Equilibrium water fraction

Set of ion concentrations in gel and outer solution Concentration of buff in acid form in outer solution Total buffer concentration in outer solution Concentration of i-th ionic spec insMe gel Concentration of i-th ionic species in outer solution Diffusion coefficient Deborah number Equilibrium water fraction Ionic strength... 

An existing lO-in. I.D. packed tower using 1-inch Berl saddles is to absorb a vent gas in water at 85°F. Laboratory data show the Henry s Law expression for solubility to be y = 1.5x, where y is the equilibrium mol fraction of the gas over water at compositions of x mol fraction of gas dissolved in the liquid phase. Past experience indicates that the Hog for air-water system will be acceptable. The conditions are (refer to Figure 9-68). 

While it is expected that the source rocks for the radionuclides of interest in many environments were deposited more than a million years ago and that the isotopes of uranium would be in a state of radioactive equilibrium, physical fractionation of " U from U during water-rock interaction results in disequilibrium conditions in the fluid phase. This is a result of (1) preferential leaching of " U from damaged sites of the crystal lattice upon alpha decay of U, (2) oxidation of insoluble tetravalent " U to soluble hexavalent " U during alpha decay, and (3) alpha recoil of " Th (and its daughter " U) into the solute phase. If initial ( " U/ U).4 in the waters can be reasonably estimated a priori, the following relationship can be used to establish the time T since deposition,... 

By analysis of hydroxyl-bearing minerals and calculation of the isotopic composition of fluids from known temperature-dependent mineral-water fractionations, assuming that minerals were precipitated from solutions under conditions of isotope equilibrium. 

Isotopic fractionation resulting from evaporation from standing water bodies can be described in terms of equilibrium and nonequilibrium fractionation effects. Equilibrium fractionation occurs when the isotopic composition of the evaporated water or lake evaporate is in thermodynamic equilibrium with the lake water (23). Equilibrium fractionation, however, can occur only when the water vapor in the air mass above the lake is 100% saturated. The process of equilibrium isotopic fractionation is described by Raleigh fractionation. The isotopic composition of water vapor in equilibrium with liquid water at any time is given by... 

Maize starch may be separated after irradiation into several fractions, based on solubility in alcohol and aqueous alcohol. The size of the fractions and their composition depends on the radiation dose, as shown in Table X which also shows the distribution of organic products of destruction (aldehydes and carboxylic acids) in particular fractions.118 The relations presented in this Table are S-shaped. Under irradiation with increasing doses, the destruction of starch obviously increases. The nature of the increase of acidity in com starch has also been studied by Athanassiades and Berger.119 Thollier and Guilbot120 have conducted similar studies on potato starch, and Raffi et al99 have extended their studies to more varieties of starch. The results expressed as free and total acidities, as well as the quantity of formic acid at equilibrium water content, are given in Table XI. These data vary rather nonlinearly with increase of the irradiation dose and water content. 

Figure 2 Calculated fraction of intracellular water remaining in (A) yeast cells and (B) human red blood cells as they cool to various temperatures at the indicated rates. Curve Eq represents the equilibrium water content. (From Ref. 22.)...

A waste-air stream containing 2 mol % of impurity A is purified to 0.02% by scrubbing with pure water in a countercurrent packed-column. The column provides 7 overall gas-phase transfer units in a height of 1.75 m. The equilibrium mole fractions of A in the vapor and liquid are related according to ... 

Equilibrium isotopic fractions rebect the combined, unidirectional kinetic isotopic fractionations. In considering the one-way buxes as in Equation (12), estimates of the one-way kinetic fracbonations are needed. Knowledge of kinetic effects is obtained from controlled experiment with pure CO2 and water or with salt solutions, but for the chemically complex system that is ocean-water, empirical values are adopted. Eor example, laboratory experiments show that the hydration of aqueous CO2 to bicarbonate involves fractionation of 13%c and the dehydration reaction fractionate by 22%c (O Leary et al., 1992). The difference between these two kinetic fractionations, 9%c, corresponds to the equilibrium fractionation depicted above (Marlier and O Leary, 1984 O Leary et al., 1992). In practice, it was estimated... 

Carbonic anhydrase, in turn, is located predominantly in the chloroplasts, and provides therefore a reasonable estimate of the specific 6 0 of water fraction with which CO2 equilibrate in the leaves, and 5i used in Equation (43) will simply be 5i = 5l, - -Seq, where Seq is the water-CO2 equilibrium fractionation. In difihising out of the leaf, a dififusional fractionation, sj must also be considered, such that the final 5 0 value of the CO2 reaching the atmosphere is 5i - - si. Note that considerable uncertainty is still associated with estimating the 5 0 value of leaf water on large scale and current estimates ranged between 4.4%o and 8.8%o (Bender etfll., 1985,1994 Dongmann, 1974 Forstel, 1978). 

Since pentane and water exhibit immiscibility, we might consider decantation as the first step. If it worked, it would be an inexpensive one to carry out. But a rigorous three-phase equilibrium calculation predicts that, in the presence of acetone and methanol, the small water fraction in the feed does not form a second liquid phase so we reject this idea. The calculation also reveals that the feed mixture is almost at the azeotropic composition for the pentane/methanol binary pair. 

In a diy atmosphere, the partial pressure and mole fraction are equal. Mole fractions for the major atmospheric gases are presented in Table 3.6, and the temperature dependence of PhjO at equilibrium with seawater, Pn o saturation equilibrium, water... 

Recently, Steinbach and Sucker (23) reported about the formation of l+-H20-molecule structures that may develop on the hydrophilic groups of surface active compounds upon dilatation of a l-H20-molecu-le structure, by adsorbing 3-water molecules from the subphase at a water-air interface. In the case of the water-oil interphase of the microemulsion, the dispersed droplet consits of an interphasal choro-na that surrounds an inner water core the free water fraction of the latter (bulk-H20)is the subphase that, acting as a reservoir, supplies H2O molecules to the interphase region. Since the formation of hydrated structures takes place at ons ant sur ace tension (23), the above mechanism allows the water-oil interface to expand without affecting the surface pressure necessary to maintain the system s equilibrium. In this way while the area of every polar head of the amphi-phile remains constant, the interphase area stabilized by a single polar head increases up to the amount corresponding to the definite area requirement of the it-H20-molecule structure (23) (3-6). 

Equilibrium mole fraction in the gas phase divided by the mole fraction in a water phase at 38°C. If base is present the equilibria of the first two compounds will affect this ratio. H2S, ki = 2.1 X 10- k2 10-14 CH3SH, k = 4.3 X 10 for aqueous solutions at 100°C. 

Figure 12.28 Comparison of experimental and calculated band profQes using the equilibrium-dispersive model. Top Experimental results on a 0.46 cm i.d. column packed with 5

Effluent air containing 0.1 mole% H2S is to be scrubbed with a caustic solution in a counterflow absorber to lower the HjS concentration in the air to 0.01 mole%. The equilibrium concentrations of H2S in the air and the liquid follow the relationship Y = 2>X, where X and Y are equilibrium mole fractions of HiS in the liquid and air, respectively. It may be assumed that water vapor in the air and air dissolved in the liquid are negligible. Determine the required number of equilibrium stages if the liquid rate is three times the minimum. 

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