Pure solids

We next treat the case of solid-liquid equilibria (SLE), solid-solid equilibria (SSE), and solid-solid-liquid equilibria (SSLE). Solids that are in equilibrium with liquids can take two forms (1) pure solids that are immiscible with other species and (2) solid solutions that, like liquid solutions, contain more than one species. Ciystalhne solids are formed within a well-defined geometrical lattice structure. While partial miscibility in liquid systems is due solely to the relative strength of like intermolecular interactions compared to unlike intermolecular interactions, the ability of solids to mix depends primarily on how well one atom fits to the lattice structure of the other species. Thus, complete solid miscibility occurs only when species are nearly the same size, have the same crystal structure, and have similar electronegativities and valences. We treat pure solids first and then address solid solutions. 

We now look at how to construct these phase diagrams from thermodynamic property data. Our criteria for species i in solid-liquid equilibrium is  

However, if the solid phase contains only pure species i, we can replace the fugacity of solid species i in the mixture with its pure species fugacity. Choosing the Lewis/Randall 

However, we can relate the right-hand side to the definition of fugacity for a pure species  

The term on the left-hand side is equal to the Gibbs energy of fusion, Agfos- Plugging in Equation (8.40) and rearranging  

---

In the phase equilibrium between a pure solid (or a liquid) and its vapour, the addition of other gases, as long as they are insoluble in the solid or liquid, has negligible effect on the partial pressure of the vapour. 

Legay-Sommaire N and Legay F 1980 Observation of a strong vibrational population inversion by CO laser exoitation of pure solid oarbon monoxide IEEE J. Quantum Electron. 16 308-14... 

Effect of impurities upon the melting point. Let us take a specific example and examine the effect of the addition of a small quantity of naphthalene to an equilibrium mixture of pure solid and liquid a-naphthol at the temperature of the true melting point (95 5°) at atmospheric pressure. 

The high boiling point residue contains p- (b.p. 173°, m.p. 53°) and o-dichloro-benzene (b.p. 179°), which may be separated, upon cooling in ice, the moderately pure solid para isomer separate out. 

To a stirred solution of 0.5 ml of 10% aqueous sodium hydroxide and 8.25 mmol of the appropriate aldehyde in 10 ml of ethanol, 8.25 mmol of 2-ace tylpyri dine was added drop wise during 2-3 hours. The temperature was kept at 0°C. After stirring for another 2 hours the reaction mixture was filtered, yielding almost pure solid 2.4a (7.26 mmol, 88%) or 2.4b (7.76 mmol, 94 %). After crystallisation... 

Even though water is a reactant (a Brpnsted base) its concentration does not appear m the expression for because it is the solvent The convention for equilibrium constant expressions is to omit concentration terms for pure solids liquids and solvents... 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

A stock solution is prepared by weighing out an appropriate portion of a pure solid or by measuring out an appropriate volume of a pure liquid and diluting to a known volume. Exactly how this is done depends on the required concentration units. For example, to prepare a solution with a desired molarity you would weigh out an appropriate mass of the reagent, dissolve it in a portion of solvent, and bring to the desired volume. To prepare a solution where the solute s concentration is given as a volume percent, you would measure out an appropriate volume of solute and add sufficient solvent to obtain the desired total volume. 

For gases, pure solids, pure liquids, and nonionic solutes, activity coefficients are approximately unity under most reasonable experimental conditions. For reactions involving only these species, differences between activity and concentration are negligible. Activity coefficients for ionic solutes, however, depend on the ionic composition of the solution. It is possible, using the extended Debye-Htickel theory, to calculate activity coefficients using equation 6.50... 

In the case of a simple eutectic system shown in Fig. 22-2, a pure solid phase is obtaiuea by cooling it the composition oFthe feed mix-... 

Figure 4.31. A comparison of the results from shock temperature measurements on Fe. Hatchured area for Fe melting is defined by the results of Bass et al. (1987), Williams et al. (1987), and the theoretical calculations of McQueen et al. (1970) predict that the shock temperatures of solid stainless steel are lower than for pure, solid iron, as observed.

Skeletal Density—SD. The actual density of the pure solid materials that make up the individual catalyst particles. For an FCC catalyst, the skeletal density can be calculated as follows ... 

Skeletal Density is the actual density of the pure solid materials that make up individual particles. 

But that is not all. For dilute solutions, the solvent concentration is high (55 mol kg ) for pure water, and does not vary significantly unless the solute is fairly concentrated. It is therefore common practice and fully justified to use unit mole fraction as the standard state for the solvent. The standard state of a close up pure solid in an electrochemical reaction is similarly treated as unit mole fraction (sometimes referred to as the pure component) this includes metals, solid oxides etc. 

The freezing point lowering, like the boiling point elevation, is a direct result of the lowering of the solvent vapor pressure by the solute. Notice from Figure 10.8 that the freezing point of the solution is the temperature at which the solvent in solution has the same vapor pressure as the pure solid solvent. This implies that it is pure solvent (e.g., ice) that separates when the solution freezes. 

The second kind of interaction takes place between solids and as a pure solid phase interaction, does not release any C02. 

Standard 0.002M potassium bromate solution. From the pure solid. 

Discussion. The turbidity of a dilute barium sulphate suspension is difficult to reproduce it is therefore essential to adhere rigidly to the experimental procedure detailed below. The velocity of the precipitation, as well as the concentration of the reactants, must be controlled by adding (after all the other components are present) pure solid barium chloride of definite grain size. The rate of solution of the barium chloride controls the velocity of the reaction. Sodium chloride and hydrochloric acid are added before the precipitation in order to inhibit the growth of microcrystals of barium sulphate the optimum pH is maintained and minimises the effect of variable amounts of other electrolytes present in the sample upon the size of the suspended barium sulphate particles. A glycerol-ethanol solution helps to stabilise the turbidity. The reaction vessel is shaken gently in order to obtain a uniform particle size each vessel should be shaken at the same rate and the same number of times. The unknown must be treated exactly like the standard solution. The interval between the time of precipitation and measurement must be kept constant. 

Fig. 1. The pressure-temperature-composition surfaces for the equilibrium between two pure solid phases, a liquid phase, and a vapor phase.

The equilibrium between a pure solid and a gaseous mixture is one of very few classes of solution for which an exact treatment can be made by the methods of statistical mechanics. The earliest work on the theory of such solutions was based on empirical equations, such as those of van der Waals,45 of Keyes,44 and of Beattie and Bridgemann.3 However, the only equation of state of a gas mixture that can be derived rigorously is the virial expansion,46 66... 

Equation 8 may be fitted to those results just described for which the vapor pressure of the pure solid is known. We show graphically the second virial coefficients derived from such fitting and those derived from conventional p-V-T measurements. 

For antibiotic production, the fermentation broth needs a pretreatment tank to produce crude and highly purified antibiotic products. The bioprocesses involved in producing antibiotics are spray or continuously dried crude solids and pure solid in the form of crystalline antibiotic. 

Matrix isolation studies suggest isolated D3h molecules, but the pure solid has a more complicated IR spectrum indicating both bridging and terminal fluorines [28]. 

According as we put dT, dp, or ds equal to zero, we have the equations representing the alteration of pressure required to keep a solution of altered concentration in equilibrium with ice at the same temperature, or the alteration of freezing-point with concentration, or the alteration of freezing-point of a given solution with pressure, respectively. Similar equations apply when the solid is the pure solid solute, e.g., a salt along with its saturated solution. 

---