Binary relative adsorptivities

The relative adsorption of component B is clearly affected by its partial pressure. Let us consider a binary system A-B where rA = 0 and B is an ideal gas with partial pressure pB. The chemical potential of B can be expressed in terms of the partial pressure of B and this is then also the case for the relative adsorption of B... 

Obtaining adsorption constant data in complicated reaction systems, such as HDS processes, is difficult as can be seen from the preceding discussion. It is often more instructive to determine the relative adsorption behaviors for competing materials in binary mixtures. This has been done by many authors and this approach is discussed next. 

Relative Adsorptivities for Binary n-Paraffin Systems over Various Zeolites... 

Hi, according to the relative adsorption of different polar solvents B, C.For binary-... 

Fig. 1 shows the uptake of pure hexane and decane frx)m their mixture with iso-octane on ZSM-S. The amounts adsorbed in the zeolite remain constant after 20 hours, indicating that the experiments were performed under equilibrium conditions. In order to verify that iso-octane can be used as inert solvent, a comparative experiment was performed in which the binary adsorption isotherm of hexane and decane was determined using isooctane and l,3,S-trimethyl benzene as respective solvents. The same adsorption isotherms are obtained with both solvent (Fig. 1 b), demonstrating that iso-octane does not interfere with the adsorption of the linear alkanes, and that the relative adsorption of the short and long n-alkanes is not influenced by the nature of the solvent, given that the solvent is not able to enter the pore system. 

Similarly to binary systems, in ternary systems without solvents the use of Eq. (8) in the calculation of relative adsorption coefficients is also questionable, because the effect of a third compound on the selectivity of hydrogenation of the remaining two may consist not only in its effect on the ratio of the adsorption coefficients, but also on the ratio of the rate constants. For this reason, the effect of a third compound on the hydrogenation of the other two was considered (99) as an effect on the ratio of reactivities of both compounds, and thus on the ratio of products of the rate and adsorption constants. 

In a binary mixture, the relative adsorption of component 2 at the liquid-air interface is defined by... 

To fix our ideas let us consider two infinite, flat, parallel plates in adsorption equilibrium with a binary solution. Suppose that at a separation H and at a given solution concentration the relative adsorption of component 2 is Tf H). We wish to know how the presence of the solution between the plates at a mole fraction x2 affects the surface tension. 

Table 1 shows the differences between nf and n and 9, and for binary adsorption of CO2 (component 1) + CH4 (component 2) mixtures on BPL carbon at soil K [13]. They were estimated at three different total gas pressure levels and at different gas-phase compositions. The table also gives the fractional adsorbate loadings (6,) of the components [0 — nT(P, T, y,)/w]. m is the saturation capacity (surface excess) for both components. The pure and binary gas adsorption isotherms for this system can be described by the Langmuir model [17]. The model parameters are given in Table 1. A value of 0.80cm /g was used as for these calculations. It can be seem from Table 1 that the differences between nf and are relatively small because CO2 (component 1) is more selectively adsorbed than CH4 on the carbon. The differences between n and 2 are, however, much larger. Furthermore, the differences between qi and q, are much larger than the corresponding differences between and. The differences between qi and qi get even bigger as the system pressure P) and the mole fraction of component 1 (y) in the gas phase are increased. These examples demonstrate the weakness of the shortcut method.

When an adsorbent is mixed with a binary solution, adsorption of both solute and solvent occurs. Since the total adsorption cannot be measured, the relative or apparent adsorption of solute is determined instead. The customary procedure is to treat a known volume of solution with a known weight of adsor nt, o volume solution/mass adsorbent. As a result of preferential adsorption of solute, the solute concentration of the liquid is observed to fall from the initial value Co to the final equilibrium value c mass solute/volume liquid. The apparent adsorption of solute, neglecting any volume change in the solution, is then o(co - c ) mass solute adsorbed/mass adsorbent. This is satisfactory for dUute solutions when the fraction of the original solvent which can be adsorbed is small. 

For a binary system, if the adsorption of compound 1 (e.g. the solvent) is zero then the relative adsorption of compound 2 (the solute) is given as ... 

The working capacity of a sorbent depends on fluid concentrations and temperatures. Graphical depiction of soration equilibrium for single component adsorption or binary ion exchange (monovariance) is usually in the form of isotherms [n = /i,(cd or at constant T] or isosteres = pi(T) at constant /ij. Representative forms are shown in Fig. I6-I. An important dimensionless group dependent on adsorption equihbrium is the partition ratio (see Eq. 16-125), which is a measure of the relative affinities of the sorbea and fluid phases for solute. 

As already discussed in Chapter 1, the relative tendency of a surfactant component to adsorb on a given surface or to form micelles can vary greatly with surfactant structure. The adsorption of each component could be measured below the CMC at various concentrations of each surfactant in a mixture. A matrix could be constructed to tabulate the (hopefully unique) monomer concentration of each component in the mixture corresponding to any combination of adsorption levels for the various components present. For example, for a binary system of surfactants A and B, when adsorption of A is 0.5 mmole/g and that of B is 0.3 mmole/g, there should be only one unique combination of monomer concentrations of surfactant A and of surfactant B which would result in this adsorption (e.g., 1 mM of A and 1.5 mM of B). Uell above the CMC, where most of the surfactant in solution is present as micelles, micellar composition is approximately equal to solution composition and is, therefore, known. If individual surfactant component adsorption is also measured here, it would allow computation of each surfactant monomer concentration (from the aforementioned matrix) in equilibrium with the mixed micelles. Other processes dependent on monomer concentration or surfactant component activities only could also be used in a similar fashion to determine monomer—micelle equilibrium. 

Since the rate of hydrogenation is sensitive to operating conditions (temperature, pressure, catalyst quantity, solvent and agitation), relative rates determined in competitive hydrogenation of binary mixtures are considered to be more reliable than measuring individual rates50. Relative reactivities thus measured are determined by the ratio of rate and adsorption constants. 

There are two properties of the metal crystals in binary systems that seem worthy of special consideration. First, since the crystals are small, they have a relatively high ratio of surface to bulk atoms hence, if bond formation during adsorption is related to a change in physical properties, as, for instance, for the case of ferromagnetism, relatively strong effects can be expected. For this reason the study of the change in ferromagnetism consequent upon adsorption was started. It was later completed by photoelectric emission and conductivity work on films, since for these studies binary catalysts are unsuitable for obvious reasons. 

Secondly, since the metal surface is large and relatively stable to a prolonged sojourn at higher temperatures, the binary systems appear interesting objects from the point of view of the study of adsorption equilibria. Contrary to films, they permit a study of equilibrium situations in which only a small fraction of the surface is covered, and therefore they serve to open a quite extensive field of investigations. 

According to Grumberg [116], it appears likely that Wvjsc may be a close approximation to the heat of mixing. Table 1.7 shows that the Wvisc values are proportional to the X values. The large negative values of WviSc for p - xylene and mesitylene in a polar solvent can be taken as experimental evidence of an effective enthalpic effect in these binary systems relative to toluene - 2 - propanol system, which influence the value of the preferential adsorption coefficient X. 

Until relatively recently, the fact that an experimental isotherm necessarily contained composite information concerning the adsorption of the two components of a binary solution was considered to be a major problem. For a rigorous interpretation it was felt necessary to process the data to obtain the so-called individual adsorption isotherm or separate adsorption isotherm of each component. However, this is not at all straightforward and requires the introduction of a number of assumptions relating to the structure of the adsorbed layer. The main problem is of course to know the composition of the adsorbed layer. One assumption often used in the case of volatile components is that introduced by Williams (1913) the solid will adsorb the same amount of each component from the vapour in equilibrium with the solution as from the solution itself. This of course implies that the adsorbed layer has the same composition at the liquid-solid and gas-solid interfaces and it requires numerous gravimetric measurements from the vapour... 

In the case of adsorption of a vapor by a porous material, a three phase system in terms of SAS is produced pore/adsorbed film or capillary condensed vapor/solid. Since the s.l.d. of H2O and D2O are known while the pore space s.l.d. equals to zero, contrast matching conditions are achieved if an appropriate mixture of H2O/D2O that has the same s.l.d. as the solid is used as the adsorbate. In this case the adsorbed film as well as the condensed cluster of pores will cease to act as scatterers, and only the remaining empty pores will produce measurable scattering. In terms of SANS, contrast matching reduces the solid/film/pore system to a binary one [1]. By determining a number of scattering curves corresponding to the same sample equilibrated at various relative pressures, for both the adsorption and desorption branches of the adsorption isotherm, a correlation of the two methods could be possible. If the predictions of the Kelvin equation are in accordance with the SAS analysis, a reconstruction of the adsorption isotherm can be obtained from the SAS data [2]. 

The application of Equations (13)-(20) is illustrated for binary mixtures of ethylene (1) and ethane (2) adsorbed on NaX zeolite (faujasite). The constants for the singlegas adsorption equations of state are given in Tables 1 and 2. The selectivity of NaX for ethylene relative to ethane is a function of temperature, pressure, and the composition of the gas. The selectivity at constant temperature (20 °C) is shown in Figure 3. The selectivity at the limit of zero pressure is the ratio of Henry s constants (Xi/X2=33.7). At constant mole fraction of ethylene in the gas, the selectivity decreases rapidly with increasing pressure. At constant pressure, the selectivity decreases with increasing mole fraction of ethylene in the gas. The selectivity at constant pressure and gas composition decreases with temperature, as shown in Figure 4. Decrease of the selectivity with temperature, pressure, and the mole fraction of the preferentially adsorbed species is typical behavior for binary adsorption. 

---