Saturated equilibrium

Equation 10.49 Indicates that as the rate of evaporation Fy increases, the yield increases. However, the energy input must also increase. If the simplifying assumption is made that the outlet concentration is the saturated equilibrium concentration C at 60°C, then ... 

In both cases the solid carbonate was in saturation equilibrium (constant pco2)- The data show that the removal of Mn(II) or Cd(II) from solution occurs in at least two stages. 

The film pressure values for the detergency system are also listed in Table 2. These quantities represent the difference in interfacial tension between two pure phases and the interfacial tension of the same two phases which are at saturation equilibrium with the third phase. Since the PEG fiber surface was assumed insoluble in either the bath or soil, = 0. 

When equilibrium is reached, solubility product constants are used to describe saturated solutions of ionic compounds of relatively low solubility. When the ion concentration in solution reaches saturation, equilibrium between the solid and dissolved ions is established. 

The difference between the minimum growing concentration and the saturation equilibrium value represents the difference in the adherence of a molecule in a plane and one adhering to the plane surface. 

Important Saturated ammonium sulfate has to have a solid salt within the flask. When preparing fresh solution, saturation equilibrium is reached after several hours. 

Figure 3.1 The five isotherm classifications according to BDDT. W, weight adsorbed F, adsorbate equilibrium pressure Pq, adsorbate saturated equilibrium vapor pressure P/Pq, relative pressure. Condensation occurs at P/Pq >1.

The scale formed under moderate temperatures is usually due to temporary (bicarbonate) hardness being converted into calcium carbonate, which occurs on heating or increase in alkalinity sufficient to result in calcium carbonate saturation. The solubility of calcium carbonate also affects corrosion since the alkalinity of dissolved carbon dioxide in the water is greatly reduced as the saturation equilibrium is approached. Ideally, at equilibrium the various forms of carbon dioxide (free C02, bicarbonate and carbonate) are so balanced that they cause neither scale nor corrosion. 

Three runs were made to determine the length of time elapsed before the product stream concentration reached that of the feed. One run was made at the start-up feed rate of 450 SCCM to determine if sufficient time had elapsed in start-up for the columns to reach saturation equilibrium conditions. Figure 9 shows that approximately 2 hours was necessary for the columns to reach equilibrium. This confirmed that, indeed, sufficient time had expired, since start-up was approximately 4 hours. 

This activity of lead would be present in the saturated equilibrium solution, due to the dissolution of the membrane. Therefore, it represents the detection limit. Because silver ion is the charge-transferring species, the membrane potential must be written in terms of the silver ion activity (6.37), which is obtained from (6.49). Thus... 

For a low-pressure absorber at constant pressure, it is common to relate the temperature and concentration at saturated equilibrium by a linear function xeq = -0.00372Teq + 1.58226. Another boundary condition suggests that the heat flux at the droplet surface is proportional to the absorbed mass of refrigerant vapor, and we have... 

Figure 4.16. [Ca ] in saturation equilibrium with CaCO for TOTC = 10 M. Note that TOTC = constant is controlled independent of the dissolution of CaC03(s).

Figure 7.21. Phosphate necessary to convert CaCOaCs) into Caio(P04)6(OH>2(s) (Example 7.18). Calculated by assuming that the solution remains in saturation equilibrium with CaC03(s) furthermore, Pj Cj and [Ca ] = C. The equilibrium constant for equation i has been taken as 10 (upper line) and 10 (lower line), respectively.

Figure 85 shows schematically the concentration distribution around spherical Si02 particles of initial radius rg during their dissolution and after the last residual solid phase has disappeared. During dissolution, the solid —liquid boundary exhibited saturated (equilibrium) concentration while the mean Si02 concentration in the... 

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... 

The superscript, sat, indicates that this is the concentration of the gas at saturation equilibrium with the atmosphere and has sometimes been called the air solubility (Weiss, 1971). Concentrations at saturation equihbrium with air are presented for the major atmospheric gases at 20 °C and 1 atm in Table 3.6. 

The temperature dependences of the Henry s Law coefficients of the different gases listed in Table 3.6 are quite variable (Fig. 3.11). Helium, the least soluble noble gas, has very little solubility temperature dependence between 0 and 30 °C. On the other hand, Kr, the second most soluble of the non-radioactive noble gases, is much less soluble at higher temperatures. More details about gas solubilities are presented in the chapter on air-sea gas exchange (Chapter 10). Another notable aspect of the temperature dependence of the gas solubilities is that they are not linear. Thus, mixing between parcels of water of different temperatures at saturation equilibrium with the atmosphere results in a mixture that is supersaturated. This effect has been observed for noble gases in the ocean and may ultimately have a utility as a tracer of mixing across density horizons. 

The concept of nutrient and O2 change along a surface of constant density in the upper ocean is illustrated in Fig. 6.18. When waters subduct (surface waters flow along density horizons into the thermo-cline) it is assumed that they carry with them O2 concentrations near saturation equilibrium with the atmosphere and preformed nutrient concentrations. The assumption of saturation equihbrium is not exactly correct but in most cases this is probably not a serious error because surface oxygen measurements indicate near-saturation equilibrium everywhere except in the Southern Ocean south of the polar front, where concentrations can be up to 10% undersaturated. As a water parcel moves along a constant-density surface into the upper thermocline, respiration consumes the O2 concentration while creating nutrients and AOU in the water mass. At any point in the ocean interior, preformed nutrient concentrations can be calculated if one knows the temperature, salinity (for determining [02 ), nutrient and O2 concentrations. 

The solution to this equation describes a straight line beginning at the initial (t = 0) condition, [Al]o (Table 9.5, Fig. 9.4). If this equation were to describe the A1 concentration throughout the reaction, then the characteristic hfe time of A1 would be equal to the final A1 concentration (that achieved when the mineral reaction stops for some reason, [Alj ) divided by the dissolution rate, [Al]j/J (Table 9.5). In practice, this relation holds only at the beginning of the dissolution reaction. If the reaction continues and the sohd is in excess, the reaction order is likely to change as saturation equilibrium between the concentration in solution and the solid is approached and precipitation and dissolution rates become comparable. 

Most readers who have seen the surface of the ocean during a moderate wind have noticed that breaking waves introduce lots of small air bubbles into the water (Fig. 10.9). The hydrostatic pressure only 1 m below the ocean surface is already equal to about 10% of the entire atmospheric pressure, so the pressure inside a bubble is c.110% of that at the ocean surface. Thus, there is a strong tendency for bubbles entrained in the downwelling limb of a breaking wave to lose some or all of their gas to the surrounding fluid by diffusion across the bubble surface. This causes the surface waters to be supersaturated with respect to saturation equilibrium. We define the degree of supersaturation, A %), as... 

The dissolution rate (R) for calcite from the laboratory experiments of Keir (1980) as a function of the degree of undersaturation, (I — fi). Lines represent the rate laws with exponents of n = 1.3 and 1.0 as reinterpreted using more realistic values for the saturation equilibrium constant by Hales and Emerson (1997a). 

Calculate both the breakthrough capacity and the working capacity of an adsorption bed given the saturation (equilibrium) capacity (SAT), mass transfer zone (MTZ), and HEEL data provided below ... 

Since much of the above data is rarely available, or just simply ignored, the working charge may be taken to be some fiaction,/, of the saturated (equilibrium) capacity of the adsorbent, i.e.. 

The above information is all that is required to perform a preliminary sizing on a spray dryer. The temperature limit of the product is given at 170°F. Using 160 F as the outlet temperature of the dryer should allow us the safety necessary so as not to exceed the temperature limit of the dry powder (product). The fact that we get evaporative cooling while drying the spherically shaped droplets to a similarly shaped powder allows us to use an inlet temperature of about 320°F. Thus the temperature difference (AT) is 160°F. This is the primary driving force in motivating the water to leave the product due to the enormous difference in saturation equilibrium between the wet droplet/dry powder and the very hot dry air. 

The formulas presented here are valid for fluids at a homogeneous one-phase equilibrium state. They are not to be directly apphed to a fluid at an unstable state, for ordinary interest is not on the unstable fluid as a homogeneous phase, but on the saturated phases that separate from the unstable fluid. Separate calculations on the separated phases need to be performed with the eos-derived formulas for the individual saturated phases, and summed if desired. The calculations to find the saturated equilibrium phases are the subject of Section 4.4. 

In experiments in which animals were supplied with food containing 0.2 ppm of labelled aldrin, a saturation equilibrium was established in 50 days. Thereafter a quantity equal to the daily intake was excreted daily. 

The lower vapour pressure of these compounds means their concentration in ambient air will also be low. If explosives are contained in an enclosure with cool surfaces the vapour concentration may be even lower than saturated values due to partitioning effects. The saturated equilibrium ambient air concentration of TNT, RDX, and PETN as a function of ambient temperature is shown in Figure 4. At room temperature there are approximately 100 picograms of TNT per mL available for detection. NG and DNT have even higher concentrations available for detection. Flowever, PETN and RDX produce less than 1 picogram per mL and hence are much more difficult to detect as vapours. For these compounds it is easier to use a wipe to extract material from surfaces and then to desorb thermally the compounds as vapours into the detection system. 

---