1. 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].

Pierotti theory[5] applies the scaled particle theory[6] to estimate solubilities, heats, entropies and molar capacities of solutions.

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[7-11].

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.

2. Experimental

Ag₂CrO₄ and Ag₃PO₄ are of the type Riedel-de-Häen AG, Seelze- Hannover was used. acetonitrile (AN), N-N, dimethylformamide (DMFA), dimethylsulphoxide (DMSO) and ethanol (EtOH) were obtained from BDH. N- methylformamide (NMFA), propylene carbonate (PC) and N- methyle-pyrrolidone (NMePy) were obtained from Merck (zur analyse). The solubilities of Ag₂CrO₄ and Ag₃PO₄ in the organic solvents under consideration were done gravimetrically with at least three measurments as explained in previous works[12-14].

3. Results and Discussion

The measured molar solubilities for Ag₂CrO₄ and Ag₃PO₄ 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 Ag₂CrO₄ were estimated by use of equation (1).

(1)

The solvated radius of the Ag₂CrO₄ 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 Ag₂CrO₄ in the solvents under consideration are represented in Table 1 also.

The measured solubilities for Ag₃PO₄ 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).

(2)

The experimental macroscopic free energies of solvation of Ag₂CrO₄ and Ag₃PO₄ in the organic solvents at 298.15K were evaluated by the use of equation (3).

(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).

(4)

The macroscopic free energies ∆G(Ma) and free energy of transfer ∆ G_t (Ma) for Ag₂CrO₄ and Ag₃PO₄ 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.

(5)

The electrostatic free energy can be calculated by using Born equation as follows[14].

Table (1). Molal solubilities, 1og activity coefficients (1ogɣ±) and solubility products of Ag2CrO4 in different solvents at 298.15 K Solvent m molal 1og ɣ± pKsp AN 1.5737x10-4 -0.0063 10.8072 NMFA 2.5495 x10-3 -0.0504 7.1938 DMFA 1.7446 x 10-4 -0.0132 3.1489 PC 1.8331 x10-4 -0.0135 10.6074 DMSO 3.0444x10-4 -0.0174 9.9474 NMePY 3.7168 x10-4 -0.0609 6.6894 EtOH 1.8325 x 10-4 -0.0135 3.1349

Table (2). Molal solubilities, 1og activity coefficients (1ogɣ±) and solubility products of Ag3PO4 in different solvents at 298.15K Solvent m molal 1og ɣ± pKsp AN 1.6237x10-5 -0.0020 17.7245 NMFA 1.3788x10-3 -0.0187 9.9918 DMFA 1.8699x10-4 -0.0069 13.5116 PC 6.7755x10-5 -0.0041 15.2406 DMSO 1.3346x10-4 -0.0058 14.0613 NMePY 1.5699x10-3 -0.0200 9.7651 EtoH 3.5986x10-4 -0.0096 12.3345

Table (3). Macroscopic experimental, electrostatic and neutral free energies for Ag2CrO4 in different solvents at 298.15 K (in kJ/mole) Solvent ∆ G(exp) Mac ∆ Gt (exp) Mac ∆ Gt (el) ∆ Gt (N) AN 61.4748 43.6423 1.1725 42.4698 NMFA 40.9159 23.0834 -6.3430 39.4264 DMFA 17.9118 0.0793 1.4640 -1.3847 PC 60.3381 42.5056 0.9238 41.5808 DMSO 56.5837 38.7512 -0.5530 39.3042 NMePy 38.0513 20.2183 2.0055 18.2133 EtOH 17.8325 0 0 0

Table (4). Macroscopic experimental, electrostatic and neutral free energies for Ag3PO4 in different solvents at 298.15 K (in kJ/mole) Solvent ∆ G(exp) Mac ∆ Gt (exp) Mac ∆ Gt (el) ∆ Gt (N) AN 100.8222 30.6599 1.0737 29.5862 NMFA 32.3567 -37.8056 -4.4626 -33.34 DMFA 76.8580 6.6957 0.9104 5.785 PC 86.6931 16.5308 -1.9366 18.4671 DMSO 79.9848 9.8225 -0.4046 10.22 NMePy 55.5468 -14.6155 1.4905 13.125 EtOH 70.1623 0 0 0

(6)

Where r is the solvated radius for Ag₂CrO₄ and for Ag₃PO₄ which is the sum of both electrolyte radius and solvent radii[15,16]. is solvent dielectric constant[13]. The calculated values of ∆ G_t (N) and ∆G_t (el) for Ag₂CrO₄ and Ag₃PO₄ 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 Ag₂CrO₄ and Ag₃PO₄ have the following order:

AN > PC > DMSO > NMFA > NMePy > DMFA

For the calculation of the microscopic free energies for Ag₂CrO₄ and Ag₃PO₄ in the organic solvents under consideration at 298.15K, the Pierotti theory[5-7] 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.

(7)

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 Ag₂CrO_{4 ,} Ag₃PO₄ 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).

(8)

All the microscopic free energies for Ag₂CrO₄ and Ag₃PO₄ solutions were calculated as explained in ref. 13 and the evaluated data are presented in Tables (5 and 6).

Table (5). The microscopic free energies of solvation of Ag2CrO4 in some organic solvents at 298.15K (in kJ/mole) Solvent Gc GL Gind Gv Gdip AN 88.9629 71.6309 1.8219 18.0307 -161.0510 NMFA 93.9556 75.4451 1.9245 15.5678 -100.6469 DMFA 84.4032 83.99.07 2.1421 14.1245 - PC 81.287 87.2097 2.2223 11.8677 -103.0410 DMSO 87.2097 81.2873 2.0734 13.6777 -80.1303 NMePy 33.3810 81.3217 2.3484 12.0739 - EtOH 95.3545 37.3149 1.7870 17.2518 -216.77

Table(6). The microscopic free energies of solvation of Ag3PO4 in some organic solvents at 298.15K (in kJ/mole) Solvent Gc GL Gind Gv Gdip AN 99.1491 79.8326 2.0305 20.0952 -179.4913 NMFA 104.7135 84.0835 2.1448 17.3503 -112.1709 DMFA 94.0673 93.6076 2.3873 15.7417 - PC 90.5943 97.1952 2.4767 13.2265 -114.8391 DMSO 97.1952 90.5946 2.3109 15.2430 -89.3052 NMePy 86.2411 90.6330 2.6173 13.4564 - EtOH 106.2725 81.7095 2.0461 19.2271 -241.5901

It was concluded that the neutral free energy is the major part (big part) in the macroscopic experimental free energies for both electrolytes Ag₂CrO₄ and Ag₃PO₄. Also it is concluded that cavity formation free energy is the major energy in the microscopic free energy[17-20].

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 Ag₂CrO₄ and Ag₃PO₄ 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 (Ag₂CrO₄ and Ag₃PO₄ ) 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 Ag₂CrO₄ and Ag₃PO₄ necessary in electroplating and photographic technology.