The Macroscopic and Microscopic Free Energies of Solvation of Silver Chromate and Silver Phosphate in Some Organic Solvents at 298.15K

The macroscopic free energies of solvation of silver chromate and silver phosphate in different solvents, acetonitrile (AN), N-methylformamide (NMFA), N-N, dimethylformamide (DMFA), propylene carbonate (PC), dimethyl suphoxide (DMSD), N-methyl-pyrrolidone (NMePy) and ethanol (ETOH) were estimated from the experimental solubility measurements at 298.15K. The macroscopic free energies ∆G(Ma) and free energy of transfer ∆ Gt (Ma) for Ag2CrO4 and Ag3PO4 in the organic solvents represent the macroscopic part of the free energies. The macroscopic free energies for both electrolytes were evaluated experimentally and compared with the microscopic free energies which calculated theoretically. The microscopic free energies of solvation of silver chromate and silver phosphate in the used solvents were theoretically calculated, which are the cavity, the lennard Jones, the induced, the volume and the dipole-dipole free energies and not only electrostatic energy as explained before. The macroscopic and microscopic free energies were compared and discussed.


Introduction
The solubility of an electrolyte is influenced by a wide range of factors, including ion association, variation in ionic activity coefficients, complexation and temperature. Solubility is an equilibrium property enable to thermodynamic parameters through the standard state free energy. Ion pairing can occur in dilute solutions for many electrolytes, particularly these with multivalent ions and for all electrolytes in concentrated solutions. Ion pairing is generally more pronounced in non-aqueous solvents which have lower dielectric constants than water. In effect, the ion pairs represent a reservoir of electrolyte in the solution and increase the solubility.The complexity of the system increases for usymmetrical electrolytes or for mixed electrolyte systems [1].Bjerrum [2] proposed, that the motion of ions would be coupled when the energy of attraction between them exceeded the thermal energy. For solely columbic interactions theory predicts a distance within which the electrostatic attraction between ions is greater than 2kT. Which will be sufficient to couple the motions of the ions .The treatment takes account of only electrostatic interactions and neglects molecularity of solvent.Nevertheless,in low concentration, strong interactions between ions and solvent molecules resulting in ion pair configuration. The three commonly assumed structures are, the first in which the ion retains their individual solvation shells, and so is separated by two solvent molecules. The second in which the ions share some part of their solvation shells so are separated by one molecule and the third where the ions are in contact and share a common solvation shell.
The presence of species such creates an experimental difficulty, the different techniques will have different sensitivities to the species present. Thus the conductance will see on the dissociated ions and the presence of ion pairs is determined by difference from experimental molar conductance and that expected for strong electrolyte [3].
The formation of complexes (complexation) provides a route to increased solubility. Several equivalent representations of the speciation in these systems have been used [4].
Good agreement between theory and experiment for evaluating the thermodynamic parameters has been obtained for a number of neutral compounds and gases in a variety of solvents [7][8][9][10][11].
Many authors like Bjerrum and others reported that the electrostatic energy plays important role in the solvation energy. In this work more work (novel) was done to explain the different types of electrostatic coulombic energy [11].
The aim of the present work is to extend the applicability of the scaled particle theory(especially applied for noble gases) as novel method for discussing the solvation of the electrolyte, silver chromate and silver phosphate in different organic solvents. Knowing the other factors affecting the solubility is very important here. Is the electrostatic energy play important role in the solubility or not.

Results and Discussion
The measured molar solubilities for Ag 2 CrO 4 and Ag 3 PO 4 in the organic solvents, AN, NMFA, DMFA, PC , DMSO, NMePY and EtOH as explained in Ref. (8) are listed in Tables (1 and 2).
Prediction of electrolyte activity coefficients is one of the classical problems in physical chemistry and is outlined in classical work [13]. The defining characteristic of ions is that they carry a net charge and so the principle interaction between ions are largest contribution to the activity coefficients are coulombic. Debye and Hückel solved the problem for system purely electrostatic interactions between point charges surrounded by a dielectric contnium .Therefore the extended Debye-Huckel equation was applied taking account of the ion size [14] From the activity coefficients ɣ± , calculated using Debye Hückel equation and from the molar solubility data. Values of pK sp Ag 2 CrO 4 were estimated by use of equation (1). 3 (1) The solvated radius of the Ag 2 CrO 4 electrolyte were calculated by summing the ionic radii of the salt [15] to the solvent radius for each organic solvent taken from ref. 13. The log activity coefficients (1ogɣ±) and the solubility products (pK sp ) calculated for Ag 2 CrO 4 in the solvents under consideration are represented in Table 1 also.
The measured solubilities for Ag 3 PO 4 as explained also in ref . 12 in the organic solvents, AN, NMFA, DMFA, PC, DMSO, NMePY and EtOH are listed in Table 2, from the activity coefficients ɣ±, calculated using Debye Hückel equation as explained in ref. 12 and from the molal solubility data. Values of pK sp were estimated by use of equation (2). were evaluated by the use of equation (3).
∆ G (Ma) = 2.303 RT pK sp (3) The macroscopic free energies of transfer ∆ G t (Ma) from ethanol (EtOH) as reference solvent to the organic solvent (s) could be calculated by using equation (4).
The macroscopic free energies ∆G(Ma) and free energy of transfer ∆ G t (Ma) for Ag 2 CrO 4 and Ag 3 PO 4 in the organic solvents, expressed the total solvation energies and represented in Tables (2 and 3). The values of the last macroscopic energies of transfer are divided into neutral (non-electrostatic) and electrostatic free energy of solvation.
Where r is the solvated radius for Ag 2 CrO 4 and for Ag 3 PO 4 which is the sum of both electrolyte radius and solvent radii [15,16]. ε is solvent dielectric constant [13]. The calculated values of ∆ G t (N) and ∆G t (el) for Ag 2 CrO 4 and Ag 3 PO 4 in the organic solvents are also given in Table s(2). It was shown from Table (2) that all the three types of free energies, ∆G t (Ma), ∆G t (el) and ∆G t (N) for Ag 2 CrO 4 and Ag 3 PO 4 have the following order: AN > PC > DMSO > NMFA > NMePy > DMFA For the calculation of the microscopic free energies for Ag 2 CrO 4 and Ag 3 PO 4 in the organic solvents under consideration at 298.15K, the Pierotti theory [5][6][7] was applies.
This model explains the solvation process through the creation of solute in the solvent followed by interaction. Therefore two difference types of free energies are present, cavity and interaction energy.
Where G c is the cavity free energy and G i is the microscopic interaction free energy the cavity free energy, necessary to form cavity of electrolyte size in solution was calculated by using Pierotti's theory based on Reiss model [13] and Ag 2 CrO 4 , Ag 3 PO 4 data are given in Table (3).
The interaction free energy (G i ) is a composite of Lennard Jones energy (G L ), the induced free energy (G ind ), the volume free energy (G v ) and the dipole-dipole free energy (G dip ).  Tables (5 and 6). It was concluded that the neutral free energy is the major part (big part) in the macroscopic experimental free energies for both electrolytes Ag 2 CrO 4 and Ag 3 PO 4 . Also it is concluded that cavity formation free energy is the major energy in the microscopic free energy [17][18][19][20].
Summing all the microscopic free energies give values in the same order as that of the macroscopic free energy values. Also it was concluded that the electrostatic coulombic energies for Ag 2 CrO 4 and Ag 3 PO 4 are the microscopic free energies, which can be theoretically calculated.These microscopic free energies are nobel and new for explaining the solvation behaviours of these important salts (Ag 2 CrO 4 and Ag 3 PO 4 ) in industry. The data were compared with that of the total macroscopic free energies evaluated from the experimental solubility data giving good results.This work gives a lot of data about the solubilities of the two used salts Ag 2 CrO 4 and Ag 3 PO 4 necessary in electroplating and photographic technology.