Differential quantities of adsorption

The differential quantities of adsorption , are the differences between the differential surface excess quantities and the same molar quantity, as in Equation (2.46) or... 

Differential heats of adsorption for several gases on a sample of a polar adsorbent (natural 2eohte chaba2ite) are shown as a function of the quantities adsorbed in Figure 5 (4). Consideration of the electrical properties of the adsorbates, included in Table 2, allows the correct prediction of the relative order of adsorption selectivity ... 

Microcalorimetry has gained importance as one of the most reliable method for the study of gas-solid interactions due to the development of commercial instrumentation able to measure small heat quantities and also the adsorbed amounts. There are basically three types of calorimeters sensitive enough (i.e., microcalorimeters) to measure differential heats of adsorption of simple gas molecules on powdered solids isoperibol calorimeters [131,132], constant temperature calorimeters [133], and heat-flow calorimeters [134,135]. During the early days of adsorption calorimetry, the most widely used calorimeters were of the isoperibol type [136-138] and their use in heterogeneous catalysis has been discussed in [134]. Many of these calorimeters consist of an inner vessel that is imperfectly insulated from its surroundings, the latter usually maintained at a constant temperature. These calorimeters usually do not have high resolution or accuracy. 

The ratio of the amount of heat evolved for each increment to the number of moles adsorbed (in the same period) is equal to the average value of the differential enthalpy of adsorption in the interval of the adsorbed quantity considered. The curve showing the differential heat variations in relation to the adsorbed amount is traditionally represented by histograms. However, for simplification, the histogram steps are often replaced by a continuous curve connecting the centers of the steps. 

Advantages and limitations of differential and integral molar quantities of adsorption... 

In any investigation of the energetics of adsorption, a choice has to be made of whether to determine the differential or the corresponding integral molar quantities of adsorption. The decision will affect all aspects of the work including the experimental procedure and the processing and interpretation of the data. 

One sees that the use of Equation (2.79) requires a knowledge of the following experimental quantities dQm (heat measured by the calorimeter), dna (amount adsorbed), dp (increase in equilibrium pressure) and Vc (dead volume of the part of the cell immersed in the heat-flowmeter of the microcalorimeter cf. Figure 3.15.). If the conditions of small and reversible introduction of adsorptive are not fulfilled, the quantity assessed by Equation (2.79) can be described as a pseudo-differential enthalpy of adsorption (see Figure 3.16a). 

In principle, the continuous procedure, where the adsorption takes place continuously and slowly, under quasi-equilibrium conditions, meets the above requirement of reversibility (Rouquerol et al. 1972). In this experiment, the basic experimental quantities from which one wishes to derive the differential enthalpy of adsorption are the rate of adsorption, f°, and the corresponding heat flow, [Pg.46]

Equilibrium capacity for adsorption of organic solutes on carbon can be predicted to increase with decreasing temperature since adsorption reactions are exothermic. The differential heat of adsorption, AH, is defined as the total amount of heat evolved in the adsorption of a definite quantity of solute on an adsorbent. Heats of vapor phase adsorption... 

This particular quantity is known as the differential heat of adsorption. 

Different types of heats of adsorption can be defined based on the variables which are kept constant during the experiment (F, F, p,/I, etc.). Here we shall discuss three such heats. The first heat is usually called the differential heat of adsorption although it is, in fact, defined as a change in internal energy the second is the isosteric enthalpy of adsorption formerly called isosteric heat of adsorption and the third is the isothermal heat of adsorption (ijth). We shall develop expressions that allow these heats to be determined from experimental calorimetric data and show how these quantities are interrelated. 

The above quantity is known as the differential heat of adsorption. Although the measurement is simple, since volumes and surface areas are kept fixed, the interpretation of the experimental measurements is more complicated than for several of the cases cited below. 

This quantity is known as the isosteric (differential) heat of adsorption. The experimental requirements are easily satisfied, but the interpretation of the results is now more complicated than for Eq. (5.3.4b). 

The above equations give a relation between 0, Ae, and N for a molecule which splits into n statistically independent parts in the adsorbed state, and afford a method of determining n by putting into equation (18) the observed differential heat of adsorption by a sparsely covered surface. 0 is being determined from the adsorbed quantity and the total measured surface area of the adsorbent. 

The adsorbed state of carbon monoxide on a platinum surface was determined by Kwan (52) as follows using the differential heat of adsorption, the covered surface fraction was calculated by means of equation (18) assuming n either 1 or 2. These values were compared with those derived from the adsorbed quantity and the surface area of the adsorbent assuming that 10 atoms per square centimeter of platinum surface are available... 

Nickel oxide prepared at 250° [NiO(250°)] presents a greater adsorption affinity toward carbon monoxide at 30° than NiO(200°) [at 2 torr, 4.5 cm /gm on NiO(200°), 5.5 cm /gm on NiO(250°)] and the differential heats of adsorption on NiO(250°) (Fig. 12) decrease more progressively than on NiO(200°) (Fig. 11). The initial heat of adsorption is lower on NiO(250°) (29 kcal/mole) than on NiO(200°) (42 kcal/mole). However, on the latter catalyst, surface oxygen ions react with carbon monoxide to give a small quantity (0.3 cm /gm) of adsorbed carbon dioxide, which accounts for the high initial heat of adsorption of carbon monoxide (42 kcal/mole) on NiO(200°). Because of the higher temperature of its... 

The importance of Eqn (7.4) is that it expresses the differential heat of adsorption in terms of a number of concepts that have a readily visuaHzed physical basis it reasserts and emphasizes that the differential heat of adsorption contains inter alia separate expressions for the adsorbate-adsorbent interaction and the adsorbate-adsorbate interaction and since aU the other experimentally determined heats of adsorption are related to q, the same conclusion also holds true for them. The quantity Uq, expressing as it does the adsorbate-adsorbent interaction stripped of all other incidental energy changes such as lateral (fluid-fluid) interaction, work terms, and kinetic and vibrational energy changes, is... 

It is found that the scaling exponent a presents universality properties, in the sense that its behavior is identical for any value of A , for the different topographies considered, for different thermodynamical quantities (i.e., adsorption isotherm and differential heat of adsorption) and for different reference curves, even a theoretical one expressed, for example, through a mean field approximation for the bp topography like ... 

This equation relates the vapor pressure, P, at which adsorption occurs, to the temperature of adsorption, T. AH is then the net enthalpy change (per mole) associated with the phase change from vapor to adsorbed state, and is a differential value. This enthalpy can be viewed as the sum of the enthalpies of condensation and adsorption of the vapor. If adsorption isotherms are collected at different temperatures, then a plot of In P (where P is the vapor pressure at which a particular quantity of adsorption occurs) against /T should be linear with a slope of —AH/R, Consequently, if the AH calculated in this way from equation 10.29 were just equal to the enthalpy of condensation of the vapor, then the phase change is simple condensation on surfaces or in pores, and does not involve true adsorption. 

When a molecule is adsorbed, the process is accompanied by a liberation of heat that can be measured calorimetrically. The experimentally measured heat can be related to a thermodynamic quantity, the differential heat of adsorption, by relationships that depend on the specifics of the calorimeter used [1, Ch. III]. The differential heat of adsorption, on a homotattic surface at any isotherm... 

The adsorption isotherms for both pesticides were Type I of the BET classification (Figure 7.27) and fitted very well to the Langmuir equation. The amount of the two pesticides adsorbed on different activated carbons varied between -18 and 36% for diquat, and between -6 and 14% for paraqnat, depending upon the surface area of the activated carbon (Table 7.10). These workers also carried out calculations for thermodynamic quantities, such as differential heat of adsorption AH and activation energy E, which indicated that the rate of removal of these pesticides by activated carbons is an endothermic process, which agreed with the suggested interparticle transport rate control mechanism. However, the eqnUibrium... 

Pore distribution in general is calculated according to the desorption isotherm, which is a desorption process with equilibrium steam pressure descending and adsorption volume reducing. The relationship between the total adsorption quantity and pore radius is shown in Fig. 7.8. The relationship between the differential values of adsorption quantity vs. pore radius is the so-called pore distribution curve, as shown in Fig. 7.9. 

Heat of adsorption is expressed as a differential heat of adsorption (q) or as an integral heat of adsorption (AH). Integral heat of adsorption can be determined by calorimetry, differential heat of adsorption (q) is calculated from the measured isosteres [dlnp/dT] = -q/RT. Differential heat of adsorption heat iq) is defined as heat that is released upon adsorption of 1 mole of gaseous substances in a quantity of the sorbent that the adsorbed amount (a) per unit mass of adsorbent remains constant. Integral heat of adsorption (AH) is the heat that is released upon adsorption of 1 mole of a substance in a quantity of the sorbent that the adsorption is just equal to the value of adsorbed amount (a) ... 

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