The Solution Process

In Chapter 4, we learned guidelines that helped us predict whether or not an ionic solid is soluble in water. We now take a more general look at the factors that determine solubility. This discussion will enable us to understand why so many ionic substances are soluble in water, which is a polar solvent and it will help us to predict the solubility of ionic and molecular compounds in both polar and nonpolar solvents. 

The intermolecular forces that hold molecules together in liquids and solids play a central role in the solution process. When the solute dissolves in the solvent, molecules of the solute disperse throughout the solvent. They are, in effect, separated from one another and each solute molecule is surroundedhy solvent molecules—a process known as solvation. The ease with which solute molecules are separated from one another and surrounded by solvent molecules depends on the relative strengths of three types of interactions  

Unlike the intermolecular forces covered in Chapter 12, all of which were between the molecules, atoms, or ions of a pure substance, solute-solvent interactions are those that exist in a mixture of different substances. Because the components of a mixture can have different properties, there is a greater variety of intermolecular forces to consider. In addition to dispersion forces, which exist between all substances, dipole-dipole forees, which exist between polar molecules, and ion-ion forces, which exist between ions, solutions ean exhibit the following intermolecular forces  

Ion-dipole. The charge of an ion is attracted to the partial charge on a polar molecule. Dipole-induced dipole. 

A solution is formed when one substance disperses uniformly throughout another. The ability of substances to form solutions depends on two factors (1) the natural tendency of substances to mix and spread into larger volumes when not restrained in some way and (2) the types of intermolecular interactions involved in the solution process. 

1 THE SOLUTION PROCESS We begin by considering what happens at the molecular level when one substance dissolves into another, paying particular attention to the role of intermolecular forces. Two important aspects of the solution process are the natural tendency of particles to mix and their accompanying changes In energy. 

We learn that when a saturated solution Is In contact with an undlssolved solute, the dissolved and undlssolved solutes are In equilibrium. The amount of solute In a saturated solution defines 

We examine several common ways of expressing concentration, including mole fraction, molarity, and molality. 

6 COLLOIDS We close the chapter by investigating colloids, mixtures that are not true solutions but consist of a solute-like phase (the dispersed phase) and a solvent-like phase (the dispersion medium). The dispersed phase consists of particles larger than typical molecular sizes. 

Why is it that some substances readily mix to form solutions while others do not Whether one substance dissolves in another substance is largely dependent on the inter-molecular forces present in the substances. For a solution to form, the solute particles must become dispersed throughout the solvent. This process requires the solute and solvent to initially separate and then mix. Another way of thinking of this is that the solute particles must separate from each other and disperse throughout the solvent. The solvent may separate to make room for the solute particles or the solute particles may occupy the space between the solvent particles. Determining whether one substance dissolves in another requires examining three different intermolecular forces present in the substances—between the 

While many ionic compounds are soluble in water, many are not. The term solubility is somewhat subjective. There are actually degrees of solubility. A substance is considered soluble if 0.1 moles of it can dissolve in 1 liter of water. If less than 0.001 mole of the substance dissolves in water, a substance is considered insoluble. Partially soluble substances fall between these two extremes. Table 11.3 summarizes the solubility of some major groups of ionic compounds in water. 

Whether an ionic compound dissolves in water depends on the strength of the ionic bond holding the compound together. Water must have sufficient strength to break the ionic bond. The strength of the 

Compounds containing alkaii metal cations or ammonium are soiuble. 

Most compounds containing CP, Br and I are solubie. Notabie exceptions are for compounds containing Ag or Pb.  

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Although the data for the silver halides suggest that silver(I) fluoride is likely to be more soluble than the other silver halides (which is in fact the case), the hydration enthalpies for the sodium halides almost exactly balance the lattice energies. What then is the driving force which makes these salts soluble, and which indeed must be responsible for the solution process where this is endothermic We have seen on p. 66 the relationship AG = — TAS and... 

The solution process consists of four steps preparation of cellulose for acetylation, acetylation, hydrolysis, and recovery of cellulose acetate polymer and solvents. A schematic of the total acetate process is shown in Figure 9. 

Vitreous sihca does not react significantly with water under ambient conditions. The solution process involves the formation of monosilicic acid, Si(OH)4. Solubihty is fairly constant at low pH but increases rapidly when the pH exceeds 9 (84—86). Above a pH of 10.7 sihca dissolves mainly as soluble sihcates. Solubihty also increases with higher temperatures and pressures. At 200—400°C and 1—30 MPa (<10 300 atm), for example, the solubihty, S, of Si02 in g/kg H2O can be expressed as foUows, where d ls the density of the vapor phase and T is the absolute temperature in Kelvin. 

Several patents describe solvent-free bulk-phase halogenation (67—69). Dry soHd butyl mbber is fed into a specially designed extmder reactor and contacted with chlorine or bromine vapor. The by-product HCl or HBr ate vented directly without a separate neutralization step. Halogenated butyl mbbers produced are essentially comparable in composition and properties to commercial products made by the solution process. 

Starting with an initial value of and knowing c t), Eq. (8-4) can be solved for c t + At). Once c t + At) is known, the solution process can be repeated to calciilate c t + 2At), and so on. This approach is called the Euler integration method while it is simple, it is not necessarily the best approach to numerically integrating nonlinear differential equations. To achieve accurate solutions with an Eiiler approach, one often needs to take small steps in time. At. A number of more sophisticated approaches are available that allow much larger step sizes to be taken but require additional calculations. One widely used approach is the fourth-order Bunge Kutta method, which involves the following calculations ... 

I FIGURE I (.49 In thermal models, the ventilation airflow rates are input parameters in airflow models, on the other hand, room air tmiperatures must be defined In the output. Since natural ventilation airflows and room air temperatures are interdependent, both parameters must be intcgratly considered in the solution process. This is possible only by an integration of the natural airflow model into the thermal model. 

Strategy To go from concentration of solute to concentration of an individual ion, you must know the conversion factor relating moles of ions to moles of solute. To find this conversion factor, it is helpful to write the equation for the solution process. 

Reality Check Notice that qieacu0n is negative, so the solution process is exothermic. That is reasonable since the temperature of the water increases. 

The effect of a temperature change on solubility equilibria such as these can be predicted by applying a simple principle. An increase in temperature always shifts the position of an equilibrium to favor an endothermic process. This means that if the solution process absorbs heat (AHsoin. > 0), an increase in temperature increases the solubility. Conversely, if the solution process is exothermic (AH < 0), an increase in temperature decreases the solubility. 

Strategy Start by writing the chemical equation for the solution process (solid on the left, ions in solution on the right). Then write the expression for fCsp) noting that—... 

It is clear that nonconfigurational factors are of great importance in the formation of solid and liquid metal solutions. Leaving aside the problem of magnetic contributions, the vibrational contributions are not understood in such a way that they may be embodied in a statistical treatment of metallic solutions. It would be helpful to have measurements both of ACP and A a. (where a is the thermal expansion coefficient) for the solution process as a function of temperature in order to have an idea of the relative importance of changes in the harmonic and the anharmonic terms in the potential energy of the lattice. 

In Benning el al. (146) some data on the kinetics of ethylene polymerization in the presence of TiCl2 activated by ball-milling are given. Polymerization was studied at 140-260°C (the solution process in cyclohexane). The first orders of the polymerization rate on the monomer and catalyst concentrations have been established. The polymerization decreased with temperature a sharp drop in rates at about 180-200°C was observed. 

The conclusion is that AmjxSm =4.66 J K I mol 1 for the solution process at 0 Kelvin. If one assumes that the entropies of the AgBr and AgCl are zero at 0 Kelvin, then the solid solution must retain an amount of entropy that will give this entropy of mixing. 

C06-0018. Adding 1.530X 10 Jof electrical energy to a constant-pressure calorimeter changes the water temperature from 20.50 °C to 21.85 °C. When 1.75 g of a solid salt is dissolved in the water, the temperature falls from 21.85 °C to 21.44 °C. Find the value of gp for the solution process. 

CO6-OO66. When 5.34 g of a salt dissolves in 155 mL of water (density = l.OOg /niL) in a coffee-cup calorimeter, the temperature rises from 21.6 °C to 23.8 °C. Determine q for the solution process, assuming that Ccal = Crater ... 

To improve the convergence of the gradient-type method, Tannor et al. [81, 93] suggested employing the Krotov iteration method [102]. In formulating their method, they utilize a penalty function of the form /[e(f)] = pe (f). In Tannor s Krotov method, the fcth iteration step of the solution process is given by... 

If it is assumed that the total free energy for the transfer of solute X from the gas phase to the stationary phase (with molecular interactions characteristic of Infinite dilution) is the linear sum of the individual free energy contributions to the transfer process then a general expression for the solution process, equation (2.11), can be written as follows... 

How do temperatures change during chemical reactions and the solution process ... 

Sodium ferric fluoride is obtained as a byproduct in the solution processing of Na2BeF6 leach liquor. It is used for substituting for sodium silicofluoride (to an extent of up to 60%) in the ore fusion reaction. 

The solution process for the cycloamyloses is somewhat more complex. Since the water molecules may interact with the hydroxyl groups located on the exterior of the cycloamylose molecule by means of hydrogen bonding,... 

The solution-processed doped silicon films described above (baked at 500 °C for 2 hr) exhibited high electrical resistivity (greater than 300 Qcm), which is the measurement limit of the instrument we used. To lower the resistivity, we tried an additional rapid thermal annealing (RTA) of the film prepared from the copolymerized solution with 1 wt% phosphorus concentration. In this RTA, the SiC plate on which the sample was placed was irradiated with infrared (IR) light from a 1-kW IR lamp. The RTA conditions were 600 °C for 2 hr, 650 °C for 20 min, 700 °C for 5 min, and 750 °C for 5 min these temperatures were that of the SiC plate, and the temperature of the Si film is estimated to be several dozens of degrees lower than that. 

Finally, silicon-based polymers, especially with hydrogen lateral groups, are very interesting, but they are not yet explored sufficiently. There are many unknown properties in these materials, including the details of the photopolymerization process and a-Si formation from polysilane. Additional academic work in this field is expected and necessary to make the solution processing of silicon devices more convenient and reliable. 

Table 8.5 summarizes the relative merits of SLP, SQP, and GRG algorithms, focusing on their application to problems with many nonlinear equality constraints. One feature appears as both an advantage and a disadvantage—whether or not the algorithm can violate the nonlinear constraints of the problem by relatively large amounts during the solution process. 

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