Associating Solutes

We now switch from solutes that dissociate completely to form ions to solutes that associate to form aggregates. We again want to find the diffusion coefficient averaged over the various species present. 

In other words, if we double the KCl concentration, we double the flux across this water-filled membrane. 

It is just as if a chemical dimerization converted the ions into a new chemical species. As before, we integrate Eq. 6.2-6 to find 

The flux is now proportional to the square of the potassium chloride concentration. This square dependence is verified experimentally, as shown in Fig. 6.2-1. 

In some cases, we may not be sufficiently astute to realize that the diffusing solutes are associating. For example, if we still thought that the ions - not the ion pairs - were diffusing, then we might analyze our data with the equation 

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For runs involving cake dewatering only, it is usually convenient to dry the total cake sample, if the associated solution contains little or no dissolved solids. 

The third category ( associated solutions ) refers to solutions in which molecular complexes may form, either through association of like or unlike species, or... 

If only one correct function exists, at most one of these equations can be right, yet each program that returned the value of 10 for its output would be allocated the same fitness. By providing a second set of input data, say a = 2, b = 4, c = 7, d = 0, and the associated solution (-8), the fitness of those programs that had found an incorrect function would be diminished when the fitness was calculated over a range of examples. 

R.F. Brebrick, Ching-Hua Su, and Pok-Kai Liao, Associated Solution Model for Ga-In-Sb and Hg-Cd-Te... 

SOL.6. 1. Prigogine, V. Mathot et A. Desmyter, Proprietes thermodynamiques des solutions associees (Thermodynamic properties of associated solutions). Bull Soc. Chim. Beiges 58, 547-565... 

Hydrogen bond formation between dissimilar molecules is an example of adduct formation, since the hydrogen atom that is bonded to an electronegative atom, such as oxygen or nitrogen, is a typical acceptor atom. The ability of molecules to donate a hydrogen bond is measured by their Taft-Kamlet solvatochromic parameter, a, (or a . for the monomer of self-associating solutes) (see Table 2.3). This is also a measure of their acidity (in the Lewis sense, see later, or the Brpnsted sense, if pro tic). Acetic acid, for instance, has a = 1.12, compared with 0.61 for phenol. However, this parameter is not necessarily correlated with the acid dissociation constant in aqueous solutions. 

G. F. Neumark and K. Kosai, Deep Levels in Wide Band-Gap III-V Semiconductors D. C. Look, The Electrical and Photoelectronic Properties of Semi-Insulating GaAs R. F. Brebrick, Chmg-Hua Su, and Pok-Kai Liao, Associated Solution Model for Ga-In-Sb and Hg-Cd-Te... 

Thus, suppose that when one wishes to measure an interfacial potential difference PDm /s, one connects the electrode with another electrode and measures the potential of this cell. Suppose one always keeps this second electrode constant in nature (i.e, the algebraic sum of the potentials associated with it is kept constant). Then, measurements of the potential of a cell in which the one (same) electrode and its associated solution were always present and the other [i.e., the first electrode mentioned here (Mt)] and its solution were changed would clearly reflect the changing interfacial potential difference FDM /s. This is in fact what is done to measure the relative values of PDM /sas Mjor S (or both) are varied. 

The partial structure factors for binary (Bhatia and Thorton, 1970) and multicomponent (Bhatia and Ratti, 1977) liquids have been expressed in terms of fluctuation correlation factors, which at zero wave number are related to the thermodynamic properties. An associated solution model in the limits of nearly complete association or nearly complete dissociation has been used to illustrate the composition dependence of the composition-fluctuation factor at zero wave number, Scc(0). For a binary liquid this is inversely proportional to the second derivative of the Gibbs energy of mixing with respect to atom fraction. 

Fig. 8. Calculated enthalpy of mixing of Ga-Sb melt at 721.9°C and experimental points from Gambino and Bros (1975). Curve 1 is fifth-power polynomial fit from Ansara et al. (1976). Curve 2 is our calculation with associated solution parameters giving the best compromise fit to the enthalpy of mixing and the liquidus points. Curve 3 is calculated using the subregular solution model and parameters given in the text.

InSb(s), one can set all of the interaction coefficients to zero to calculate the mole fraction of the associated species at x = and T=TAC for an ideal associated solution. For GaSb the value is 0.415, while for InSb it is 0.28. These are to be compared with the best fit values of z in Table VI. 

In the development of the associated solution model used a number of general features have been obtained, which hopefully should prove useful. In particular it is shown in Appendix that the model behavior includes the occurrence of miscibility gaps in the liquid that do not require interaction coefficients that are large in magnitude and that are associated with an uncommon form for the Gibbs energy of mixing isotherms. 

The miscibility gap behavior contained in the associated solution model would appear to be complex and has only been touched upon here. Miscibility... 

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