Chemical Distribution among Phases

calculate the sample standard deviation for the BOD using either Eq. [1-25] or a preprogrammed function on a calculator  

Given that seven samples were taken and a 95% confidence interval is of interest, the approximation for the t statistic presented in Eq. [1-28] can be used  

the inspector can be 95% confident that the true BOD mean lies within the range 10.1 0.2 mg/liter. There is a 5% probability that the true BOD mean lies outside the range a 2.5% chance that the true mean exceeds 10.3 mg/liter and a 2.5% chance that it is less than 9.9 mg/liter. 

Thus far the discussion of the transport and reactions of chemicals has predominantly focused on processes occurring in one of two fluids air or water. Of course, the natural environment contains more than these two media furthermore, one medium often contains different phases. For example, the atmosphere contains not only air, but also water and solids (particulate matter) in small, varying amounts surface waters often contain solid particles and gas bubbles. The subsurface medium contains not only solids, but also a substantial volume of water and air. Therefore, a consideration of the principles that determine how a chemical becomes distributed among air, water, and solid phases is necessary, not only to understand chemical movement between media (atmosphere to surface water, soil to atmosphere, etc.), but also to understand the behavior of a chemical within a single environmental medium. 

Pure air is an example of a gas phase pure water is an example of the aqueous phase. Solid phases include soil grains, solid particles suspended in water or air, and pure solid chemicals. In addition, an immiscible liquid (i.e., a liquid that does not mix freely with water) can form its own nonaqueous 

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In the discussion of chemical distribution among phases, it is assumed that chemicals are not transformed (i.e., no chemical bonds are formed or broken). For example, when liquid gasoline evaporates and enters the air in a partially empty gas tank, the bonds within individual molecules of the chemicals that compose gasoline are not being disrupted the molecules are simply moving from a nonaqueous liquid phase to the gas phase without changing their identities. The rate at which this chemical movement occurs from one phase to another, relative to the timescale of interest, determines whether the problem is an equilibrium problem or a kinetics problem. Examples of both types abound in the environment this section, however, refers only to the principles that govern equilibrium. 

The essential input data are (a) the bulk chemical composition of the cement, (b) the quantitative phase composition of the cement and the chemical compositions of its individual phases, (c) the fraction of each phase that has reacted, (d) the w/c ratio, (e) the COj content of the paste and an estimate of how it is distributed among phases, and (0 the composition of each hydrated phase for the specified drying condition. If (b) is unknown, it may be estimated as described in Section 4.4, and if (c) is unknown, it may be estimated from the age as described by Parrott and Killoh (P30), or, more simply though less precisely, by using empirical equations (D12,T37). If the phase composition by volume and porosities are to be calculated, densities of phases are also required. 

These problems lead to the second major branch of thermodynamics, which we will now formulate. It deals only with equilibrium systems. It should be pointed out that this branch still uses the same observations of nature (conservation of energy and directionality) that we have already studied. In these problems, however, we wish to calculate how species distribute among phases when more than one phase is present (phase equilibria) or what types of species are formed and how much of each type is produced as systems approach equilibrium when the molecules in the system chemically react (chemical reaction equilibria). We will consider phase equilibria first. These calculations are restricted to equilibrium systems therefore, they give information on the direction of the driving force for a given system (i.e., the system will spontaneously move toward its equilibrium state) but no information on the rate at which it will reach equilibrium. 

The chemical speciation of the metal is defined as its distribution among different phases and different dissolved forms. When heavy metals enter aquatic... 

Partition processes determine how a substance is distributed among the liquid, solid, and gas phases and determine the chemical form or species of a substance. Partitioning usually does not affect the toxic properties of the substance. Partitioning can, however, affect the mobility of the waste, its compatibility with the injection zone, or other factors that influence fate in the deep-well environment. The major partition processes are as follows ... 

For a multiphase equilibria containing a number of components distributed among them, the chemical potential of any component is the same in all the phases. 

Process-scale models represent the behavior of reaction, separation and mass, heat, and momentum transfer at the process flowsheet level, or for a network of process flowsheets. Whether based on first-principles or empirical relations, the model equations for these systems typically consist of conservation laws (based on mass, heat, and momentum), physical and chemical equilibrium among species and phases, and additional constitutive equations that describe the rates of chemical transformation or transport of mass and energy. These process models are often represented by a collection of individual unit models (the so-called unit operations) that usually correspond to major pieces of process equipment, which, in turn, are captured by device-level models. These unit models are assembled within a process flowsheet that describes the interaction of equipment either for steady state or dynamic behavior. As a result, models can be described by algebraic or differential equations. As illustrated in Figure 3 for a PEFC-base power plant, steady-state process flowsheets are usually described by lumped parameter models described by algebraic equations. Similarly, dynamic process flowsheets are described by lumped parameter models comprising differential-algebraic equations. Models that deal with spatially distributed models are frequently considered at the device... 

Metal concentrations and metal activities in the pore water are dependent upon both the metal concentration in the solid phase and the composition of both the solid and the liquid phase. In matrix extrapolation, and with emphasis on the pore water exposure route, it is therefore of great practical importance to have a quantitative understanding of the distribution of heavy metals over the solid phase and the pore water. A relatively simple approach for calculating the distribution of heavy metals in soils is the equilibrium-partitioning (EP) concept (Shea 1988 van der Kooij et al. 1991). The EP concept assumes that chemical concentrations among environmental compartments are at equilibrium and that the partitioning of metals among environmental compartments can be predicted based on partition coefficients. The partition coefficient, Kp, used to calculate the distribution of heavy metals over solid phase and pore water is defined as... 

Table 4.3 Distribution of oxide components among phases in a typical Portland cement clinker, calculated from the bulk chemical analysis... 

For a system containing N chemical species distributed at equilibrium among % phases, the phase-rule variables are temperature and pressure, presumed uniform throughout the system, and N - 1 mole fractions in each phase. The number of these variables is 2 -H (N - 1)tc. The masses of the phases are not phase-rule variables, because they have nothing to do with the intensive state of the system. 

When the partition dynamics are rapid, the solute distribution in vesicles will obey the same laws as the distributions in micelles. However, when the transmembrane diffusion time of molecules entrapped within the aqueous vesicle core or incorporated into the hydrocarbon phases exceeds the characteristic time of their chemical transformation in chemical reactions, then their partitioning is set by their initial statistical distribution rather than their migration dynamics. In this case also, a Poisson law is appropriate to approximate their distribution among vesicles. This follows because the volume of the inner aqueous phase generally exceeds 10 A, and the maximiun number of molecules that can be entrapped inside the vesicle is correspondingly large. 

Now that solubility and vapor pressure have been defined, consider how a volatile chemical partitions, or distributes itself, between water and air phases at equilibrium. In general, a partition coefficient is the ratio of the concentrations of a chemical in two different phases, such as water and air, under equilibrium conditions. The Henry s law constant, H (or KH), is a partition coefficient usually defined as the ratio of a chemical s concentration in air to its concentration in water at equilibrium. [Occasionally, a Henry s law constant is interpreted in an inverse fashion, as the ratio of a chemical s concentration in water to its concentration in air see, e.g., Stumm and Morgan (1981, p. 179). Note that in that table, KH is equivalent to 1/H as H is defined above ] Values of Henry s law constants are tabulated in a variety of sources (Lyman et al, 1990 Howard, 1989, 1991 Mackay and Shiu, 1981 Hine and Mookerjee, 1975) Table 1-3 lists constants for some common environmental chemicals. When H is not tabulated directly, it can be estimated by dividing the vapor pressure of a chemical at a particular temperature by its aqueous solubility at that temperature. (Think about the simultaneous equilibrium among phases that would occur for a pure chemical in contact with both aqueous and gas phases.) Henry s law constants generally increase with increased temperature, primarily due to the significant temperature dependency of chemical vapor pressures as previously mentioned, solubility is much less affected by the changes in temperature normally found in the environment. 

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