Fusion, Gibbs energy

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Here A,xx°(v >l) is the change in chemical potential or Gibbs energy on fusion of pure i. By using G = H-TS we have... 

Figure 4.6 Gibbs energy of fusion of Ge and Si. The solid lines represent experimental data [4] while the broken lines are calculated neglecting the heat capacity difference between liquid and solid.

Here /g,hq and y ,ss are the activity coefficients of component B in the liquid and solid solutions at infinite dilution with pure solid and liquid taken as reference states. A fus A" is the standard molar entropy of fusion of component A at its fusion temperature Tfus A and AfusGg is the standard molar Gibbs energy of fusion of component B with the same crystal structure as component A at the melting temperature of component A. 

In equation 33, the superscript I refers to the use of method I, a T) is the activity of component i in the stoichiometric liquid (si) at the temperature of interest, AHj is the molar enthalpy of fusion of the compound ij, and ACp[ij] is the difference between the molar heat capacities of the stoichiometric liquid and the compound ij. This representation requires values of the Gibbs energy of mixing and heat capacity for the stoichiometric liquid mixture as a function of temperature in a range for which the mixture is not stable and thus generally not observable. When equation 33 is combined with equations 23 and 24 in the limit of the AC binary system, it is termed the fusion equation for the liquidus (107-111). 

The essential thermodynamic quantity for the liquid trihalides is the heat capacity, which in combination with the data for the solid phase gives the enthalpy/entropy of fusion. With these two quantities the Gibbs energy of the liquid phase can be calculated and extrapolated to the super-cooled state, if needed. 

K regardless of its stability. For example, if the vapor pressure over liquid copper is analyzed using Cu(/) Gibbs energy functions, the result is the enthalpy of vaporization of the liquid at 298.15 K. To calculate the enthalpy of sublimation of Cu(cr) it is necessary to add the enthalpy of fusion at... 

The standard Gibbs energy may be obtained from the standard Gibbs energies of fusion and dissolution of solid AB. 

The pressures for the liquid are calculated with an estimated enthalpy of fusion of 41.84 kJ moT, as noted above. Thus the selected value for the Gibbs energy of formation is ... 

Since is the chemical potential of the pure liquid, p°(T, p) — PsoUd(T, p) = AGf s, where AGfuj is the molar Gibbs energy of fusion of the pure solvent at the temperature T. Equation (13.11) becomes... 

LetAGi = — i(s), the Gibbs energy of fusion of the pure component at temperature... 

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