Adsorption heat of

Adsorption is accompanied by evolution of heat since adsorbate molecules are more stabilized on the adsorbent surface than in the bulk phase Adsorption is accompanied by phase change and thus depending on the occasion it may involve mechanical work For this reason, the amount of heat evolution by unit adsorption depends on the system adopted 

Differential heat of adsorption, Qm, is defined as heat evolution when unit adsorption takes place in an isolated system. This heat is directly measurable by calorimeter. 

Isosteric heat of adsorption, Qu, is defined from isotherms at different temperatures by Eq. (3-29). Qa is bigger than Qmi since it requires work equivalent to pV(=RT). 

Qn is related to adsorption isotherms at different temperatures by the van t Hoff equation 

For the Henry equation and the Langmuir equation, g., is related to the equilibrium constant, K, as 

the heat of adsorption is dependent on the fractional coverage, its calculation from thermodynamics is a complex matter. In this section, we will only derive some basic parameters. When equilibrium is reached between the adsorbate and adsorptive gas molecules, the reversible free energy change of adsorbed gas molecules on the solid (adsorbate), dGads, is equal to the non-adsorbed gas molecules (adsorptive), dGg in the medium. Then, we may write from Equation (126), given in Section 3.1.1, for a total number of moles of gas and unit area of adsorbent 

Vg yads, and if we assume ideal gas conditions, that is [Vg = RT/P2, then Equation (633) becomes 

When we write n is a constant in Equation (634), we mean a constant fractional coverage, Of, because the number of moles of adsorbed gas is constant. This is called isosteric, which means the same coverage. If the process is reversible, we may write the entropy difference from thermodynamics as 

On the other hand, two more heats of adsorption are also in use in adsorption science the integral heat of adsorption, Q is an experimentally found quantity from constant volume calorimeter measurements, using the simple expression 

The second type of heat of adsorption is differential heat of adsorption (-AH), which can be expressed as Joules per g mole of the adsorbate. Let us suppose we have a solid that has already adsorbed x grams of a gas or vapor. The solid is allowed to adsorb additional Ax grams of the adsorbate and, in so doing, the solid evolves AQ Joules. The differential heat of adsorption (-AH) is then equal to 

The Clapeyron equation (Eq. 5.5) applies to equilibrium between any two phases of a pure substance. If we wish to apply it to the adsorbed phase and the gas or vapor in equilibrium with it, we see that because the vapor pressure of the adsorbed phase depends not only on the temperature but also on the amount adsorbed per mass of adsorbent, we must specify the amount adsorbed as well. Thus, for equilibrium between the adsorbed phase and gas or vapor, Eq. 5.5 becomes 

For the low pressures normally involved in adsorption, the Clausius-Clapeyron simplifications (Eqs. 5.8, 5.9, and 5.10) 

Where 4//average is the average heat of adsorption over the temperature range (assumed to be a constant in the integration leading to Eq. 5.10.) 

As previously mentioned, the phenomena of adsorption embody energy. Heat is released when a vapor is adsorbed, and conversely, heat is required to evaporate (desorb) an adsorbed vapor. The heat 

Heat of adsorption is further discussed in Chapter 9, Section 17. 

Physics and Chemistry of Surfaces, Oxford University Press, London, 1941. 

Adamson, A. W Physical Chemistry of Surfaces, Interscience Publishers, Inc., New York, I960. 

Alexander, J., Colloid Chemistry, 6 volumes Chemical Catalog Co. and Reinhold Publishing Corporation, New York, 1926— 1946. 

In the last section, we summarized the different contributions to the potential energy for the interactions between an adsorbate molecule (or atom) and an atom on the solid surface. To calculate the interaction energy between the adsorbate molecule and all atoms on the surface, pairwise additivity is generally assumed. The task is then to sum the interactions, pairwise, with all atoms on the surface, by integration. 

It can be shown (Barrer, 1978 Ross and Olivier, 1964) that the isosteric heat of adsorption (AH) at low coverage is related to the sorbate-sorbent interaction potential ( / ) by 

The nonelectrostatic energies depend directly on the polarizability of the sorbate molecule, x makes a contribution to the dispersion energy, and x also increases with molecular weight. 

A comparison of N2 and 02 is of particular interest for the application of air separation. Both molecules are nonpolar and have very similar 

we summarized the different contributions to the potential energy for the interactions between an adsorbate molecule (or atom) and an atom on the soUd surface. Pairwise additivity is generally assumed when calculating the interaction 

EFFECTS OF ADSORBATE PROPERTIES ON ADSORPTION POLARIZABILITY (a), DIPOLE MOMENT (/it), AND QUADRUPOLE MOMENT (Q) 

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The adsorption of nonelectrolytes at the solid-solution interface may be viewed in terms of two somewhat different physical pictures. In the first, the adsorption is confined to a monolayer next to the surface, with the implication that succeeding layers are virtually normal bulk solution. The picture is similar to that for the chemisorption of gases (see Chapter XVIII) and arises under the assumption that solute-solid interactions decay very rapidly with distance. Unlike the chemisorption of gases, however, the heat of adsorption from solution is usually small it is more comparable with heats of solution than with chemical bond energies. 

There are numerous references in the literature to irreversible adsorption from solution. Irreversible adsorption is defined as the lack of desotption from an adsoibed layer equilibrated with pure solvent. Often there is no evidence of strong surface-adsorbate bond formation, either in terms of the chemistry of the system or from direct calorimetric measurements of the heat of adsorption. It is also typical that if a better solvent is used, or a strongly competitive adsorbate, then desorption is rapid and complete. Adsorption irreversibility occurs quite frequently in polymers [4] and proteins [121-123] but has also been observed in small molecules and surfactants [124-128]. Each of these cases has a different explanation and discussion. 

The example of Section XI-5B may be completed as follows. It is found that 0 = 0.5 at a butanol concentration of 0.3 g/100 cm. The heat of solution of butanol is 25 cal/g. The molecular area of adsorbed butanol is 40 A. Show that the heat of adsorption of butanol at this concentration is about 50 ergs/cm. ... 

The general type of approach, that is, the comparison of an experimental heat of immersion with the expected value per square centimeter, has been discussed and implemented by numerous authors [21,22]. It is possible, for example, to estimate sv - sl from adsorption data or from the so-called isosteric heat of adsorption (see Section XVII-12B). In many cases where approximate relative areas only are desired, as with coals or other natural products, the heat of immersion method has much to recommend it. In the case of microporous adsorbents surface areas from heats of immersion can be larger than those from adsorption studies [23], but the former are the more correct [24]. 

As also noted in the preceding chapter, it is customary to divide adsorption into two broad classes, namely, physical adsorption and chemisorption. Physical adsorption equilibrium is very rapid in attainment (except when limited by mass transport rates in the gas phase or within a porous adsorbent) and is reversible, the adsorbate being removable without change by lowering the pressure (there may be hysteresis in the case of a porous solid). It is supposed that this type of adsorption occurs as a result of the same type of relatively nonspecific intermolecular forces that are responsible for the condensation of a vapor to a liquid, and in physical adsorption the heat of adsorption should be in the range of heats of condensation. Physical adsorption is usually important only for gases below their critical temperature, that is, for vapors. 

The heat of adsorption is an important experimental quantity. The heat evolution with each of successive admissions of adsorbate vapor may be measured directly by means of a calorimeter described by Beebe and co-workers [31]. Alternatively, the heat of immersion in liquid adsorbate of adsorbent having various amounts preadsorbed on it may be determined. The difference between any two values is related to the integral heat of adsorption (see Section X-3A) between the two degrees of coverage. See Refs. 32 and 33 for experimental papers in this area. 

The basic assumption is that the Langmuir equation applies to each layer, with the added postulate that for the first layer the heat of adsorption Q may have some special value, whereas for all succeeding layers, it is equal to Qu, the heat of condensation of the liquid adsorbate. A furfter assumption is that evaporation and condensation can occur only from or on exposed surfaces. As illustrated in Fig. XVII-9, the picture is one of portions of uncovered surface 5o, of surface covered by a single layer 5, by a double-layer 52. and so on.f The condition for equilibrium is taken to be that the amount of each type of surface reaches a steady-state value with respect to the next-deeper one. Thus for 5o... 

The constants in Eqs. XVII-88-XVI1-90 may be calculated fiom theory to give the Henry s law constant K from Eq. XVII-87, the experimental n /P dien gives the surface area. Alternatively, the constants may be arrived at from an experimental K (assuming that A is known) and either the isosteric heat of adsorption... 

Fig. XVII-20. Isosteric heat of adsorption of Xe on a stepped Pd surface [8(100) x (110)]. (From Ref. 111.)...

The heat evolved will now be a differential heat of adsorption, equal at constant volume to Qd or per mole, to qd - AI2, where Ae2 is the change in partial molar energy. It follows that... 

The quantity 2 has been called (by Hill) the equilibrium heat of adsorption. It follows from the foregoing definitions that... 

The adsorbed state often seems to resemble liquid adsorbate, as in the approach of the heat of adsorption to the heat of condensation in the multilayer region. For this reason, a common choice for the standard state of free adsorbate is the pure liquid. We now have... 

There are alternative ways of defining the various thermodynamic quantities. One may, for example, treat the adsorbed film as a phase having volume, so that P, V terms enter into the definitions. A systematic treatment of this type has been given by Honig [116], who also points out some additional types of heat of adsorption. 

The integral heat of adsorption Qi may be measured calorimetrically by determining directly the heat evolution when the desired amount of adsorbate is admitted to the clean solid surface. Alternatively, it may be more convenient to measure the heat of immersion of the solid in pure liquid adsorbate. Immersion of clean solid gives the integral heat of adsorption at P = Pq, that is, Qi(Po) or qi(Po), whereas immersion of solid previously equilibrated with adsorbate at pressure P gives the difference [qi(Po) differential heat of adsorption q may be obtained from the slope of the Qi-n plot, or by measuring the heat evolved as small increments of adsorbate are added [123]. 

Fig. XVn-21. (a) Differential heat of adsorption of N2 on Graphon, except for Oand , which were determined calorimetrically. (From Ref. 89.) (b) Differential heat of adsorption of N2 on carbon black (Spheron 6) at 78.5 K (From Ref. 124).

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. XVII-21. Continued) (c) Isosteric heats of adsorption of n-hexane on ice powder Vm = 0.073 cm STP. (From Ref. 125). (d) Isosteric heats of adsorption of Ar on graphitized carbon black having the indicated number of preadsorbed layers of ethylene. (From Ref. 126.)...

Fig. XVII-22. Isosteric heats of adsorption for Kr on graphitized carbon black. Solid line calculated from isotherms at 110.14, 114.14, and 117.14 K dashed line calculated from isotherms at 122.02, 125.05, and 129.00 K. Point A reflects the transition from a fluid to an in-registry solid phase points B and C relate to the transition from the in-registry to and out-of-registry solid phase. The normal monolayer point is about 124 mol/g. [Reprinted with permission from T. P. Vo and T. Fort, Jr., J. Phys. Chem., 91, 6638 (1987) (Ref. 131). Copyright 1987, American Chemical Society.]...

Brunauer (see Refs. 136-138) defended these defects as deliberate approximations needed to obtain a practical two-constant equation. The assumption of a constant heat of adsorption in the first layer represents a balance between the effects of surface heterogeneity and of lateral interaction, and the assumption of a constant instead of a decreasing heat of adsorption for the succeeding layers balances the overestimate of the entropy of adsorption. These comments do help to explain why the model works as well as it does. However, since these approximations are inherent in the treatment, one can see why the BET model does not lend itself readily to any detailed insight into the real physical nature of multilayers. In summary, the BET equation will undoubtedly maintain its usefulness in surface area determinations, and it does provide some physical information about the nature of the adsorbed film, but only at the level of approximation inherent in the model. Mainly, the c value provides an estimate of the first layer heat of adsorption, averaged over the region of fit. 

Most microporous adsorbents have a range of micropore size, as evidenced, for example, by a variation in or in calorimetric heats of adsorption with amount adsorbed [227]. As may be expected, a considerable amount of effort has been spent in seeing how to extract a size distribution from adsorption data. 

Gas A, by itself, adsorbs to a of 0.02 at P = 200 mm Hg, and gas B, by itself, adsorbs tod = 0.02 at P = 20 mm Hg Tisll K in both cases, (a) Calculate the difference between (2a and (2b> the two heats of adsorption. Explain briefly any assumptions or approximations made, ib) Calculate the value for 6 when the solid, at 77 K, is equilibrated with a mixture of A and B such that the final pressures are 200 mm Hg each, (c) Explain whether the answer in b would be raised, lowered, or affected in an unpredictable way if all of the preceding data were the same but the surface was known to be heterogeneous. The local isotherm function can still be assumed to be the Langmuir equation. 

When plotted according to the linear form of the BET equation, data for the adsorption of N2 on Graphon at 77 K give an intercept of 0.004 and a slope of 1.7 (both in cubic centimeters STP per gram). Calculate E assuming a molecular area of 16 for N2. Calculate also the heat of adsorption for the first layer (the heat of condensation of N2 is 1.3 kcal/mol). Would your answer for Vm be much different if the intercept were taken to be zero (and the slope the same) Comment briefly on the practical significance of your conclusion. 

Consider the case of the BET equation with c = 1. Calculate for this case the heat of adsorption for the process ... 

The nitrogen adsorption isotherm is determined for a finely divided, nonporous solid. It is found that at = 0.5, P/P is 0.05 at 77 K, gnd P/F is 0.2 at 90 K. Calculate the isosteric heat of adsorption, and AS and AC for adsorption at 77 K. Write the statement of the process to which your calculated quantities correspond. Explain whether the state of the adsorbed N2 appears to be more nearly gaslike or liquidlike. The normal boiling point of N2 is 77 K, and its heat of vaporization is 1.35 kcal/mol. 

It is not surprising, in view of the material of the preceding section, that the heat of chemisorption often varies from the degree of surface coverage. It is convenient to consider two types of explanation (actual systems involving some combination of the two). First, the surface may be heterogeneous, so that a site energy distribution is involved (Section XVII-14). As an example, the variation of the calorimetric differential heat of adsorption of H2 on ZnO is shown in Fig. 

Fig. XVIII-11. Calorimetric differential heat of adsorption of H2 on ZnO. Dashed line differential heat of desorption. (From Ref. 104.)...

The second general cause of a variable heat of adsorption is that of adsorbate-adsorbate interaction. In physical adsorption, the effect usually appears as a lateral attraction, ascribable to van der Waals forces acting between adsorbate molecules. A simple treatment led to Eq. XVII-53. 

We consider first some experimental observations. In general, the initial heats of adsorption on metals tend to follow a common pattern, similar for such common adsorbates as hydrogen, nitrogen, ammonia, carbon monoxide, and ethylene. The usual order of decreasing Q values is Ta > W > Cr > Fe > Ni > Rh > Cu > Au a traditional illustration may be found in Refs. 81, 84, and 165. It appears, first, that transition metals are the most active ones in chemisorption and, second, that the activity correlates with the percent of d character in the metallic bond. What appears to be involved is the ability of a metal to use d orbitals in forming an adsorption bond. An old but still illustrative example is shown in Fig. XVIII-17, for the case of ethylene hydrogenation. 

Process 2, the adsorption of the reactant(s), is often quite rapid for nonporous adsorbents, but not necessarily so it appears to be the rate-limiting step for the water-gas reaction, CO + HjO = CO2 + H2, on Cu(lll) [200]. On the other hand, process 4, the desorption of products, must always be activated at least by Q, the heat of adsorption, and is much more apt to be slow. In fact, because of this expectation, certain seemingly paradoxical situations have arisen. For example, the catalyzed exchange between hydrogen and deuterium on metal surfaces may be quite rapid at temperatures well below room temperature and under circumstances such that the rate of desorption of the product HD appeared to be so slow that the observed reaction should not have been able to occur To be more specific, the originally proposed mechanism, due to Bonhoeffer and Farkas [201], was that of Eq. XVIII-32. That is. 

Just as the surface and apparent kinetics are related through the adsorption isotherm, the surface or true activation energy and the apparent activation energy are related through the heat of adsorption. The apparent rate constant k in these equations contains two temperature-dependent quantities, the true rate constant k and the parameter b. Thus... 

The apparent activation energy is then less than the actual one for the surface reaction per se by the heat of adsorption. Most of the algebraic forms cited are complicated by having a composite denominator, itself temperature dependent, which must be allowed for in obtaining k from the experimental data. However, Eq. XVIII-47 would apply directly to the low-pressure limiting form of Eq. XVIII-38. Another limiting form of interest results if one product dominates the adsorption so that the rate law becomes... 

Some early observations on the catalytic oxidation of SO2 to SO3 on platinized asbestos catalysts led to the following observations (1) the rate was proportional to the SO2 pressure and was inversely proportional to the SO3 pressure (2) the apparent activation energy was 30 kcal/mol (3) the heats of adsorption for SO2, SO3, and O2 were 20, 25, and 30 kcal/mol, respectively. By using appropriate Langmuir equations, show that a possible explanation of the rate data is that there are two kinds of surfaces present, 5 and S2, and that the rate-determining step is... 

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