International Journal of Theoretical and Mathematical Physics 2012, 2(2): 1-4 DOI: 10.5923/j.ijtmp.20120202.01 The Microscopic Free Energies of Solvation for K + , Rb + and Cs + in Mixed Methanol (MeOH)-Dimethylformamide (DMFA) Solvents at 298.15 K Esam A. Gomaa Chemistry Department, Faculty of Science, Mansoura University,35516-Mansoura, Egypt Abstract The microscopic charging ( ∆ G t charging), ion-dipole ( ∆ G t ion-dipole) and ion-induced dipole ( ∆ G t ion- induced dipole) free energies of transfer for some ions from methanol to mixed methanol (MeOH)-dimethylformamide (DMFA) solvents were calculated. These ions are potassium, rubidium and cesium. These theoretical free energies were compared with that of experimental values and the difference excess free energies of solvation were discussed. I t was ob- served that the excess free energies for all ions are positive and follow the following order: ∆ G T (excess) K + > ∆ G T (excess) Rb + > ∆ G T (excess) Cs + . Indicating more solvation behaviour by increasing the percentage of DMFA in the mixed solvents due to more attraction of these ions in the range rich in DMFA Keywords Microscopic free energy, potassium,robedium, cesium,excess free energy, organic solvents 1. Calculations and Results The electrostatic free energies of transfer ∆ G t (el) is known as the microscopic free energies of interaction[1]. The solvation free energies of ions is important in the ap- plications of all fields,chemistry,physics and theoretical sciencesto obtain the corresponding energies of salts.Also chemical reactions can be theoreticaly expected to happen by knowing the free energy values for reactants and products. When we know the free energies of the ions we can easily obtain that for any simple, heavy element, lanthanide and actinide salts,which facilitate the explanation of different reactions.The salvation free energy of an ion has been for- mulated by number of authors cited by Covington[1] as a composite of neutral and electrostatic contribution.A neutral part may be considered to be equivalent to the salvation energy of uncharged molecules analogous to the ion in structure and size. The electrostatic contribution of the free energy is not exact evaluated before.In this work we did simple view to evaluate the electrostatic free energies and compare it with the available experimental values done by using the asymmetric Ph 4 AsPh 4 B (tetraphenylarsonium tetraphenylborate) assumption for evaluating single ion thermodynamics[Popovych...][2]. * Corresponding author: esam1947@yahoo.com (Esam A. Gomaa) Published online at http://journal.sapub.org/ijtmp Copyright © 2012 Scientific & Academic Publishing. All Rights Reserved Transfer values are the difference in the thermodynamic functions in solvents or mixed solvents and that of methanol as reference solvent. The electrostatic microscopic free en- ergies of transfer is composite of energy contributions from charging a sphere, ion induced dipole, ion induced di- pole/and the ion quadrupole interactions. The last one the ion-quadrupole interaction are very small that can be ne- glected[1]. The charging of sphere can be calculated by using Born equation[2]. Other microscopic terms may be evaluated according to Buckingham model[3]. The neutral free energy is almost the same for ions that having the same electronic shells. But the microscopic free energies are only different and need evaluation. Table (1): Physical Parameters of MeOH and DMFA at 298.15 K. Physical Properties MeOH (a) DMFA (a) Diameter σ (in A°) Dipole moment 18 ( 10 ) X esu µ − Dielectric Constant ε Polarizability 24 3 ( 10 ) X cm α − 3.84 1.76 32.7 3.26 4.962 3.82 36.8 (b) 7.88 (a) ref: .7 (b) ref: .8 2. Individual Microscopic Energies The individual microscopic interaction energies are given below for positive ions K + , Rb + and Cs + .