Solute behaviour ideal

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

The activity coefficient of component i, y(-, is now defined as a measure of the deviation from the ideal solution behaviour as the ratio between the chemical activity and the mole fraction of i in a solution. 

By using a thermodynamic model based on the formation of self-associates, as proposed by Singh and Sommer (1992), Akinlade and Awe (2006) studied the composition dependence of the bulk and surface properties of some liquid alloys (Tl-Ga at 700°C, Cd-Zn at 627°C). Positive deviations of the mixing properties from ideal solution behaviour were explained and the degree of phase separation was computed both for bulk alloys and for the surface. 

The activity coefficient of component i, y, is a measure for the deviation from ideal solution behaviour... 

At basic pH values the rate of 3-MPA formation is reduced, but continues at measurable rates even at a pH value as high as 10. These results indicate that acrylate ion possesses significant reactivity, although the undissodated form is much more reactive. In the addic pH ranee, the rate of 3-MPA formation in seawater is similar to that in Milli-Q water, but at basic pH values, the rates in seawater are higher than those in Milli-Q water (Figure 4). In an ionic medium such as seawater, for reactions involving ions, the Bronsted-Bjerrum equation predicts that ionic interactions cause deviations from ideal-solution behaviour (Equation 5) (451. 

One of the most successful applications of crystal field theory to transition metal chemistry, and the one that heralded the re-discovery of the theory by Orgel in 1952, has been the rationalization of observed thermodynamic properties of transition metal ions. Examples include explanations of trends in heats of hydration and lattice energies of transition metal compounds. These and other thermodynamic properties which are influenced by crystal field stabilization energies, including ideal solid-solution behaviour and distribution coefficients of transition metals between coexisting phases, are described in this chapter. 

Criteria for ideal solution behaviour The criteria for ideal solution behaviour are discussed in most chemical thermodynamic texts (e.g., Lewis and Randall, 1961, p. 130 Nordstrom and Munoz, 1986, p. 401). The conditions may be summarized as follows. 

The relationships expressed in eqs (7.2) to (7.5) lead to the following necessary conditions for ideal solid-solution behaviour. First, the heat of mixing, AHm, must be zero... 

A necessary condition for an ideal solid-solution behaviour is that there be zero heat of mixing in forming the solution from its components, eq. (7.6). This condition cannot be fulfilled when differences exist between CFSE s of cations in the end-member components and in the solid-solutions. 

This calculation shows that the formation of intermediate liebenbergite by mixing of Mg2Si04 and Ni2Si04 components is accompanied by an excess CFSE of mixing of -5.65 kJ/mole. These results suggest that Mg2+-Ni2+ olivines depart considerably from ideal solution behaviour (Bish, 1981). This is further demonstrated in fig. 7.4 by the compositional variation of excess CFSE of mixing for the suite of synthetic Mg2+-Ni2+ olivines for which site occupancy and CFSE data are available (table 7.2). 

Only in calcic clinopyroxenes, in which Ca2+ ions completely fill the M2 sites and Fe2+ and other transition metal ions occur in the Ml sites alone, is ideal solution behaviour to be expected. This is because cation ordering is not possible in one-site atomic substitution in the pyroxene Ml site. Furthermore, there is an insignificant variation of the CFSE of Fe2+ across the diopside-hedenbergite series ( 5.5.3). 

Figure 33.3 Henry s Law behaviour for solutes in ideal dilute solutions. Reproduction of Figure 33.2 but with tangents (C K, DL, HJ and Gl) appropriately drawn to the partial vapour pressure curves at the ends where they are acting as solute. ...

In Frame 39, section 39.3 we consider the question of deviations from ideal dilute solution behaviour at higher molalities. 

The variation in composition with cmc at the solid-solution interface now more closely resembles that expected for ideal mixing. The air-solution behaviour, where a monolayer is adsorbed, is associated with the different preferred... 

The Flory-temperature or theta-temperature (0F) is defined as the temperature where the partial molar free energy due to polymer-solvent interactions is zero, i.e. when y = 0, so that the polymer-solvent systems show ideal solution behaviour. If T = 0F, the molecules can interpenetrate one another freely with no net interactions. For systems with an upper critical solution temperature (UCST) the polymer molecules attract one another at temperatures T < 0F. If the temperature is much below 0F precipitation occurs. On the other hand for systems with a lower critical solution temperature (LOST) the polymer molecules attract one another at temperatures T > F. If the temperature is much above 0F precipitation occurs. Aqueous polymer solutions show this behaviour. Systems with both UCST and LCST are also known (see, e.g. Napper, 1983). 

For a solute in solution. For a solute in a liquid or solid solution the standard state is referenced to the ideal dilute behaviour of the solute. It is the (hypothetical) state of solute B at the standard molality m, standard pressure and exhibiting infinitely diluted solution behaviour. The standard chemical potential is defined as... 

The molecular structure of binary HBD/HBA solvent mixtures is largely determined by intermolecular hydrogen bonding between the two components, which usually leads to pronounced deviations from ideal solution behaviour [306, 325-327]. Representative examples are trichloromethane/acetone [326] and trichloromethane/dimethyl sulfoxide mixtures [327], which readily form hydrogen-bonded 1 1 and 2 1 complexes, respectively, with distinct changes in their physical properties as a consequence. 

The non-ideal behaviour of a wide selection of binary solvent mixtures has been studied experimentally mainly by means of suitable solvatochromic dyes, the UV/Vis absorptions of which are solvent-dependent [cf. Section 6.2.1) see references [380-385] for some more recent examples. Conversely, the largely non-ideal solute behaviour in binary solvent mixtures has been used for the quantitative determination of the compositions of such solvent mixtures, e.g. for the determination of small water contents in organie solvents [386-388]. 

The term activity is used in the description of the departure of the behaviour of a solution from ideality. In any real solution, interactions occur between the components which reduce the effective concentration of the solution. The activity is a way of describing this effective concentration. In an ideal solution or in a real solution at infinite dilution, there are no interactions between components and the activity equals the concentration. Nonideality in real solutions at higher concentrations causes a divergence between the values of... 

Table 7.1 shows the wide variation which exists in solution behaviour. The acetone/carbon disulphide system is far from ideal this non-ideality will also show up in properties such as the vapour pressure curves, and the boiling point diagram. As a result of all this, we could say that u, for a compound i (the subscript implies a mixture) depends not only on the nature of the compound, but also on the environment in which it finds itself. In this more complete sense, u, is known as the partial molar free energy,... 

Electrolyte solutions are non-ideal, with non-ideality increasing with increase in concentration. When experimental results on aspects of electrolyte solution behaviour are analysed, this non-ideality has to be taken into consideration. The standard way of doing so is to extrapolate the data to zero ionic strength. However, it is also necessary to obtain a theoretical description of non-ideality, and to deduce theoretical expressions which describe non-ideality for electrolyte solutions. Non-ideality is taken to be a manifestation of the electrostatic interactions which occur as a result of the charges on the ions of an electrolyte, and these interactions depend on the concentration of the electrolyte solution. Theoretically this non-ideaUty is taken care of by an activity coefficient for each ion of the electrolyte. 

This chapter describes the behaviour of electrolyte solutions under ideal conditions. Chapter 12 describes the theoretical attempts made to cope with the problems introduced when non-ideality is considered. 

An Arrhenius plot, i.e. the (lnA, ) versus (1/7) function, brings information about the departure from an ideal solution behaviour (cooperativeness). A linear function is characteristic of the absence of cooperative effects (Fig. 9.13). The deviations from linearity increase with the value of the interaction parameter y. 

Zeolites Y dealuminated by Si/Al substitution using SiCU (DAY-S) and dealuminated thermochemically in steam (DAY-T) were investigated by X-ray powder diffraction, infrared spectroscopy and wet chemical methods. The dependence of lattice constants (a) on the molar ratio X = (1+Si/Al) show non-ideal solid solution behaviour. In a first approximation the change in a (in nm) can be described as a = 0.187x+2.412, for 0.1 < x < 0.5. For x < 0.1 the change in lattice constant saturates towards a = 2.425 nm. A similar shift in the double ring mode (wdr) is observed, tailing off. 

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