Condensed volume

Figure 2.38 shows that a volume of 1000 L (chamber and condenser) will be evacuated to 0.01 mbar in -8 min by a pump with the capacity of 100 m3/h. For a volume of 100 L, a pump with a capacity of 10 m3/h is sufficient. The pump for evacuation only can be relatively small. A pump with 100 m3/h has this capacity also at a pressure of 0.05 mbar however, at this low pressure 100 m3/h represents only 1.4 mbar L/s or 1.1 x 10 3 g/s. This pumping capacity is more than sufficient if the leak rate is smaller than 0.01 mbar L/s, which can be expected for most plants. The critical dimension for the pump size can be the gas from the product. In a chamber of 700 L (plus 300 L condenser volume), there may be, e.g., 10 kg of product, which may have a minimum of 10 g (but often 100 g) of air dissolved within, which may become free... 

Example Exhaust vapors from a process operation contain 95 percent steam at 200 °F at 11.5 psia. The maximum evaporation rate in the cooker is 2,000 lb per hour. Steam is to be condensed at 200 °F and cooled to 140 °F in a contact condenser. A vacuum pump removes uncondensable vapors at the condenser and maintains a slight vacuum on the cooker. Determine the volume of 60 °F fresh water required and the resultant condensate volume. The solution to this problem is as follows ... 

Fig. 1. Capillary condensation in the contact zone of elementary particles of radius and two particle packing types (a) shaded zone is a condensing volume enclosed by a hypothetical rolling sphere of radius r in contact with larger spheres of radius R (b) P.P. type (c) S.C. type.

Two theoretical force curves calculated by using Eqs (25) and (26) are shown in Fig. 18. In these calculations we used a Kelvin radius of 320 nm and an interfacial tension difference of 3.3 mN/m. The measured force curves fall in between the extreme cases of full equilibrium, where the volume of the condensate is changing with distance to minimize the free energy, and the case of no change in condensate volume with separation. Long-range forces due to capillary condensation have been observed previously by Petrov et al. who foimd that water condensed between two surfaces immersed in a microemulsion. (83). Capillary condensation of sparingly soluble surfactants between surfaces close to each other in surfactant solutions has also been reported (84). 

When using the Kelvin equation to determine the pore size distribution, with the capillary condensation part of the Type IV isotherms, the adsorbing gas should be nitrogen, so that both surface area and pore size distribution can be obtained from one isotherm. If the volume of the gas adsorbed on external surface of the solid is smaller than that adsorbed inside the pores, the voliune of the pores can be obtained, when the volume of the gas adsorbed Vg is converted to a liquid or condensed volume 14- The relationship between Vg and is given by ... 

Due to the necessity of producing a condensed volume, the content of this book has been devoted to a limited part of physics and physical chemistry that excludes more complicated systems. More sophisticated Formal Objects that are the distributed dipoles and systems with assemblies of these objects have not been studied further. These concepts enable us to handle systems with several energy levels that are of paramount importance in condensed matter physics and in many other fields. The Maxwell distribution of velocities in a gas is one of the important systems that are modeled with this Formal Object. 

Counterion condensation theory (CCT) predicts the concentration of bound counterions (1-5). However, traditional experim tal methods only measure the fraction of counterions bound and not their concentration within e condensed volume. The chemical trapping method provides this information (7-11). Here, we use chemical trapping to estimate e concentration of counterions in the condensed volume of an anionic polyelectrolyte, sodium polyaciylate, NaPAA and compare our result with that obtained from CCT. 

CCT has been described in detail (1,12,13). The concentration of univalent counterions in the condensed volume, cj°° (7), can be calculated from ... 

In aqueous solutions of NaPAA containing added l-ArN2 the distribution of the two cations between die condensed volume and the bulk water is described by an exchange constant ... 

The equilibrium constant for this exchange was obtained by using Na NMR (15,16) to measure the change in the relaxation time of Na as a function of added [l-ArN2l. We assume that the total number of counterions in the condensed volume remains constant, i.e. one-to-one exchange of counterions. The assumption of one-to-one exchange is supported by the repeated observation that the fraction of counterions bound to a polyelectrolyte is unaffected by dilution or added electrolyte (1,6,12,13,11,18). 

Solutions of sodium acetate/acetic acid were used as a model system for the condensed volume. l-ArN2 reacts with water and acetate ion, Scheme 1, and also acetic acid to give stable products. The selectivity of the l-ArN2 toward acetate versus water is then defined as (7) ... 

We assume that net surface charge density (5) and similarly die fraction of bound counterions to NaPAA, are is independent of counterion type. Thus the total concentration of Na" and l-ArN2 counterions is 65% of that of the pendent carboxylate groups, ti = 0.65, Over a 5-fold polymer dilution, the average interfacial counterion concentration in the condensed volume, Ccv around NaPAA is about 0.14 M estimated by chemical trapping. 

Chemical trapping with an arenediazonium ion provides the first experimental estimate of counterion concentration in the condensed volume around an anionic polyelectrolyte, NaPAA. The method can be applied to other polyelectrolyte systems. Inherent advantages of the method are the low selectivity of the probe towards a variety of nucleophiles and its insensitivity to medium effects such that product yields are almost directly proportional to nucleophile concentration. We are currendy using chemical trapping to estimate the concentration of condensed counterions around sodium polystyrene... 

There is negligible liquid or vapor hold-up in the reflux condenser. Volume changes in the reacting mixture are negligible, and the volume of liquid in the reactor remains constant at 1.46 m /kg mol of initial benzene charge. 

Vc is the condensed volume adsorbed, F is the degree of volume filling, Vfmcro is the volume of micropores and Sme and Sma are the surface areas of the meso and macropores. Kadlec also proposed a method of evaluating F which was later applied by Dubinin etal, [106]. 

Pore volue and pore surface distribution may be determined from gas adsorption isotherms. If the amount of gas adsorbed on the external surface is small compared with the amount adsorbed in the pores, the total pore volume is the condensed volume adsorbed at saturation pressure. 

The limits of integration being the maximum measured relative pressure (circ 0.99) and the relative pressure at which the hysteresis loop closes (x 0.40). If the condensed volume, is in cm3 g-1, Sp is in m2 g-1 with a constant of 4939. 

Sp may be evaluated by graphically integrating a plot of log x against condensed volume or by a tabular method [73], an example of which is given in Table 3.1. 

Kiselev [74] employed this method successfully for the determination of the total surface area of a number of adsorbents, having only wide pores, and the results were in good agreement with BET surface areas. For narrow pores, core and pore surface differ considerably. In terms of volume distributions, this technique is equivalent to plotting condensed volume desorbed (V ) against half the Kelvin radius. 

The condensed volume desorbed (AV j is related to the pore surface (AS J by the following equation ... 

As the pressure falls from to /V-1 condensed volume Vf. is desorbed where ... 

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