Composition of solutions

This chapter begins by explaining how the composition of solutions is defined and how solutions are prepared. It is important to master these concepts, because the properties and behavior of solutions are determined by their composition. With this background, we give quantitative descriptions of chemical reactions and phase equilibria in solutions, and relate these events to the nature of the species in the solution. 

Several measures are used to specify the composition of a solution. Mass percentage (colloquially called weight percentage), frequently used in everyday applications, is defined as the percentage by mass of a given substance in the solution. In quantitative chemistry, the most useful measures of composition are mole fraction, molarity, and molality. 

The mole fraction of a substance in a mixture is the number of moles of that substance divided by the total number of moles present. This term was introduced in the discussion of gas mixtures and Dalton s law (see Section 9.4). In a binary mixture containing ni mol of species 1 and U2 mol of species 2, the mole fractions Xi and X2 are 

The mole fractions of all the species present must add up to 1. When a clear distinction can be made between solvent and solutes, the label 1 denotes the solvent and higher numbers are given to the solutes. If comparable amounts of two liquids such as water and alcohol are mixed, the assignment of the labels 1 and 2 is arbitrary. 

The concentration of a substance is the number of moles per unit volume. The SI units moles per cubic meter are inconveniently large for chemical work, so instead we use the molarity, defined as the number of moles of solute per liter of solution  

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Smith [113] studied the adsorption of n-pentane on mercury, determining both the surface tension change and the ellipsometric film thickness as a function of the equilibrium pentane pressure. F could then be calculated from the Gibbs equation in the form of Eq. ni-106, and from t. The agreement was excellent. Ellipsometry has also been used to determine the surface compositions of solutions [114,115], as well polymer adsorption at the solution-air interface [116]. 

System in which the solid phases consist of the pure components and the components are completely miscible in the liquid phase. We may now conveniently consider the general case of a system in which the two components A and B are completely miscible in the liquid state and the solid phases consist of the pure components. The equilibrium diagram is shown in Fig. 1,12, 1. Here the points A and B are the melting points of the pure components A and B respectively. If the freezing points of a series of liquid mixtures, varying in composition from pure A to pure B, are determined, the two curves represented by AC and BC will be obtained. The curve AC expresses the compositions of solutions which are in equilibrium, at different temperatures, with the solid component A, and, likewise, the curve BC denotes the compositions... 

By analogy with the mechanisms of nitration in other media, and from a knowledge of the composition of solutions of acetyl nitrate in acetic anhydride, the following may be considered possible nitrating species in these solutions ... 

We have already come across one example of the qualitative application of acid-base titrimetry in assigning the forms of alkalinity in waters (see Example 9.5). This approach is easily extended to other systems. For example, the composition of solutions containing one or two of the following species... 

Table 60. Initial dissolution rates (RJ of niobium and tantalum dissolved from columbite or tantalite in different solutions, at 80% . (Compositions of solutions are given in mol/l)(qfter Majima et al. [415]).

The composition of solutions that are used for washing and stripping of extracts is also different and is adjusted for each specific case however, some common conditions can be noted. It is recommended that the extract obtained following collective extraction, which contains both tantalum and niobium, be washed (scrubbed) using sulfuric acid solutions that contain at least 6 mol per liter of H2SO4. Collective stripping of the elements, on the other hand, can be... 

The rest of this chapter is a variation on a theme introduced in Chapter 9 the use of equilibrium constants to calculate the equilibrium composition of solutions of acids, bases, and salts. We shall see how to predict the pH of solutions of weak acids and bases and how to calculate the extent of deprotonation of a weak acid and the extent of protonation of a weak base. We shall also see how to calculate the pH of a solution of a salt in which the cation or anion of the salt may itself be a weak acid or base. 

Equilibria considerations on solution-grown zinc chalcogenide compounds have been put forward by Chaparro [28] who examined the chemical and electrochemical reactivity of solutions appropriate for deposition of ZnS, ZnSe, ZnTe (and the oxide ZnO) in order to explain the results of recipes normally used for the growth of such thin films. The author compared different reaction possibilities and analyzed the composition of solutions containing zinc cations, ammonia, hydrazine, chalcogen anions, and dissolved oxygen, at 25 °C, by means of thermodynamic diagrams, applicable for concentrations usually employed in most studies. 

The pressure above a solution relates to the composition of solution, according to Henry s law see Section 5.6. 

Generally, the activity coefficient y depends on the composition of solution. In the ranges of our narrow purposes of investigations of the macromolecules chemical potential conformation term influence on the osmotic pressure of polymeric solutions we will be neglect by the change of y lying y = const in all range of the macromolecules concentrations into solution. This permits to write... 

Equilibrium composition of solutions in contact with freshly precipitated, Al(OH)3 and Fe(OH)3, calculated, using representative values for the equilibrium constants for solubility and hydrolysis equilibria. Shaded areas are approximate operating regions in water treatment practice coagulation in these systems occurs under conditions of oversaturation with respect to the metal hydroxide. 

Two other conventions exist for the choice of standard states for components of a solution. One convention chooses the pure component at 1 bar of pressure, for conformance with the usual standard state for pure components. This choice has the disadvantage that it requires aterm for the effect of pressure in the relation between the chemical potentials of the pure component and of the component in solution. The other convention chooses the pure component at the vapor pressure of the solution. This choice has the disadvantage of having different standard states for each composition of solution. 

Figure 17.3. Data for vapor pressure and composition of solutions of methyl rert-butyl ether Pi and chloroform p2 at 313.15 K. Data from Ref. 2.

The data in Table 17.3 are for vapor pressure and vapor and liquid composition of solutions of methyl tert-butyl ether (1) and acetonitrile (2), (9). The symbol Xi represents the mole fraction of (1) in the liquid phase, and yi represents the mole fraction of (1) in the vapor phase. P is the equilibrium vapor pressure of the solution. The temperature is 313.15 K. 

An infinitesimal transfer of glycine from the sohd phase to the solution at constant temperature, pressure, and composition of solution results in a corresponding change dJ in the thermodynamic property J of the system composed of crystalline glycine and a 1-molal aqueous solution of glycine. The application of Equation (9.32) leads to the expression... 

The ion selectivity of a membrane can be established by measuring the potential difference between two identical reference electrodes. One electrode is immersed in the specimen solution, the other in a reference solution, and the membrane is interposed between them. The composition of solution 2 is constant, and, if both solutions contain monovalent ions, the ion-exchange process can be described as follows ... 

If the composition of solution 2 is assumed to remain unchanged, the above reduces to ... 

Furthermore, if the overall concentration of positive charges is the same on both membrane surfaces and if the composition of solution 2, which contains cations of the I2+ sort only, remains constant, then ... 

Table I.—Percentage Composition of Solutions of Perchloric Acid of Specific Gravity between 1-00 and 1-67 at 15°.

B) Composition of solution to be distilled (silver plating solntion and silver drag-out for silver recovery) ... 

The composition of aqueous solutions of D-arahino-2-hexulose (d-fructose) has also been studied by laser-Raman spectroscopy.45 (The composition of solutions of D-fructose appears to have been determined by more methods, and more often, than that of any other sugar.20)... 

Before discussing the composition of solutions of individual sugars, it will be instructive to look at the relative stabilities of the various forms of the sugars. These considerations will give a general overview, and also provide explanations for some of the results. 

The equilibrium compositions of aqueous solutions of some aldoheptoses are listed in Table III. Because the additional carbon atom in the side chain does not introduce additional steric interactions, the composition of solutions of heptoses is similar to that of the homomorphous hexoses, with only one exception, namely, n-glycero-n-ido-heptose, 92 a-D-Idopyranose in solution is a mixture of the 4Ci and 1C4 conformant) S. J. Angyal and R. J. Beveridge, Carbohydr. Res., 65 (1978) 229-234. 

The composition of solutions of the 2-heptuloses has been determined, and discussed, by Angyal and Tran.92 These ketoses are different from other reducing sugars inasmuch as there are two hydroxymethyl side chains attached to the pyranose ring. In the a-pyranose form, they are cis to each other and will therefore both be equatorial in the preponderant chair form. In the / -pyranose, however, one or other of the hydroxymethyl groups has to be axial and, in consequence, the / anomers are disfavored in only one solution (that of the altro isomer) was the yS-pyra-nose detected in the 13C-n.m.r. spectrum.92... 

Whereas the composition of solutions of the unsubstituted aldoses and ketoses has been systematically investigated, very few studies have been conducted on substituted and on derived sugars, such as amino sugars,... 

Here is how we calculate the pH and composition of solutions prepared from different forms of a diprotic acid (H2A, HA, or A2 ). 

Table 8 Percentage Composition of Solutions of 3-Substituted Indolizines in Trifluoroacetic Acid (66jcs(B)44)...

Figure 2. pH dependence of the computed composition of solutions, which were 0.003M in nickel(II)nitrate and 0.003M or 0.0003M in L-threonine, at 37°C and 0.15M in potassium nitrate, using the values of constants summarized in Table 1... 

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