Enthalpy electrostatic contribution

A thermodynamic analysis regarding the relation between enthalpy and entropy values on the one hand and non-bulk electrostatic contributions on the other leads to the same result144). 

The transformed enthalpy of a biochemical reaction is a function of temperature, pH, and ionic strength. Knowledge of AfG°, AfH°, and CPm for all the species in a biochemical reaction makes it possible to calculate ArG °, ArH °, ArC P°, and K for the biochemical reaction at the desired T, pH, and ionic strength. Note that when ions are involved there is an electrostatic contribution that varies with temperature (see Section 3.7). 

Since the electrostatic component of AGsoi depends on the permittivity of the solvent, e, and on the cavity size (represented by means of the vector normal to the cavity surface, n), the electrostatic contribution to the enthalpy of solvation, A//ele, can be determined as indicated in Eq. 4-10 ... 

Previous studies have shown that there is a correlation between the enthalpy of hydration of alkanes and their accessible surface area [30,31] or related magnitudes. Moreover, relationships between the hydration numbers calculated from discrete simulations for hydrocarbons and both the free energy and enthalpy of hydration of these molecules have also been reported [32] and have been often used to evaluate solvation enthalpies. Analysis of our results, illustrates the existence of a linear relationship between A//n eie and the surface of the van der Waals cavity,. SVw, defined in MST computations for the calculation of the non-electrostatic contributions (Figure 4-1). In contrast, no relationship was found for the electrostatic component of the hydration enthalpy (A//eie data not shown). Clearly, in a first approximation, one can assume that the electrostatic interactions between solute and solvent can be decoupled from the interactions formed between uncharged solutes and solvent molecules. 

Notwithstanding the fact that several literature data on the enthalpy of charge formation are not yet well established (agreement between directly obtained calorimetric data and values derived from dpH°/dT has not always verified and tlie absence of an electrostatic contribution has not always been... 

Empirically determined parameters, Ea and Ca, are assigned to an acid while, Eb and Cb are assigned to a base. When substituted into equation (2), they give the enthalpy of adduct formation for the acid-base pair. Ea and Eb parameters supposedly represent the electrostatic contributions to adduct stability, while Ca and Cb parameters are the susceptibility of the acid and base, respectively, to form covalent bonds. With increasing amount of reliable enthalpy data, the E C model was extended to many different acids and bases. 

In the symmetric experiment the difference between the initial pH and pHp c is the same as the difference between pHp c and the final pH, so that the surface potentials of the initial and final states are same in magnitude but opposite in sign, and consequently the electrostatic contributions cancel. Accordingly, the calculated enthalpies are the standard reaction enthalpies. These standard enthalpies are defined in the same way as those which one obtains from the temperature dependency of pHp c-... 

Energies in kcal mol unrelaxed HF/6-31G(d) geometries the total contribution (TOT ) to the activation free enthalpy is due to the cavitation+solute/solvent dispersion+solvent structural rearrangement term (CDS ) and to the electronic+nuclear- polarization term (ENP ) in the AMSOL model in the Tomasi model CDR is the cavitation-rdispersion+repulsion term and ELEC is the electrostatic contribution ab initio calculations are standard HF/6-31G(d). 

In all the evaluations of Table 4, the solvent effects on the activation free enthalpies are positive, increase with increasing solvent dielectric constants and tend to be larger for the endo than for the exo adducts. This behaviour, in accord with the experimental trend, is due to the electrostatic contribution the CDS and CDR contributions, in fact, are rather independent of the isomeric reaction considered and, moreover, appear to obtain comparable values in every 1,3-dipolar cycloaddition. For the Tomasi parametrisation in water, for example, the CDR" contribution for the cycloadditions of diazomethane and nitrile oxides to substituted alkenes amounts to -1.85 0.14 kcal mok This finding can be traced back to the view that the CDR term is approximately proportional to the solvent accessible surface area (the cavity area) of solutes and to the feature of TSs of having very alike structures of the new forming pentatomic ring so that the changes of the cavity areas from reactants to TSs are similar. 

Despite the simplifying assumptions in the derivation, such as assuming that the medium, water, is a continuum with no structure, and that the only work is electrostatic, and even more assumptions in calculating the properties of individual ions from the measured properties of electrolytes, as estimated by the Born function comes reasonably close to the measured Gibbs energy of ion solvation, as shown in Figure 6.7. Other thermodynamic properties such as the volume, entropy and enthalpy of solvation can also be obtained by appropriate differentiation of Equation (6.5). As a result, ever since its inception the Born equation has been used as a primitive model for the electrostatic contribution to the properties of an ion in a dielectric solvent. 

Since depends on and is completely independent of T, it is at once apparent that there is no electrostatic contribution to the enthalpy, and that the constant-pressure heat capacity is just 3Nk, or exactly what would have been obtained for an ideal one-di-... 

The absence of any difference between the plasma and an ideal gas as regards the enthalpy means that the electrostatic part of the free energy is entirely an entropy term the electrostatic contribution to the entropy is therefore simply... 

A further check was obtained through the study of the effects of alcohols on the oxygen affinity of hemoglobin at various temperatures. This allowed the determination of non bulk-electrostatic contributions, due to the presence of alcohols, to the standard enthalpy and entropy differences between T and R states of hemoglobin. 

More recently, in addition to the adsorption equilibria studies, calorimetry was employed in examining of the metal oxide aqueous interface. The results deal either with relatively simple situations, such as protonation and deprotonation reactions at the surface or with the heats of the adsorption of organic molecules onto surfaces. In both cases, one encounters two problems. The first one is due to the fact that, upon addition of a reactant, several reactions take place in the calorimeter. In order to evaluate enthalpy of a specific surface reaction, one has to be able to distinguish between different contributions to the heat and also to determine the extents of all reactions taking place in the system. The next problem is related to the electrostatic contribution to the enthalpy. Recently, an experimental design was developed which enabled the proper interpretation of the calorimetric data so that one... 

Thus, from these measurements, one cannot obtain the singular reaction enthalpy but only the difference, which does not include the electrostatic contribution. This enthalpy difference may be obtained from the slope in presentation pHp, vs VT. 

As stated in (22), die experiment in which initial and final pH values are related to p.z.c. by (19) yields the difference in standard enthalpies describing chemical interactions only and does not incorporate the electrostatic effects, just as in the case of the value obtained from p.z.c. dependence on temperature. The compensation of the electrostatic effect is based on the assumption of symmetrical surface potential with respect to p.z.c. and does not necessarily assume Nemstian behavior. It is sufficient that surface equilibria results, e.g., half pH unit below p.z.c., positive surface potential equal in magnitude to that one half pH unit above p.z.c. If such a behavior is found within a certain temperature range, then the derivative of potential with respect to temperature is again the same in magnitude but opposite in sign. Since the electrostatic contribution to the total enthalpy exhibits the same behavior as a derivative of the potential, the compensation of electrostatic contribution to the enthalpies takes place. 

The method described here enables the proper assignment of the enthalpy to a certain surface reaction. It also makes possible to avoid electrostatic contribution to the enthalpy. The next step should deal with different initial and final conditions to enable the determination of singular values of AJf° and Ab// and also to examine the electrostatic effect on the enthalpy. 

It is worth noting that, depending on the type of PE used, the electrostatic contribution for PEs are the dominating force and therefore it is possible to omit the Hory enthalpy term in this cases [23]. If the PE is very weak, the free enthalpy of dilution, AH, is only correctly obtained, when the electrostatic and Flory-Huggins polymer dilution enthalpy terms are added [49]. 

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