Thermodynamics solvation energy

The A X transition energy of liquid water increases with the addition of salts, and the increase in the energy linearly correlates with the thermodynamic solvation energies of the cations [43, 44]. Figure 4.6 shows the ATR-FUV spectra of 1 M Group I metal nitrate solutions and pure water at 25 °C. The same counter-anion, nitrate, was employed for all the electrolyte solutions to negate the effect of counter-... 

Correlation methods discussed include basic mathematical and numerical techniques, and approaches based on reference substances, empirical equations, nomographs, group contributions, linear solvation energy relationships, molecular connectivity indexes, and graph theory. Chemical data correlation foundations in classical, molecular, and statistical thermodynamics are introduced. 

Kamlet-Taft Linear Solvation Energy Relationships. Most recent works on LSERs are based on a powerfiil predictive model, known as the Kamlet-Taft model (257), which has provided a framework for numerous studies into specific molecular thermodynamic properties of solvent—solute systems. This model is based on an equation having three conceptually expHcit terms (258). 

It has been possible to obtain thermodynamic data for the ionization of alkyl chlorides by reaction with SbFs, a Lewis acid, in the nonnucleophilic solvent S02C1F. It has been foimd that the solvation energies of the carbocations in this medium are small and do not differ much from one another, making comparison of the nonisomeric systems possible. As long as subsequent reactions of the carbocation can be avoided, the thermodynamic characteristics of this reaction provide a measure of the relative ease of carbocation formation in solution. 

Solvation can be studied by thermodynamic methods, often combined with ex-trathermodynamic assumptions so as to express results for individual ions (rather than for neutral electrolytes). The solvation energy is the free energy change upon transferring a molecule or ion from the gas phase into a solvent at infinite dilution. This sometimes can be obtained from a consideration of the following processes, written for a 1 1 electrolyte ... 

Figure 16.2 An exainple of a thermodynamic cycle for calculating differences in solvation energies...

The main point of this exercise and considerations is that you can easily examine the feasibility of the desolvation hypothesis by using well-defined thermodynamic cycles. The only nontrivial numbers are the solvation energies, which can however be estimated reliably by the LD model. Thus for example, if you like to examine whether or not an enzymatic reaction resembles the corresponding gas-phase reaction or the solution reaction you may use the relationship... 

Thus it is concluded that while destabilization of the ground-state charges may be used in enzymes to reduce Ag, it is not used in enzymes that optimize kzJKM. Furthermore, we argue that the feasibility of any proposed desolvation mechanism can be easily analyzed (and in most cases disproved) by the reader once the relevant thermodynamic cycle is defined and the solvation energies of the reacting fragments are estimated. 

When the gas-phase reactions, such as the relative acidities or basicities were compared with their counterparts in solution (in a solvent such as water) it was generally found16,17 that the energetics in the solvent were strongly affected by solvation effects and particularly the solvation of the ionic reactants. Relationships between the gas-phase and solution-phase reactions and the solvation energies of the reactants are generally obtained through thermodynamic cycles. From the cycle,... 

Because the acid dissociation constants in solution are generally known, and also, often the solvation energies of the neutral AH have been determined by neutral gas-phase solution equilibria, equation 8 can be used to obtain the sum of the solvation energies AG°ol(A-) + AG°ol (H30+). When this approach is applied to a series of acids AH, values for the solvation energies AG°ol (A-), relative to the constant AG, (H30+), can be obtained. Such thermodynamic determinations of the... 

The complexation of the alkaline earth metals is reminiscent of the behaviour of several of the naturally occurring antibiotics and, like the latter, the crown often exhibits remarkable selectivity for particular ions. The thermodynamic factors underlying the selectivity of many of the crowns have been studied in some depth and the results related to such parameters as cavity size, number of donor atoms present, possible ring conformations on complex formation and the solvation energies of the various species involved. 

It is especially interesting to examine the thermodynamics of reaction (i) for the trityl and dityl (diphenylmethyl) cations as initiating salts for isobutylene because we can thus provide a theoretical explanation of the experimental fact that trityl salts do not initiate isobutylene polymerisation, but dityl salts do Table 2 shows the relevant data. The solvation energy terms have been omitted since on the basis of a... 

Although the potential energy functions can be made to reproduce thermodynamic solvation data quite well, they are not without problems. In some cases, the structure of the ion solvation shell, and in particular the coordination number, deviates from experimental data. The marked sensitivity of calculated thermodynamic data for ion pairs on the potential parameters is also a problem. Attempts to alleviate these problems by introducing polarizable ion-water potentials (which take into account the induced dipole on the water caused by the ion strong electric field) have been made, and this is still an active area of research. 

Various potentiometric indicator electrodes work as sensors for ion solvation. Metal and metal amalgam electrodes, in principle, respond in a thermodynamic way to the solvation energy of the relevant metal ions. Some ion-selective electrodes can also respond almost thermodynamically to the solvation energies of the ions to which they are sensitive. Thus, the main difficulty in the potentiometric study of ion solvation arises from having to compare the potentials in different solvents, even though there is no thermodynamic way of doing it. In order to overcome this difficulty, we have to employ a method based on an extra-thermodynamic assumption. For example, we can use (1) or (2) below ... 

Although the entire discussion of electrochemistry thus far has been in terms of aqueous solutions, the same principles apply equaly well to nonaqueous solvents. As a result of differences in solvation energies, electrode potentials may vary considerably from those found in aqueous solution. In addition the oxidation and reduction potentials characteristic of the solvent vary with the chemical behavior of the solvent. as a result of these two effects, it is often possible to carry out reactions in a nonaqueous solvent that would be impossible in water. For example, both sodium and beryllium are too reactive to be electroplated from aqueous solution, but beryllium can be electroplated from liquid ammonia and sodium from solutions in pyridine. 0 Unfortunately, the thermodynamic data necessary to construct complete tables of standard potential values are lacking for most solvents other than water. Jolly 1 has compiled such a table for liquid ammonia. The hydrogen electrode is used as the reference point to establish the scale as in water ... 

As we have mentioned at the beginning of this section, in condensed media, besides the free and quasi-free states, an ejected electron can also be in the solvated state. The energy released in this case is the solvation energy Vs. From the thermodynamical point of view, the ionization with solvation of the ejected electron is more advantageous since the required energy equals 7C + Vs (Vs is always negative and is of the order of 1-2 eV). Physically, such an ionization may correspond to preionization from an excited state as a result of the electron tunneling from the excited molecule to the nearest trap (see the discussion in Refs. 197 and 198). 

I cite three papers to show that standard continuum calculations can give satisfactory first-principles pKa values Shields and coworkers used a thermodynamic cycle with gas phase and continuum calculations to obtain satisfactory results for six simple carboxylic acids [46]. These were absolute calculations in the sense that no acid was used as a reference point, although the experimental gas phase free energy and aqueous solvation energy of the proton were resorted to. Not quite as esthetically satisfying perhaps, were relative calculations in which acetic acid was used as a reference compound [47]. Similar to the absolute acid calculations was work with phenols that was said to be among the most accurate of any such calculations for any group of compounds [48]. 

Statistical thermodynamics gives us the recipes to perform this average. The most appropriate Gibbsian ensemble for our problem is the canonical one (namely the isochoric-isothermal ensemble N,V,T). We remark, in passing, that other ensembles such as the grand canonical one have to be selected for other solvation problems). To determine the partition function necessary to compute the thermodynamic properties of the system, and in particular the solvation energy of M which we are now interested in, of a computer simulation is necessary [1],... 

The use of thermodynamically averaged solvent distributions replaces the discrete description with a continuum distribution (expressed as a distribution function). The discrete description of the system, introduced at the start of the procedure, is thus replaced in the final stage by a continuous distribution of statistical nature, from which the solvation energy may be computed. Molecular aspects of the solvation may be recovered at a further stage, especially for the calculation of properties, but a new, less extensive, average should again be applied. 

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