Gas-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 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. 

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

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

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. 

Table 1. Gas-Phase Thermodynamic Parameters (Enol-Keto) from Integrated h...

The gas-phase thermodynamic (van t Hoff) parameters AH°, A5°, and AG029g for the syn-anti conformer interconversion of these gaseous alkyl nitrites are presented in Table 2. For MeONO this data compared well with those obtained by direct integration of slow exchange spectra. [27,22] The agreement of these gas-phase NMR thermodynamic parameters with microwave and theoretical data reinforce the validity of this technique applied to the syn-anti equilibria. Comparison of these gas-phase data with solution values yields information on the effects solvents have on the conformer equilibria, which in the particular case of these alkyl nitrites reflect a balance of steric and dielectric effects. 

Table 1.5 Definition of most important gas-phase thermodynamic data.

Carbon-centered radicals play an important role in organic synthesis, biological chemistry, and polymer chemistry. The radical chemistry observed in these areas can, to a good part, be rationalized by the thermodynamic stability of the open shell species involved. Challenges associated with the experimental determination of homolytic bond dissociation energies (BDEs) have lead to the widespread use of theoretically calculated values. These can be presented either directly as the enthalpy for the C-H bond dissociation reaction described in Equation 5.1, the gas-phase thermodynamic values at the standard state of 298.15K and 1 bar pressure being the most commonly reported values. 

Up to now our attention was mainly devoted to calculations of the energy and other quantities referring to free, isolated molecules. The computational techniques and their applications were demonstrated to be profitable in the exploration of physico-chemical properties of free molecules and their reactivity in the gas phase (thermodynamic functions, equilibrium and rate constants). However, the gas-phase processes represent only a special minor part of chemistry. Not only processes in biological systems, but also processes in laboratory conditions proceed typically in the liquid phase - or expressed more specifically - in the solution. It is therefore not surprising that the effort for applications of ab initio calculations is also still increasing in this very important field . ... 

Now the feeling is undergoing a further change in that gas-phase thermodynamic measurements can be used with great utility as standards for the understanding of—and even in anticipating—major new advances of ion thermochemistry in solution. 

In summary, we would like to emphasize the two current capabilities of the CHETAH program. The first is the estimation of gas phase thermodynamic data over the range of 25-1200°C, using Benson s second order group contribution method. The second capability of CHETAH is a hazard appraisal. This uses thermodynamic data to... 

TABLE 3-1 Pure-Component Gas-Phase Thermodynamic Properties for CO, H2, and CH3OH... 

TABLE 3-3 Pure-Component Gas-Phase Thermodynamic Properties at 298 K for CeHs, Hz, and C Hiz (cal/g mol)... 

Table 3.11 Ideal Gas-Phase Thermodynamic Properties of vinyl-hydroperoxides...

This section discusses how gas-phase thermodynamic properties can be calculated from molecular quantities such as the electronic energy, the equilibrium geometry, and the vibrational frequencies. 

Stronger acidity and for certain reactions are preferred for that reason. For microporous solids, it is the product selectivity that they impart, particularly in complex hydrocarbon transformations, that makes them so valuable. This shape selectivity, as it is generally termed, is a consequence of the geometry of the channels and cages from which the active sites are accessed. In a manner analogous to that of enzymes, the combination of active site, local environment and the available pathways to and from the particles external surface controls the product selectivities, often to product distributions well away from gas phase thermodynamic equilibrium. 

For the specific example, the heat of the CO activation reaction in gas-phase (CO <-> C + 0) at 298 K evalnated by the DFT method nsed here, inclnding temperature correction, is 247.3 kcal/mol as compared to 257.1 kcal/mol calcn-lated from [36]. This difference (of 10kcal/mol in this example) makes the DFT calculations inconsistent with high-level ab initio methods nsed to compnte thermodynamic properties in the gas phase. Use of DFT valnes only, without employing literature or ab initio gas-phase thermodynamics, can overcome this inconsistency at the expense of having less accurate thermodynamics with implications for error in energy balances, eqnilibrium conversions, and gas-phase species concentrations. Similarly to enthalpic inconsistency, entropic inconsistency may also exist. 

Kjaer, J. Computer Methods in Gas Phase Thermodynamics , Topsoe, Vedbaek, DK (1972) (Section 1.2.1)... 

---