Isosteric adsorption enthalpies

Just as with gas adsorption, an isosteric enthalpy of adsorption can also be defined for adsorption from solution. In sec. 2.3d we have refrained from deriving from isotherms, measured at different temperatures because a... 

Table 2 Constants ofEq. (3) for differential enthalpy (isosteric heat) of adsorption of gases in NaX zeolite at 298.15 K. Virial coefficients Z),- in units ofkJ kg mol< >...

One, called isosteric (because, for gas adsorption, it requires comparing two states with same amount adsorbed, i.e., same volume adsorbed), is the calculation of the differential adsorption enthalpy by using a set of two (or, better, three) adsorption isotherms at different temperatures. In dilute solution, the calculation of the isosteric enthalpy from adsorption isotherms at different temperatures is done by applying the following equation ... 

Representative anion isosteric adsorption enthalpies at several surface coverages for goethite are compiled in Table III. 

Table III. Isosteric adsorption enthalpies for representative anions and several fractional surface coverages (0) of goethite...

Table IV. Residual solution concentrations at 5, 20, 25 and 35 C and average isosteric adsorption enthalpies calculated using equation (8) for cadmium, zinc and nickel onto hematite at pH=6 and a total metal concentration of 10/xM. Concentration data from (25)...

Furthermore, on polystyrene it was found that the adsorption of HPA in the low surface coverage region increased with increasing temperature, except at the isoelectric point (i.e.p.) of the protein where the adsorption appeared to be independent of the temperature. According to Clapeyron s law a positive value for (6r/6T) implies an endothermic adsorption process under isosteric conditions. Although with protein adsorption isosteric conditions are difficult to establish, the qualitative conclusion is that at pHf i.e.p. the adsorption enthalpy is positive. Hence, under those conditions, adsorption must be entropically driven. We will return to this subject in section 5. 

On principle calorimetric data of adsorbed phases can be calculated from adsorption equilibria data, i. e. adsorption isotherms, if these are available for different temperatures. From the Clausius-Clapeyron equation applied to the phase equilibrium in the ideal sorptive gas (f) - adsorbate (a) system, one can derive an equation for the isosteric differential adsorption enthalpy or isosteric differential heat of adsorption [2.2, p. 43], [2.26, p. 38]... 

The adsorption enthalpies fiir n-butane determined in this work are in the (rather wide) ran of those reported in the literature. Hu et d. [12] and Do and Do [13] determined adsorption enthalpies of approximately 16 and 35 LI moT in the micropore and meso-macropore region, respectively. Allen et al. [14] measured isosteric heats of adsorption of 32 and 66 kJ mol" for n-butane adsorption over a non-porous carbon and over a molecular sieve carbon, respectively. Liu et al. [15] determined an adsorption enthalpy of 53.9 kJ mol" at zero coverage. Linders et. al. [16] fmmd adsorption enthalpies between 45 and 50 kJ moT for two diflEerent carbons in a Multitrack apparatus a technique similar to the TAP system described... 

For the adsorption of hydrogen, it may be readily shown that = —SR for a variety of adsorbents [18]. For the delivery cycle reasonable values of adsorption and desorption pressures may be taken as Pi = 30 bar and P2 = 1.5 bar respectively, which upon substitution in Eq.(2) yield = —15.1 kJ/mole at r = 298 K. Thus, for optimum delivery of hydrogen between pressures of 30 bar and 1.5 bar at 298 K, an adsorption enthalpy change of -15.1 kJ/mole is desired. The isosteric heat of adsorption of hydrogen on carbons is substantially less, typically about 5.8 kJ/mole. However, if cryogenic conditions are acceptable then one may determine an optimum teu terature of operation in the case of activated carbon, for which delivery is maximized. Following Eq.(2), this ten terature is obtained as... 

From the temperature dependence of the adsorption the isosteric enthalpy of adsorption can also be obtained, using... 

Fig. 4 Comparison between the isosteric adsorption enthalpy (region II) of DPC on Na-kaolinite, pH = 50, CNaci = 10 M, curve 1, with the enthalpy of micellization according to different sources (curves 2 and 3) further discussion in the text...

Fig. 7.11 Grapliic determination of adsorption enthalpy and entropy from isothermal adsorption data measured at various temperatures, a Van t Hoff method applied to the adsorption equilibrium constant deduced from the parameter of a thermodynamic model like Henry or Langmuir fitting well the adsorption isotherms, h Clausius-Clapeyron or isosteric method the isosters he below a limit Une, which corresponds to the liquefaction equihbrium of the adsorptive...

If the van t Hoff and isosteric methods are simple ways for estimating the adsorption enthalpy of single component from isothermal adsorption data, they have the disadvantage to not take into account the temperature dependence on the enthalpy and entropy and to be not enough accurate. Moreover they are not adapted to the adsorption of gas mixtures. The best mean to determine the adsorption and coadsorption enthalpy is to measure them by using a differential calorimetry technique coupled with others techniques allowing the measure of adsorbed amount and composition as for example the manometry and the chromatography. 

Thus, the molar adsorption heat measured by differential calorimetry at constant temperature corresponds to the differential molar adsorption enthalpy. This value is equivalent to the isosteric enthalpy of adsorption [11]. 

Fig. 7.29 Comparison of adsorption enthalpies of ethylmercaptan on NaX zeolite at 298 K measured by calorimetry (red points) and calculated with the isosteric method (green points)...

The paper by Martin-Martinez et al provides a good example of how adsorption enthalpy measurements can yield a clearer understanding of the mechanisms of micropore filling and surface coverage. An improved isosteric method has been developed by Rees and his co-workers. Their measurements have revealed energetic heterogeneity in the adsorption of ethane and propane by Silicalite I. 

Now A. the diflerential molar enthalpy of adsorption, is often termed the isosteric enthalpy of adsorption (or alternatively the isosteric heat of adsorption) and is given the opposite sign. Thus... 

The shift in the C=C frequency, vi, for adsorbed ethylene relative to that in the gas phase is 23 cm-1. This is much greater than the 2 cm-1 shift that is observed on liquefaction (42) but is less than that found for complexes of silver salts (44) (about 40 cm-1) or platinum complexes (48) (105 cm-1). Often there is a correlation of the enthalpy of formation of complexes of ethylene to this frequency shift (44, 45). If we use the curve showing this correlation for heat of adsorption of ethylene on various molecular sieves (45), we find that a shift of 23 cm-1 should correspond to a heat of adsorption of 13.8 kcal. This value is in excellent agreement with the value of 14 kcal obtained for isosteric heats at low coverage. Thus, this comparison reinforces the conclusion that ethylene adsorbed on zinc oxide is best characterized as an olefin w-bonded to the surface, i.e., a surface w-complex. 

Calculate an isosteric enthalpy of adsorption for each value of V/Vm ... 

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