Adsorption at equilibrium

The variation of activation energy as a function of alloy composition is shown in Fig. 23. There is a fairly sharp rise in activation energy from about 0.4 kcal/mole at 50% Ag to 5.9 kcal/mole on pure Ag, but the increase observed with Pd-Au wires 127) was more abrupt. Pd-Ag alloy wires 148) showed a gradual increase from about 2 kcal/mole for pure Pd to 4 kcal/mole at 60% Ag, followed by a more rapid, smooth increase from 4.9 kcal/mole at 80% Ag to 11.5 kcal/mole on pure Ag. The results on films were also used to derive heats of adsorption at equilibrium coverage. Values increased from 1.29 kcal/mole on the 68% Ag alloy to 2.89 kcal/mole on pure Ag. 

Cu(NH3)2BTC2/3 and finally copper hydroxide in the presence of water. The formation of the BTC salts was supported by the collapse of the structure after interaction of ammonia with unsaturated copper centers. The release of BTC and copper oxide centers provides sites for reactive adsorption of ammonia during the course of the breakthrough experiments. Interestingly, even though the structure collapses, some evidence of the structural breathing of the resulting materials caused by reactions with ammonia was found, based on the ammonia adsorption at equilibrium and the analysis of the heat of interactions [51]. 

Any solid is capable of adsorbing a certain amount of gas, the extent of adsorption at equilibrium depending on temperature, the pressure of the gas and the effective surface area of the solid. The most notable adsorbents are, therefore, highly porous solids, such as charcoal and silica gel (which have large internal surface areas - up to c. 1000 m2 g-1) and finely divided powders. The relationship at a given temperature between the equilibrium amount of gas adsorbed and the pressure of the gas is known as the adsorption isotherm (Figures 5.1, 5.5-5.6, 5.8, 5.11, 5.13). 

There is also no lack of evidence that, in many cases, increasing molecular weight, without increase in groups capable of bonding, brings about greater adsorption at equilibrium and decreased rate of desorption. 

Balmforth et al. (jf.S.D.C., 1966, 82, 408) showed that there is a ma.xi-mum concentration of the carrier above which the take-up of the dye by the fibre decreases. This optimum carrier concentration corresponds approximately with the amount necessary to saturate both fibre and dyebath phases of the system. Excess will introduce a third phase, namely undissolved carrier, which will compete with the fibre for the dye. Increase in adsorption at equilibrium is brought about by bisphenyl, orthophcnyl-phenol and phenyl salicylate in the order in which they are set out. Benzoic acid, on the other hand, decreases the adsorption by the fibre at equilibrium and only increases the dyeing rate, probably by promoting the solubility of the dye. It is suggested, in fact, that water soluble carriers such as benzoic acid really act as extremely efficient dispersing agents. 

These equations are statements of the essentially equilibrium nature of the adsorption. At equilibrium the concentration of the adsorbed monoalkyl is [S]0a with an analogous expression for M. 

The rate of desorption equals to the rate of adsorption at equilibrium ... 

In this expression, the term between braces, which represents the change of the Gibbs energy of adsorption at equilibrium, is null and thus... 

The adsorption at equilibrium is defined on the basis of the equilibrium monomer density p(x) profile along the normal direction x, with wall geometrical position defining x = 0. At p = 0, kT/s = 1 and for a particular value of the wall attraction intensity e described above, we define the equilibrium adsorption (keeping the thermodynamic state (p, T, M) implicit) as... 

Smith [113] studied the adsorption of n-pentane on mercury, determining both the surface tension change and the ellipsometric film thickness as a function of the equilibrium pentane pressure. F could then be calculated from the Gibbs equation in the form of Eq. ni-106, and from t. The agreement was excellent. Ellipsometry has also been used to determine the surface compositions of solutions [114,115], as well polymer adsorption at the solution-air interface [116]. 

H2O/100 kg of adsorbent. At equilibrium and at a given adsorbed water content, the dew point that can be obtained in the treated fluid is a function only of the adsorbent temperature. The slopes of the isosteres indicate that the capacity of molecular sieves is less temperature sensitive than that of siUca gel or activated alumina. In another type of isostere plot, the natural logarithm of the vapor pressure of water in equiUbrium with the desiccant is plotted against the reciprocal of absolute temperature. The slopes of these isosteres are proportional to the isosteric heats of adsorption of water on the desiccant (see... 

Adsorptive Equilibrium The fraction of the surface covered by A at equilibrium is... 

Adsorption — An important physico-chemical phenomenon used in treatment of hazardous wastes or in predicting the behavior of hazardous materials in natural systems is adsorption. Adsorption is the concentration or accumulation of substances at a surface or interface between media. Hazardous materials are often removed from water or air by adsorption onto activated carbon. Adsorption of organic hazardous materials onto soils or sediments is an important factor affecting their mobility in the environment. Adsorption may be predicted by use of a number of equations most commonly relating the concentration of a chemical at the surface or interface to the concentration in air or in solution, at equilibrium. These equations may be solved graphically using laboratory data to plot "isotherms." The most common application of adsorption is for the removal of organic compounds from water by activated carbon. 

Now, we would like to investigate adsorption of another fluid of species / in the pore filled by the matrix. The fluid/ outside the pore has the chemical potential at equilibrium the adsorbed fluid / reaches the density distribution pf z). The pair distribution of / particles is characterized by the inhomogeneous correlation function /z (l,2). The matrix and fluid species are denoted by 0 and 1. We assume the simplest form of the interactions between particles and between particles and pore walls, choosing both species as hard spheres of unit diameter... 

Langmuir (1916), whp put forward the fir quantitative theory of the adsorption of a gaS, assumed that a gas molecule condensing from the gas phase-would adhere to the surface fora short time before evaporating and that the condensed layer was only one atom or molecule thick. If 0 is the fraction of the surface area covered by adsorbed molecules at any time, the rate of desorption is proportional to 0 and equal to k 0 where is a constant at constant temperature. Similarly the rate of adsorption will be proportional to the area of bare surface and to the rate at which the molecules strike the surface (proportional to the gas pressurep). At equilibrium the rate of desorption equals the rate of adsorption... 

In highly diluted solutions the surfactants are monodispersed and are enriched by hydrophil-hydrophobe-oriented adsorption at the surface. If a certain concentration which is characteristic for each surfactant is exceeded, the surfactant molecules congregate to micelles. The inside of a micelle consists of hydrophobic groups whereas its surface consists of hydrophilic groups. Micelles are dynamic entities that are in equilibrium with their surrounded concentration. If the solution is diluted and remains under the characteristic concentration, micelles dissociate to single molecules. The concentration at which micelle formation starts is called critical micelle concentration (cmc). Its value is characteristic for each surfactant and depends on several parameters [189-191] ... 

Baviere et al. [41] determined the adsorption of C18 AOS onto kaolinite by agitating tubes containing 2 g of kaolinite per 10 g of surfactant solution for 4 h in a thermostat. Solids were separated from the liquid phase by centrifugation and the supernatant liquid titrated for sulfonate. The amount of AOS adsorbed is the difference between initial solution concentration and supernatant solution concentration at equilibrium. 

Adsorption Coefficient (K c)—The ratio of the amount of a chemical adsorbed per unit weight of organic carbon in the soil or sediment to the concentration of the chemical in solution at equilibrium. 

There are, however, a number of criticisms of these theories. Beidler argued that, as Renqvist had assumed that the magnitude of response is proportional to the amount of stimulant adsorbed per unit time, it is evident that, at equilibrium, the net velocity of adsorption is zero. It would follow that taste intensity should be zero, and the receptors completely adapted. However, Beidler showed that the receptors do not adapt completely, but reach a steady level of response that is consistent for the duration of stimulation. Therefore, he concluded that human taste-adaption is dominated by events in the central nervous system, and not by the peripheral receptor. The same facts also prove Lasarefl s assumption to be incorrect, as his experimental data also depended on a change in adaption that is not seen at the receptor level. 

The adsorption isotherms for each chemical, Triton X-100 or phenanthrene, on the activated carbons were shown in Figs. 1 and 2. The adsorption isotherms are expressed as qg [g g ], the amount of compounds adsorbed per unit mass of adsorbent, as a fimction of Q [g l ], the concentration in solution at equilibrium [5, 6]. The best-fit parameters for Freimdlich isotherms (g = or linear isotherms (q - Kj C ) were summarized in Table 2. The... 

If we now assume that this surface at temperature T is in equilibrium with a gas then the adsorption rate equals the desorption rate. Since the atoms/molecules are physisorbed in a weak adsorption potential there are no barriers and the sticking coefficient (the probability that a molecule adsorbs) is unity. This is not entirely consistent since there is an entropic barrier to direct adsorption on a specific site from the gas phase. Nevertheless, a lower sticking probability does not change the overall characteristics of the model. Hence, at equilibrium we have... 

At low temperatures the reaction is negatively affected by the lack of oxygen on the surface, while at higher temperatures the adsorption/desorption equilibrium of CO shifts towards the gas phase side, resulting in low coverages of CO. As discussed in Chapter 2, this type of non-Arrhenius-like behavior with temperature is generally the case for catalytic reactions. 

CO oxidation is often quoted as a structure-insensitive reaction, implying that the turnover frequency on a certain metal is the same for every type of site, or for every crystallographic surface plane. Figure 10.7 shows that the rates on Rh(lll) and Rh(llO) are indeed similar on the low-temperature side of the maximum, but that they differ at higher temperatures. This is because on the low-temperature side the surface is mainly covered by CO. Hence the rate at which the reaction produces CO2 becomes determined by the probability that CO desorbs to release sites for the oxygen. As the heats of adsorption of CO on the two surfaces are very similar, the resulting rates for CO oxidation are very similar for the two surfaces. However, at temperatures where the CO adsorption-desorption equilibrium lies more towards the gas phase, the surface reaction between O and CO determines the rate, and here the two rhodium surfaces show a difference (Fig. 10.7). The apparent structure insensitivity of the CO oxidation appears to be a coincidence that is not necessarily caused by equality of sites or ensembles thereof on the different surfaces. 

Adsorption The separation achieved depends in part on the selectivity of adsorption at the bubble surface. At equilibrium, the adsorption of dissolved material follows the Gibbs equation (Gibbs, Collected Works, Longmans Green, New York, 1928). 

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