Equilibrium problems Solubility

The solubility of a precipitate can be improved by adding a ligand capable of forming a soluble complex with one of the precipitate s ions. For example, the solubility of Agl increases in the presence of NH3 due to the formation of the soluble Ag(NH3)2°" complex. As a final illustration of the systematic approach to solving equilibrium problems, let us find the solubility of Agl in 0.10 M NH3. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

Cubic and higher order polynomial expressions also arise naturally in a wide range of problems in chemistry, particularly in solubility and equilibrium problems. If we try to dissolve lead (II) chloride (PbCl2) instead of silver chloride, the solubility product expression becomes... 

The calculations involved in complex equilibria are the major subject of this chapter. The systematic approach to solving multiple-equilibrium problems is described. The calculation of solubility when the equilibrium is influenced by pH and the formation of complexes is also discussed. 

Solution of a multiple-equilibrium problem requires us to develop as many independent equations as there are participants in the system being studied. For example, if we wish to compute the solubility of barium sulfate in a solution of acid, we need to be able to calculate the concentration of all the species present in the solution. There are five species [Ba ], [SOj"l, [HSOj], [H30" ], and [OH ]. To calculate the solubility of barium sulfate in this solution rigorously, it is then necessary to develop five independent algebraic equations that can be solved simultaneously to give the five concentrations. 

So far, we have learned that if we know the chemical equilibria involved in a system, we can write a corresponding system of equations that allows us to solve for the concentrations of all species in the system. Although the systematic method gives us the means to solve equilibrium problems of great complexity, it is sometimes tedious and time consuming, particularly when a system must be solved for various sets of experimental conditions. For example, if we wish to find the solubility of silver chloride as a function of the concentration of added chloride, the system of five equations and five unknowns must be solved repetitively for each different concentration of chloride (see Example 11-9). 

We have only discussed two of the sixteen fields given in the figure, the prediction of the direction in which a reaction can proceed spontaneously by means of the chemical potential and the temperature and pressure dependence of p and its application. A next step would be to go over to mass action, i.e., the concentration dependence of p. This leads directly to the deduction of the mass action law, calculation of equilibrium constants, solubilities, and many other data. An expansion of the concept to colligative phenomena, diffusion processes, surface effects, electrochemical processes, etc., is easily possible. Furthermore, the same tools allow solving problems even at the atomic and molecular level that are usually treated by quantum statistical methods. 

Problem Solubility equilibrium of a salt is not limited to the concentrations of the ions that deliver the pure salt solution. If, for example, a large amount of chloride ions are added to the saturated sodium chloride solution, then the equilibrium deviates in such a way that solid sodium chloride is formed and precipitates (Le Chatelier s principle of getting rid of the stress ). This way, the position of equilibrium is altered however, the product of concentrations of sodium ions and chloride ions remain constant solubility product. 

These are used extensively in emf work to find, in particular, equilibrium constants, solubility products and equilibrium constants for complexing and ion-pair formation. Practice is necessary in recognising such situations and in handling them, and this is given in Worked Problems 9.23 to 9.27. 

The discussion in this section has been concerned with the distribution of a solute between two liquid, phases whose equilibrium is unaffected by the added solute. This will occur if the amount of added solute is very small, or if the solvents are essentially immiscible at all conditions. However, if the amount of dissolved solute is so large as to affect the miscibility of the solvents, the solute addition can have a significant effect on the solvents, including the increase (salting in) or decrease (saltin out) of the mutual solubility of the two solvents, as was discussed in Sec. 11.2. It is important to emphasize that such situations are described by the methods in Sec. 11.2 as a multicomponent liquid-liquid equilibrium problem, in contrast to the procedures in this section, which are based on the assumption that the partial or complete immiscibility of the solvents is imaffected by the addition of the partitioning solute. 

Solubility is an oft ill-defined term, used rather indiscriminately to refer to small amounts of a solute of one phase dissolved in a solvent of another phase. Invariably, the solvent is a liquid or dense fluid, though it may contain any number of components, while the solute may be gas, liquid, or solid. Solubility problems are really phase-equilibrium problems and are attacked using the general strategies presented in Chapter 10. In this section we describe the three common solubility problems gas solubility, which refers to supercritical gases dissolved in liquids ( 12.2.1) solid solubility, which refers to solids dissolved in liquids ( 12.2.2) and solubilities in near-critical... 

The impact of these liquid phase reactions on the phase equilibrium properties is thus an increased solubility of NH3, CO2, H2S and HCN compared with the one calculated using the ideal Henry s constants. The reason for the change in solubility is that only the compounds present as molecules have a vapour pressure, whereas the ionic species have not. The change thus depends on the pH of the mixture. The mathematical solution of the physical model is conveniently formulated as an equilibrium problem using coupled chemical reactions. For all practical applications the system is diluted and the liquid electrolyte solution is weak, so activity coefficients can be neglected. 

PROBLEM STRATEGY This problem is the reverse of the preceding ones instead of finding K p from the solubility, here you calculate solubility from the K p. You follow the three steps for equilibrium problems, but since the molar solubility is not hnmediately known, you assign it the value x. For Step 1, you obtain the concentration of each ion by multiplying x by the coefficient of the ion in the chemical equation. In Step 2, you obtain AT as a cubic in x. In Step 3, you solve the equilibrium-constant equation... 

If you add the solubility equilibrium and the complex-ion equilibrium (the two equations just before this example), you obtain the overall equilibrium for the dissolving of AgCl in NH3. The equilibrium constant for this reaction equals the product of the equilibrium constants for solubility and complex-ion formation. (We will show that in the solution to this example however, we discussed the general principle at the end of Section 15.2.) Once you have the equilibrium constant, you can solve the equilibrium problem. 

Often we know the value of Kgp for a compound and are asked to calculate the compound s molar solubility. The procedure for solving such a problem is essentially identical to the p ocedure for solving weak acid or weak base equilibrium problems ... 

We can calculate the exact value of the solubility by working an equilibrium problem in which the concentration of the common ion is accounted for in the initial conditions, as shown in Example 16.10. 

If auxiliary chemical reactions are involved in concentration determinations using ion-selective electrodes (end point titration, standard addition or subtraction, indirect procedures), extreme caution is required with variable sample temperatures. This is because in addition to the electrochemical effects discussed, purely chemical phenomena may become problematic (temperature dependence of equilibrium constants, solubility products, complex formation constants and activity coefficients). With the low sample flow rates commonly encountered (a few ml/minute), thermostating the solution and sample cell with the help of a quickly responding proportional controller (Orion, Series 1,000) presents no problem. 

Numerous attempts to determine the equilibrium constants using titration microcalorimetry failed, due to solubility problems encountered at the higher concentrations of catalyst and dienophile that are required for this technique. 

Now interpret phase X as pure solute then Cs and co become the equilibrium solubilities of the solute in solvents S and 0, respectively, and we can apply Eq. (8-58). Again the concentrations should be in the dilute range, but nonideality is not a great problem for nonelectrolytes. For volatile solutes vapor pressure measurements are suitable for this type of determination, and for electrolytes electrode potentials can be used. 

In some cases, the Q ions have such a low solubility in water that virtually all remain in the organic phase. ° In such cases, the exchange of ions (equilibrium 3) takes place across the interface. Still another mechanism the interfacial mechanism) can operate where OH extracts a proton from an organic substrate. In this mechanism, the OH ions remain in the aqueous phase and the substrate in the organic phase the deprotonation takes place at the interface. Thermal stability of the quaternary ammonium salt is a problem, limiting the use of some catalysts. The trialkylacyl ammonium halide 95 is thermally stable, however, even at high reaction temperatures." The use of molten quaternary ammonium salts as ionic reaction media for substitution reactions has also been reported. " " ... 

The problem asks for an equilibrium constant, which means we need to find equilibrium concentrations of the species involved in the solubility reaction. Use the seven-step strategy, which we present here without step numbers. 

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. 

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