Total mass adsorbed

Gravimetry can also be associated with adsorption manometry, which is a simple and safe way to study co-adsorption of two gases, provided their molar masses are sufficiently different (Keller et al, 1992). The manometric experiment provides a total amount adsorbed n°a = n° + n%, whereas the gravimetric experiment provides the total mass adsorbed m t=m° + m. Since n°Mx = m and n M1 = m" we have two unknowns, n° and n, and two equations. From these we can obtain, for instance ... 

As the thickness (d) of the adsorbed layer is ill-defined we again have to use an approximation for (V ) which may be related to the total mass adsorbed by... 

From equations (1.34), (1.35) the total mass adsorbed (m ) can be calculated from density measurements and calculations of the sorptive gas (p, p ) and given data of the corresponding helium experiments (mHj,p[,J and after choosing or calculating the reference density (pj ) of the sorbate phase. 

In physical terms fi gives the total mass adsorbed, i. e. the sum of the masses of both components (m + mj) minus the buoyancy correction term caused by the volume (V ) of both the sorbent (s) and the adsorbate phase (a), cp. Eq. (44). 

In Fig. 6.22 the spectrum of the initial state is indicated by Vac. . It can be seen that within the first hour of the adsorption process the capacitance of the system increases with a shift of its maximum value to somewhat higher frequencies. This effect is possibly due to a primary adsorption process of the CO-molecules at locations in macro- and mesopores of the AC where, due to their permanent dipole moment (pco = 0.1 D), they add to both the capacitance and the resonance frequency of the loaded AC. Now microbalance measurements have shown that approximately 80 % of the total mass adsorbed during the whole process is adsorbed within the first hour. In view of this, the changes of the capacitance spectrum which were observed afterwards for nearly 40 h are doubtless due to an internal diffusion or dissoziation process of the CO molecules taking place without uptake of more molecules from the gas phase. 

Schneider et al. [67] studied flie kinetics of adsorption of atactic PMMA polymers of different molar mass from dilute CCI4 solution on to oxidized silicon. They measiued the number of hydrogen bonds to the surface (as calculated from the intensity of the infrared carbonyl peak) as a function of the total mass adsorbed (Fig. 25). A unique relation was obtained, independent of molar mass, solution concentration, solvent, and temperature. It was concluded fliat die first chains could spread... 

FIG. 25 Bound mass of atactic PMMA polymers of molar masses ranging from 7700 to 130,000 plotted against total mass adsorbed. (From Ref. 67.)... 

From the concentration of the solute in the solvent, and the total amount added the quantity of solute adsorbed on the stationary phase was also calculated. The results obtained for the solutes anisole and nitrobenzene are shown as graphs in Figure 12. One pair of curves refers to the polar solvent and relates the concentration of ethyl acetate in the solvent (Em) and the concentration of ethyl acetate in the stationary phase (Es) to the total mass of solute added. The other pair of curves refers to the... 

We express the altered concentration in terms of the adsorption excess. If all the adsorbed substance were contained to the extent of k gr. per cm.2 on a superficial layer of zero thickness and surface total mass present in the volume Y would be m = V + kto. The layer of altered concentration must, however, have a certain thickness. We will therefore imagine a plate 2 placed in front of the surface and parallel to it, and define the adsorption excess as the concentration in the included layer minus the concentration in the free liquid. That this result is independent of the arbitrarily chosen thickness is easily proved when we remember that the problem is exactly the same as that of finding the change of concentration around an electrode in the determination of the transport number of an ion by Hittorf s method. 

Most primary and secondary minerals found in soil systems are barely soluble in the soil solution. The amount of mass from the bulk phase to hydrated ions in soil solution is negligible compared to the total mass of the solid phase. In arid and semi-arid soils, concentrations of most trace metals in soil solution may be controlled by their carbonates and to some extent by their hydroxides. Other than carbonates, trace elements in arid and semi-arid soils may also occur as sulfate, phosphate or siliceous compounds, or as a minor component adsorbed on the surface of various solid phase components. The solubility of carbonates, sulfates and other common minerals of trace elements in arid and semi-arid soils will be discussed in Chapter 5. Badawy et al. (2002) reported that in near neutral and alkaline soils representative of alluvial, desertic and calcareous soils of Egypt, the measured Pb2+ activities were undersaturated with regard to the solubility of... 

F = flow rate through the charcoal bed in cnr/min Y = volume fraction of adsorbate in the gas phase leaving the ith stage at time t M = total mass of the adsorber in grams t = time in minutes. 

Figure 5.15. A simplified one-dimensional adsorbent molecule having three binding sites. The total mass of the molecule ihq is distributed equally at three points a, b, and c. The mass at any site is when it is unoccupied, and + rtti when occupied by a ligand of mass m. ...

Mo Total mass of particles in a sample pressure p/po of adsorbate... 

Note that the gravimetric procedure involves an integral measurement at any time, the total amount adsorbed is known from the total mass uptake, with an accuracy which does not depend on the number of previous equilibrium points. Another interesting feature stems from the relatively large volume of adsorption balances... 

A pertinent question is as the volume of the adsorbed phase increases, do we have to take into account the corresponding increase of buoyancy (e.g. the buoyancy doubles after saturation of an adsorbent with 50% porosity). The answer is no, provided we want to assess the surface excess mass m°. As illustrated in Figure 3.22, because of the buoyancy effect, we do not measure the total mass of the adsorbed layer (shaded+hatched areas) but simply a surface excess mass (hatched area only). Thus, adsorption gravimetry and the Gibbs representation are highly compatible (Findenegg, 1997). 

Here mp is the total mass of the particles ivith radius R placed in the contactor ivith a useful volume V. In some cases, the surface diffusion is considered the sloivest process because organic components such as hydrocarbons are generally strongly adsorbed on activated carbon [3.65, 3.66]. Indeed, we can consider here that, at the surface of the particle, the adsorption equilibrium is achieved faster than the surface diffusion process. In these conditions the batch model equations are ... 

Because n, is the total mass confmed in the adsorbed phase, it must vary with the experimental condition, therefore, should be determined as a function of temperature and pressure. A straightforward method was proposed by the author [18-19]. It is known from Eq.l that /i = /i, if Fg/Og can be neglected comparing to n. Therefore, we can use the experimental values of n that comply with the constraint to formulate the model of absolute adsorption. The experimental data experienced twice transformations to reach a linear plot as was usually done for the establishment of a model for a set of data. The experimental data were utilized to the utmost in the transformation processes, and the data that do not comply with the constraint were sifted out. A plot of ln[ln(<9n)] versus np (p in kPa) was thus constructed. Parameter S was used to adjust the magnitude of n in order to avoid evaluating the logarithm of negative numbers. Its value could be set at 1, 10 or 100. A model with two parameters were obtained from the linear plots for the absolute adsorption isotherms ... 

A catalyst is characterized as a substance which adsorbs reactant. When it is adsorbed it may be transported either by desorption into the pore space or by migration to an adjacent site on the surface. The contribution of surface diffusion must be added to the diffusion in the pore volume to obtain the total mass transport. 

---