Solubility molality

Molal solubility -> Molality of a saturated solution of a substance... 

Correlation of water solubility (molality) with W has also been determined for the saturated alcohols ... 

The solubility of boric acid in water (Table 6) increases rapidly with temperature. The heat of solution is somewhat concentration dependent. For solutions having molalities in the range 0.03—0.9 the molar heats of solution fit the empirical relation (49) ... 

In the case of a sparingly soluble substance, if each of the quantities in (64) is divided by Avogadro s constant, we confirm the statement made above— namely, that, if AS at per ion pair is added to the contribution made to the entropy of the crystal by each ion pair, in this way we evaluate the contribution made by one additional ion pair to the entropy of the saturated solution and it is important to grasp that this contribution depends only on the presence of the additional pair of ions in the solution and does not depend on where they have come from. They might have been introduced into the solution from a vacuum, instead of from the surface of a solid. In (64) the quantities on the right-hand side refer to the solution of a crystal, but the quantity (S2 — Si) does not it denotes merely a change in the entropy of a solution due to the presence of additional ions, which may have come from anywhere. When Si denotes the entropy of a sufficiently large amount of solution, (S2 — Si) is the partial molal entropy of the solute in this solution. 

Let x and x denote the mole fractions of the two sparingly soluble solids in their respective saturated solutions let y and y denote their mole ratios, m and ml their molalities, and a and a their activities on the molality scale. If the saturated solutions are sufficiently dilute, we may, with sufficient accuracy, neglect the differences between the four ratios x/x, y/yf, m/m, and a/a. We can express the difference between the cratic terms by means of any of these quantities, thus,... 

Finally, as an example of a highly soluble salt, we may take sodium chloride at 25° the concentration of the saturated solution is 6.16 molal. The activity coefficient of NaCl, like that of NaBr plotted in Fig. 72, passes through a minimum at a concentration between 1.0 and 1.5 molal and it has been estimated2 that in the saturated solution the activity coefficient has risen to a value very near unity. Writing y = 1.0, we find that the work required to take a pair of ions from the surface of NaCl into pure water at 25° has the rather small value... 

Solubilities of quartz and amorphous silica in aqueous solutions increase with increasing of temperature (Holland and Malinin, 1979). Solubility of barite depends on salinity and temperature (Blount, 1977). The solubility of barite in hydrothermal solution having more than 1 molal NaCl concentration increases with increasing temperature, while a solubility maximum exists in the solution with NaCl concentration less than ca. 0.2 molal (Blount, 1977). 

Figure 1.55. The relationships between the concentration product, (Ba " )i(S04 )i, at the initiation of barite precipitation, and morphologies of barite crystals (Shikazono, 1994). The dashed line represents the boundary between dendritic barite crystals and well-formed rhombohedral, rectangular, and polyhedral barite crystals. The 150°C data are from Shikazono (1994) the others from other investigations. D dendritic (spindle-like, rodlike, star-like, cross-like) barite Dp feather-like dendritic barite W well-formed rectangular, rhombohedral, and polyhedral barite. The boundary between the diffusion-controlled mechanism (Di) and the surface reaction mechanism (S) for barite precipitation at 25°C estimated by Nielsen (1958) The solubility product for barite in 1 molal NaCl solution at 150°C based on data by Helgeson (1969) and Blount (1977). A-B The solubility product for barite in 1 molal NaCl solution from 25 to 150°C based on data by Helgeson (1969).

Marshall, W.L., Slusher, R. and Jones, E.V. (1964b) Aqueous systems at high temperatures, XIV Solubility and thermodynamic relationships for CaSOa in NaCl-H20 solutions from 40°C to 200°C, 0 to 4 molal NaCl. J. Ghent. Eng. Data, 9, 187-191. 

If a2/ax = gim2lgxmx m2/mx (a = activity, g = molal activity coefficient, m = molality) if Henry s law is obeyed and a = gm, mh and m2 are the molal solubilities of the polymorphs, and if the standard molar enthalpies and standard molar entropies of solution are, respectively,... 

Figure 16 Van t Hoff plot of molal solubility versus reciprocal absolute temperature for theophylline in water. (Reproduced with permission from Ref. 50.)...

In this chapter, you learned about solutions. A solution is a homogeneous mixture composed of a solvent and one or more solutes. Solutions may be unsaturated, saturated, or supersaturated. Solution concentration units include percentage, molarity, molality, and mole fraction. The solubility of solids in liquids normally increases with increasing temperature, but the reverse is true of gases dissolving in liquids. The solubility of gases in liquids increases with increasing pressure. 

The procedure of Beutier and Renon as well as the later on described method of Edwards, Maurer, Newman and Prausnitz ( 3) is an extension of an earlier work by Edwards, Newman and Prausnitz ( ). Beutier and Renon restrict their procedure to ternary systems NH3-CO2-H2O, NH3-H2S-H2O and NH3-S02 H20 but it may be expected that it is also useful for the complete multisolute system built up with these substances. The concentration range should be limited to mole fractions of water xw 0.7 a temperature range from 0 to 100 °C is recommended. Equilibrium constants for chemical reactions 1 to 9 are taken from literature (cf. Appendix II). Henry s constants are assumed to be independent of pressure numerical values were determined from solubility data of pure gaseous electrolytes in water (cf. Appendix II). The vapor phase is considered to behave like an ideal gas. The fugacity of pure water is replaced by the vapor pressure. For any molecular or ionic species i, except for water, the activity is expressed on the scale of molality m ... 

Solubility. Assume now that the solubility of KC1 is to be predicted at 100°C in 3.48 molal NaCl which when saturated with KC1 is known to be 5.34 molal in this latter salt. To predict this molality, it is merely necessary to know and q, at... 

Salts for Low Solubility. A different test of these relations involves calculating solubilities of salts of low solubility in mixed solutions at 25°C. Thus a pure solution saturated with Gypsum, namely CaSC I O, has a molality of 0.0156 (7), hence... 

Solving Gypsum s solubility mgyp is found to be 0.047 molal,... 

The partial molal volumes of gases in water are needed to apply the Krichevsky-Kasarnowsky and the Krichevsky-Ilinskaya equations. A survey of the available experimentally measured partial molal volumes is given in Table VII. The results of Tiepel and Gubbins (2 ) seem especially reliable. The recent results of Popov and Drakin 26) usually appear to be much too high, possibly because of Popov and Drakin depended on literature solubility values for the concentration to be used in their calculation of the partial molal volume from the density data. 

Khodakovskiy (16) used this assumption to extrapolate dissociation constants for acids, Henry s law constants for gases and solubility products for salts. In a variation of this technique Khodakovskiy (17) has extrapolated partial molal heat capacities of ions and neutral molecules by using C = bT. 

KsjjMgl stoichiometric solubility product of MgC03 m molality... 

J mol The solubility of this sugar in 80% ethanol at this temperature is 20 g kg solvent, and the solute obeys Henry s law up to saturation in this solvent. Compute AfG for this sugar at 298 K in 80% ethanol. The standard state for this dissolved solute is a hypothetical 1-molal solution. 

The solubility of monoclinic sulfur in CS2 is 22-molal. What is the solubility of rhombic sulfur in the same solvent Assume that the activity coefficient for both forms of dissolved sulfur is 1. 

In the most dilute solutions studied, the molality of chloride ion was considerably greater than the molality of the hydrogen ion, because of the solubility of AgCl. Therefore, the mean molality m+ is tabulated, rather than the molality of either ion. 

Solubility concentratiorrs can be expressed many ways, including molarity (mol/L), molality (mol/kg), mole fraction, weight percent, mass per unit volume (e g., g/L), etc. The conversion formttlas for solutiotts having different concentration units are presented in Table 1. 

If the metal concentration in solution is sufficiently low to remain below the solubility product, increasing the pH, with molal concentration, T, and P remaining equal, hydrolysis proceeds by further solvation of H2O molecules, with proton loss according to the scheme... 

The adjustable interaction constants Q can be evaluated from the experimental data for three-component systems these constants can then be employed for concentration of temperature interpolations and also for calculation of phase equilibria in multicomponent systems. Moreover, the constants Q usually depend very little on temperature, as the relative molalities, related to the solubility of the substance in the pure solvent, are employed hence calculations of other isotherms can be carried out easily. 

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