Liquid solutions phase rule

The general XT E problem involves a multicomponent system of N constituent species for which the independent variables are T, P, N — 1 liquid-phase mole fractions, and N — 1 vapor-phase mole fractions. (Note that Xi = 1 and y = 1, where x, and y, represent liquid and vapor mole fractions respectively.) Thus there are 2N independent variables, and application of the phase rule shows that exactly N of these variables must be fixed to estabhsh the intensive state of the system. This means that once N variables have been specified, the remaining N variables can be determined by siiTUiltaneous solution of the N equihbrium relations ... 

The curves in Fig. 10 were drawn for the particular instance of a volatile solute dissolved in a volatile solvent, such as would exist for the acetone-chloroform system (whose diagram is very nearly like that of Fig. 10B). For many nonvolatile solutes, it not possible to trace smooth partial pressure curves across the entire range of mole fractions. This is especially true for aqueous salt solutions, where at a certain concentration of solute the solution becomes saturated. Any further addition of crystalline solute to the system does not change the mole fraction in the liquid phase, and the partial pressure of water thereafter remains constant, in accord with the phase rule. This phenomenon permits the use of saturated salt solutions as media to establish fixed relative humidity values in closed systems [12],... 

The behavior of carbonates will be used to illustrate heterogeneous processes, with emphasis upon the formation of inorganic surface coatings and solid solutions. This is a vital topic in the study of solid-solution interactions since it is coatings rather than bulk phases which are sensed by liquid solutions. Homogeneous reactions will be studied in terms of the competition of coulombic ion pairs with true complexes for anions. An extended form of the phase rule will be used. 

Once a quantity of a third substance (solute) is added to a system of two immiscible liquids, it will distribute or divide between the layers in definite proportions. Applying the phase rule to such a system reveals that we have a system of three components (C) and two phases (P). Thus, the system has three degrees of freedom (F), that is, pressure, temperature, and concentration. 

For solid-liquid equilibrium in a quaternary system, the Gibbs phase rule allows four degrees of freedom. If T, P, xc, and xD (in which x is the mole fraction of component i in liquid solution) are specified, then xA, x, t/, and xAC (in which x is the mole fraction of component ij in solid solution) are determined, and the system is invariant. These variables are defined by the following equations ... 

The solubility of solid and liquid solutes in liquid solvents generally increases with increasing temperature. There are a few exceptions to this rule, but not many. This is why there are a few medications that are stored at room temperature. For example, a concentrated mannitol solution will crystallize if stored at low temperatures. Warming the solution will cause the crystallized solid to redissolve. Temperature has the opposite effect on the solubility of gaseous solutes in liquid solvents. As the temperature increases, the vapor pressure of the gaseous solutes increases to the point that they can escape the solvent into the gas phase. 

The lacking special description of the Gibbs phase rule in MEIS that should be met automatically in case of its validity is very important for solution of many problems on the analysis of multiphase, multicomponent systems. Indeed, without information (at least complete enough) on the process mechanism (for coal combustion, for example, it may consist of thousands of stages), it is impossible to specify the number of independent reactions and the number of phases. Prior to calculations it is difficult to evaluate, concentrations of what substances will turn out to be negligibly low, i.e., the dimensionality of the studied system. Besides, note that the MEIS application leads to departure from the Gibbs classical definition of the notion of a system component and its interpretation not as an individual substance, but only as part of this substance that is contained in any one phase. For example, if water in the reactive mixture is in gas and liquid phases, its corresponding phase contents represent different parameters of the considered system. Such an expansion of the space of variables in the problem solved facilitates its reduction to the CP problems. 

The dimensions of the space available are in the nanometer range. At this length scale, water is supposed to behave as a constrained liquid, which follows rules of diffusion, flow and structuring more akin to those of gels than to those observed in free liquids [108]. Furthermore, if the silk is present as a gel phase, the structured nature of the water molecules is even more enhanced. This in turn affects the activities of the ions within this medium, especially where polyelectrolytes are also involved. This speculative scenario envisages that the chemical environment of nucleation is very different from a simple saturated solution, and that the thermodynamics and kinetics of nucleation are more akin to crystallization from hydrogels. The same situation exists also in collagen-mediated mineralization, where the tiny apatite crystals form inside the... 

A study of the curves m fig. 50 is particularly interesting from the point of view of the Phase Rule. AB represents the various states of equilibrium between ice and feme chloride solutions, a minimum temperature being reached at the ervohydnc point B. which is —553 C. At this point ice, solution, and the dodeeahydrate of ferric chloride are in equilibrium. The number of degrees of freedom is nil—in other words, the system is invariant, and if heat be subtracted the liquid phase will solidify without change of temperature until the whole has become a solid mass of ice and dodeeahydrate. Further abstraction of heat merely lowers the temperature of the system as a whole. 

The phase rule plays an important part in chemistry. For example, it helps to answer the controversial question of long standing whether the solubility of solids in liquids depends only on temperature, or also on pressure. Inasmuch as such a system is composed of two phases (liquid solution and a solid) and two components (solvent and solute), then... 

The Phase Rule—A Method of Classifying Al Systems in Equilibrium. We have so far discussed a number of examples of systems in equilibrium. These examples include, among others, a crystal or a liquid in equilibrium with its vapor (Chap. 4), a crystal and its liquid in equilibrium with its vapor at its melting point (Chap. 4), a solution... 

Let us now consider the application of this rule. We ask Is it ever possible for four phases to exist together in equilibrium The answer is seen to be that it is, provided that there are at least two components -—it is not possible for a one-component system, such as that made of pure water-substance. If there are only two components, the four phases can co-exist only at exactly fixed temperature and pressure. For example, we might add copper sulfate to the water in our system. The components would then be 2 in number (C = 2). With icc, liquid solution, and water vapor present (P 3), the temperature could still be varied somewhat, by varying the concentration of copper sulfate in the liquid solution. The variance would then be I, with three phases. On lowering the temperature there would ultimately be formed crys... 

When multicomponent gas and liquid phases are in equilibrium, a limited number of intensive system variables may be specified arbitrarily (the number is given by the Gibbs phase rule), and the remaining variables can then be determined using equilibrium relationships for the distribution of components between the two phases. In this section we define several such relationships and illustrate how they are used in the solution of material balance problems. 

The Gibbs phase rule shows that specifying temperature and pressure for a two-component system at equilibrium containing a solid solute and a liquid solution fixes the values of all other intensive variables. (Verify this statement.) Furthermore, because the properties of liquids and solids are only slightly affected by pressure, a single plot of solubility (an intensive variable) versus temperature may be applicable over a wide pressure range. 

Suppose the mass fraction of ammonia in a liquid solution of NH3 and H2O al 1 atm is specified to be 0.25. According to the phase rule, the system temperature and the mass fraction of NH3 in the vapor phase are uniquely determined by these specifications. (Verify.) A tie line may therefore be drawn on the enthalpy-concentration chart from x - 0.25 on the liquid-phase curve to the corresponding point on the vapor-phase curve, which is at y = 0.95 and the... 

Let us now consider the systems which have one degree of freedom (so-caUed monovariant systems). According to the phase rule, these must consist of three phases, and may contain gas, solution, and sohd phase, or gas and two sohd phases. Systems composed of sohd phases alone, or of sohd and liquid phases alone, are caUed condensed systems. Condensed systems See Abegg, Handb. d. anorg. Chemie, vol. ii. p. 95. 

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