Partial molal enthalpies and entropies

In Figure 6 we show that good theoretical representations are obtained for different temperatures with a small change in the parameter a. On such evidence we might expect to obtain a consistent description of partial molal enthalpies and entropies. However, discussion of these quantities, along with a fuller consideration of solvation aspects, the a parameters, and the dielectric decrements (27, 28), is deferred until a later stage. 

Enthalpy, Entropy, and Heat Capacity of Protein—Water Systems Below 0°C. A number of investigators have reported the apparent enthalpy of fusion as a function of temperature and composition for several hydrated proteins. MacKenzie and coworkers (10) determined absorption isotherms at low temperatures and found that 1) these absorption isotherms have essentially the same sigmoidal shapes as those observed above zero degrees 2) the magnitudes of the values for partial molal enthalpy and entropy increase as the content of unfrozen water decreases 3) the heat of fusion decreases as the content of unfrozen water decreases and 4) the heat capacity of the system increases as the content of unfrozen water increases. Taking these findings all together, the thermodynamic properties of unfrozen water are not very different from those of supercooled water at comparable temperatures. 

It should be mentioned that since the hydrogen solubility of hydrogen in the metal phase is relatively low, the contribution from the enthalpies (and entropies) of solution pf hydrogen in the metal phase is neglected. For completeness, however, eqs. (26.5) and (26.6) should include a term containing the partial molal enthalpy (and entropy) of hydrogen in the metal phase. 

The standard partial molal volumes (V ), heat capacities (C >), and entropies (S ) of aqueous /i-polymers, together with their standard partial molal enthalpies AHj) and Gibbs free energies of formation from the elements AGf), are linear functions of the number of moles of carbon atoms in the alkyl chains (figure 8.28). 

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... 

Values of the partial molal enthalpies (H) and entropies (S) were calculated from the temperature coefficient of G(()z). The values of (— S) consistently increased with x in UC +a, and tended to 0 as x - 0 much higher values of (—S) were obtained for the U4Os 2/ phase, increasing as y increased. Values obtained for the entropy change, AS, for the reaction... 

Partial molal free energies, enthalpies and entropies were calculated from the activity data. The integral free energy, enthalpy and entropy of mixing were... 

Partial molal excess enthalpy and entropy of toluene m the mixture polystyrene ... 

Table 9.3. Standard chemical potential jj°, standard partial molar enthalpy h°, and standard partial molar entropy s,° for a few hydrated ions Standard state 101.3 kPa, 298 K, unit activity in molality scale.

The partial molal entropies are calculated from the partial molal free energies and enthalpies. The change in the partial molal entropy of water increases monotonically to a value near zero with increasing amount adsorbed. The partial molal entropy of barium sulfate decreases with increasing amount adsorbed. 

The upper limit for the enthalpy of activation is somewhat harder to set. An attempt can be made by noting that the partial molal entropy of e m is estimated to be positive. It is unprecedented for solution of a charged species to cause an increase in entropy of the surrounding medium, and the effect, if real, must be associated with the very dispersed charge of the hydrated electron. If the enthalpy of activation for the reverse of Reaction 1 is greater than the value estimated in Table II, then the partial molal entropy of the hydrated electron in Table I must... 

A single homogeneous phase such as an aqueous salt (say NaCl) solution has a large number of properties, such as temperature, density, NaCl molality, refractive index, heat capacity, absorption spectra, vapor pressure, conductivity, partial molar entropy of water, partial molar enthalpy of NaCl, ionization constant, osmotic coefficient, ionic strength, and so on. We know however that these properties are not all independent of one another. Most chemists know instinctively that a solution of NaCl in water will have all its properties fixed if temperature, pressure, and salt concentration are fixed. In other words, there are apparently three independent variables for this two-component system, or three variables which must be fixed before all variables are fixed. Furthermore, there seems to be no fundamental reason for singling out temperature, pressure, and salt concentration from the dozens of properties available, it s just more convenient any three would do. In saying this we have made the usual assumption that properties means intensive variables, or that the size of the system is irrelevant. If extensive variables are included, one extra variable is needed to fix all variables. This could be the system volume, or any other extensive parameter. 

Thermodynamic properties of solutions are not only useful for estimating the feasibility of reactions in solution, but they also offer one of the better methods of investigating the theoretical aspects of solution structure. This is particularly true for the standard partial molal entropy, heat capacity, and volume of the solutes, values of which are sensitive to the arrangement of solvent molecules around a solute molecule. They have been examined extensively in aqueous solution for the purpose of structure interpretation and more recently in non-aqueous solutions. Enthalpies and free energies of solvation and transfer between... 

Partial molal entropy data in ethanol are nearly as sparse as the heat capacity data. The only comprehensive entropy data in this solvent are those of Jakuszewski and Taniewska-Osinska, who report 5 for HCl and several alkali metal halides in ethanol. Ionic entropies have been calculated for the alkali metals from free energies and enthalpies of solvation, but since extra-thermodynamic assumptions were necessary, the meaning of the values is questionable. Ionic entropies in ethanol are somewhat more negative than in methanol and considerably more negative than in water. 

Marky LA, Kupke DW (2000) Enthalpy-entropy compensations in nucleic acids contribution of electrostriction and stmctural hydration. Meth Enzymol 323 419-441 Masterton WL, Lee TP (1970) A classical model for the low-energy electron(positron)-atomic hydrogen(l s) elastic scattering. J Phys Chem 79 1776-1782 Mathieson JG, Conway BE (1974) Partial molal compressibilities of salts in aqueous solution and assignment of ionic contributions. J Sol Chem 3 455-477 Mauzerall D, Hou J-M, Boichenko VA (2002) Volume changes and electrostriction in the primary photoreactions of various photosynthetic systems estimation of dielectric coefficient in bacterial reaction centers and of the observed volume changes with the Drude-Nernst equation. Photosyn Res 74 173-180... 

Because partial molar volume, enthalpy, and heat capacity are the same anywhere on the Henry s law tangent, including both the state of infinite dilution and the ideal one molal solution, either of these states can serve as the standard state for these properties. We have chosen to say that the infinitely dilute solution is the standard state, but many treatments prefer to say that the standard state for these properties, as well as for the Gibbs energy and entropy, is the ideal one molal solution. For some reason, these treatments (e.g., Klotz, 1964, p. 361) then define the reference state for enthalpy, volume and heat capacity... 

This table contains standard state thermodynamic properties of positive and negative ions in aqueous solution. It includes enthalpy and Gibbs energy of formation, partial molar entropy, and partial molar heat capacity. The standard state is the hypothetical ideal solution with molality equals 1 mol/kg. 

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