The Free Energies of Hydration of Gaseous Ions

1948 ◽  
Vol 1 (4) ◽  
pp. 480 ◽  
Author(s):  
NS Hush
Keyword(s):  
Free Energy ◽  
Water Molecule ◽  
Pure Water ◽  
Free Energies ◽  
The Real ◽  
Free Energy Of Formation ◽  
Energy Of Hydration ◽  
Free Energy Of Hydration ◽  
Molecule Interaction ◽  
Energy Of Formation

Values of hydration energies of individual ions have usually been obtained by division of sums of energies of hydration of pairs of ions, and those calculated by different authors are usually mutually inconsistent. " Experimental " figures, whenever these are quoted, have always been obtained by assuming the truth of theoretical equations whose accuracy has not been independently checked. The distinction between free energy of ion/water-molecule interaction and the real free energy of hydration of a gaseous ion is pointed out, and the importance of Klein and Lange's measurement of the Volta-potential Hg/Hg+ (soln.), which makes possible the direct calculation of real free energies of hydration of individual ions, thus providing a check on theoretical values, is emphasized. Utilizing this value, the equation - ΔFh� = - ΔFf� + ΔFi� + ΔFs�- 103.92 z kcal. (where ΔFs� is the free energy of formation of the gaseous monatomic element, ΔFi� is the free energy of ionization, ΔFf�is the free energy of formation of the aqueous ion, and ΔFh� is the real free energy of hydration of the ion, of valency z, at 298.2� K.) is derived from fundamental considerations. By means of this equation, the real free energies of hydration of 49 ions are calculated, using the most reliable data. It is proposed that these be provisionally accepted as standard values. Several subsidiary values for important ions are calculated indirectly. The difference between ΔFh� and the free energy of ion/water-molecule interaction is discussed in relation to the surface structure of water : a value of -0.30 v. is derived for the X-potential at the surface of pure water, and it is concluded that at the water/gas interface the positive poles of the surface layer are oriented towards the gas phase. The applicability of a modified Born equation in the calculation of free energies of hydration is discussed, and a modified equation is proposed which yields values of ΔFh� for gaseous ions with noble gas structure in excellent agreement with those calculated independently by the method described above.

The enol content of simple carbonyl compounds: a thermochemical approach

1979 ◽  
Vol 57 (2) ◽  
pp. 240-248 ◽  
Author(s):  
J. Peter Guthrie ◽  
Patricia A. Cullimore
Keyword(s):  
Aqueous Solution ◽  
Free Energy ◽  
Carbonyl Compounds ◽  
Free Energy Change ◽  
Energy Change ◽  
Free Energies ◽  
Enol Ethers ◽  
Free Energy Of Formation ◽  
Hydrolysis Of ◽  
Energy Of Formation

From the heats of hydrolysis of enol ethers, the heats of formation of the enol ethers, and thence the free energies of formation of the enol ethers in aqueous solution can be calculated. For this calculation it was necessary to determine the free energies of transfer from the gas phase to aqueous solution. By methods previously published it was possible to estimate the free energy change for the hypothetical hydrolysis reaction leading from the enol ether to the enol, which in turn made possible calculation of the free energy of formation of the enol. Finally the free energy change for enolization in aqueous solution could be calculated using the known free energy of formation of the corresponding keto tautomer. In this way the following were determined: carbonyl compound, pKenol = −log ([enol]/[keto]): acetaldehyde, 5.3; propionaldehyde, 3.9; isobutyraldehyde, 2.8; acetone, 7.2; 2-butanone, 8.3; 3-pentanone, 7.8; cyclopentanone, 7.2; cyclohexanone, 5.7; acetophenone, 6.7.

scholarly journals Estimating Free Energies of Formation of Titanate () and Zirconate () Pyrochlore Phases of Trivalent Lanthanides and Actinides

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Anpalaki J. Ragavan ◽  
Dean V. Adams
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Linear Free Energy Relationship ◽  
Free Energies ◽  
Empirical Parameter ◽  
Trivalent Lanthanides ◽  
Linear Free Energy ◽  
Free Energy Of Formation ◽  
The Difference ◽  
Energy Of Formation

A linear free energy relationship was developed to predict the Gibbs free energies of formation (, in kJ/mol) of crystalline titanate (M2Ti2O7) and zirconate (M2Zr2O2) pyrochlore families of trivalent lanthanides and actinides (M3+) from the Shannon-Prewitt radius of M3+ in a given coordination state (, in nm) and the nonsolvation contribution to the Gibbs free energy of formation of the aqueous M3+ (). The linear free energy relationship for M2Ti2O7 is expressed as . The linear free energy relationship for M2Zr2O7 is expressed as . Estimated free energies were within 0.73 percent of those calculated from the first principles for M2Ti2O7 and within 0.50 percent for M2Zr2O7. Entropies of formation were estimated from constituent oxides (J/mol), based on an empirical parameter defined as the difference between the measured entropies of formation of the oxides and the measured entropies of formation of the aqueous cation.

Standard Gibbs free energy of formation of ZrOS

1990 ◽  
Vol 163 (1) ◽  
pp. 109-113 ◽  
Author(s):  
Zhi-Tong Sui ◽  
Xing-Yi Xiao ◽  
Ke-Qin Huang ◽  
Chang-Zhen Wang
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Standard Gibbs Free Energy ◽  
Free Energy Of Formation ◽  
Energy Of Formation

Thermodynamical study of (CaGa2S4)x(BaGa2S4)1−x solid solutions

2021 ◽  
pp. 2150469
Author(s):  
T. G. Naghiyev ◽  
R. M. Rzayev
Keyword(s):  
Free Energy ◽  
Solid Solutions ◽  
Calculation Method ◽  
Solid Phase ◽  
Ternary Compounds ◽  
Free Energy Of Formation ◽  
Concentration Dependences ◽  
Solid Phase Reactions ◽  
Two Phases ◽  
Energy Of Formation

The solid solutions of [Formula: see text] were synthesized by solid-phase reactions from powder components of CaS, BaS, and Ga2S3. The temperature-concentration dependences of the Gibbs free energy of formation of [Formula: see text] solid solutions from ternary compounds and phase diagrams of the CaGa2S4–BaGa2S4 were determined by a calculation method. It was revealed that continuous solid solutions are formed in these systems. The spinodal decomposition of [Formula: see text] solid solutions into two phases is predicted at ordinary temperatures.

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