Energy of dilution

G. N. Lewis and H. Storch, "The Potential of the Bromine Electrode the Free Energy of Dilution of Hydrogen Bromide the Distribution of Bromine Between Several Phases". J. Am. Chem. Soc., 39, 2544-2554 (1917). 

The free energy of dilution of a solution can be shown to be given by ... 

There have been many attempts to describe the process of mixing and solubility of polymer molecules in thermodynamic terms. By assuming that the sizes of polymer segments are similar to those of solvent molecules, Flory and Huggins derived an expression for the partial molar Gibbs free energy of dilution that included the dimensionless Flory Higgins interaction parameter X = ZAH/RT, where Z is the lattice coordination number. It is now... 

According to M. Berthelot, heat is absorbed by the soln. of sodium chloride in water at 15°, less heat is absorbed at 76°, and heat is neither absorbed nor evolved at 100°. S. Arrhenius, A. E. Stearn, R. F. Schneider, and G. McP. Smith measured the heats of dilution of aq. soln. of sodium and potassium chlorides alone or mixed with strontium or barium chlorides and A. J. Allmand and W. G. Polack, the free energy of dilution of soln. of sodium chloride. The heats of dilution in cals, are negative, rather greater numerically for potassium chloride than for sodium chloride. 

The driving force for this process is the free energy change AG associated with the concentration gradient (Q> — Cf), sometimes known as the free energy of dilution ... 

It has been seen in Chapter 7 that the use of macromolecules as dispersion stabilisers depends in part on the osmotic forces arising from the interaction of solvated polymer chains as neighbouring particles approach (see Fig. 7.7). It is thus important to know how factors such as temperature and additive affect this interaction. Flory has given the free energy of dilution (the opposite process to the concentration effect discussed in section 7.2)... 

The first and third half-reactions have half-cell potentials (AgCl CH Ag) and (Hg2Cl2 cr Hg)that can be combined and called A ef because they make a constant contribution to the cell voltage. The second reaction is the source of a variable potential in the cell, corresponding to the free energy of dilution of H30 from a concentration of 1.0 M to an unknown and variable concentration, and its potential exists across the thin glass membrane of the glass electrode. The Nernst equation for the cell can therefore be written as... 

Show that the free energy of dilution of a solution from one molality (m) to another (m ), i e., the difference in the partial molar free energy (y) of the solute in the two solutions, is equal to... 

In order to obtain the thermodynamic degree of ionisation, a, Lewis and Linhart combme the above empirical expression with the thermodynamic equation connecting the free energy of dilution with the lowenng of freezing point, finally arriving at the following useful formula —... 

Nafion membranes are composed of hydrophobic-hydrophilic comonomers. When the ionic form of Nafion is exposed to water, some swelling takes place. However, in order to minimize the free energy of the system, water will be taken up in such a way as to avoid contact with the hydrophobic TFE units of the copolymer. At equilibrium, for a fixed structure, there will be a balance between the free energy of dilution (osmotic swelling) and the free energy of hydration of the TFE units. As a result of these two opposing effects, water of hydration is contained in ion clusters which reduces the necessity of water-TFE interaction and yields a system of minimum energy. Several models... 

Sato and Sieglaff (1980) argue that three free energies determine whether or not desorption of the solvation layers can take place. These are the free energy of dilution of the bulk polymer solution the thermal energy of the... 

It is more useful to express Equation 8.30 in terms of the chemical potentials of the pure solvent (Pi), by differentiating the expression with respect to the number of solvent molecules, to obtain the partial molar Gibbs free energy of dilution (after multiplying by Avogadro s number). 

From Equation 8.33 it can be seen that the excess free energy of dilution is... 

The chemical potential gives the partial molar Gibbs energy of dilution. The partial molar dilution enthalpy and the partial molar dilution entropy are given by... 

The parameter will vary with PS molecular weight and with the free energy of dilution (Flory, 1953), kT jj2 — Q/T)v, where is the entropy of dilution, 9 is the Flory theta temperature, and V2 is the volume fraction of solute. 

It will further be obvious that the relations (16) also apply to the difference between ho and hi, etc. In other words, the heat of dilution can be derived from the Gibbs free energy of dilution and its temperature coefficient, while the entropy Aso of dilution follows from Ago and Aho or from the temperature coefficient of Ago. ... 

Thus, from the vapour pressure p of the mixture and the vapour pressure p"" of the pure solvent we derive the Gibbs free energy of dilution... 

The result obtained regardii the ideal character of all solutions in the limit of small concentrations may be expressed by saying that the free energy of dilution is of the form Ago + terms of a higher order than the first... 

At high concentrations most polymer solutions assume gel-like behaviour. (Compare chapter on gels, p. 494). The osmotic pressure of a gel is usually called swelling pressure, although from a physical point of view these quantities are identical they both represent the pressure difference between solution and solvent separated by a semipermeable membrane when equilibrium is reached. In particular, the vapour pressure p and the swelling pressure of a gel are related to the free energy of dilution accordii to the usual formula... 

Fig. 22. Free energy of dilution per mole acetone in the system cellulose nitrate-acetone plotted on a logarithmic scale against percentage by weight of the cellulose nitrate.

Gibbses free energy of dilution with concentration T is negative for all values... 

Lin, C. L. and R. H. Wood. 1996. Prediction of the free energy of dilute aqueous methane, ethane, and propane at temperatures from 600 to 1200 degrees C and densities from 0 to 1 g cm using molecular dynamics simulations. Journal of Physical Chemistry. 100, 16399. 

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