Mixing, enthalpy entropy

So far, we have seen that deviation from ideal behavior may affect one or more thermodynamic magnitudes (e.g., enthalpy, entropy, volume). In some cases, we are able to associate macroscopic interactions with real (microscopic) interactions of the various ions in the mixture (for instance, coulombic and repulsive interactions in the quasi-chemical approximation). In practice, it may happen that none of the models discussed above is able to explain, with reasonable approximation, the macroscopic behavior of mixtures, as experimentally observed. In such cases (or whenever the numeric value of the energy term for a given substance is more important than actual comprehension of the mixing process), we adopt general (and more flexible) equations for the excess functions. 

Most multicomponent systems undergo phase separation because of their positive mixing enthalpies coupled with low entropy of mixing. Morphological features have been central to the study of multicomponent systems, because domain sizes, shapes, and interfacial bonding characteristics determine the mechanical properties. A proper understanding of these features often allow synergistic behavior to be developed. 

C) Commercial instant ice packs are available that contain a mixture of ammonium nitrate and water separated by a barrier. When the ice pack is twisted, the barrier breaks and the two substances mix. The temperature rapidly decreases as the ammonium nitrate dissolves in the water. Describe the changes in enthalpy, entropy, and free energy during this process. 

In the simplest case of linear AB diblock and ABA triblock copolymers, the phase behavior has been the subject of numerous theoretical and experimental studies over recent decades and is relatively well understood [89-96]. As mentioned before, the self-assembly process is driven by an unfavorable mixing enthalpy and small mixing entropy, while the covalent bond connecting the blocks prevents... 

Electromotive force measurements of the cell Pt, H2 HBr(m), X% alcohol, Y% water AgBr-Ag were made at 25°, 35°, and 45°C in the following solvent systems (1) water, (2) water-ethanol (30%, 60%, 90%, 99% ethanol), (3) anhydrous ethanol, (4) water-tert-butanol (30%, 60%, 91% and 99% tert-butanol), and (5) anhydrous tert-butanol. Calculations of standard cell potential were made using the Debye-Huckel theory as extended by Gronwall, LaMer, and Sandved. Gibbs free energy, enthalpy, entropy changes, and mean ionic activity coefficients were calculated for each solvent mixture and temperature. Relationships of the stand-ard potentials and thermodynamic functons with respect to solvent compositions in the two mixed-solvent systems and the pure solvents were discussed. 

Pursuing more realistic formulae for calculation of the adsorption enthalpy, we will incorporate the mixed adsorption entropy S /R. From Eqs. 5.42 and 5.70 it follows that the entropy change for the each partial adsorption isotherm is ... 

Only solid solutions were present under the conditions of the investigation of the Fe-Co [242], Ni-Cu [250], and SnTe-PbSe [262] systems given in Table 7. The thermodynamic activities, excess Gibbs energies, mixing enthalpies and excess entropies were determined by the use of the ion intensity ratio method for the Fe-Co and Ni-Cu systems as described for the melts. The partial pressure of the molecules SnTe, SnSe, PbTe, and PbSe were obtained for different compositions of the quasi-binary system SnTe-PbSe using the isothermal evaporation technique. 

In the case of NaCl and especially NH4NO3 dissolving in water, AH o r > but the increase in entropy that occurs when the crystal breaks down and the ions mix with water more than compensates for the increase in enthalpy. (The enthalpy/entropy interplay in physical and chemical systems is covered in depth in Chapter 20.)... 

The contributions Z ° and are represented by generalised functions containing as parameters the reduced temperature and pressure. These have been obtained by using a special form of the BWR-EOS. Mixture critical parameters and acentric factor are calculated by means of mixing rules, which do not have interaction parameters. Tables of values for hand calculations may be found in Reid et al. (1987). Graphical representations of contributions are presented in Perry (1997). Note that this method can be used to compute phase properties (specific volume, enthalpy, entropy) for both vapour and liquid phase. It has been accepted as accurate option for enthalpy and entropy of hydrocarbons and slightly polar components. 

The improvement in AT-values does not automatically ensure accuracy of other properties. In this example the estimation of liquid volume is poor for SRK, but acceptable for PR. Without interaction coefficients the prediction of the liquid volume is even better Note that when the volumetric properties are important, as in reservoir engineering, special equation of state or mixing rules should be applied, as Teja-Sandler EOS given in Chapter 5. The same observation holds for the enthalpy of vaporisation, which could be in serious error. Another method for enthalpy/entropy computation should be used, as for example based on the principle of corresponding states. 

Change in Enthalpy, Entropy and Gibbs Free Energy of Mixing... 

The entropy of mixing of small molecules can be so large that it overwhelms the positive mixing enthalpy and forces the components to mix under a wide range of temperature and compositions. This is why polyolefins. 

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