Moving between Phases

Chemical substances can move between different phases in a system that is not at equilibrium. Modelers sometimes refer to the movement of chemicals between environmental compartments via such mechanisms, that is, between soil, water, sediment, and air. 

A substance released to the environment can volatilize from water to air, or sublime from solid to vapor phase. It can also be washed out of the air with rainfall that deposits the substance on land or in surface water. Scientists characterize the tendency of a chemical substance to partition between air and water by its vapor pressure and solubility in water, or, in dilute solutions at equilibrium, by the Henry s law coefficient (which can be measured or calculated from the ratio of the vapor pressure to solubility at a specified temperature). The Henry s law coefficient is sometimes referred to as an air-water partition coefficient. 

Chemicals in water can sorb to sediment or soil in a reversible process that reflects the attraction and adhesion of molecules to solids. (Less commonly considered in environmental mass balances, some air pollutants can sorb to particulates in the atmosphere.) The n-octanol/water partition coefficient (K ) of a substance provides a crude indication of the tendency to partition to solids from water a high value indicates that a substance is hydro-phobic/lipophilic and would tend to sorb to solids. More sophisticated tests determine a distribution coefficient (KJ or adsorption isotherm to relate the concentration in solution to the concentration sorbed to solids. The sorption coefficient is the ratio between the concentration of a chemical in soil to the concentration in water which is in contact with the soil. Normalized to the organic carbon content of the soil, this coefficient becomes (K = I i/ fraction organic carbon in soil) [4]. 

Calculations that represent interphase transport must account for the difference between ideal and nonideal behavior. The substances in an ideal system precisely obey simplified laws describing their behavior. An ideal gas, for example, would obey the familiar ideal gas law. 

For a more elegant and rigorous explanation of fugacity, see Multimedia Emnronmental Models The Fugacity Approach [5]. 

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Explaining the kinetic molecular theory Moving between phases... 

Figure 24.11 X-ray diffraction pattern of tetramethylammonium dicyanamide shows the change in lattice parameters on moving between phases. As the temperature increases, there is a loss of some peaks and the appearance of new ones, indicating a change in unit cell. Generally, the diffraction patterns become simpler on moving to lower phases, culminating in only one peak for the phase I species. Leaving the material for two days does not appear to have any effect on the diffraction pattern and hence on the structure of the salt.

Still want to consider a system that is closed overall, but within which matter is free to move between phases, i.e., in which the phases are open. Still, because the system is closed overall, the same criterion (dUs,v = 0) applies. If we denote the various phases in the system by accents, we can consider that during any increment of change of energy dU the various phases contribute dU, dU", etc., so that... 

Now that we have seen how mass moves between phases and those factors that control the rate of this process, we can bore in at the molecular level on mass action, especially adsorption. 

The ion exchange membranes are used in systems where ions of specific charge must be transported. They are used as separators in fuel cells and for electrodialysis where ions must move between phases. 

Another method to remove pollutants from air is to absorb the pollutants into a nonvolatile liquid such as oil. During absorption, pollutants move from the gas phase to the liquid phase. This movement is an example of mass transfer. To move between phases, the pollutants must cross the liquid-gas interface. Increasing the interfacial area increases the rate of mass transfer. An easy way to increase the interfacial area is to bubble the gas through the liquid. This concept is effective in delivering oxygen to water in fish tanks and it is effective in delivering benzene to oil. 

The system of primary interest, then, is that of a condensable vapor moving between a Hquid phase, usually pure, and a vapor phase in which other components are present. Some of the gas-phase components may be noncondensable. A simple example would be water vapor moving through air to condense on a cold surface. Here the condensed phase, characterized by T and P, exists pure. The vapor-phase description requiresjy, the mole fraction, as weU as T and P. The nomenclature used in the description of vapor-inert gas systems is given in Table 1. 

The stagnant-film model discussed previously assumes a steady state in which the local flux across each element of area is constant i.e., there is no accumulation of the diffusing species within the film. Higbie [Trans. Am. Jn.st. Chem. Eng., 31,365 (1935)] pointed out that industrial contactors often operate with repeated brief contacts between phases in which the contact times are too short for the steady state to be achieved. For example, Higbie advanced the theory that in a packed tower the liquid flows across each packing piece in laminar flow and is remixed at the points of discontinuity between the packing elements. Thus, a fresh liquid surface is formed at the top of each piece, and as it moves downward, it absorbs gas at a decreasing rate until it is mixed at the next discontinuity. This is the basis of penetration theoiy. 

We have covered a body of material in this chapter that deals with movement of mass along gradients and between phases. We have examined the commonalities and differences between linear driving forces, net rates of adsorption, and permeation. Each has the common feature that reaction is not involved but does involve transport between apparently well-defined regions. We move now to chemically reactive systems in anticipation of eventually analyzing problems that involve mass transfer and reaction. 

Several observations show that saturated solutions are at dynamic equilibrium. For example, if O2 gas enriched in the oxygen-18 isotope is introduced into the gas phase above water that is saturated with oxygen gas, the gas in the solution eventually also becomes enriched in the heavier isotope. As another example, if finely divided ciystalline salt is in contact with a saturated solution of the salt, the small crystals slowly disappear and are replaced by larger crystals. Each of these observations shows that molecules are moving between the two phases, yet the concentrations of the saturated solutions remain constant. 

Porosity correction is constant in both time and space. Chemicals move between the three soil phases much more rapidly than they diffuse in the air phase. This means that they appear to be in equilibrium. Adsorption is reversible. 

Ctl is the mass transfer term and arises because of the finite time taken for solute molecules to move between the two phases. Consequently, a true equilibrium situation is never established as the solute moves through the system, and spreading of the concentration profiles results. The effect is minimal for small particle size and thin coatings of stationary phase but increases with flow rate and length of column or surface. 

Surface renewal theory (King, 1966) the theory describes the replacement of a surface liquid film by the action of eddies that move between the bulk water phase and the surface film. The surface renewal rate thereby determines the exchange between the surface and the bulk water. 

A molecule carried along in the mobile phase must contact the stationary phase if the system is an equilibrium separation method. That means that a molecule moving between particles must sense the chemical potential in the direction of the stationary phase and move toward it. 

Gas chromatography is a method of separation wherein gaseous or vaporised components are distributed between a moving gas phase and a fixed liquid phase or solid adsorbent. By a continuous succession of adsorption or elution steps, occurring at a specific rate for each component, separation can be achieved. The components can be detected by one of various methods as they emerge successively from the chromatographic column. From the detector signal, proportional to the instantaneous concentration of the dilute component in the gas stream, information about the number, nature and amounts of the components present is obtained. 

There are two generally accepted mechanisms for simple phase transfer reactions under neutral conditions. The first of these is a mechanism in which the whole cation-anion complex moves between the two phases as shown in Scheme 5.6 [42],... 

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