilute aqueous solution of potassium carbonate (Eq. 10.24).54... 

By now, water exchange has been studied on more than one hundred Gdm complexes with the help of 170 NMR, and the large body of data available has been reviewed recently (48). Variable temperature 170 transverse relaxation rate measurements provide the rate of the water exchange, whereas the mechanism can be assessed by determining the activation volume, AVt, from variable pressure 170 T2 measurements (49,50). The technique of 170 NMR has been described in detail (51). 

J. Rimmelin and G. Jenner, Tetrahedron, 30, 3081 (1974). A recent measurement of the pressure and temperature dependence of die electrocyclic ring-closure of Z-l,3,5-hexatriene to 1,3-cyclohexadiene in the range of 200 to 2500 bar and 100 to 125 °C does not show a significant temperature dependence of die activation volume (M. K. Diedrich and F. -G. Klarner, unpublished results). 

In two earlier studies (106, 107), the oxidation of two Schiff base complexes were studied at room temperature, but in these cases only activation parameters for the overall process could be obtained since it was not possible to detect the formation of an intermediate species which could be attributed to a peroxo species. Nevertheless, the kinetic measurements provided indirect evidence for the existence of this intermediate. In both studies negative values for the activation entropies and the activation volumes were obtained. The oxidation of [Cu2(H-BPB-H)(CH3CN)2](PF6)2 (H-BPB-H = l,3-bis[iV-(2-pyridylethyl)-formidoyl]benzene) is accompanied by an activation entropy of -53 11 J K-1 mol-1 and an activation volume of -9.5 0.5 cm3 mol-1. In... 

Figure 15. Room temperature pressure evolution of the rate constant for different activation volume values that have been assumed to be constant over the entire pressure range.

Eontanella and co-workers studied the effect of high pressure variation on the conductivity as well as the H, H, and O NMR spectra of acid form Nafionl 17 membranes that were exposed to various humidities. Variation of pressure allows for a determination of activation volume, A V, presumably associated with ionic and molecular motions. Conductivities (a) were obtained from complex electrical impedance diagrams and sample geometry, and A V was determined from the slope of linear isothermal In a versus p graphs based on the equation A E = —kJ d In a/d/j] t, where p is the applied pressure. At room temperature, A Ewas found to be 2.9 cm mol for a sample conditioned in atmosphere and was 6.9 cm mol for a sample that was conditioned in 25% relative humidity, where the latter contained the lesser amount of water. 

The mole fractions of labeled water at t = 0 and at equilibrium are noted as Xq and Xoo, respectively (Pig. 4). In the end, the signal of bound water becomes small and difficult to quantify. But, this does not influence the quality of the measured rate constant because the mole fraction at equilibrium, x, is known from the concentration of the metal ion and the coordination number. These experiments can be performed at variable temperature and at variable pressure to obtain activation enthalpies and entropies as well as activation volumes. 

The standard enthalpy difference between reactant(s) of a reaction and the activated complex in the transition state at the same temperature and pressure. It is symbolized by AH and is equal to (E - RT), where E is the energy of activation, R is the molar gas constant, and T is the absolute temperature (provided that all non-first-order rate constants are expressed in temperature-independent concentration units, such as molarity, and are measured at a fixed temperature and pressure). Formally, this quantity is the enthalpy of activation at constant pressure. See Transition-State Theory (Thermodynamics) Transition-State Theory Gibbs Free Energy of Activation Entropy of Activation Volume of Activation... 

Since the activation energy for ionic recombination is mainly due to viscosity we use the activation energy for viscous flow (10kJ.mol l). AH ] and 3 were determined from conductance as 44.2kJ.mol and 11,4kJ.mol From the data presented in Table III it is clear that the temperature dependence of the slope is very satisfactorily described by A% +l/2(AHd-AH3). Another, and rather critical, test for the applicability of eq. 14b is the effect of pressure since the slope of eq. 14b is largely pressure independent so that we ask here for a compensation of rather large effects. From Table III we Indeed see an excellent accordance between the experimental value and the pressure-dependence calculated from the activation volume of viscous flow (+20.3 ctPmol ), AVd (-57.3 cnAnol" ) and (-13.9 cnAnol ) the difference between the small experimental and calculated values is entirely with the uncertainties of compressibility - corrections and experimental errors. 

This conclusion was based only upon a supposed increase in the heat of activation with temperature, which was interpreted as proof that the wall reaction which predominates at lower temperatures is superseded by a true gas reaction. Hinshelwood and Topley f found, by varying the ratio surface/ volume, that the reaction taking place in a silica vessel was predominantly heterogeneous up to 1,044° abs. at least. Since the total velocity as measured in these experiments was actually rather less than that in the experiments of Trautz and Bhandarkar, it seems clear that the reaction measured by the latter observers must have been heterogeneous also. Re-examination of their experimental data, moreover, fails to substantiate the conclusion that there is any real increase in the heat of activation with temperature. 

The change in rate constant at various pressures and temperatures, calculated from eqn. 3.2-53 for several values of Av is presented in Fig. 3.2-6. The rate-constant changes exponentially with the pressure. The effect is steeper when the activation volume is large and the temperature is low, and vice versa. 

The half-life time, Tm, of decomposition of di(t-butyl)peroxide at a temperature of 463 K and ambient pressure is 50 s. One may calculate the rate constant and the half-life time for decomposition at 300 MPa and the same temperature, when the activation volume is Av = +13 cm3 mol"1. 

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