American Journal of Systems Science

2014;  3(1): 12-17

doi:10.5923/j.ajss.20140301.02

Thermodynamics of the Solvation of Potassium Chromate in Mixed DMF-H2O Solvents at 301.15 K

Esam A. Gomaa

Chemistry Department, Faculty of Science, Mansoura University, 35516-Mansoura, Egypt

Correspondence to: Esam A. Gomaa, Chemistry Department, Faculty of Science, Mansoura University, 35516-Mansoura, Egypt.

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Abstract

The Gibbs free energies for K2CrO4 were evaluated in mixed dimethylformamide (DMF)-H2O solvents at 301.15 K from the experimental solubility measurements. From the experimental solubility data also the ionic radii of potassium and chromate ions are evaluated . The total free energy of the salt is divided into its individual contribution in the mixtures used. Libration Gibbs free energy for moving K2CrO4 from standard gas state to standard solution state was calculated according to specific cycle for the solvation process using the solubility product. Also the lattice energy for solid K2CrO4 (cr) was also calculated and used for further evaluation. The conventional Gibbs free energies for the cation (K+) and the anion (CrO42-) were estimated theoretically and also the Gibbs free energy of CrO42- gas was evaluated and all values were discussed.

Keywords: Thermodynamics, Gibbs Free Energies, Potassium Chromate, Solvation, Solubility, Aqueous and Dimethylformamide Mixtures

Cite this paper: Esam A. Gomaa, Thermodynamics of the Solvation of Potassium Chromate in Mixed DMF-H2O Solvents at 301.15 K, American Journal of Systems Science, Vol. 3 No. 1, 2014, pp. 12-17. doi: 10.5923/j.ajss.20140301.02.

Article Outline

1. Introduction
2. Relative and Conventional Solvation Free Energies of Ions
3. Conventional Gibbs Free Energies from Reduction Potentials
4. Experimental
5. Results and Discussion
6. Conclusions

1. Introduction

For neutral species experimental solvation Gibbs free energies have been tabulated large number of solutes in both aqueous[1-7] and non-aqueous[7, 8] solvents. Typically, these solvation free energies are determined experimentally [8] and their uncertainty is relatively low (~ 0.8 KJ/mol)[9].
Determining accurate values for the Gibbs free energies of ionic solutes like K2CrO4 is important than that of neutral solutes. Understanding the partitioning of single ions between different liquid phases is important in many areas of biology. For example, the electrical signals sent by nerve cells are activated by changes in cell potential that are caused by the movement of various ions across the neuronal membrane[10]. The division of thermodynamic Gibbs free energies of solvation of electrolytes into ionic constituents is conventionally accomplished by using the single ion solvation Gibbs free energy of one reference ion, conventionally, the proton, to set the single ion scales[11, 12]. The aim of this work is to estimate the single ion Gibbs free, energies for K+ & CrO42- ions in mixed DMF H2O solvents at 301.15 K.
Sums of solvation free energies of cations and anions are well defined through the use of thermochemical cycles involving calorimetric or electrochemical measurements [13-17]. A number of different extra thermodynamic approximations have been used[18-25] for partition the sums of cation and anion Gibbs free energies into single ion contribution. Solvation Gibbs free energies for single ions are necessary for theoretical calculations.

2. Relative and Conventional Solvation Free Energies of Ions

The Gibbs solvation free energies of ions as relative free energies by settling the free energy of solvation of some reference ion equal zero[26]. Proton was chosen as reference ion. For ions, this result in a set of conventional free energies of solvation that the cations are shifted from their absolute values by the value for the absolute Gibbs solvation free energy of the proton.
The conventional Gibbs free energies of solvation for anions are shifted by an equal amount in the opposite direction.

3. Conventional Gibbs Free Energies from Reduction Potentials

When the convention for the absolute Gibbs free energy of the proton is followed, the solution-phase free energy change associated with the half cell for reduction of hydrogen gas is equal to zero. Reduction potentials following this convention for hydrogen electrode are referred as standard reduction potentials. From the half cell reaction for the reduction of metal cation to crystalline phase and the half reduction reaction of hydrogen gas, the redox reaction can be illustrated through the use of thermochemical cycle[12]. This last procedure can be used to estimate the gas free energy of formation for CrO42- ion, to explain the ionic behaviour.

4. Experimental

Potassium chromate K2CrO4 Griffinkamp and N-N, dimethylformamide (DMF) from Merck Co, were used.
Saturated solutions of K2CrO4 were prepared by dissolving different amounts of the salt in closed test tubes containing different DMF-H2O mixtures. These mixtures were then saturated with nitrogen gas as inert atmosphere. The tubes were placed in a shaking thermostat (Model Gel) for a period of four days till equilibrium reached. The solubility of K2CrO4 in each mixture was measured gravimetrically by evaporating 1 ml of the saturated solution in small cup using I. R. lamp. The measurements were done by three readings for each solution at 301.15 K.

5. Results and Discussion

The molar solubility (S) for K2CrO4 was measured gravimetrically in mixed DMF-H2O solvent at 301.15 K. The solubility values with an average number of the second number after comma are cited in Table (1). These (S) value in water agreed well with that in literature values[27]. The activity coefficients were calculated by the use of Debye-Hückel equation[28, 29].
(1)
Where I is the ionic strength calculated from S values. These data were tabulated also in Table (1).
The solubility product was calculated by the use of equation 2[30].
(2)
The solubility product (pKsp) data are given in Table (1). From solubility products the Gibbs free energies of solvation and the transfer Gibbs free energies from water to mixed solvents were calculated by using equations (3) and (4). Their values are tabulated also in Table (1)[31, 32].
(3)
(4)
s, w denote solvent and water respectively.
It was concluded that the Gibbs free energies of transfer increase in negativity by increasing the mole fraction of DMF in the mixed DMF-H2O solvents. This is due to more solvation behaviour in the mixed solvents than that of water (see Fig. 1).
Figure 1. Gibbs free energies of transfer for K2CrO4 versus the mole fraction of DMF at 301.15 K
Table (1). Solubility and Gibbs free energies for K2CrO4 in mixed DMF-H2O solvents at 301.15 K
     
Single ion Gibbs free energies and convention free energies for K+ and CrO42- ions.
It was well known that the preferrentional single ion thermodynamic parameters depend on the ionic radii of two ions (cation and anion). Therefore the ionic radii ratio between K+ and CrO42- were evaluated from exact radii values given in literature[35] and found to be 0.4399.
Multiply the ionic radii ratio for K+ / CrO42- by the Gibbs free energies of K2CrO4 we get the ionic Gibbs free energies for K+ ion. Then subtract K+ Gibbs free energies from K2CrO4 Gibbs free energy we obtain the Gibbs free energies for CrO42- anion in K2CrO4. The obtained values for single ions are presented in Table (2). The conventional Gibbs free energies for potassium ion in solvents are shifted from their absolute values by the absolute free energy of the proton[34] according to equation (5).
(5)
and for (CrO42-) anion is shifted by an equal amount in the opposite direction (equation 6).
(6)
Where are the Gibbs free energies of solvation for potassium, chromate and proton in solvents.
From the mean values of Gibbs free energies for the proton in water and other solvents given in literature[12, 35, 36], a straight line was drown between these mean proton values and the diameter for each solvent taken from[37]. From this line the proton solvation free energies in pure water and DMF were obtained and found to be 1523 and 1561 K J/mol, respectively. Multiplying these values by the mole fraction of each solvent and then sum the results. The mixed solvent proton free energies in DMF-H2O mixtures were obtained and their values are given in Table (2). Apply equations (5) and (6) we get the conventional Gibbs free energies for the cation K+ and the anion CrO4- , their values are given also in Table (2). Cation conventional free energy values are negative indicating exothermic character and anion values are positive indicating endothermic character. Both values conventional Gibbs free energies for potassium and chromate ions increase with increase of the mole fraction of DMF due to more solvation and the sum of them gives the values for the neutral salt.
Table (2). Single ion Gibbs free energies for K+, chromate CrO42- and their half conventional energies at 301.15 K. in mixed DMF-H2O solvents (in KJ/mol)
     
Libration Gibbs free energies for K2CrO4 in mixed DMF-H2O solvents:
The libration Gibbs free energies for K2CrO4 in mixed DMF/H2O solvents at 301.15 K were calculated following thermochemical cycle 1 (cycle 1) as applied in literature[12] for silver salts following solubility product concept.
Where is the lattice free energy, (g) and (s) denote the gas and solution cases. The lattice energy was calculated following Bartlett’s relationship following equation (7)[38-41].
(7)
The volumes for soild K2CrO4 was calculated by dividing its molecular weight by the density of solid given in literature[4] and apply it in equation (7) to obtain 198.938 KJ/mol as for K2CrO4.
On the use of equation (8) cycle (1), the liberation free energy for K2CrO4was obtained (99.468 KJ/mol).
(8)
The, the free energy change associated with moving K2CrO4 from standard gas phase at 1 atmosphere to solution phase. This free energy change has been referred as “compression” work of the gas or liberation free energy.
Conventional free energies from reduction potentials:
The absolute Gibbs free energy of the proton is followed solution phase free energy change associated with the following half cell.
(9)
The half cell reaction for the reduction of cation is:
(10)
The symbol (cr) is the crystal phase. The sum of the two half cells is:
(11)
Through the thermochemical cycle 2, the conventional free energy of K+ can be written as:
(12)
Where are the gas free energy of formation for H+ and K+ ions. F faraday’s constant, equal = 23.061 Kcal/mol and Ec is the standard reduction potential of K+.
Also the conventional free energy of the chromate ion can be written following Truhlar[ 12 ] explanation as:
(13)
Apply last equation the , gas free energies of formation for the anion CrO42- and K+ estimated in the mixed DMF H2O solvents and their values are given in Table (3) and Fig. (2). The values increase by increase of the mole fraction of DMF favoring less solvation.
Table (3). Gas formation free energy for CrO42- anion and K+ cation in mixed DMF-H2O solvents at 301.15 K (in KJ/mol)
     
Figure 2. Relation between against the mole fraction of DMF at 301.15 K

6. Conclusions

By the use of combination of experimental gas-phase free energies of formation and solution-phase reduction potentials, we determined conventional solvation free energies of K2CrO4 in mixed DMF-H2O solvents at 301.15 K from the experimental solubility measurements. Libration Gibbs free energy associated with moving K2CrO4 in standard gas state to standard stat in solution was evaluated according to thermochemical cycle for the solvation process using the solubility product. Also the lattice energy for solid K2CrO4 (cr) was also calculated and used for further evaluation. These conventional solvation free energies were then combined with experimental and calculated gas-phase clustering free energies to determine conventional solvation free energies of ion-solvent clusters containing up to solvent molecules. The values for the absolute solvation free energy of the proton obtained in this work should be useful as standards against which the absolute solvation free energies of other single ions can be derived.

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