Calculation on the Free Energy of Mixing of some Silane Systems

2011 ◽  
Vol 391-392 ◽  
pp. 1017-1021
Author(s):  
Ru Zhang ◽  
Yan Fen Wu ◽  
Ping Hu
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Activity Coefficients ◽  
Influence Factors ◽  
Critical Parameters ◽  
Model Parameters ◽  
Free Energies ◽  
Wilson Model ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

Six binary silane systems were chosen to calculate the activity coefficients (γ) and free energies of mixing (ΔGm). These systems included: methyldichlorosilane + methyltrichlorosilane, methyldichlorosilane + methylvinyldichlorosilane, methyldichlorosilane + toluene, methyltrichlorosilane + methylvinyldichlorosilane, methyltrichlorosilane + toluene, methylvinyldichlorosilane + toluene. Based on the Antoine constants, critical parameters of the pure components and Wilson model parameters, γ and ΔGmwere calculated. The influence factors of these thermodynamic properties were also discussed.

The statistical thermodynamics of multicomponent systems

1951 ◽  
Vol 205 (1081) ◽  
pp. 247-269 ◽  
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Potential Energy ◽  
Multicomponent Systems ◽  
Reference Species ◽  
Two Phase ◽  
Energy Of Mixing ◽  
Volume Of Mixing ◽  
Two Component Systems ◽  
Free Energy Of Mixing

This paper describes a new statistical approach to the theory of multicomponent systems. A ‘conformal solution’ is defined as one satisfying the following conditions: (i) The mutual potential energy of a molecule of species L r and one of species L s at a distance ρ is given by the expression u rs (ρ) = f rs u 00 ( g rs ρ ), where u 00 is the mutual potential energy of two molecules of some reference species L 0 at a distance ρ , and f rs and g rs are constants depending only on the chemical nature of L r and L s . (ii) If L 0 is taken to be one of the components of the solution, then f rs and g rs are close to unity for every pair of components. (iii) The constant g rs equals ½( g rr + g ss ). From these assumptions it is possible to calculate rigorously the thermodynamic properties of a conformal solution in terms of those of the components and their interaction constants. The non-ideal free energy of mixing is given by the equation ∆* G = E 0 ƩƩ rs x r x s d rs , where E 0 equals RT minus the latent heat of vaporization of L 0 , x r is the mole fraction of L r and d rs denotes 2 f rs — f rr — f ss . This equation resembles that defining a regular solution, with the important difference that E 0 is a measurable function of T and p , which makes it possible to relate the free energy, entropy, heat and volume of mixing to the thermodynamic properties of the reference species; and the predicted relationships between these quantities agree well with available data on non-polar solutions. The theory makes no appeal to a lattice model or any other model of the liquid state, and can therefore be applied both to liquids and to imperfect gases, and to two-phase two-component systems near the critical point.

scholarly journals A Theoretical study of thermodynamic properties of Cd-Bi liquid alloy

BIBECHANA ◽  
1970 ◽  
Vol 8 ◽  
pp. 90-95
Author(s):  
D Adhikari
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Liquid Alloy ◽  
Theoretical Study ◽  
Energy Parameter ◽  
Heat Of Mixing ◽  
Liquid Alloys ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Good Agreement

Flory’s model has been used for the study of thermodynamic properties of Cd-Bi liquid alloys. Free energy of mixing, heat of mixing, entropy of mixing and activity of Cd have been determined. All of these computed quantities have been found to be in a good agreement with observed values.Keywords: Flory’s model; thermodynamic properties; Cd-Bi liquid alloy; weakly interacting system; interaction energy parameter  DOI: http://dx.doi.org/10.3126/bibechana.v8i0.5693  BIBECHANA 8 (2012) 90-95

Excess free energies of mixing at temperatures below 25°. Isopiestic measurements on the systems H2O-NaCl-Na2SO4 and H2O-NaCl-MgSO4

1971 ◽  
Vol 24 (12) ◽  
pp. 2487 ◽  
Author(s):  
CW Childs ◽  
RF Platford
Keyword(s):  
Free Energy ◽  
Vapour Pressure ◽  
Excess Free Energy ◽  
Pressure Measurements ◽  
Experimental Uncertainty ◽  
Free Energies ◽  
Isopiestic Measurements ◽  
Temperature Range ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

Isopiestic vapour pressure measurements have been made on the systems H2O-NaCl-Na2SO4 and H2O-NaCl-MgSO4 at 15� and 0�. Excess free energies of mixing the aqueous salts hare been calculated for various ionic strengths, and the results have been compared with those previously obtained at 25�. ��� Within experimental uncertainty the excess free energies of mixing of aqueous NaCl with aqueous Na2SO4 are the same at 0�, 15�, and 25�. However, the excess free energy of mixing aqueous NaCl with aqueous MgSO4 shows differences which may be just larger than experimental uncertainty over the same temperature range.

Activity coefficients of NaNO3 in (Mg, Ca, Sr, and Ba)(NO3)2 + H2O systems at 298 K by EMF methods

1993 ◽  
Vol 71 (3) ◽  
pp. 384-389 ◽  
Author(s):  
Stephen N. Smith ◽  
S. Sarada ◽  
Ramamurthy Palepu
Keyword(s):  
Free Energy ◽  
Ionic Strength ◽  
Gibbs Free Energy ◽  
Activity Coefficients ◽  
Interaction Parameters ◽  
Excess Gibbs Free Energy ◽  
Experimental Activity ◽  
Energy Of Mixing ◽  
Total Ionic Strength ◽  
Free Energy Of Mixing

The activity coefficients of NaNO3 in Mg(NO3)2, Ca(NO3)2, Sr(NO3)2 and Ba (NO3)2 were determined at constant total ionic strength of 0.1, 0.5, 0.75, 1.0, 1.5, and 2.0 mol kg−1 at 298 K using EMF methods. The experimental activity coefficients were analyzed using four different formalisms, namely, Reilly–Wood–Robinson, Scatchard, Pitzer, and Harned equations, and the interaction parameters were evaluated. Excess Gibbs free energy of mixing and trace activity coefficients were calculated and the results are discussed.

scholarly journals Regular Associated Solution Model for the Estimation of Free Energy of Mixing of Binary Liquid Alloys

1970 ◽  
Vol 8 (8) ◽  
pp. 30-33
Author(s):  
D Adhikari ◽  
BP Singh ◽  
IS Jha
Keyword(s):  
Free Energy ◽  
Equilibrium Constants ◽  
Solution Model ◽  
Interaction Energies ◽  
Free Energies ◽  
Scientific World ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Associated Solution Model ◽  
Associated Solution

We have found the equilibrium constants and pairwise interaction energies between the species and the complexes of liquid CuSn, AgAl, FeSi, CdNa and HgNa alloys on the basis of regular associated solution model. These parameters are then used to estimate the free energies of mixing of each alloy. The observed asymmetry in the free energy of mixing of each alloy with respect to concentration is well explained. Key Words: Free energy of mixing; Asymmetry; Binary alloys; Interaction energy. DOI: 10.3126/sw.v8i8.3842 Scientific World Vol.8(8) 2010 pp.30-33

Thermodynamic Properties of Liquid Binary Transition-Metal Alloys in the Bretonnet-Silbert Model

2007 ◽  
Vol 263 ◽  
pp. 105-110 ◽  
Author(s):  
N.E. Dubinin ◽  
L.D. Son ◽  
N.A. Vatolin
Keyword(s):  
Free Energy ◽  
Transition Metal ◽  
Thermodynamic Properties ◽  
Excess Entropy ◽  
Thermodynamic Perturbation Theory ◽  
Exchange Correlation ◽  
Transition Metal Alloys ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Model Pseudopotential

In the present study, we apply the Bretonnet-Silbert local model pseudopotential, which takes into account the s-d hybridization in interacting between ion and s-electron to calculate the thermodynamic properties of binary transition-metal liquid alloys. The Wills-Harrison approach is used to take into account the d-electron terms in the free energy. We use the simplest variant of the variational method of the thermodynamic perturbation theory (with the hard-sphere reference system), the Vashishta-Singwi exchange-correlation function, and the Lorenz form of the density of d-electron states. The free energy of mixing, internal energy of mixing, and excess entropy of mixing are calculated for a Fe-Co liquid alloy at different compositions near the melting temperature. The agreement with the experimental data is quite satisfactory.

scholarly journals THEORETICAL STUDY OF THERMODYNAMIC PROPERTIES OF Cu-Pb LIQUID ALLOYS AT DIFFERENT TEMPERATURE BY OPTIMIZATION METHOD

2017 ◽  
Vol 22 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Ganesh Kumar Shrestha ◽  
Bijay Kumar Singh ◽  
Indu Shekhar Jha ◽  
Ishwar Koirala
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Energy Parameter ◽  
Concentration Fluctuations ◽  
Size Ratio ◽  
Liquid Alloys ◽  
Order Energy ◽  
Energy Of Mixing ◽  
Different Temperatures ◽  
Free Energy Of Mixing

A theoretical assessment on thermodynamic properties and concentration fluctuations of Cu-Pb liquid alloys at a specified temperature has been made by using the fitted values for size ratio ( ) and order energy parameter (W) of the alloys in Quasi-Lattice Theory where the combined effect of size ratio, entropic and enthalpic effect is considered. The order energy parameter (W) of the alloys is temperature dependent and its value at the required temperature has been determined by using the value of order energy parameter at the given temperature and temperature derivative of order energy parameter ( ). The values of W at different temperatures have been used to determine the free energy of mixing of the alloys at different temperatures which are then used for the optimization procedure in order to calculate the corresponding values of partial excess free energy of mixing and activity of the constituents involved in the alloy at different temperatures. These parameters have been used to predict the concentration fluctuations in long wavelength limit (Scc(0)) at different temperatures in the entire range of concentration. Journal of Institute of Science and TechnologyVolume 22, Issue 1, July 2017, page: 25-33

THERMODYNAMICS OF COMPOUND FORMING MOLTEN Cu–In ALLOYS

2008 ◽  
Vol 22 (27) ◽  
pp. 4833-4844 ◽  
Author(s):  
Y. A. ODUSOTE
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Gibbs Free Energy ◽  
Chemical Diffusion ◽  
Interaction Parameters ◽  
Ideal Behavior ◽  
Mixing Properties ◽  
Long Wavelength ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

A study of the thermodynamic properties of Cu in molten Cu – In alloys has been explained using a compound formation model. We use the model to deduce information on thermodynamic properties of the alloy such as the Gibbs free energy of mixing, the enthalpy and entropy of mixing. In this study, we first model the Gibbs free energy in terms of the interaction parameters. Sequel to this, the interaction parameters are utilized to quantify properties such as the concentration–concentration fluctuations in the long wavelength limit, the Warren–Cowley short-range order parameter, and the chemical diffusion. Both positive and negative deviations from Raoultian behavior and concentration-dependent asymmetry in the mixing properties of CuIn 4 liquid alloys were reported. Our analysis suggest that the liquid alloy undergoes a transformation from an ordered ( In -rich end) to segregating ( Cu -rich end) state. The system also exhibits ideal behavior at the Cu -rich end.

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