Henry’s treatment

Henry s Treatment Henry s treatment [18] apphes to intermediate cases where kR is not too small or too large, Henry derived the following expression (which can be applied at all kR values),... 

Henry s calculations are based on the assumption that the external field can be superimposed on the field due to the particle, and hence it can only be applied for low potentials (f < 25 mV). It also does not take into account the distortion of the field induced by the movement of the particle (relaxation effect). Wiersema, Loeb and Overbeek [19] introduced two corrections for the Henry s treatment, namely the relaxation and retardation (movement of the hquid with the double layer ions) effects. A numerical tabulation of the relationship between mobility and zeta-potential has been provided by Ottewill and Shaw [20]. Such tables are useful for converting u to f at aU practical values of kR. 

Wiersema, Loeb and Overbeek [25] introduced two corrections to Henry s treatment, namely the relaxation and retardation (movement of the liquid with the double layer ions) effects and Ottewill and Shaw have compiled a numerical tabulation of the relation between mobility and zeta potential [26]. Such tables are useful for converting u into C at all practical values of kR. 

B In Huckel s and Henry s treatment of electrophoresis the reader who is familiar with the theory of the conductivity of strong electrolytes will have missed the so-cailed time-of-relaxation effect This effect, originating in the deformation of the double layer also has a retarding influence on the electrophoresis. In the applied field the charge of the double layer is displaced in a direction opposite to the movement of the particle Not only does this charge retard the electrophoresis by its movement (electrophoretic retardation see 6a), but also by the dissymmetry of the double layer resulting from this displacement a retarding potential difference is set up. 

The results of a comparison between values of n estimated by the DRK and BET methods present a con. used picture. In a number of investigations linear DRK plots have been obtained over restricted ranges of the isotherm, and in some cases reasonable agreement has been reported between the DRK and BET values. Kiselev and his co-workers have pointed out, however, that since the DR and the DRK equations do not reduce to Henry s Law n = const x p) as n - 0, they are not readily susceptible of statistical-thermodynamic treatment. Moreover, it is not easy to see how exactly the same form of equation can apply to two quite diverse processes involving entirely diiferent mechanisms. We are obliged to conclude that the significance of the DRK plot is obscure, and its validity for surface area estimation very doubtful. 

Low concentrations of oil can be removed by dissolved air flotation (DAF). In this process, an effluent recycle is pressurized in the presence of excess air, causing additional air to go into solution, in accordance with Henry s Law. When this water is discharged to the inlet chamber of the flotation unit at close to atmospheric pressure, the dissolved air comes out of solution in the form of tiny air bubbles which attach themselves to and become enmeshed in suspended solids and oil globules. The primary design criteria is the air/solids ratio, which is defined as the mass of air released divided by the mass of solids fed. Sufficient air must be released to capture the solids in the influent wastewater. The performance of DAF for the treatment of several... 

However, as can be seen in Figure 6.15, which is a graph of the fugacity of HC1 against molality in dilute aqueous solutions of HC1 (near. i = 1), f2 approaches the m axis with zero slope. This behavior would lead to a Henry s law constant, kn.m = 0. given the treatment we have developed so far. Since the activity with a Henry s law standard state is defined as a —fi/kwnu this would yield infinite activities for all solutions. 

The extension of the ideas presented in Sections 5.8 and 5.10 to the theoretical treatment of isotope separation by gas chromatography is straightforward. The isotope effects observed in chromatography are governed by the isotopic ratio of Henry s Law constants (for gas-liquid separations), or adsorption constants (for... 

In water, neither volatilization nor sorption to sediments and suspended particulates is expected to be an important transport mechanism. Using the Henry s Law constant, a half-life of 88 days was calculated for evaporation from a model river 1 m deep with a current of 1 m/second, and with a wind velocity of 3 m/second (Lyman et al. 1982). The biological treatment of waste water containing phenol has shown that less than 1% of phenol is removed by stripping (Kincannon et al. 1983 Petrasek et al. 1983). 

HEMOGLOBINS POLYMERIZATION RESONANCE RAMAN SPECTROSCOPY HEMOGLOBIN-S POLYMERIZATION HENDERSON-HASSELBALCH EQUATION HENDERSON PLOT Henri-Brown treatment,... 

Volatilization from surface waters is not expected to be a significant source of isophorone in the atmosphere, since this is anticipated to be a slow process (based on the Henry s Law Constant of 4.55x10 atm m mol"). Wastewater treatment plants may, however, emit some isophorone from influent water to the air, particularly if gas stripping methods are used (Hawthorne and Sievers 1984, Hawthorne et al. 1985). Drinking water plants that practice aeration of influent water may also emit small amounts of isophorone to air. 

In this chapter we will focus on another special case, that is, the case in which we assume that Yu is different from 1 but is constant over the concentration range considered. This situation is primarily met when we are dealing with dilute solutions. As we have seen for the solvent water (Table 5.2), for many organic compounds of interest to us, Ylw does not vary much with concentration, even up to saturated solutions. Hence, for our treatment of air-water partitioning, as well as for our examples of air/organic solvent partitioning at dilute conditions, we will assume that Yu is constant. This allows us to modify Eq. 6-1 to a form known as Henry s Law ... 

Due to the complexity of most waste waters and unknown oxidation products, differences in lumped parameters such as COD or preferably DOC are used to quantify treatment success. A model to describe the oxidation process, including physical and chemical processes, based on a lumped parameter has been tried (Beltran et al., 1995). COD was used as a global parameter for all reactions of ozone with organic compounds in the chemical model. The physical model included the Henry s law constant, the kLa, mass transfer enhancement (i. e. the determination of the kinetic regime of ozone absorption) as well as the... 

Here ng is the density of the gas molecules, c is the average thermal velocity and 7 is the mass accommodation coefficient This is the maximum flux of gas into a liquid. In many circumstances, however, the actual gas uptake is smaller. It may be limited tty several processes, the most important of which are gas phase diffusion and Henry s Law saturation. The treatment of Henry s Law saturation in turn involves liquid phase diffusion and, in some cases, liquid phase chemical reactions. 

The Henry constant J Cis a function of T but not P. (In some theoretical treatments, the Henry constant is the ratio of fugacity to quantity adsorbed, i.e., the inverse of the sense used here.) It is generally expected that adsorption will be governed by Henry s law at sufficiently low pressures. It is possible to construct theoretical models for adsorption in which an isotherm does not reduce to Henry s law, Equation (2.3), even in the limit P —> 0, but it is not clear that such situations obtain in practice and doubtful that they are important in noble gas geochemistry. 

Chapter 6 dealt with the application of vacuum technology in three areas of the chemical sciences. The first was concerned with its use in chemical technology, particularly in purification/separation operations such as distillation and evaporation. For distillation, the use of the Clapeyron and Clausius-Clapeyron equations was demonstrated (Examples 6.1 and 6.2) whilst Raoult s and Henry s laws were stated and applied (Examples 6.3, 6.4). The removal of water (drying) is an important but poorly understood operation. Aspects of this were discussed in Examples 6.5-6.7. Condensers, particularly in conjunction with vacuum pumps, are indispensable in applications such as distillation and drying. Simple treatment of condenser theory was stated and applied in Examples 6.7-6.9. 

A number of different empirical equations have been proposed to allow for the deviations of physisorption isotherms from Henry s law. An approach which is analogous to that used in the treatment of imperfect gases and non-ideal solutions is to adopt a virial treatment. Kiselev and his co-workers (Avgul et al. 1973) favoured the form... 

Natural attenuation studies of MTBE are limited and the physicochemical characteristics of MTBE, including relatively high aqueous solubility and low Henry s law constant, are such that removal by traditional treatment technologies, such as pump-and-treat, is difficult. 

The most commonly encountered coexisting phases in industrial practice are vapor and liquid, although liquid/liquid, vaporlsolid, and liquid/solid systems are also found. In this chapter we first discuss the nature of equilibrium, and then consider two rules that give the lumiber of independent variables required to detemiine equilibrium states. There follows in Sec. 10.3 a qualitative discussion of vapor/liquid phase behavior. In Sec. 10.4 we introduce tlie two simplest fomiulations that allow calculation of temperatures, pressures, and phase compositions for systems in vaporlliquid equilibrium. The first, known as Raoult s law, is valid only for systems at low to moderate pressures and in general only for systems comprised of chemically similar species. The second, known as Henry s law, is valid for any species present at low concentration, but as presented here is also limited to systems at low to moderate pressures. A modification of Raoult s law that removes the restriction to chemically similar species is treated in Sec. 10.5. Finally in Sec. 10.6 calculations based on equilibrium ratios or K-values are considered. The treatment of vapor/liquid equilibrium is developed further in Chaps. 12 and 14. 

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