Adsorption at constant temperature

Let us now consider the most common situation in adsorption calorimetry, a gas-solid open system in which adsorption is brought about by continous or stepwise admission of the adsorptive at constant temperature but not necessarily at the same temperature as the calorimeter. Initially the system contains... 

The efficiency of dynamic adsorption at constant temperature decreased with increasing the SO2 partial pressure, as shown in Figure 9. Within the flow rate range of 5-10 liters/min the adsorption efficiency at a given partial pressure was found first to increase with the flow rate and then to decrease. 

Starting with the equation for the molar integral change of the free energy of adsorption at constant temperature... 

The basics of adsorption phenomena require definitions. In experimental adsorption systems, the gas or vapor of a gas phase, or the solute in a solution, is called the adsorptive (when not in the adsorbed state). It is called the adsorbate when existing as an adsorbed phase within a solid, and the solid is referred to as the adsorbent. Note The terms absorb and absorption refer to such processes as the absorption of light or of X-ray radiation internally by the entire material, where internal surfaces may not exist.) The variations of extents of adsorption n in mmol g ) with relative pressure iplp ) of the adsorptive at constant temperature, when plotted, make up the adsorption isotherm (Figure 4.1(a)). The variation of extents of adsorption (n in mmol g ) with temperature of adsorption Tin K), at constant relative pressure, is the adsorption isobar (Figure 4.1(b)). The variation of the relative pressure of the adsorptive (p/p ), with adsorption temperature (T in K), to maintain a constant amount of adsorbate adsorbed on the adsorbent (n in mmolg ) is the adsorption isostere (Figure 4.1(c)). 

Hydrophilic surfactants adsorb best on aqueous phases, whereas hydrophobic surfactants adsorb best on lipophilic surfaces (oils). Data on adsorption at constant temperature are usually plotted as a function of the surfactant equilibrium concentration plots for solid substrates are termed Langmuir isotherms. From such isotherms the maximum surfactant concentration at the interface (Fmax) can be derived and the maximum area occupied by the surfactant at the interface ( max) can be calculated. In addition, the Gibbs adsorption equation can be extracted. 

Fig. 7.3 Pressure range of adsorption at constant temperature in the liquid-gas phase diagram of the adsorptive. The pressure cannot exceed the saturated vapour pressure ps of the fluid at the adsorption temperature Tads...

Figure Bl.19.13. (a) Tliree STM images of a Pt(l 11) surface covered witli hydrocarbon species generated by exposure to propene. Images taken in constant-height mode. (A) after adsorption at room temperature. The propylidyne (=C-CH2-CH2) species that fomied was too mobile on the surface to be visible. The surface looks similar to that of the clean surface. Terraces ( 10 mn wide) and monatomic steps are the only visible features. (B) After heating the adsorbed propylidyne to 550 K, clusters fonn by polymerization of the C H...

The hydration shell is formed with the increasing of the water content of the sample and the NA transforms from the unordered to A- and then to B form, in the case of DNA and DNA-like polynucleotides and salt concentrations similar to in vivo conditions. The reverse process, dehydration of NA, results in the reverse conformational transitions but they take place at the values of relative humidity (r.h.) less than the forward direction [12]. Thus, there is a conformational hysteresis over the hydration-dehydration loop. The adsorption isotherms of the NAs, i.e. the plots of the number of the adsorbed water molecules versus the r.h. of the sample at constant temperature, also demonstrate the hysteresis phenomena [13]. The hysteresis is i( producible and its value does not decrease for at least a week. 

Equations (1.2) and (1.3) are expressions of the adsorption isotherm, i.e. the relationship, at constant temperature, between the amount of gas adsorbed and the pressure, or relative pressure, respectively. 

In the simplest case, adsorption occurs at constant temperature and volume and we can then write... 

In considering the differential energy of adsorption, it is useful to picture an experimental procedure which allows the adsorption to proceed at constant temperature and in infinitely small stages. Then... 

Thus by measuring the small amount of heat 5Q which is evolved when the adsorption increases by the small amount 6n mole at constant temperature, the differential molar energy of adsorption can be evaluated calorimetri-... 

In the first step, in which the molecules of the fluid come in contact with the adsorbent, an equihbrium is established between the adsorbed fluid and the fluid remaining in the fluid phase. Figures 25-7 through 25-9 show several experimental equihbrium adsorption isotherms for a number of components adsorbed on various adsorbents. Consider Fig. 25-7, in which the concentration of adsorbed gas on the solid is plotted against the equilibrium partial pressure p of the vapor or gas at constant temperature. At 40° C, for example, pure propane vapor at a pressure of 550 mm Hg is in equilibrium with an adsorbate concentration at point P of 0.04 lb adsorbed propane per pound of silica gel. Increasing the pressure of the propane will cause... 

The basic measurement of adsorption is the amount adsorbed v, which usually is given in units of cm of gas adsorbed per gram of adsorbent. Usually this quantity is measured at constant temperature as a function of pressure p (in mm Hg), and hence is termed an isotherm. Isobars and isosteres also can be measured, but have little practical utility. It has been found that isotherms of many types exist, but the five basic isotherm shapes are shown in Figure 1, where />ois the vapor pressure. 

The adsorption process generally is of an exothermal nature. With increasing temperature and decreasing adsorbate concentration the adsorption capacity decreases. For the design of adsorption processes it is important to know the adsorption capacity at constant temperature in relation to the adsorbate concentration. Figure 11 shows the adsorption isotherms for several common solvents. 

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... 

The adsorption of a component j in a given system depends on temperature T and on the component s concentration, Cyj, in the bulk phase. The overall adsorption equation can be written as Aj =f(T, Cyj). The relation between adsorption and the adsorbate s bulk concentration (or pressure, in the case of gases) at constant temperature is called the adsorption isotherm the relation between adsorption and temperature at constant concentration is called the adsorption isobar. From the shape of the adsorption isotherms, the adsorption behavior can be interpreted. In the case of monolayer adsorption, the isotherms are usually written in the form 9 =f(Cyj). (The subscript j is dropped in what follows.)... 

Heats of Adsorption. Temperature effects were determined by measuring adsorption at three temperatures. As seen from TABLE IV, the K values vary with temperature such that for butylate, K increases with temperature, while for alachlor and metolachlor, K decreases with temperature. These results indicate that butylate becomes more adsorbed to Keeton soil as the temperature increases while alachlor and metolachlor become less adsorbed as temperature increases. In order to obtain a quantitative measure of these effects, heats of adsorption (AH) were calculated as described previously in the Materials and Methods section (equation 3). TABLE IV contains values for the average molar distribution constants (Kd) for butylate, alachlor, and metolachlor which were plotted vs the inverse temperatures (1/°K) to obtain the AH s shown in Figure 3. 

Whatever the mechanism of the adsorption process, it occurs spontaneously, at constant temperature and pressure, only if the Gibbs energy, G, of the system decreases ... 

Adsorption is often described in terms of isotherms which show the relationship between the bulk activity (concentration) of adsorbate and the amount adsorbed at constant temperature. 

This expression is analogous to Henry s Law for gas-liquid systems even to the extent that the proportionality constant obeys the van t Hoff equation and Ka = K0e AH/RT where AH is the enthalpy change per mole of adsorbate as it transfers from gaseous to adsorbed phase. At constant temperature, equation 17.1 becomes the simplest form of adsorption isotherm. Unfortunately, few systems are so simple. 

In-situ infrared spectroscopy has been used in much the same fashion at TGA, but temperature profiles have been combined with monitoring changes at constant temperature. " IR spectroscopy does not yield the same direct information about the complete removal of organic residues that TGA provides. On the other hand, CO adsorption experiments performed along with dendrimer decomposition experiments provide direct information regarding metal availability. Further, IR experiments provide... 

Fusions to thermostable enzymes will allow us to evaluate adsorption at higher temperatures. When a column containing Abg-CBDcex/ adsorbed to cellulose at pH 7.0, was eluted with an increasing or decreasing pH gradient (constant ionic strength), protein (enzymatically inactive) was eluted above pH 9, but there was no desorption evident at low pH. (Ong, E. Gilkes, N.R Miller, R.C., Jr. Warren, R.A.J. Kilbum, D.G. Enzyme Microb, TechnoL, in press). 

Lietti and co-workers studied the kinetics of ammonia adsorption-desorption over V-Ti-O and V-W-Ti-O model catalysts in powder form by transient response methods [37, 52, 53[. Perturbations both in the ammonia concentration at constant temperature in the range 220-400 °C and in the catalyst temperature were imposed. A typical result obtained at 280 °C with a rectangular step feed of ammonia in flowing He over a V2O5-WO3/TiO2 model catalyst followed by its shut off is presented in Figure 13.5. Eventually the catalyst temperature was increased according to a linear schedule in order to complete the desorption of ammonia. 

The amount of gas adsorbed at constant temperature plotted as a function of the equilibrium pressure (adsorption isotherm I). 

---