Ionization thermodynamics

Gibbs energy of formation in solution Gibbs energy of solution heat capacities, entropies ionization thermodynamics solubilities... 

The Monte Carlo approach, although much slower than the Hybrid method, makes it possible to address very large systems quite efficiently. It should be noted that the Monte Carlo approach gives a correct estimation of thermodynamic properties even though the number of production steps is a tiny fraction of the total number of possible ionization states. 

The ketone is added to a large excess of a strong base at low temperature, usually LDA in THF at -78 °C. The more acidic and less sterically hindered proton is removed in a kineti-cally controlled reaction. The equilibrium with a thermodynamically more stable enolate (generally the one which is more stabilized by substituents) is only reached very slowly (H.O. House, 1977), and the kinetic enolates may be trapped and isolated as silyl enol ethers (J.K. Rasmussen, 1977 H.O. House, 1969). If, on the other hand, a weak acid is added to the solution, e.g. an excess of the non-ionized ketone or a non-nucleophilic alcohol such as cert-butanol, then the tautomeric enolate is preferentially formed (stabilized mostly by hyperconjugation effects). The rate of approach to equilibrium is particularly slow with lithium as the counterion and much faster with potassium or sodium. 

TABLE 1-51. THERMODYNAMICS OF THE AQUEOUS IONIZATION OF THIAZOLIUM IONS (322). 

Parallel to the determination of pK, the thermodynamic constants of the ionization reaction... 

TABLE III-15. THERMODYNAMIC CONSTANTS OF IONIZATION FOR ALKYL-THIAZOLES (151)... 

Source J. J. Christensen, L. D. Hansen, and R. M. Izatt, Handbook of Proton Ionization Heats and Related Thermodynamic... 

Hydrogen chloride is completely ionized in aqueous solutions at all but the highest concentrations. Thermodynamic functions have been deterrnined electrochemicaHy for equations 7 and 8. Values are given in Table 7. 

Internal and External Phases. When dyeing hydrated fibers, for example, hydrophUic fibers in aqueous dyebaths, two distinct solvent phases exist, the external and the internal. The external solvent phase consists of the mobile molecules that are in the external dyebath so far away from the fiber that they are not influenced by it. The internal phase comprises the water that is within the fiber infrastmcture in a bound or static state and is an integral part of the internal stmcture in terms of defining the physical chemistry and thermodynamics of the system. Thus dye molecules have different chemical potentials when in the internal solvent phase than when in the external phase. Further, the effects of hydrogen ions (H" ) or hydroxyl ions (OH ) have a different impact. In the external phase acids or bases are completely dissociated and give an external or dyebath pH. In the internal phase these ions can interact with the fiber polymer chain and cause ionization of functional groups. This results in the pH of the internal phase being different from the external phase and the theoretical concept of internal pH (6). 

Local Thermodynamic Equilibrium (LTE). This LTE model is of historical importance only. The idea was that under ion bombardment a near-surface plasma is generated, in which the sputtered atoms are ionized [3.48]. The plasma should be under local equilibrium, so that the Saha-Eggert equation for determination of the ionization probability can be used. The important condition was the plasma temperature, and this could be determined from a knowledge of the concentration of one of the elements present. The theoretical background of the model is not applicable. The reason why it gives semi-quantitative results is that the exponential term of the Saha-Eggert equation also fits quantum-mechanical expressions. 

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. 

The quantities AH and AH require consideration. These are molar heats of ionization at the conditions of the kinetic measurements. The thermodynamic heat of ionization of water in pure water, A//°, is a function of temperature Hamed and Owen - pp give for this quantity... 

These same dependencies will, in general, apply to the heat of ionization of the buffer acid, AH. Thermodynamic quantities, namely, AH°, have been reported for some buffer substances, and it is found that A//° is temperature dependent. Bates and Hetzer studied the temperature dependence of for the important buffer tris(hydroxymethyl)aminomethane (TRIS), finding... 

Table 11. Thermodynamic functions of interaction between Hb and CP as a function of the degree of CP ionization...

The relationship of thermodynamic functions of selective bonding of Hb to a series of carboxylic CP in the variation of the degree of ionization of carboxylic groups is expressed by the effect of enthalpy-entropy compensation (Fig. 18). The compensation effect of enthalpy and entropy components is the most wide-spread characteristic of many reactions in aqueous solutions for systems with a cooperative change in structure [78],... 

R.C. Oliver et al, USDeptCom, Office Tech-Serv ..AD 265822,(1961) CA 60, 10466 (1969) Metal additives for solid proplnts formulas for calculating specific impulse and other proplnt performance parameters are given. A mathematical treatment of the free-energy minimization procedure for equilibrium compn calcns is provided. The treatment is extended to include ionized species and mixing of condensed phases. Sources and techniques for thermodynamic-property calcns are also discussed... 

The major source of error In calculating the free energies of Pu0(g) and Pu02(g) from Battles et al. probably results from the derived equations for the partial pressures of 0(g) and Pu(g) as a consequence of uncertainties In Ionization cross sections. The thermodynamic assessments of Ackermann et al. Involve extrapolations of oxygen potentials reported by Markin and Rand (4) In temperature of the order of 500 K. However, a second and third... 

In contrast to the situation observed in the trivalent lanthanide and actinide sulfates, the enthalpies and entropies of complexation for the 1 1 complexes are not constant across this series of tetravalent actinide sulfates. In order to compare these results, the thermodynamic parameters for the reaction between the tetravalent actinide ions and HSOIJ were corrected for the ionization of HSOi as was done above in the discussion of the trivalent complexes. The corrected results are tabulated in Table V. The enthalpies are found to vary from +9.8 to+41.7 kj/m and the entropies from +101 to +213 J/m°K. Both the enthalpy and entropy increase from ll1 "1" to Pu1 with the ThSOfj parameters being similar to those of NpS0 +. Complex stability is derived from a very favorable entropy contribution implying (not surprisingly) that these complexes are inner sphere in nature. 

This calculation demonstrates that a nonpolar solvent can accelerate S 2 reactions. However, this is not what we are asking the relevant quantity is the overall activation energy for the reaction in a nonpolar enzyme which is surrounded by water. Thus, as is indicated in the thermodynamic cycle of Fig. 9.3, we should include the energy of moving the ionized R-O- from water to the nonpolar active site (AAg j1). Thus the actual apparent change in activation barrier is... 

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