Vapor-adsorbate equilibria

Table 2.4-4 Adsorbed solution theories for the description or prediction of multicomponent adsorption equilibria. In the light gray area new theoretical models are listed. The theories in the double-framed area require experimental data of binary adsorptives. VLE denotes vapor liquid equilibrium. The meaning of VAE is vapor adsorbate equilibrium...

Where Pg is the pressure of vapor in equilibrium with the adsorbed film. The characteristic curve is now just PF In Pq/P versus x (or against [Pg.627]

The trapping efficiency of polymeric, microporous adsorbents [e.g., polystyrene, polyurethane foam (PUF), Tenax] for compound vapors will be affected by compound vapor density (i. e., equilibrium vapor pressure). The free energy change required in the transition from the vapor state to the condensed state (e.g., on an adsorbent) is known as the adsorption potential (calories per mole), and this potential is proportional to the ratio of saturation to equilibrium vapor pressure. This means that changes in vapor density (equilibrium vapor pressure) for very volatile compounds, or for compounds that are gases under ambient conditions, can have a dramatic effect on the trapping efficiency for polymeric microporous adsorbents. 

After the end of the 4-day exposure, the detectors were returned to EML for analysis. The amount of radon adsorbed on the carbon device was determined by counting the gamma rays of radon progeny in equilibrium with radon. The concentrations of radon in the buildings were determined from the radioactivity in the device and the calibration factor, obtained in a radon chamber, that takes into consideration the length of exposure and a correction for the amount of water vapor adsorbed during the exposure. The lower limit of detection with this technique is 0.2 pCi/1 for a measurement period of 4 days when the test sample is counted for 10 min, 4 days after the end of exposure. More than 90% of the radon monitoring devices were analyzed successfully. Most of the unsuccessful measurements were due to delays or losses caused by the participants. 

The equilibrium adsorption characteristics of gas or vapor on a solid resemble in many ways the equilibrium solubility of a gas in a liquid. Adsorption equilibrium data are usually portrayed by isotherms lines of constant temperature on a plot of adsorbate equilibrium partial pressure versus adsorbent loading in mass of adsorbate per mass of adsorbent. Isotherms take many shapes, including concave upward and downward, and S-curves. Equilibrium data for a given adsorbate-adsorbent system cannot generally be extrapolated to other systems with any degree of accuracy. 

To some extent adsorption always occurs when a clean solid surface is exposed to vapor. Invariably the amount adsorbed on a solid surface will depend upon the absolute temperature T, the pressure P, and the interaction potential E between the vapor (adsorbate) and the surface (adsorbent). Therefore, at some equilibrium pressure and temperature the weight W of gas adsorbed on a unit weight of adsorbent is given by... 

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.

Measurements of binary vapor-liquid equilibria can be expressed in terms of activity coefficients, and then correlated by the Wilson or other suitable equation. Data on all possible pairs of components can be combined to represent the vapor-liquid behavior of the complete mixture. For exploratory purposes, several rapid experimental techniques are applicable. For example, differential ebulliometry can obtain data for several systems in one laboratory day, from which infinite dilution activity coefficients can be calculated and then used to evaluate the parameters of correlating equations. Chromatography also is a well-developed rapid technique for vapor-liquid equilibrium measurement of extractive distillation systems. The low-boiling solvent is deposited on an inert carrier to serve as the adsorbent. The mathematics is known from which the relative volatility of a pair of substances can be calculated from the effluent trace of the elutriated stream. Some of the literature of these two techniques is cited by Walas (1985, pp. 216-217). 

Individuals of multicomponent mixtures compete for the limited space on the adsorbent. Equilibrium curves of binary mixtures, when plotted as x vs. y diagrams, resemble those of vapor-liquid mixtures, either for gases (Fig. 15.5) or liquids (Fig. 15.6). The shapes of adsorption curves of binary mixtures, Figure 15.7, are varied the total adsorptions of the components of the pairs of Figure 15.7 would be more nearly constant over the whole range of compositions in terms of liquid volume fractions rather than the mol fractions shown. 

An essential step is to realize that the factor [3 is equal to P/Po- To see this let us consider the adsorption of a vapor to its own liquid at equilibrium and hence at Po. We take this situation to be similar to the situation of the vapor adsorbing to the th (not the first) layer. Taking the rate of binding equal to the rate of desorption we write... 

The measurement of contact angles is a wet chemical technique and since TTe is determined with a liquid film adsorbed from vapor in equilibrium with the liquid, it could also qualify as a wet chemical technique in contrast with vacuum techniques. 

Vapors in equilibrium with liquid in fine capillaries or pores will have depressed vapor pressure as a result of the Kelvin effect. In fact, if the pores are adequately small, the vapor will condense at pressures far below normal. By measuring the volume of nitrogen adsorbed at a relative pressure, i.e., p/po, of 0.99 and with prior knowledge of the surface area, the average pore diameter can be calculated. 

This study was undertaken to obtain the necessary vapor-liquid equilibrium data and to determine the distillation requirements for recovering solvent for reuse from the solvent-water mixture obtained from adsorber regeneration. Previous binary vapor-liquid equilibrium data (2, 3) indicated two binary azeotropes (water-THF and water-MEK) and a two phase region (water-MEK). The ternary system was thus expected to be highly nonideal. 

Where W is the equilibrium adsorption capacity. Wo is the total volume of the micropores aecessible to the given adsorbate, k is a characteristic constant related to the pore structure of the adsorbent, P is an affinity coefficient, Csai is the saturation concentration in the gas phase of liquid adsorbate at the adsorption temperature T, and C is the eoncentration of adsorbate vapor in equilibrium. Plotting ln(W) versus [RTln(Csai/C)] the parameters K/p and Wo in the DR equation were determined by the slope and the intercept of the linear lines respeetively. The obtained results and correlation coefficients are eompiled in Table 2. This Table shows the DR equation parameters and the... 

Material balance calculations on separation processes follow the same procedures used in Chapters 4 and 5. If the product streams leaving a unit include two phases in equilibrium, an equilibrium relationship for each species distributed between the phases should be counted in the degree-of-freedom analysis and included in the calculations. If a species is distributed between gas and liquid phases (as in distillation, absorption, and condensation), use tabulated vapor-liquid equilibrium data, Raoult s law, or Henry s law. If a solid solute is in equilibrium with a liquid solution, use tabulated solubility data. If a solute is distributed between two immiscible liquid phases, use a tabulated distribution coefficient or equilibrium data. If an adsorbate is distributed between a solid surface and a gas phase, use an adsorption isotherm. 

The pore size distribution is ealculated based on the water vapor or nitrogen gas adsorption isotherm. Before the calculation, it is essential to obtain an accurate adsorption isotherm. The amount of nitrogen gas adsorbed on the collagen fiber is extremely low in comparison to the amount of water vapor adsorbed on it. Approximately. 1 x 10 kg of collagen fiber, therefore, is put in the adsorption glass bulb. The amount adsorbed on the collagen fiber is measured at equilibrium pressures of 6.7, 13.3, 20.0, 26.7, 33.3, 40.0, 53.3, 66.7, 80.0, 93.3, and 101.3 kPa in order to get an accurate quantity. The adsorption isotherm for each... 

Here (Po) is the (fictitious) density of the adsorbate. A physically reasonable assumption is to consider Po to be either the density of the sorptive in its liquid triple state or in its liquid boiling state at system s temperature, if it exists. For low sorptive gas densities, i. e. p p , m" moe But for high gas densities, i. e. p - pj , we have m oo, indicating the occurrence of a liquid phase outside the sorbent material according to vapor-liquid-equilibrium (VLB) of the sorptive fluid, cp. also Chaps. 1, 8. 

---