Solubility, equilibrium

The equilibrium between a hydrated or otherwise solvated solid phase of salt MAx and its solution in an organic solvent, may be formulated as 

Heats of solution, for reasonably soluble salts, either in water or in organic solvent, in the absence of strong chemical reaction with the solvent, 

For solution in organic media, therefore, the experimental quantity of significance is not the lattice energy of the crystalline solid, but its heat of sublimation. Thus, the heat of sublimation (to monomeric gas molecules) of NaCl is given (Table 1) as 54.3 kcal/mole. Therefore, any solution process must produce an energy evolution of the order of 50 to 60 kcal/mole for the process which we shall write as 

The alkaline earths, particularly the lighter ones, have more definite water coordination, and a probable coordination number of 4. The heats of sublimation (Table I) of the magnesium salts are about 50 kcal/mole or higher, those for the calcium halides are over 60 kcal/mole, and for the heavier alkaline earths they run over 70 kcal/mole. For the beryllium halides other than the fluoride, however, the values are 30 to 33 kcal/mole. In 

For the alkali metal halides for which vapor interatomic-distance data and heat-of-sublimation data are available, the M+—X distances computed 

The solubility equilibrium, subject to natural processes in the subsurface matrix, was examined in Chapter 2. The process of contaminant dissolution is affected by the molecular properties of the compound, the composition of the aqueous solution, and the ambient temperature. Here, we focus our discussion on pollutant behavior. 

Solubility equihbrium is the final state to be reached by a chemical and the subsurface aqueous phase under specific environmental conditions. Equihbrium provides a valuable reference point for characterizing chemical reactions. Equilibrium constants can be expressed on a concentration basis (/ ), on an activity basis (K ), or as mixed constants (K ) in which all parameters are given in terms of concentration, except for H, OH , and e (electron) which are given as activities. 

we provide a short description of the reactions involving transfer of protons and electrons that affect the solubility equihbria. 

Acid-base equilibria are described by a group of reachons covering the transfer of protons, in which the proton donor is an acid and the acceptor is a base, acid base + proton, with the equilibrium constant given by 

Water is the ever-present proton acceptor in the subsurface. During the dissocia-hon of an acid in subsurface water, H3O is one of the dissociation products and the acid strength is a measurable parameter. In a dilute solution the activity of the hydrated protons equals that of H3O and the pH value characterizes the H-ion achvity. Substituting for pH in Eq. 6.1, we obtain 

The solubility of a solid in a solvent depends on the temperature. Solubility is the concentration when the solid solute is in equilibrium with the solution it is 

For dilute nonionic solutions, we may assume ideality and use the expression 

In this form the temperature dependence of the solubility is not explicit because AGfus is itself a function of T. This expression can also be written in terms of the enthalpy of fusion, Afffus, by differentiating it with respect to T and using the Gibbs-Helmholtz equation d AG/T)/dT — —AH/T (5.2.14)  

Since A/ffus does not change much with T, this expression can be integrated to obtain a more explicit dependence of solubility with temperature. 

Ionic solutions, also called electrolytes, are dominated by electrical forces which can be very strong. To get an idea of the strength of electrical forces, it is 

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In our first example, the stress to the equilibrium was applied directly. It is also possible to apply a concentration stress indirectly. Consider, for example, the following solubility equilibrium involving AgCl... 

A third method, or phenomenon, capable of generating a pseudo reaction order is exemplified by a first-order solution reaction of a substance in the presence of its solid phase. Then if the dissolution rate of the solid is greater than the reaction rate of the dissolved solute, the solute concentration is maintained constant by the solubility equilibrium and the first-order reaction becomes a pseudo-zero-order reaction. 

Common ion effect The tube at the left contains a saturated solution of silver acetate (AgC2H302). Originally the tube at the right also contained a saturated solution of silver acetate. With the addition of a solution of silver nitrate (AgNOs), the solubility equilibrium of the silver acetate is shifted by the common ion Ag+ and additional silver acetate precipitates. 

The simple form of the equilibrium expression (4) follows directly from the dynamic nature of the solubility equilibrium. There must be a dynamic balance between the rate that iodine molecules leave the ciystal and the rate that iodine molecules return to the crystal. To understand this dynamic balance, we must consider the factors that determine these two rates. 

Expression (2) applies to a solubility equilibrium, provided we write the chemical reaction to show the important molecular species present. In Section 10-1 we considered the solubility of iodine in alcohol. Since iodine dissolves to give a solution containing molecules of iodine, the concentration of iodine itself fixed the solubility. The situation is quite different for substances that dissolve to form ions. When silver chloride dissolves in water, no molecules of silver chloride, AgCl, seem to be present. Instead, silver ions, Ag+, and chloride ions, Cl-, are found in the solution. The concentrations of these species, Ag+ and Cl-, are the ones which fix the equilibrium solubility. The counterpart of equation (7) will be... 

Solubility equilibrium constants, such as (20) and (22), are given a special name—the solubility product. It is symbolized K,p. A low value of K,p means the concentrations of ions are low at equilibrium. Hence the solubility must be low. Table 10-11 lists solubility products for some common compounds. 

The concentrations of free carbonate and bicarbonate ions determined at solubility equilibrium as a function of pH. Decrements of the concentration near pH = 10 suggest the formation of the Pu(0H)2C03 precipitate and hence lowering solubilities of Pu02 (cf. Figure 2). 

The equilibrium constant for the solubility equilibrium between an ionic solid and its dissolved ions is called the solubility product, Ksp, of the solute. For example, the solubility product for bismuth sulfide, Bi2S3, is defined as... 

When a precipitate has been formed during the qualitative analysis of the ions present in a solution, it may be necessary to dissolve the precipitate again to identify the cation or anion. One strategy is to remove one of the ions from the solubility equilibrium so that the precipitate will continue to dissolve in a fruitless chase for equilibrium. Suppose, for example, that a solid hydroxide such as iron(IIl) hydroxide is in equilibrium with its ions in solution ... 

C12-0055. Draw a molecular picture illustrating the solubility equilibrium between KCl(s) and KCl(aq). 

A molecular view of the solubility equilibrium for a solution of sodium chloride in water. At equilibrium, ions dissolve from the crystal surface at the same rate they are captured, so the concentration of ions in the solution remains constant. 

By convention, a solubility equilibrium is written in the direction of a solid dissolving to give aqueous ions, and the equilibrium constant for this reaction is called the solubility product ( sp). Here, for example, is the reaction... 

When equal volumes of 0.100 M solutions of sodium bromide and silver nitrate are mixed, a white solid precipitates from the solution. Identify the precipitate, write the net ionic reaction for the solubility equilibrium, and identify any spectator ions. 

All sodium salts are soluble, and so are all nitrate salts, so It makes sense that neither of these ions participates in a solubility equilibrium. Furthermore, nitrate and sodium cations are neither acidic nor basic, so it makes sense that neither participates in an acid-base equilibrium. 

Over the eons, the flow and evaporation of water inside a cavern creates a stunning array of rock sculptures. Stalagmites grow upward from the floor, sometimes joining stalactites to form massive columns. Limestone dams create beautiful pools of water. Limestone draperies fall like curtains from water flowing around overhanging rock. Delicate mineral flowers sprout from the walls. All these features result from the aqueous solubility equilibrium of calcium carbonate. 

Identify the precipitate, write the net ionic equation for the solubility equilibrium, and identify the spectator species. 

The limestone deposits that decorate Carlsbad and other caverns are the result of the solubility equilibrium of calcium carbonate in groundwater, as described in Chapter 16 ... 

Now set up a concentration table. The equilibrium constant for precipitation is very large, so imagine the precipitation in two steps (see Example ). First, take the reaction to completion by applying limiting reactant stoichiomehy. Then switch on the solubility equilibrium ... 

A tiny amount of Cd (OH)2 dissolves in this approach to equilibrium, so we use the solubility equilibrium and Ksp — [Cd ]gg [OH ]gg = 7.2 x 10 The variable y represents the change to equilibrium in a reaction with a small equilibrium constant, so make the approximation that y will be small compared with 6.0 X 10... 

The problem asks for the g/L solubility of PbCl2 in pure H2 O and in 0.55 M NaCl. The same solubility equilibrium applies to each solution. 

Calcium carbonate is insoluble in pure water but dissolves in weakly acidic water. The role of this solubility phenomenon in the geochemistry of caverns is described in Box. We can understand this dependence on pH by examining the acid-base properties of the species involved in the solubility equilibrium. 

C18-0073. For the following salts, write a balanced equation showing the solubility equilibrium and write the solubility product expression for each (a) silver chloride (b) barium sulfate (c) iron(H) hydroxide and (d) calcium phosphate. 

By convention, [HA(s)] = [B(s)] = 1. Eqs. (6.1) represent the precipitation equilibria of the uncharged species, and are characterized by the intrinsic solubility equilibrium constant, Sq. The zero subscript denotes the zero charge of the precipitating species. In a saturated solution, the effective (total) solubility S, at a particular pH is defined as the sum of the concentrations of all the compound species dissolved in the aqueous solution ... 

Fig. 17.4. Absorbance versus wavelength (nM) spectroscopic measurement for acetazolamide compound. The solubility equilibrium is obtained at 72 hours after dissolution.

When having a look at variable conversion degrees, the different gas phase concentrations affect the liquid phase concentrations via the solubility equilibrium, as shown in Table 12.3. 

A In each case, we first write the balanced equation for the solubility equilibrium and then the equilibrium constant expression for that equilibrium, the Ksp expression ... 

A We use the solubility equilibrium to write the Kv expression, which we then solve to obtain the molar solubility, s, of Fe(OH)3. 

An ion pair is a close association of a cation and an anion in solution, whereas the ion product is the value obtained when the initial concentrations for the dissolved ions involved in the solubility equilibrium are inserted into the equilibrium constant expression. 

The solubility product as a measure of solubility was introduced in Chapter 3. For the solubility equilibrium... 

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