Enthalpy ideal mixing

For an ideal vapor mixture of m components, there is no enthalpy of mixing. The enthalpy of such a mixture is then... 

In Equation (15), the third term is much more important than the second term. The third term gives the enthalpy of the ideal liquid mixture (corrected to zero pressure) relative to that of the ideal vapor at the same temperature and composition. The second term gives the excess enthalpy, i.e. the liquid-phase enthalpy of mixing often little basis exists for evaluation of this term, but fortunately its contribution to total liquid enthalpy is usually not large. 

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

The ideal enthalpy of mixing is easily obtained from equations (7.7) and (7.8) and the relationship... 

A particular type of nonideal solution is the regular solution which is characterized by a nonzero enthalpy of mixing but an ideal entropy of mixing. Thus, for a regular solution,... 

The first term is the ideal entropy of mixing while the second term is the enthalpy of mixing in the regular solution approximation ... 

At 42°C the enthalpy of mixing of 1 mole of water and 1 mole of ethanol is — 343.1 J. The vapor pressure of water above the solution is 0.821 p and that of ethanol is 0.509 P2, in which p is the vapor pressure of the corresponding pure liquid. Assume that the vapors behave as ideal gases. Compute the excess entropy of mixing. 

Thermodynamic definitions show that the first term of Eq. (1) is the enthalpy of mixing, AHu, while the second term is the negative of the excess entropy of mixing, ASm, multiplied by T. When all four parameters are zero, the liquid is ideal with a zero enthalpy and excess entropy of mixing. What has been called the quasiregular model, a = b = 0, has been used by Panish and Ilegems (1972) to fit the liquidus lines of a number of III—V binary compounds. The particular extension of this special case of Eq. (1) to a ternary liquid given by... 

The relative partial molar enthalpies of the species are obtained by using Eqs. (70) and (75) in Eq. (41). When the interaction coefficients linear functions of T as assumed here, these enthalpies can be written down directly from Eq. (70) since the partial derivatives defining them in Eq. (41) are all taken at constant values for the species mole fractions. Since the concept of excess quantities measures a quantity for a solution relative to its value in an ideal solution, all nonzero enthalpy quantities are excess. The total enthalpy of mixing is then the same as the excess enthalpy of mixing and a relative partial molar enthalpy is the same as the excess relative partial molar enthalpy. Therefore for brevity the adjective excess is not used here in connection with enthalpy quantities. By definition the relation between the relative partial molar entropy of species j, Sj, and the excess relative partial molar entropy sj is... 

Using an automated film balance the behavior of mixed monomolecular films exhibiting deviations from ideality was studied. Particular attention was paid to condensation effects obtained when cholesterol is mixed with a more expanded component. The deviations at various film pressures are discussed in terms of the partial molecular areas of the film components. Slope changes in these plots are caused by phase transitions of the expanded monolayer component and do not indicate the formation of surface complexes. In addition, the excess free energies, entropies, and enthalpies of mixing were evaluated, but these parameters could be interpreted only for systems involving pure expanded components, for which it is clear that the observed condensation effects must involve molecular interactions. 

Data. Assume for Al-Zn alloys that a2Y is isotropic, the enthalpy of mixing of Al-Zn solutions is independent of temperature, and the entropy of mixing, s, is ideal that is,... 

PI 7.1 At T= 315 K, the enthalpy of mixing of 1 mole of water with 1 mole of ethanol is -343 J-mol-1. For this solution at this temperature, the vapor pressure of the water is 0.821/7 and that of the ethanol is 0.509/7, where p and p are the vapor pressures of the pure liquids. Assume the vapors are ideal and calculate 5 for the mixing process. 

Consider the case of an ideal solution involving a solute, which is a crystalline material at the solution temperature, dissolved in a liquid solvent. Even though the partial molal enthalpy of mixing is still zero because it is an ideal solution, there is an enthalpy requirement to overcome the crystal structure interactions. The van t Hoff equation (Adamson, 1979) gives... 

Substituting Equation 2.35 for the partial molal enthalpy of mixing, along with Equation 2.2 for the partial molal entropy of mixing, which is still considered ideal, and Equation 2.10 for the free energy change in Equation 2.6, gives... 

The change of enthalpy on mixing, AHM[T, P, x], at constant temperature and pressure is seen to be zero for an ideal solution. The change of the heat capacity on mixing at constant temperature and pressure is also zero for an ideal solution, as are all higher derivatives of AHM with respect to both the temperature and pressure at constant composition. Differentiation of Equations (8.57), (8.59), and (8.60) with respect to the pressure yields... 

For instance, separating a two-gas mixture requires a minimum amount of energy equal to their free enthalpy of mixing therefore for separating N moles of two gases with an x molar fraction for the first gas we have, assuming a mixture of two ideal gases ... 

Therefore, according to this calculation, there is an excess CFSE (enthalpy) of mixing of about -1.6 kJ/(mole of olivine). Similarly, the formation of all intermediate olivines by mixing of Mg2Si04 and Fe2Si04 components results in an excess CFSE of mixing. This is illustrated in fig. 7.3. These results imply that there is a heat of mixing term and that the olivine series is not an ideal solid-solution of forsterite and fayalite. 

Hildebrand has defined a regular solution13 as one in which deviations from ideality are attributed only to the enthalpy of mixing the intermo-lecular forces are limited to dispersion forces. The equation that defines his model is... 

For an ideal mixture, the enthalpy of mixing is zero and so a measured molar enthalpy of mixing is the excess value, HE. The literature concerning HE -values is more extensive than for GE-values because calorimetric measurements are more readily made. The dependence of HE on temperature yields the excess molar heat capacity, while combination of HE and GE values yields SE, the molar excess entropy of mixing. The dependences of GE, HE and T- SE on composition are conveniently summarized in the same diagram. The definition of an ideal mixture also requires that the molar volume is given by the sum, Xj V + x2 V2, so that the molar volume of a real mixture can be expressed in terms of an excess molar volume VE (Battino, 1971). 

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