Dilution, Gibbs energy

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. 

Here /g,hq and y ,ss are the activity coefficients of component B in the liquid and solid solutions at infinite dilution with pure solid and liquid taken as reference states. A fus A" is the standard molar entropy of fusion of component A at its fusion temperature Tfus A and AfusGg is the standard molar Gibbs energy of fusion of component B with the same crystal structure as component A at the melting temperature of component A. 

The local compostion model is developed as a symmetric model, based on pure solvent and hypothetical pure completely-dissociated liquid electrolyte. This model is then normalized by infinite dilution activity coefficients in order to obtain an unsymmetric local composition model. Finally the unsymmetric Debye-Huckel and local composition expressions are added to yield the excess Gibbs energy expression proposed in this study. 

As an example, consider phenol as the solute and water and toluene as two solvents. The parameters for phenol are A = 5.7, A = -12.9, A = -18.3, and A5 = 0.0091, whereas Aq is unspecified, but a negative quantity. With the solvent parameters from Tables 2.1 and 2.3, the standard Gibbs energy of solvation of phenol in water becomes Aq + 3.39, and in toluene Ao -1- 4.11 kJ mol". It is seen that As i,Gb is lower in water than in toluene, so that the transfer of phenol from water to toluene entails an increase in AjoItGb. The consequence of this is that phenol prefers water over toluene, since work would be required to make this transfer. It should be remembered that the standard Gibbs energies of solvation refer to the state of infinite dilution of the solute (solute-solute... 

From Eq. 6-24 it follows that the Gibbs energy change for dilution from one activity a1 to another a2 is ... 

The molar Gibbs energy of micelle formation is the Gibbs energy difference between a mole of monomers in micelles and the standard chemical potential in dilute solution ... 

As a last example, we consider the binary phase diagram of water and 1-butanol (Figs. 6.16 and 6.17). There is a negative heat of mixing, HE, but a positive excess Gibbs energy of mixing, GE. The infinite dilution activity coefficient of 1-butanol in water is very... 

The Legendre transform that defines the further transformed Gibbs energy G", which provides the criterion for spontaneous change and equilibrium in dilute... 

This calculation using equcalcc involves the problem that Af G° H2 O) is used in the calculation of the equilibrium constant K, but the expression for the equilibrium constant does not involve the concentration of H2 O. Thus in effect oxygen atoms are not conserved, because in dilute aqueous solutions they are drawn for th essentially infinite reservoir of the solvent. Therefore, the further transformed Gibbs energy G has to be used. The conservation matrix with C and P as components and GlcP2-, Glc, and HP042"as species is given by... 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

Thus the activity coefficient of a species in solution becomes unity as the species becomes pure. At the other limit, where xf - 0 and species i becomes infinitely dilute, In y,- is seen to approach some finite limit, which we represent by In y In the limit as - 0, the dimensionless excess Gibbs energy GB/RT as given by Eq. (11.69) becomes... 

AG 0°° partial excess Gibbs energy of mixing at infinite dilution of a solute i in a... 

Molar heat capacities Cp "(crystalline reactant) can be determined down to about 10 K, and the Debye equation that applies at very low temperatures can be used to estimate heat capacities below 10 K. The Debye equation is Cpm ° = kT Heat of combustion measurements can be used to obtain AfH ° (298.15 K) of the crystalline substance at 298.15 K, and the heat of solution makes it possible to calculate AfH ° (aq soln,298.15 K). When third law measurements have been made, the standard Gibbs energy of formation of the substance in dilute aqueous solution can be calculated using... 

---