Solutions Of Solids In Liquids

The amount of a solid that will dissolve in a liquid is a function of the temperature, the nature of the solvent, and the nature of the solute (solid). The broad concepts of unsaturated, saturated, and supersaturated solutions are generally treated quite adequately in courses in general science and chemistry. However, the significance of crystal or particle size and the influence of temperature on solubility are not always adequately discussed.

Significance of Particle Size

The solubility of solids has been shown to increase as particle size diminishes. For example, coarse granular CaS04(s) dissolves to the extent of 2.08 g/L at 25°C, whereas finely divided CaS04(i) dissolves to the extent of 2.54 g/L. This phenomenon is considered to be due to the increased ratio of surface area to mass and to an increase in vapor pressure of the solid as particle size decreases. Particles of colloidal size are considered to have the greatest solubility because of their submicroscopic size.

In quantitative analysis, advantage is often taken of the fact that solubility varies with particle size. In gravimetric analysis, such as in the determination of sulfate by precipitation as BaS04(i), the precipitate first formed is highly colloidal in nature. However, if some care is used in the precipitation procedure, a few crystals of larger size will be formed. If the precipitated material is allowed to stand for a period of time before filtration, the colloidal-size particles will tend to dissolve and then precipitate out on the large crystals present. The rate of transfer is a function of the number of crystals present, the differential in solubilities, and the temperature. The difference in solubility is known to increase with temperature, as well as the rate of exchange; consequently, "digestion" of precipitates is normally done at temperatures near the boiling point of the solvent.

Temperature Relationships

In general, the solubility of solids in liquids increases as the temperature increases. There are a number of exceptions, however. The influence of temperature on solubility depends mainly upon the total heat effects of the solution. If the heat of solution is endothermic, the solubility increases with an increase in temperature; if the heat of solution is exothermic, the solubility decreases with an increase in temperature; and if there is little thermal change, the solubility is influenced very little by change of temperature. These considerations are all in accord with Le Chatelier's principle and the thermodynamic principles discussed in Sec. 3.2.

Temperature, °C

Figure 3.4

Relationship between solubility in water and heat of solution.

Temperature, °C

Figure 3.4

Relationship between solubility in water and heat of solution.

chapter 3 Basic Concepts from Physical Chemistry

Figure 3.4 shows solubility curves for a number of solids in water and illustrates the relationship to heat of solution. The solubility curves for some solids, such as sodium sulfate, show abrupt changes because of a change in molecular composition and heat of solution.

3.7 I MEMBRANE PROCESSES: OSMOSIS AND DIALYSIS

Membrane processes are being used increasingly to remove particulates and solutes from waters, wastewaters, and gas. More stringent environmental regulations coupled with advances .in membrane technology and more favorable economics are primarily responsible for this increased use. In general, membrane processes are classified by the size of the pollutants being removed. The following table gives a general classification of the common membrane processes (1 ^m = 1 micron = KT6 m).

Membrane proccss

Applicable particle or solute size range, ßm

Macrofiltration

>10-100

Microfiitration

0.1-10

Ultrafiltration

0.005-0.1

Nanofiltration

0.001-0.005

Reverse osmosis

<0.001

Dialysis

<0.001

Reverse osmosis and dialysis can remove dissolved ions from solution. In the rest of this section, the principles of osmosis and dialysis are discussed in some detail.

Osmosis

Osmosis is the movement of a solvent through a membrane that is impermeable to a solute. The direction of flow is from the more dilute to the more concentrated solution. For example, if a salt solution is separated from water by means of a semipermeable membrane, as shown in Fig. 3.5, water will pass through the membrane in both directions, but it will pass more rapidly in the direction of the salt solution. As a result, a difference in hydrostatic pressure develops. The tendency for the solvent to flow can be opposed by applying pressure to the salt solution. The excess pressure that must be applied to the solution to produce equilibrium is known as the osmotic pressure and is denoted by it.

The net flow of solvent across a membrane results in response to a driving force which can be estimated by the difference in vapor pressure of the solvent on either side of the membrane. The transfer of solvent across the membrane from the less concentrated to the more concentrated solution will continue until the effect of hydrostatic pressure overcomes the driving force of the vapor pressure differential. For an incompressible solvent, the osmotic pressure at equilibrium it (expressed in atmospheres) can be estimated from the following:

vA "A

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Figure 3.5

The process of osmosis and the development of osmotic pressure.

Figure 3.5

The process of osmosis and the development of osmotic pressure.

where R = 0.08206 L atmAnol ■ K T = temperature, K P°A = vapor pressure of solvent in dilute solution PA = vapor pressure of solvent in concentrated solution VA = volume per mole of solvent (= 0.018 L/mol for water)

Raoult's law, discussed in Sec. 2.10, indicates that for dilute solutions the reduction in vapor pressure of a solvent is directly proportional to the mole fraction of other species in solution. From this fact, the osmotic pressure can be related to the molar concentration of dissolved substances c in the concentrated solution:

This equation is valid in a strict sense only for dilute solutions in which Raoult's law holds true.

An application of osmotic pressure principles is in the demineralization of salt-laden (brackish) water by the reverse osmosis process. Reverse osmosis is also used to remove specific contaminants such as nitrate and radium from waters. As the name implies, this process is the reverse of osmosis, and water is caused to flow in a reverse manner through a semipermeable membrane from brackish to dilute fresh water. This is accomplished by exerting a pressure on the brackish water in excess of the osmotic pressure. The semipermeable membrane acts like a ¡filter to retain the ions and particles in solution on the brackish water side, while permitting water alone to pass through the membrane. Theoretically, the process will

CHAPTER 3 Basic Concepts from Physical Chemistry 73

work if a pressure just in excess of the osmotic pressure is used. In practice, however, a considerably higher pressure is necessary to obtain an appreciable flow of water through the membrane. Also, as fresh water passes through the membrane, the concentration of salts in the brackish water remaining increases, creating a greater osmotic pressure differential. The theoretical minimum energy required to remove salts from water in such a process is equal to the osmotic pressure multiplied by the volume of water being demineralized.

EXAMPLE 3.8

(a) What would be the approximate osmotie pressure difference across a semipermeable

. _.1 1. „Vi fi. .met mtn/->r[:(!_frpp vj.':;i?pr on ihf' nfhpT"'

(a) What would be the approximate osmotie pressure difference across a semipermeable

. _.1 1. „Vi fi. .met mtn/->r[:(!_frpp vj.':;i?pr on ihf' nfhpT"'

c = 0.02 + 0.015 + 0.01 + 0.001 + 0.025 + 0.001 + 0.002 + 0.012 -^■'P-0^206

(¿0 If in part (a), a yield of 75 percent fresh water were dc ------------

•! would he rcauired to balance the osmotic pressure dif:

■ For a 75 percent yield, the'salts originally present water would be concentrated in one volume of brackish w^ter left bciiind the; ; ; . membrane after three volumes Of fresh water have passed through the membrane: Thus, the molar concentration of salt in the blackish water would be four times that

/ . ,. V : ; . v = 0.344 X 0.08206 X .298 ='8.41 atm orl:24psi; . 7 '

■ At this point the pressure required to push the fresh water through the :membrane . would be in excess of 124 psi. ■;.

Dialysis

By choice of a membrane of a particular permeability, which is wetted by the solvent, it is possible to cause ions to pass through the membrane while large molecules of organic substances or colloidal particles are unable to pass. Thus, a separation of solutes can be accomplished. This process is termed dialysis.

Dialysis is used extensively to remove electrolytes from colloidal suspensions to render the latter more stable. Dialysis is used to recover sodium hydroxide from certain industrial wastes that have become contaminated with organic substances, as

Figure 3.6

A simple dialysis cell for recovery of sodium hydroxide from an industrial waste.

shown in Fig. 3.6. In the process, the waste material is placed in cells with permeable membranes, and the cells are surrounded with water. The sodium and hydroxide ions pass through the cell wall into the surrounding water and some water may pass into the cell. The NaOH solution is evaporated to recover the sodium hydroxide, and the organic waste remaining in the cells is disposed of separately. Waste caustic solutions must be quite concentrated before recovery by dialysis can be justified economically. Mercerizing wastes of the cotton textile industry are an example.

In another application, the dialysis principle can be used for demineralization of brackish water. In this case, the brackish water is placed both inside and outside the cell. Electrodes are placed in the water outside the cell, and when a current is applied, the ions within the cell are caused to flow through the semipermeable membrane and to concentrate in the water outside. The cations flow toward the cathode and the anions flow toward the anode, as discussed in Sec. 3.10. By this method, the water within the cell is demineralized. This process, termed electrodial-ysis, uses electrical energy to cause the flow of ions against a concentration gradient. In practice, a large number of thin, continuous-flow cells are used to make the process efficient for large-scale usage. Electrodialysis is also used to remove specific pollutants such as heavy metals, nitrate, hardness (Ca2+ and Mg2+), and radium from contaminated waters.

3.8 I PRINCIPLES OF SOLVENT EXTRACTION

Industrial and hazardous wastes often contain valuable constituents that can be recovered most effectively and economically by means of extraction with an immiscible solvent [commonly called NAPL (non-aqueous-phase liquid)], such as petroleum

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Figure 3.6

A simple dialysis cell for recovery of sodium hydroxide from an industrial waste.

ether, diethyl ether, benzene, hexane, dichloromethane, or some other organic solvent'Also, many methods for water analysis involve extraction of a constituent or complex from the water sample as one step in the determination. This is true of some procedures for measurement of surface active agents, organic compounds, and various heavy metals. Because of the importance of this operation in environmental engineering practice, a discussion of the principles involved is merited.

When an aqueous solution is intimately mixed with an immiscible solvent, the solutes contained in the water distribute themselves in relation to their solubilities in the two solvents. For low-to-moderate concentrations of solute, the ratio of distribution is always the same:

Cwater

The equilibrium constant K, or the ratio of distribution, is known as the distribution coefficient. In actual practice the immiscible solvent is selected for its ability to dissolve the desired material, and the values for K are normally greater than 1. A distribution coefficient of particular interest is the octanol-water partition coefficient (J0J. Use of Km is described in Sec. 5.34,

If the volume of solvent used is equal to the volume of the sample being extracted, the mathematics involved are rather simple. For a system with a distribution coefficient of 9, 90 percent of the material would be extracted in the first step, and 90 percent of the material remaining in each successive step. After three extractions with fresh solvent, 99.9 percent of the material would be removed.

In actual practice it is seldom feasible to use a volume of solvent equal to the waste volume, and calculations become somewhat involved. The question in industrial waste treatment that usually requires answering is this: How much remains in the aqueous phase after n extractions? The expression defining the distribution coefficient may be written in terms of the amounts of the substance extracted and the volumes of the liquids involved,

cw WtiVw where W0 = weight of substance originally present in aqueous phase Wi = weight remaining in water after one extraction V, = volume of solvent V„ = volume of water

Simplifying, we obtain

In the second step of the extraction, w = w —^— (3.28)

or, in terms of the original sample,

and after n extractions the weight of substance remaining in the water is

Equation (3.30) has general application and may be used to calculate the volume of a solvent needed to reduce the concentration of a material in the aqueous phase to definite levels with a fixed number of extractions, or the number of extractions needed with a fixed volume of a solvent, provided that the distribution coefficient is known.

A related phenomenon of significance to environmental engineers is the "cosol-vent" effect. An important example is the use of ethanol as a fuel oxygenate in gasoline formulations. The purpose of adding ethanol to gasoline is to increase the oxygen content as mandated by the 1990 Clean Air Act amendments. The presence of ethanol in gasoline may cause unintended problems.1 The presence of ethanol, which is miscible with water, as a cosolvent will increase the water solubility of gasoline components such as benzene, toluene, ethylbenzene, and xylene (BTEX). Second, if the ethanol-gasoline mixture (ethanol and gasoline are miscible) becomes contaminated with enough water, the gasoline will separate into two phases: a gasoline-rich phase that will float on top of an ethanol-water phase. This behavior prevents distribution of ethanol-gasoline formulations by pipeline.

Another, more complex example is cosolvent flushing of soils contaminated with NAPL [they may be less dense than water (LNAPL) or more dense than water (DNAPL)]. Water-miscible cosolvents such as ethanol may be added to increase the solubility of the NAPL and enhance its extraction and recovery.2 Surfactants have also been employed.3 In this application, the effects of properties such as surface tension (capillary forces), density, and viscosity, among others, are also important.

Electrochemistry is concerned with the relationships between electrical and chemical phenomena. A knowledge of electrochemistry has several applications in environmental engineering. It is germane to an understanding of corrosion as well as

!S. E. Powers, D. Rice, B, Dooher, and P. J. J. Alvarez, Will Ethanol-B tended Gasoline Affect Groundwater Quality, Env. Sci. Tech., 30: 24A-30A (2001),

2J. W. Jawitz, R. K. Sillan, M. D. Amiable, P. S, C. Rao, and K. Warner, In-Situ Alcohol Flushing of a

DNAPL Source Zone at a Dry Cleaner Site, Env. Sci. Tech., 34: 3722-3729 (2000). SK. D. Fennel, G. A, Pope, and L. M. Abriola, Influence of Viscous and Buoyancy Forces on the Mobilization of Residual Tetrachloroethylene during Surfactant Flushing, Env. Sci. Tech., 30: 1328-1335 (1996).

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