Free energy and enthalpy

Fig. XVII-23. (a) Entropy enthalpy, and free energy of adsorption relative to the liquid state of N2 on Graphon at 78.3 K (From Ref. 89.) b) Differential entropies of adsorption of n-hexane on (1) 1700°C heat-treated Spheron 6, (2) 2800°C heat-treated, (3) 3000°C heat-treated, and (4) Sterling MT-1, 3100°C heat-treated. (From Ref 18.)...

It is possible to detemiine the equilibrium constant, K, for the bimolecular reaction involving gas-phase ions and neutral molecules in the ion source of a mass spectrometer [18]. These measurements have generally focused on tln-ee properties, proton affinity (or gas-phase basicity) [19, 20], gas-phase acidity [H] and solvation enthalpies (and free energies) [22, 23] ... 

Enthalpy and free energy functions can also be tabulated using T = 298.15 K as a reference temperature by making use of the relationships... 

H-bond acceptor enthalpy and free energy thermodynamic Fa, Ca 27... 

H-bond donor enthalpy and free energy factors thermodynamic Ed, Q 27... 

A multiplicative approach to describe the enthalpy and free energy of H-bonding was developed by Raevsky et al. [3, 24—27]. From a large number of their own... 

Thus, the statishcal criteria for Eqs. (5) and (6) show that the approach provides a reasonably reliable method to calculate H-bond enthalpy and free energy. 

From 163 calculated H-bond donor and 195 calculated H-bond acceptor factors, one can get enthalpy and free energy values for 31785 reactions using Eqs. (3) and (4). Later, the number of H-bond factor values was significantly increased. A special program for calculating factor values was created and included in the HYBOT (Hydrogen Bond Thermodynamics) program [28, 29]. The current version, HYBOT-2006, has about 20000 values of H-bond acceptor factors and about 5000... 

Table 6.2 demonstrates large intervals of enthalpy and free energy H-bond donor and acceptor factor values as result of a different nature of H-bonding atoms as well as an infiuence of substituents at those atoms on its H-bond capability. 

Tab. 6.2 Enthalpy and free energy H-bond donor and acceptor factor values for a few chemicals [28].

However, even the best experimental technique typically does not provide a detailed mechanistic picture of a chemical reaction. Computational quantum chemical methods such as the ab initio molecular orbital and density functional theory (DFT) " methods allow chemists to obtain a detailed picture of reaction potential energy surfaces and to elucidate important reaction-driving forces. Moreover, these methods can provide valuable kinetic and thermodynamic information (i.e., heats of formation, enthalpies, and free energies) for reactions and species for which reactivity and conditions make experiments difficult, thereby providing a powerful means to complement experimental data. 

Figure 3.1 (A) Plots for the change in enthalpy and free energy of a reaction...

Table XII contains the enthalpy and free-energy differences of the critical intermediate species for the anthraphos Rh catalyst. Although no experimental results are available yet, our predicted energies show a much smaller dissociation energy for H2 loss, the first step in the dissociative mechanism (8 is more stable by 13 kcal/mol relative to 4). In contrast, the oxidative addition intermediate of the first step in the associative mechanism, the M(V) species 5, is 14 kcal/mol less stable...

More recently, ionic enthalpies and free energies of hydration have been determined relative to jj+.88 168 171 This can be done, for example, by means of appropriate thermodynamic cycles.170,171 Then by assigning the AHhydTation and AGhydration of H+ on some basis, these quantities can be evaluated for the other ion. Rashin and Honig took AHhydTation (H+) to be -262.18 kcal/mole,88 while Florian and Warshel assumed that AGhydratj0n (H+) is -259.5 kcal/mole.171... 

In Table 10 are listed some computed ionic enthalpies and free energies of hydration, as well as the corresponding experimental ones. The range in some of the latter illustrates the uncertainty associated with the experimental data, discussed in the previous Section. This must of course be taken into account in evaluating the calculated results. 

Calculated (By Simulations) And Experimental Ionic Enthalpies And Free Energies of Hydration, in kcal/mole... 

Armentrout and Rogers also suggest more suitable anchor points for the LCA scale, e.g. the lithium cation bond energies to methanol or dimethyl ether. They further examined the kinetic energy dependences of the CID of Li+—ROH with and reported that the dominant dissociation process in all cases is the loss of alcohol. The thresholds for Li+—ROH dissociations were determined and converted to enthalpies and free energies at 298 and 373 K for comparison with previous equihbrium data on these systems. LCA values at 298 K for a series of alcohols are summarized in Table 3. The experimental results are compared with enthalpies of binding (PA) at 298 K (Figure 2) and a linear correlation between the LCA and the PA is found. 

The driving force for such reactions is found in the values of entropy, enthalpy and free energy according to the equation ... 

As such, thermochemical analogies don t help us decide which tautomer is more stable. From the literature we conclude that the quinone oxime tautomer is somewhat the more stable, the precise enthalpy and free energy difference depending on the solvent, substituents and reaction conditions (see the recent paper. Reference 60, and references cited therein). 

Tabulated values of standard enthalpies and free energies of formation [8]... 

Table 4 Comparison of reaction pathway energetics (kcal/mol) for benzylperoxy radical and 2-picolinylperoxy radical at 298 K, via B3LYP/6-311+G //B3LYP/6-31G. Numbers refer to pathways depicted in Fig. 18. All enthalpies and free energies are relative to the peroxy radical (2) when preceded by TS, the relative data are the enthalpy and free energies of activation...

Table 2-2 lists some important chemical reactions along with their standard state enthalpies and free energies of reaction, all in kj/mole. 

Standard State Enthalpy and Free Energy Changes in This Book. All values are in kj/mole of the first... 

Dynamic NMR measurements gave estimates of enthalpies and free energies for equilibria of... 

The wave functions for the periodic motions (i.e., vibrations) of the nuclei and the associated vibrational energy levels can then be obtained from the geometries and the second derivatives of the energy at the stationary points. As described in Sections 2.3 and 2.4, the vibrational energies are necessary to correct the difference between the electronic energies of two stationary points into differences between their enthalpies and free energies. 

Equation (4.70) is a starting point in the determination of diffusivities in liquid metal alloys, but in most real systems, experimental values are difficult to obtain to confirm theoretical expressions, and pair potentials and molecular interactions that exist in liquid alloys are not sufficiently quantified. Even semiempirical approaches do not fare well when applied to liquid alloy systems. There have been some attempts to correlate diffusivities with thermodynamic quantities such as partial molar enthalpy and free energy of solution, but their application has been limited to only a few systems. 

State-of-the-art calorimetry allows the accurate determination of enthalpies and free energies of ionization with micromolar amounts of weak acids and bases. The acidic pKs as well as the neutralization enthalpies of imidazole and pyrazole have been determined by calorimetry. 

In the case of azoles, where protonation enthalpies and free energies are linearly related (86UP1), we have... 

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