Heat of liquefaction

Differential heats of adsorption generally decrease steadily with increasing amount adsorbed and, in the case of physical adsorption tend to approach the heat of liquefaction of the adsorbate as P approaches P. Some illustrative data... 

Fig. 5.2 Type III isotherms, (a) n-hexane on PTFE at 25°C (b) n-octane on PTFE at 20 C (c) water on polymethylmethacrylate at 20°C (d) water on bis(A-polycarbonate) (Lexan) at 20°C. The insets in (c) and (d) give the curves of heat of adsorption against fractional coverage the horizontal line marks the molar heat of liquefaction. (Redrawn from diagrams in the original papers, with omission of experimental points.)...

This concept is now applied to the liquefaction of methane initially at atmospheric pressure and 105°F, 105°F being selected because it is a common industrial heat rejection temperature. The theoretical quantity of work (expressed in Btu of work equal to 778 ft-lb, of work) required to cool 1 lb of methane down to its liquefaction point and then to absorb the 219.7 Btu of latent heat of liquefaction at -258°F, is shown in Figure 3-2. It amounts to 510.8 Btu of work per pound of methane and is not to be confused with Btu of heat, although the quantities in this case are not very different. This amount of work per pound of methane is equivalent to 352 hp/MMcfd. An actual process with its expected inefficiencies would require twice this much work. 

A number of the assumptions used in the BET theory have been questioned for real samples [6]. One assumption states that all adsorption sites are energetically equivalent, which is not the case for normal samples. The BET model ignores lateral adsorbate interactions on the surface, and it also assumes that the heat of adsorption for the second layer and above is equal to the heat of liquefaction. This assumption is not valid at high pressures and is the reason for using adsorbate pressures less than 0.35. In spite of these concerns, the BET method has proven to be an accurate representation of surface area for the majority of samples [9,10]. 

Type III isotherms are characterized principally by heats of adsorption which are less than the adsorbate heat of liquefaction. Thus, as adsorption proceeds, additional adsorption is facilitated because the adsorbate interaction with an adsorbed layer is greater than the interaction with the adsorbent surface. 

A further criticism of the BET theory is the assumption that the heat of adsorption of the second and higher layers is equal to the heat of liquefaction. It seems reasonable to expect that polarization forces would induce a higher heat of adsorption in the second layer than in the third, and so forth. Only after several layers are adsorbed should the heat of adsorption equal the heat of liquefaction. It is, therefore, difficult to resolve a model of molecules adsorbed in stacks while postulating that all layers above the first are thermodynamically a true liquid structure. The apparent validity of these criticisms contributes to the failure of the BET equation at high relative pressures (P/Pq > 0.35). However, in the range of relative pressure leading to coverage near W/ = 1, the BET C values... 

The very low water adsorption by Graphon precludes reliable calculations of thermodynamic quantities from isotherms at two temperatures. By combining one adsorption isotherm with measurements of the heats of immersion, however, it is possible to calculate both the isosteric heat and entropy change on adsorption with Equations (9) and (10). If the surface is assumed to be unperturbed by the adsorption, the absolute entropy of the water in the adsorbed state can be calculated. The isosteric heat values are much less than the heat of liquefaction with a minimum of 6 kcal./mole near the B.E.T. the entropy values are much greater than for liquid water. The formation of a two-dimensional gaseous film could account for the high entropy and low heat values, but the total evidence 22) indicates that water molecules adsorb on isolated sites (1 in 1,500), so that patch-wise adsorption takes place. 

The heat curves, themselves, are informative. The kaolin-based pellet catalyst has a few more active sites then attapulgite, but its site activity decreases rapidly and to values only about 3 kcal./mole above the heat of liquefaction of the liquid at maximum coverage. Obviously, a distinction cannot be made between physical adsorption and chemisorption for some of the amine adsorbed at full coverage on the cracking catalyst. On the other hand, attapulgite has a much narrower distribution of adsorption energies, and the lowest heats are about double the heat of liquefaction of butyl amine. Therefore, it appears safe to conclude that the amount remaining after evacuation at 25° is chemisorbed. 

We see in Section 9.5b (Example 9.5) that Type III behavior occurs when the heat of liquefaction is more than the heat of adsorption. 

Vanadium tetrachloride is, in fact, stable only at high temperatures. The last figure is, however, unreliable, since it is considerably affected by (a) the experimental errors involved in the reactions (ii) and (iii) above, and (b) the heat of liquefaction of vanadium tetrachloride, which is at present unknown. 

The theory of Brunauer, Emmett and Teller167 is an extension of the Langmuir treatment to allow for multilayer adsorption on non-porous solid surfaces. The BET equation is derived by balancing the rates of evaporation and condensation for the various adsorbed molecular layers, and is based on the simplifying assumption that a characteristic heat of adsorption A Hi applies to the first monolayer, while the heat of liquefaction, AHL, of the vapour in question applies to adsorption in the second and subsequent molecular layers. The equation is usually written in the form... 

In all the layers, except the first one, the heat of adsorption is equal to the molar heat of liquefaction (q ) of the adsorptive at the adsorption temperature. 

Enthalpies of wetting are sometimes used to obtain (integral) enthalpies of adsorption by subtracting the enthalpy of condensation. This procedure is not exact because it presupposes a model in which the interaction between the first and the second surface layer is Interpreted as purely identical to that in condensation (BET theory assumes the same). However, the heat of adsorption of the second layer Is not exactly Identical to the heat of liquefaction and the configuration of the first layer is affected by the presence of a second. In other words, entropic factors also have to be considered, and. in this connection, the packing in the first layer must be known to convert A H (in J m ) into A H (in J mol 2). Notwithstanding these reservations, a certain similarity may be expected. 

The values are presented in figure 3 (left part) as a function of the amount adsorbed. The heat of adsorption at very low coverage (75 kJ/mol) is well above the heat of liquefaction of bulk water (44 kJ/mol) which means that the surface is hydrophilic, as previously deduced from the shape of adsorption isotherm at low pressure. We also report the result obtained by Markova, et. al. [27] on vycor. The agreement is quite good, taking into account the fact that our sample has pores slightly smaller than real vycor which errhances the strength of the interaction. 

Table I shows that the differential heat of adsorption of n-alkane on "as received" carbon fibers Is low and closely approximates Its heat of liquefaction. This Indicates a low concentration of high energy sites on the "as received" fibers. The differential heat of adsorption on "cleaned fibers, especially T-300, Is greater than on "as received" fibers, suggesting that some of the high energy sites on the carbon fiber surfaces were occupied by physically adsorbed species. GC analysis of desorption products, collected In a liquid nitrogen trap, showed the presence of water and carbon dioxide.

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