Gibbs energy 96 Ionization

Fig. 1.1 (a) The ionization enthalpies of dipositive lanthanide ions with configurations of the type [Xe]4f" (upper plot left-hand axis), (b) The standard Gibbs energy change of reaction 1 (lower plot right-hand axis estimated value ... 

We shall look more closely at this equation. On one hand, the standard chemical potentials of Ox and Red depend on their standard Gibbs solvation energies, AG ox and AG°Red, and, on the other hand, on the standard Gibbs energy of ionization of Red in the gas phase, AGlon Red. This quantity is connected with the ionization potential of Red, /Rcd, which is, however, a sort of enthalpy so that it must be supplemented by the entropy term, -TA5 on Red. Thus, Eq. (3.1.17) is converted to the form... 

The difference between the electronic energies of the final and initial states must include the energy of ionization of the ion B(z-1)+ in vacuo (where its ionization potential is complemented by the entropy term TA5/), the interaction energy of the ions Bz+ and B(z-1)+ with the surroundings, i.e. the solvation Gibbs energies, and finally the energy of an electron at the Fermi level in the electrode. These quantities can be expressed most simply... 

The standard enthalpy change for the ionization of water is +55.83 kJ mol", which means that the reverse reaction, which occurs when acids are neutralized by bases, is exothermic, i.e. ArH = —55.83 kJ mol-1. The corresponding change in standard Gibbs energy is —79.9 kJ mol - . The reaction ... 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

By introducing this scale, we can separate the total emf of the cell into two quantities, for which the contributions (AGsubi, AGion, and AG are the sublimation, ionization, and real hydration -> Gibbs energies, respectively) can be experimentally determined. For the -> hydrogen electrode it holds that... 

Thus, the Gibbs energy difference AAG for the ionization of a mol of HA in solvent 1 and solvent 2 with relative permittivities er(i) and r(2), respectively, provided that the radii of the reactants are the same in both solvents, is given by Eq. (4-9). 

This kind of procedure, i. e. empirical estimation of solvent polarity with the aid of actual chemical or physical reference processes, is very common in chemistry. The well-known Hammett equation for the calculation of substituent effects on reaction rates and chemical equilibria, was introduced in 1937 by Hammett using the ionization of meta-ox /iflra-substituted benzoic acids in water at 25 °C as a reference process in much the same way [10]. Usually, the functional relationships between substituent or solvent parameters and various substituent- or solvent-dependent processes take the form of a linear Gibbs energy relationship, frequently still referred to as a linear free-energy (LFE) relationship [11-15, 125-127]. 

The thermodynamic functions for the first and second ionization processes were evaluated from Equations 6, 7, and 8 (for pKi) and 12, 13, and 14 (for pK2) in 10, 30, and 50 mass % THF-H20, respectively, using the customary thermodynamic formulae. The values of the standard Gibbs energy (AG°), enthalpy (AH°), entropy (AS°), and heat capacity... 

Table 6-6 Ionization of Acids at 25°C Gibbs Energies of Hydrolysis at 25°C... 

Their partial pressure (J ) should be free of large error from Error does arise from uncertainties in the evaporation coefficients, ionization cross sections and total flux of species ( ). An extreme example of this error is the formation of o-AlgOg, which is biased by -9 kcal mol" if calculated from the reported ( ) pressures of Al and 0. Our assigned uncertainty includes contributions from this error and that of the Gibbs-energy function. 

The properties selected for evaluation include most of the thermodynamic properties which we normally evaluate in the course of our work in the data centers. They include enthalpies of formation, solution, and dilution Gibbs energies of formation and solution entropies of formation and solution heat capacities and equilibrium constants (solubility, ionization, etc) as well as activity and osmotic coefficients, relative apparent molal enthalpies and apparent molal heat capacities. 

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