Molar enthalpy of mixing

Integral and partial molar enthalpies of mixing in solid solutions may be derived by similar investigations of a series of solid solutions with systematic variation in composition. 

Substituting for the partial molal change in molar enthalpy of mixing with respect to the solute (Equation 2.5) gives... 

Then, at the minimum solubility, the partial molar enthalpy of mixing of... 

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). 

If the molar enthalpy of mixing of the system is known, the molar Gibbs energy of mixing can be expressed as follows... 

The following data are reported for the molar enthalpy of mixing for the system discussed in question 3. 

Generally, it is known that partial molar enthalpies of mixing (or dilution) of the solvent can also be determined from the temperature dependence of the activity of the solvent, a ... 

Partial molar enthalpies of mixing at infinite dilution and ... 

Fig. 4. The molar enthalpy of mixing of a nickel-silicon melt at 1800 K.

From the thermodynamic viewpoint, miscibility is determined by the molar Gibb s free energy of mixing (AG ) which in turn is governed by the combinatorial molar entropy of mixing and molar enthalpy of mixing as shown in... 

Partial molar enthalpies of mixing at infinite dilution of water and enthalpies of solution of water vapor in molten polymers from inverse gas-liquid chromatography (IGC) Polymer (B) polyester (hyperbranched) 2009DOM Characterization M /g.mor = 6500,M yg.mor = 9750, fatty acid modified, Boltom U3000, Perstorp Specialty Chemicals AB, Perstorp, Sweden ... 

Gas Permeation Parameters and Other Physicochemical Properties 39 Table 2.5 Enthalpy of sorption, AHj, partial molar enthalpy of mixing, AHm, and partial... 

The quantity related to the solubility parameters of the two components of solution is the partial molar enthalpy of mixing of the injected substance with the polymer at infinite dilution, AFf, (eqn (3.35)). Eqn (3.35) has been deduced for mixtures containing both non-polar solvent and solute it can be extended to polar interactions if the two components of the mixture have approximately equal interactions [73]. 

The partial molar enthalpy of dissolution in the chromatographic column is given by eqn (4.22). This is related to the partial molar enthalpy of mixing by the relationship (4.29). The latter is also given by eqn (5.33). ASf can be thus correctly determined from gas-chromatographic data. 

The partial molar quantities of mixing were determined for normal and branched alkanes (O5 — Cio), cyclohexane, benzene and tetrachloromethane in polyisobutylene [57]. Partial molar enthalpies of mixing were measured for normal alkenes in low and high density polyethylene, polypropylene, polybutene-1, polystyrene, poly(methyl acrylate), poly(vinyl chloride), polyCN-isopropyl-acrylamide), ethylene-vinyl acetate copolymer, ethylene-carbon oxide copolymer [88] normal, branched and cyclic alkanes, benzene, n-butylbenzene, ois- and ra s-decalin, tetraline and naphthalene in polystyrene at 183, 193 and 203°C [60] these solutes in poly (methyl acrylate) [57] n-nonane, n-dodecane and benzene in polystyrene in the range 104.8 — 165.1 C [71] O7—C, C12 normal alkanes and aromatic hydrocarbons in polystyrene at an average temperature of 204.9°C [72], C7—Cg normal alkanes in poly(ethylene oxide) at an average temperature of 66.5 "C [72] normal alkanes in ethylene oxide—propylene oxide block copolymers (Pluronics L 72, L 64 and F 68) at the same average temperature [72]. 

The global solubility parameters of polymers were determined from partial molar enthalpies of mixing [60, 71, 72], from partial molar free energies of mixing [60] and from the polymer-solute interactions parameters [60, 68, 101, 108, 109] all these functions were obtained by GLC. For normal, branched and cyclic alkanes, aromatic hydrocarbons and tetraline in polystyrene, eqns (5.40) and (5.42) yield Sj = 7.6 0.2 and 82 = 7.4 i 0.4 cali/2 "cm /z [60] at an average column temperature of 193°C. The same substances in poly(methyl acrylate) give 82 = 8.7 0.3... 

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