Free energy integral molar

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

The relative partial molar free energy of A is written in terms of the integral molar free energy of the solution as... 

When the formation of one mole of the solution is considered, the integral molar free energy of mixing, AGM, is given by... 

The equality of aA and PA/PA has been explained earlier. It may be recalled that the activity of the component A in the solution is defined by this equality. For the binary solution A-B, the integral molar free energy of mixing is then... 

The relationships presented thus far for partial, integral and relative partial molar free energies are applicable in a similar manner to entropy, enthalpy and also volume. 

The partial and integral molar free energies of mixing are, therefore, given by AG, d = R TlnXA AG, d = R TlnXB AGM,id = RT(XA lnXA + XB lnXB)... 

Thus the integral molar excess free energy of mixing as well as the enthalpy of mixing are independent of temperature for a regular solution. 

The integral extends from LH to Ld. Equation 5.47b demonstrates that the solvent solubility IE offers a convenient way to determine the IE on the standard state partial molar free energy for the salt provided the concentration dependence of its activity coefficient in one solvent, most likely H20, is available at high concentration. 

The differential molar entropies can be plotted as a function of the coverage. Adsorption is always exothermic and takes place with a decrease in both free energy (AG < 0) and entropy (AS < 0). With respect to the adsorbate, the gas-solid interaction results in a decrease in entropy of the system. The cooperative orientation of surface-adsorbate bonds provides a further entropy decrease. The integral molar entropy of adsorption 5 and the differential molar entropy are related by the formula = d(n S )ldn for the particular adsorbed amount n. The quantity can be calculated from... 

Assuming again that y follows the Debye-Hiickel law, the total pressure P is measured as a function of the solute concentration, then the vapor phase y, the only unknown in Equation 4, can be calculated, and hence the activities a and a2 can also be calculated, provided the activities ai° and a of each solvent prior to the addition of the solute are known dG°/dZ can be obtained next from Equation 1. Finally, integration of dG°/<9Zi with respect to Z leads to the standard molar free energy of transfer AG°t between Z = 1 (if water is chosen as the reference solvent) and any value of Z. ... 

It is the energy difference between Na moles of gas adsorbed U"n (per mol) and the same amount free in the gas phase U. The next important quantities are the integral molar enthalpy of adsorption... 

They are defined in complete analogy to the integral molar energy. The difference between the energy and the enthalpy of adsorption is usually small. If we treat the free gas as being ideal, the difference is AadU = AadHm1 + RT. At 25°C RT is only 2.4 kJ/mol. For this reason we do not need to worry too much about whether a heat of adsorption is the adsorption enthalpy or the internal adsorption energy, if we only want to estimate is. 

Therefore, at steady-state, the integral of all molar free energy contributions must be zero. 

This is called the relative integral molar free energy or the molar free energy of mixing. Hie method of tangential intercepts which we have applied for determination of partial molar quantities from the integral molar quantities can also apply to the relative quantities ... 

Calculate the relative integral molar free energy of the solution, Gv. 

This is called the excess partial molar free energy of i. The excess integral molar free energy or the excess molar free energy of solution is given by... 

The free energy of mixing of the solution, or the relative integral molar free energy, G, for a A-B binary solutions given by... 

Some Relations between Macroscopic and Microscopic Adsorption Parameters The molar integral change of free energy at a temperature T during adsorption is [2,13]... 

In case of a solution, like the FeO-MnO solid solution, the integral molar free energy of mixing would be related to the partial molar values, as per their definition, in the following manner ... 

One of the most important consequences of Euler s integral theorem, as applied to stability criteria and phase separation, is the expansion of the extensive Gibbs free energy of mixing for a multicomponent mixture in terms of partial molar properties. This result is employed to analyze chemical stability of a binary mixture. 

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