Phase thermodynamics

The free energy of activation at the QCISD(T)/6-31 H-- -G(d,p) level amounts to 21.1 kcal/mol. According to the authors, the large electron density redistribution arising upon cyclization makes it necessary to use extended basis sets and high-order electron correlation methods to describe the gas-phase thermodynamics, which indicates clearly the gas-phase preference of the azido species. However, the equilibrium is shifted toward the tetrazole as the polarity of a solvent is increased. For instance, SCRF calculations (e = 78.4) yield a relative free energy of solvation with respect to the cw-azido isomer of —2.4 kcal/mol for the tmns-zziAo compound and of —6.8 kcal/mol for the tetrazole isomer. At a much lower level, the... 

Part of the gas can escape from the solution at a specific concentration and a fixed temperature, as the pressure level falls to under P < Pg. This takes place in two phases appearance of nuclei, and growth of bubbles of the free gas phase. Thermodynamic conditions for stable nucleation are formulated in [1], They are analogous to the conditions for starting the boiling of low-molecular liquids. The following changes take... 

In addition to deciding on the method of normalization of activity coefficients, it is necessary to undertake two additional tasks first, a method is required for estimating partial molar volumes in the liquid phase, and second, a model must be chosen for the liquid mixture in order to relate y to x. Partial molar volumes were discussed in Section IV. This section gives brief attention to two models which give the effect of composition on liquid-phase thermodynamic properties. 

In this paper we describe (1) the gas-phase thermodynamic functions (2) the condensed-phase thermodynamic functions (3) the oxygen potential (and the phase boundaries that are consistent with It) and (4) the resulting vapor pressure and composition as functions of temperature and composition of the condensed phase. 

The uncertainties in the condensed-phase thermodynamic functions arise from (1) the possible existence of a solid-solid phase transition in the temperature range 2160 to 2370 K and (2) the uncertainty in the estimated value of the liquid heat capacity which is on the order of 40%. While these uncertainties affect the partial pressures of plutonium oxides by a factor of 10 at 4000 K, they are not limiting because, at that temperature, the total pressure is due essentially entirely to O2 and 0. 

Klamt, A. (ed.), COSMO-RS From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design, Elsevier, Amsterdam, 2005. 

Wilson et al. [27] showed that the introduction of steric hindrance in the 6-position of one or two of the pyridine groups was sufficient to fine-tune the ligand field and obtain crossover compounds. These systems have been investigated using a number of different techniques, both in the solid and solution phases. Thermodynamic parameters have been derived from variable temperature magnetic susceptibility data for the single methyl-substituted (23 ) (AH°=19.7 kj mol"1, A5°=39.8 J mol"1 K"1), the double methylsubstitut-... 

Martinez, M. R., "Estimation of Gas-Phase Thermodynamic Parameters," Quantum Chemistry Program Exchange, Program 244 (1974). 

Many matrix molecules are acidic and can produce protons that attach to the gas-phase substrate molecules, producing protonated ions. Metal complexes examined by MALDI should have the ability to be stable in an acidic environment. A study of some metal complexes, by comparing the solid state, solution state, and gas-phase ions produced by MALDI, indicate that preformed species due to reaction of the complexes with the matrix can be predicted on the basis of condensed-phase thermodynamics (67). 

Gas-Phase Thermodynamics of Reactions of XeOTeFs+ with CFnX4 n (X =... 

Despite the importance of the precipitation of calcium phosphates, there is still considerable uncertainty as to the nature of the phases formed in the early stages of the precipitation reactions under differing conditions of supersaturation, pH, and temperature. Although thermodynamic considerations yield the driving force for the precipitation, the course of the reaction is frequently mediated by kinetic factors. Whether dicalcium phosphate dihydrate (CaHPO HoO, DCPD), octacalcium phosphate (Ca HfPO, 2.5 H20, OCP), hydroxyapatite (Cag (PO fOH), HAP), amorphous calcium phosphate (ACP), or a defect apatite form from aqueous solution depends both upon the driving force for the precipitation and upon the initiating surface phase. Thermodynamically, the relative supersaturation, o, is given by... 

In the conversion of fossil and nuclear energy to electricity, the value of high temperature solution phase thermodynamics in improving plant reliability has been far less obvious than that of classical thermodynamics in predicting Carnot cycle efficiency. Experimental studies under conditions appropriate to modern boiler plant are difficult and with little pressure from designers for such studies this area of thermodynamic study has been seriously neglected until the last decade or two. 

The MARTINI model effectively replaces three to four heavy atoms with a bead, parameterized to reproduce condensed-phase thermodynamic data of small molecules [23]. The MARTINI model has been used to investigate many biological processes, such as lung surfactant collapse [24], nanoparticle permeation in bilayers [25], large domain motion of integral membrane proteins [26], vesicle fusion [27,28], and lateral domain formation in membranes [29]. 

The definition of crystal is itself a developing concept, as demonstrated by the ongoing discussions [5, 6]. Most ot the theoretical background proposed in this chapter is valid for a perfect crystal, i.e., an infinite mathematical object with an idealized crystal structure ideal crystal) in thermodynamic equilibrium at a given presstrre P and temperature T. In textbooks, only the gas phase thermodynamics is usually discussed in detail, whereas little attention is paid to the solid state. A full thermodynamic treatment of solids is beyond the scope of this chapter and the reader is referred to specific books on the subject, for example [7]. 

If two or more different sequences of steps lead from reactants to products, these sequences must describe the same gas phase thermodynamics. This is the principle of thermodynamic consistency. 

This book has two primary aims. The first is to provide an accurate but accessible introduction to the theory of chemical and phase thermodynamics as first enunciated by J. Willard Gibbs. The second is to exhibit the transcendent beauty of the Gibbsian theory as expressed in the mathematical framework of Euclidean and Riemannian geometry. 

Classical and Geometrical Theory of Chemical and Phase Thermodynamics. By Frank Weinhold Copyright 2009 John Wiley Sons, Inc. 

The second law is more subtle and difficult to comprehend than the first. The full scope of the second law only became clear after an extended period of time in which (as expressed by Gibbs) truth and error were in a confusing state of mixture. In the present chapter, we focus primarily on the work of Carnot (Sidebar 4.1), Thomson (Sidebar 4.2), and Clausius (Sidebar 4.3), which culminated in Clausius clear enunciation of the second law in terms of the entropy function. This in turn led to the masterful reformulation by J. W. Gibbs, which underlies the modem theory of chemical and phase thermodynamics and is introduced in Chapter 5. 

The metric geometry of equilibrium thermodynamics provides an unusual prototype in the rich spectrum of possibilities of differential geometry. Just as Einstein s general relativistic theory of gravitation enriched the classical Riemann theory of curved spaces, so does its thermodynamic manifestation suggest further extensions of powerful Riemannian concepts. Theorems and tools of the differential geometer may be sharpened or extended by application to the unique Riemannian features of equilibrium chemical and phase thermodynamics. 

QUANTUM STATISTICAL THERMODYNAMIC ORIGINS OF CHEMICAL AND PHASE THERMODYNAMICS... 

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