Break-point concentration

Data for drying nitrogen with molecular sieve type 4A are given by Collins. Calculate the saturation capacity from the breakthrough curve, and determine the length of unused bed based on a break-point concentration c/e of 0.05 ... 

After the break-point time is reached, the concentration c rises very rapidly up to point c, which is the end of the breakthrough curve where the bed is judged ineffective. The break-point concentration represents the maximum that can be discarded and is often taken as 0.01 to 0.05 for c /Co. The value cjc is taken as the point where Cj is approximately equal to c. ... 

EXAMPLE 12.3-1. Scale-Up of Laboratory Adsorption Column A waste stream of alcohol vapor in air from a process was adsorbed by activated carbon particles in a packed bed having a diameter of 4 cm and length of 14 cm containing 79.2 g of carbon. The inlet gas stream having a concentration of 600 ppm and a density of 0.00115 g/cm entered the bed at a flow rate of 754 cm /s. Data in Table 12.3-1 give the concentrations of the breakthrough curve. The break-point concentration is set at dCg = 0.01. Do as follows. 

In the case of precipitation by monovalent salts (NaCl), the phase separation was taken at the initial break points in the resulting optical density versus NaCl concentration curves obtained at 600 nm. This method has been also used to detect the phase separation with CuCl2 at very low polymer concentrations. 

Fig. n.7 Sharp-break PLIMSTEX curves at high protein concentration [23], Line (a) melittin (a 26-amino-acid peptide) titration. Line (b) mastoparan (a 16-amino-acid peptide) titration of 15 pM Ca +-saturated porcine calmodulin (CaM-4Ca) in 50 mM HEPES, 100 mM KCI, 0.49 mM Ca +, 99% D2O, apparent pH 7.4. Data points are based on the average of t /o runs for each titration system, and the breaking point clearly indicates 1 1 protein-ligand binding stochiomet. ... 

The equivalent conductivity of the 6ED-LiF0S mixed solutions was measured, with the concentrations of 5ED fixed below and above the CMC. The break point corresponding to the CMC in the graph of equivalent conductivity vs. concentration of LiFOS disappeared gradually. The values of equivalent conductivity decreased with increasing the fixed 6ED concentration. 

The break point corresponding to the CMC of SDS did not shift in several fixed NF concentrations, and the values of equivalent conductivity were almost the same at the same SDS concentration in the mixed solutions. Therefore, it is concluded that the NF molecules can not penetrate into the SDS micelles, and that pure component NF and SDS micelles exist. 

Figure 1 shows the plots of the interfacial tension against temperature at various values for = 7.54 mmol kg". All the curves except for the concentrated solution of dodecylammonium chloride have a break point which represents the phase transition from the condensed to expanded state. The phase transition temperature lowers with increasing and disappears above a certain ni2 value. 

The TS of the compacted samples was determined by transverse compression with a custom-built tensile tester. Tensile failure was observed for all the rectangular compacts when compressed between flat-faced platens at a speed ranging between 0.006 and 0.016 mm/sec. Platen speed was adjusted between materials to maintain a time constant of 15 2 seconds to account for viscoelastic differences the constant is the time between the sample break point and when the measured force equals Fbreak/e in the force versus time profile, where the denominator is the mathematical e. Specially modified punch and die sets permitted the formation of square compacts with a centrally located hole (0.11 cm diameter) that acted as a stress concentrator during tensile testing. This capability permitted the determination of a compromised compact TS and thus facilitated an assessment of the defect sensitivity of each compacted material. At least two replicate determinations were performed for each mechanical testing procedure and mean values are reported. 

Usually, the supply of the feed solution is stopped when the ratio of the adsorbate concentration in the effluent to that in the feed has reached a predetermined value (the break point ). Then, in the elution operation the adsorbate bound to the adsorbent particles is desorbed (i.e., eluted) by supplying a suitable fluid (eluent) that contains no adsorbates. In this way, adsorbent particles are regenerated to their initial conditions. However, in some cases the column may be repacked with new adsorbent particles. 

Integration of this equation between the break point and exhaustion point, where the ratio of the adsorbate concentration in the effluent to that in the feed becomes a value of (1 - the ratio at the break point), gives... 

Estimate the break point at which the concentration of A in the effiuent becomes 0.1 C g. 

One simple way to analyze the performance of a fixed-bed adsorber is to prepare a breakthrough curve (Figure 10.12) by measuring the solute concentration of the effluent as a function of time. As the solution enters the column, most of the solute will be adsorbed in the uppermost layer of solid. The adsorption front will move downward as the adsorption progresses. The solute concentration of the effluent will be virtually free of solute until the adsorption front reaches the bottom of the bed, and then the concentration will start to rise sharply. At this point (tb in Figure 10.12), known as the break point, the whole adsorbent is saturated... 

It has been well documented that surfactants self-associate in aqueous solution to minimize the are of contact between their hydrophobictails and the aqueous solution (Mukerjee, 1979 Tanford, 1980). This phenomenon occurs at a critical concentration of surfactant, the critical micelle concentration or CMC (see Figure 12.4) above where the surfactant molecules exist predominantly as monomeric units and above which micelles exist. The CMC can be measured by a variety of techniques, for example, surface tension, light scattering, osmometry, each of which shows a characteristic break point in the plot of the operative property as a function of concentration. Knowing the CMC of the particular surfactant system and understanding the conditions that may raise or lower that critical concentration is important to the design of a formulation based on micellar solubilization. 

In general, the tensile strength of the composites based on concentrated emulsions is higher than that based on bulk polymerization the elongation at the break point and the toughness are, however, a little lower. 

In the case of strongly polluted surface water, chlorination is the first purification step and is carried out after removal of any coarse foreign matter. Sufficient chlorine is added to ensure a free chlorine concentration of ca. 0.2 to 0.5 mg/L in the water after treatment (break-point chlorination). Chlorine reacts with water forming hydrochloric acid and the hypochlorite anion, depending upon the pH. 

Figure 15. Arsenic concentrations in coals of the Black Warrior basin, Alabama. Shaded areas show the extent of coalfields of Alabama. The proportionally sized symbols. show the content of arsenic in coal samples analyzed by the USGS. Some symbols that plot inside each other are from the same core or coal face. The break points for the symbol groups were calculated using the natural breaks algorithm in the computer program Arcview . Dashed lines are contours of vitrinite reflectance data from coals. We are presently evaluating whether the tack of correspondence of high arsenic content with high vitrinite reflectance values is an artifact due to low sample density or reflects an actual trend in the data.

Another important point can be made from the y-log C curves. At a concentration just before the break point there is a condition of constant slope, which indicates that saturation adsorption has been reached ... 

At concentrations just before the break point, the slope of the y-log C curve is constant. 

Each of the EPA tables show a break in the exponential relationships, and it is necessary to solve each of the pair of equations to determine the distance that could be attained by toxic endpomt concentrations. If the distance exceeds the break point, the long-distance equation would apply. 

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