Yielding pressure dependence

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

Because shear and compressive strengths s andp depend in a similar way on material properties such as lattice stmcture and bond strength,yis often in a rather narrow range of about 0.20—0.35 for a wide variety of materials. The following are typical data for sliding on steel with bearing materials varying several hundredfold in yield pressure ... 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

An interesting feature is the sometimes observed pressure dependence of the reaction. The Michael addition of dimethyl methylmalonate 12 to the bicyclic ketone 13 does not occur under atmospheric pressure, but can be achieved at 15 Kbar in 77% yield ... 

The question of which channels account for the difference between the observed CH5 + cross-section and the CH4 + loss is illuminated by studying the isotopic system CH4-CD4. When mixtures of CH4 and CD4 were subjected to electron impact, a pressure dependent yield of CH2D+ was observed which established the reaction mechanism ... 

The kinetic data fit a mechanism of successive reactions sequent to only one primary ion equally well, provided that the first step can yield 1.37 methyl radical/100 e.v. and is pressure dependent and that the succeeding pressure independent step yields methyl radicals with a lesser efficiency and leads to a pressure independent yield of 0.58 methyl radicals/100 e.v. If the first step is either Reaction 9a or Reaction 17b, one can once more use the rate constant ratios given earlier to estimate the yields of the possible primary precursor ions. Hence, either G-(C2H2+) = 1.9 ions/100 e.v., or G(C2H4+) = 1.52 ions/100 e.v. The... 

Kinetic examination of the methane yield shows behavior quite similar to that of methyl radical a pressure dependent yield of 0.406 molecule/100 e.v., a pressure independent yield of 0.126 molecule/100 e.v., and a rate constant ratio of kq/kf = 1.5 X 106 mole-1 cc. for the competing steps. 

In all cases, glycine oligomers were obtained, from the dimer up to the decamer yields were pressure dependent. The rate of polymerisation increased during the first 8 days and then remained constant until the 31st day. The authors conclude from their experimental results that abiotic polymerisation reactions during diagenesis were more likely to have occurred in deep-lying sediments than in the primeval ocean (Ohara et al 2007). 

If the pressure dependence of the molar volume of the liquid is neglected, integration from a flat interface (r = oo) yields... 

The photoablation behaviour of a number of polymers has been described with the aid of the moving interface model. The kinetics of ablation is characterized by the rate constant k and a laser beam attenuation by the desorbing products is quantified by the screening coefficient 6. The polymer structure strongly influences the ablation parameters and some general trends are inferred. The deposition rates and yields of the ablation products can also be precisely measured with the quartz crystal microbalance. The yields usually depend on fluence, wavelength, polymer structure and background pressure. 

Somewhat surprisingly, the pressure dependence of quantum yields from the photolysis of NO at 1236 A, where the primary process is almost entirely photoionization199, is very similar to that observed for 1470-1650 A198. Clearly, recombination of the ionic fragments must lead to an excited state of NO which predissociates upon collision. However, the neutralization reaction... 

While claiming no finality for their mechanism, the authors pointed out that it accounted satisfactorily for the zero-order dependence on NC13 concentration, the intensity exponent of unity and many other characteristics of the reaction. However, a serious defect lies in the apparent absence of any effect of pressure on the rate of diffusion of NC14 to the reaction vessel surface. Such an effect would be expected under their conditions and it would yield a dependence of the reaction rate on total pressure opposite to that observed. 

In kinetics, similar relationships apply, but the volume of activation AV can be determined only from the pressure dependence of the rate coefficient k, since the partial molal volumes V of transition states are not directly measurable. Conversely, however, equation 4 can yield values of V. ... 

Fourier-transform infrared (FT-IR) spectroscopy and small-angle X-ray (SAXS) and neutron (SANS) scattering studies have shown the existence of a further pressure induced gel phase in DPPC bilayers." " Pressure dependent NMR studies yielded complementary information on the pressure-induced gel phases. The gel state of DPPC bilayers shows a variation in lineshapes which depend on the particular pressure and temperature. The types of lineshapes seen in a high pressure investigation of dg2-DPPC by Jonas et al. are... 

Fig. 8. Data showing (a) the pressure dependence of the quantum yield of H2 produced in the 184.9 nm pyi dysis of borazine and (b) the build-up of solid polymer during the pyrolysis reaction...

Transition state theory yields rate coefficients at the high-pressure limit (i.e., statistical equilibrium). For reactions that are pressure-dependent, more sophisticated methods such as RRKM rate calculations coupled with master equation calculations (to estimate collisional energy transfer) allow for estimation of low-pressure rates. Rate coefficients obtained over a range of temperatures can be used to obtain two- and three-parameter Arrhenius expressions ... 

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