Net heat of adsorption

Even so, it is of interest to calculate the BET monolayer capacity from the composite isotherm of Fig. 5.12(b). Though the isotherm did not conform very closely to the BET equation, the isosteric net heat of adsorption was... 

The experimental isotherms were fitted to the BET and Langmuir isotherms, selecting the best fit. The values of the monolayer capacity, the specific surface and the net heats of adsorption were calculated. 

The hypothesis that liquids in contact with charcoal were actually compressed on the surface of the solid was originally suggested by Lagergren Bihang till k. Svenska Vet. Akad. Handl. 24, ii. 4, 1898) who assumed the existence of surface pressures of the order of 10,000 atmospheres. Lamb and Coolidge (J.A.G.S. XLII. 1146,1920) considered that the net heat of adsorption was due to compression alone and that with charcoal the compressive force was substantially the same for all liquids, viz. 37,000 atmospheres. A similar conclusion was arrived at by Harkins and Ewing. 

An estimation of the average electrostatic field of the rutile surface is possible, since the net heat of adsorption, or the heat of wetting directly... 

Another common model which also describes multilayer adsorption is the Brunauer-Emmett-Teller equation [Eqs. (4.3) and (4.4), often called the BET equation or the BETmethod], published in 1938 [82], Here Vis the amount adsorbed, Vm is the amount adsorbed in one monolayer, p is the pressure, p° is the saturation pressure, C is a constant which relates to the net heat of adsorption, and N [in the cases of Eq. (4.4)] is the maximum number of layers which can form in a pore. 

Healy et al. (134) studied experimentally the heats of adsorption of many polar and nonpolar gases on polar and nonpolar surfaces by means of their heats of immersion. It was found that the heat of immersion of rutile on a series of straight-chain compounds was a linear function of the dipole moment of the wetting liquid. In a later article (135)- this work was extended and it is shown that nearly the entire heat effect on immersion of the clean solid surface is due to adsorption of molecules in the first layer. From the slope of the line, giving the values found for the net heat of adsorption as a function of the dipole moments, the average field strength, F, of rutile can be found by means of Eq. (22). The experimental value found by these investigators is... 

Because of the importance of the surface chemistry of bone mineral in physiological systems, we have undertaken a series of gas adsorption studies on hydroxyapatite in the form of anorganic bone. In a recent publication from this laboratory (4) results of calorimetric studies of the adsorption of water and methanol vapors on bone mineral and on synthetic hydroxyapatite were reported. The adsorption potential for nitrogen on dehydrated hydroxyapatite, whether from bone or from synthetic sources, was rather profoundly altered by the addition to the surface of chemisorbed methanol or water prior to the adsorption of nitrogen at —195° C. This effect was reflected in the specific surface areas, in the BET C values, and in the resultant values of Ex — EL (net heats of adsorption) as shown in Table I of the above paper. 

The negative of the enthalpy change for this particular process corresponds to the net heat of adsorption, since the process involves the transfer of the adsorbate from its liquid state to the surface of the adsorbent. (The net heat of adsorption of liquid adsorbate is in turn the difference between the heat of adsorption of the adsorbate vapor and the heat of condensation of the vapor.)... 

As pointed out above, Affi for the process studied here is the net heat of adsorption. AH2 is then a net differential heat of adsorption. AHJ is the same as it would be for the adsorption process involving adsorption of vapor instead of liquid. 

Originally Ex - EL was known as the net heat of adsorption (Lamb and Coolidge, 1920). It is now recommended that the more general term net molar energy of adsorption should be adopted (cf. Chapter 2). 

In principle, isotherms at low partial pressures of the sorbate may be used to determine specific surface areas by the Brunauer-Emmett-Teller (BET) method (G64). In this method, it is assumed that molecules of the sorbate are adsorbed on surfaces that can include the walls of pores, provided that the distance between molecules on opposing walls is large compared with molecular dimensions. From a plot derived from the isotherm, and given the effective cross-sectional area of the sorbate molecule, the specific surface area of the sorbent and the net heat of adsorption are obtained. Using water as sorbate, specific surface areas of about 200 m per g of D-dried paste have typically been obtained for mature cement pastes of normal w/c ratios... 

With n the amoxmt adsorbed, /im the monolayer capacity, c a parameter related to the net heat of adsorption, p/po the partial pressure and x a parameter differing from one experiment to another. 

The last parameter, c, is related to the net heat of adsorption and, consequently, depends on both adsorbent and adsorptive. As Ar and N2 are quite similar adsorptives, c should only be dependent on the adsorbent. This is reflected in the results for activated carbons c varied between 25000 and 35000 (with a value of 30000 for the ACF), and for zeolites c was situated between 2500 and 3000. The limited variation of c for a given type of adsorbent shows the general applicability of the equation. 

Thickness of mass transfer film around catalyst pellet (m) Net heat of adsorption of component i (kJ/kmol)... 

Phenomena related to heat of adsorption have engaged the interest of a number of investigators. Many have noted a relation between the heat of adsorption and heat of liquefaction. Lamb and Cool-idge59 suggested considering the heat of adsorption as consisting of two components the heat of liquefaction and a remainder which they termed the net heat of adsorption. They found that this net heat of adsorption—expressed as calories per milliliter of adsorbed liquid—was practically identical for all eleven vapors used in their... 

The net heat of adsorption is the isosteric heat minus the heat of vaporization, i.e. ... 

Figure 3.2-17 shows the reduced net heat of adsorption qne/RgT versus the fractional loading with E/RgT as the varying parameter. The heat of adsorption is infinite at zero loading, and the higher is the characteristic energy the higher is the isosteric heat of adsorption. 

Figure 3.2-17 Plots of the reduced net heat of adsorption versus fractional loading...

The enthalpy of immersion is the amount of heat released if adsorption is taken place in a bulk liquid adsorbate. Since adsorption is from the liquid phase there is no phase change associated with the condensation of vapors to liquid phase hence the net heat of adsorption is used in the calculation of the heat of immersion. This heat of immersion is given by ... 

Figure 4.2-7 Net heat of adsorption versus fractional loading with E = 15 kJ/mol, n = 2, T = 300K...

Integration of the net heat of adsorption versus the fractional loading from 0 to 1 would give the molar enthalpy of immersion into the corresponding liquid (Stoeckli and Krahenbuhl, 1981, 1989), that is ... 

However, (he case of locating Point B depends upon (he shape of the knee of the adsorption isotherm. If the value of c the net heat of adsorption is high, the knee is sharp and the Point B can be accurately located even when the linear branch of the isotherm is short. When c has a small value, the knee is rounded so that (he location of Point B becomes difficult, and the estimated value of Xg may differ significantly from the BET monolayer capacity X . Thus, it is the value of c that makes the two values agree with each other. Gregg and Sing has suggested that the adsorption isotherms, for which the value of c is below 20, may not be used to obtain values of X from the Point B, because in such cases it is difficult to locate Point B. 

We used the Brunauer-Emmett-Teller (BET) theory [4], as a standard procedure, to determine specific surface area of samples, asEr and net heat of adsorption, AQ. For the various adsorbates abet was calculated at relative pressure, p/p (where p and p were the equilibrium and the saturation pressure, respectively), in the range 0.01-0.35, which was the validity domain of the linear BET plot. 

BET parameters for CH4 adsoiption on samples at 77 K ubet, specific surface area AQ, net heat of adsorption, ubet/ g is calculated using the CH4 molecular area equal to 0.178 nm. ... 

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