Pressure and Temperature Dependencies

Schroeder J, Schwarzer D, Troe J and Voss F 1990 Cluster and barrier effects in the temperature and pressure dependence of the photoisomerization of trans.stilbene J. Chem. Phys. 93 2393-404... 

Song K and Hase W L 1998 Role of state specificity in the temperature- and pressure-dependent unimolecular rate constants for H02->H+02 dissociation J. Phys. Chem. A 102 1292-6... 

A recent example of laser flash-lamp photolysis is given by Hippier etal [ ], who investigated the temperature and pressure dependence of the thennal recombmation rate constant for the reaction... 

The experimentally measured dependence of the rates of chemical reactions on thermodynamic conditions is accounted for by assigning temperature and pressure dependence to rate constants. The temperature variation is well described by the Arrhenius equation. 

From fundamental thermodynamic relations, the temperature and pressure dependence of Henry s constant can be shown (18,50,51) to be ... 

The most notable theoretical analysis of the instability problem has been presented by McClure and Hart (M5). These investigators postulated a generalized combustion zone that includes a temperature-dependent and pressure-independent solid-phase reaction zone, and a temperature- and pressure-dependent gas-phase reaction zone. From this general model, Hart... 

While the Gibbs phase rule provides for a qualitative explanation, we can apply the Clapeyron equation, derived earlier [equation (5.71)], in conjunction with studying the temperature and pressure dependences of the chemical potential, to explain quantitatively some of the features of the one-component phase diagram. 

Sulfur vapor contains all molecules with between 2 and 8 atoms which are related by temperature- and pressure-dependent equilibrium reactions ... 

This reaction was investigated by Klippenstein and Harding [57] using multireference configuration interaction quantum chemistry (CAS + 1 + 2) to define the PES, variable reaction coordinate TST to determine microcanonical rate coefficients, and a one-dimensional (ID) master equation to evaluate the temperature and pressure dependence of the reaction kinetics. There are no experimental investigations of pathway branching in this reaction. 

The same group has looked into the conversion of NO on palladium particles. The authors in that case started with a simple model involving only one type of reactive site, and used as many experimental parameters as possible [86], That proved sufficient to obtain qualitative agreement with the set of experiments on Pd/MgO discussed above [72], and with the conclusion that the rate-limiting step is NO decomposition at low temperatures and CO adsorption at high temperatures. Both the temperature and pressure dependences of the C02 production rate and the major features of the transient signals were correctly reproduced. In a more detailed simulation that included the contribution of different facets to the kinetics on Pd particles of different sizes, it was shown that the effects of CO and NO desorption are fundamental to the overall behavior... 

Ren P, Ponder JW (2003) Temperature and pressure dependence of AMOEBA water model. J Phys Chem B 107 5933... 

Here functions Qnt X), Qj(X), and QP(X) can be determined experimentally using calibration samples. If these functions are linear independent then the parameters Ank, A, and Ap can be uniquely determined from the variation of P /1, , n2,. .. /( . /. / considered as a function of X. In particular, the side effects, i.e., the temperature and pressure dependences, can be eliminated from the transmission spectrum. The sensing method based on this simple idea was applied in Ref. 69 for determination of microfluidic refractive index changes in two microcapillaries coupled to a single MNF illustrated in Fig. 13.26c. The developed approach allowed to compensate the side temperature and pressure variation effects. 

Iron(III)-catalyzed autoxidation of ascorbic acid has received considerably less attention than the comparable reactions with copper species. Anaerobic studies confirmed that Fe(III) can easily oxidize ascorbic acid to dehydroascorbic acid. Xu and Jordan reported two-stage kinetics for this system in the presence of an excess of the metal ion, and suggested the fast formation of iron(III) ascorbate complexes which undergo reversible electron transfer steps (21). However, Bansch and coworkers did not find spectral evidence for the formation of ascorbate complexes in excess ascorbic acid (22). On the basis of a combined pH, temperature and pressure dependence study these authors confirmed that the oxidation by Fe(H20)g+ proceeds via an outer-sphere mechanism, while the reaction with Fe(H20)50H2+ is substitution-controlled and follows an inner-sphere electron transfer path. To some extent, these results may contradict with the model proposed by Taqui Khan and Martell (6), because the oxidation by the metal ion may take place before the ternary oxygen complex is actually formed in Eq. (17). 

The objective function or the constraint functions may be defined in terms of complicated interactions of the variables. A familiar case of interaction is the temperature and pressure dependence in the design of pressure vessels. For example, if the objective function is given as / = I5.5xxx2m, the interaction between xx and x2 precludes the determination of unique values of xx and x2. Many other more complicated and subtle interactions are common in engineering systems. The interaction prevents calculation of unique values of the variables at the optimum. 

Recent interpretations of diffraction data suggest that water may contain regular clusters of as many as 280 molecules [2], These large clusters have icosohedral symmetry and adopt two forms, expanded and compressed, (the latter appearing somewhat similar to a deflating soccer ball), which are thought to exist in a temperature and pressure dependent equilibrium. 

The density of a SCF is typically less than half that of the liquid state, but two orders of magnitude greater than that of a gas. Viscosity and diffusivity are also temperature and pressure dependent. 

SURFTHERM Coltrin, M. E. and Moffat, H. K. Sandia National Laboratories. SURFTHERM is a Fortran program (surftherm.f) that is used in combination with CHEMKIN (and SURFACE CHEMKIN) to aid in the development and analysis of chemical mechanisms by presenting in tabular form detailed information about the temperature and pressure dependence of chemical reaction rate constants and their reverse rate constants, reaction equilibrium constants, reaction thermochemistry, chemical species thermochemistry, and transport properties. 

A single N(ls) peak at 402 eV is observed on preoxidized nickel [with clean nickel at 80 K the N(ls) peak is at 399.5 eVj. The intensity of the 402-eV peak is both temperature and pressure dependent, increasing in intensity with decreasing temperature and increasing pressure (46). 

Both viscosity and diffusivity change from gas-fike to fiquid-like with increasing pressure Viscosity and diffusivity (which is strongly related to viscosity) are also temperature- and pressure-dependent and, in general, an order of magnitude lower and higher at least than in the liquid phase, respectively. 

It can be seen from Equation (7.70) that to calculate AG at any temperature and pressure we need to know values of AH and AS at standard conditions (P= 100 kPa, T = 298 K), the value of ACp as a function of temperature at the standard pressure, and the value of AEj- as a function of pressure at each temperature T. Thus, the temperature dependence of AC/> and the temperature and pressure dependence of AVj-are needed. If such data are available in the form of empirical equations, the required integrations can be carried out analytically. If the data are available in tabular form, graphical or numerical integration can be used. If the data are not available, an approximate result can be obtained by assuming ACp and AVp are constant... 

An interesting example of a one-component systems is SiOa, which can exist in five different crystalline forms or as a liquid or a vapor. As C = 1, the maximum number of phases that can coexist at equilibrium is three. Each phase occupies an area on the T P diagram the two-phase equilibria are represented by curves and the three-phase equilibria by points. Figure 13.1 (2, p. 123), which displays the equUi-brium relationships among the sohd forms of Si02, was obtained from calculations of the temperature and pressure dependence of AG (as described in Section 7.3) and from experimental determination of equUibrium temperature as a function of equilibrium pressure. 

Calcium carbonate solubility is also temperature and pressure dependent. Pressure is a 6r more important fector than temperature in influencing solubility. As illustrated in Table 15.1, a 20°C drop in temperature boosts solubility 4%, whereas the pressure increase associated with a 4-km increase in water depth increases solubility 200-fold. The large pressure effect arises from the susceptibility of the fully hydrated divalent Ca and CO ions to electrostriction. Calcite and aragonite are examples of minerals whose solubility increases with decreasing temperature. This unusual behavior is referred to as retrograde solubility. Because of the pressure and temperature effects, calcium carbonate is fer more soluble in the deep sea than in the surfece waters (See the online appendix on the companion website). 

The data thus clearly shows that, depending on the gramicidin concentration, the structure of the temperature- and pressure-dependent lipid bilayer is significantly altered by the insertion of the polypeptide. It has also been shown... 

Raheim A. and Green D. H. (1974). Experimental determination of the temperature and pressure dependence of the Ee-Mg partition coefficient for coexisting garnet and clinopyro-xene. Contrib. Mineral Petrol, 48 179-203. 

Palmer MR, Slack JF (1989) Boron isotopic composition of tourmaline from massive sulfide deposits and tourmalinites, Contr Miner Petrol 103 434 51 Palmer MR, Swihart GH (1996) Boron isotope geochemistry an overview. Rev Miner 33 709-744 Palmer MR, Spivack AJ, Edmond JM (1987) Temperature and pH controls over isotopic fractionation during the absorption of boron on marine clays, Geochim Cosmochim Acta 51 2319-2323 Palmer MR, London D, Morgan GB, Babb HA (1992) Experimental determination of fractionation of B/ °B between tourmaline and aqueous vapor a temperature- and pressure-dependent isotopic system, Chem Geol 101 123-129... 

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