Molar adsorption enthalpies

Elements 108 - 116 are homologues of Os through Po and are expected to be partially very noble metals. Thus it is obvious that their electrochemical deposition could be an attractive method for their separation from aqueous solutions. It is known that the potential associated with the electrochemical deposition of radionuclides in metallic form from solutions of extremely small concentration is strongly influenced by the electrode material. This is reproduced in a macroscopic model [70], in which the interaction between the microcomponent A and the electrode material B is described by the partial molar adsorption enthalpy and adsorption entropy. By combination with the thermodynamic description of the electrode process, a potential is calculated that characterizes the process at 50% deposition ... 

It is assumed that the binding energy of an adsorbed single molecule to the surface approximately equals its partial molar adsorption enthalpy at zero surface coverage. In the adsorbed state at zero surface coverage the individual variations of the entropy are partly but not completely suppressed. Hence, it is expected that this adsorption enthalpy is proportional to the standard sublimation enthalpy, which characterizes the volatility properties of pure solid phases as an integral value, ... 

Figure 4-13 gives the differential molar adsorption enthalpy for the adsorption of different hydrocarbons on active carbon. 

Further information is obtained if the amount of liquid adsorbed on the surface of the particle is also determined, permitting the combination of the data on heat of immersion with those on the amount of adsorbed liquid. Thus, molar adsorption enthalpies can be given for the characterization of the stabilizing adsorption layer [12-16]. A further benefit of adsorption excess isotherms is that it is possible to calculate from them the free enthalpy of adsorption as a function of composition. When these data are combined with the results of calorimetric measurements, the entropy change associated with adsorption can also be calculated on the basis of the second law of thermodynamics. Thus, the combination of these two techniques makes possible the calculation of the thermodynamic potential functions describing adsorption [14,17-19]. 

The interaction of adsorbents with various surface energies with the liquid components studied are adequately characterized by the differences in molar adsorption enthalpies between components 1 and 2, h - (l/r )ft, listed in Table 1. In the case of the adsorption of the methanol-benzene liquid pair, these enthalpy differences in the adsorption layer are decreased by the effect of hydropho-bization. 

Abstract The adsorption of ionic surfactants on different soil components such as silica, clay minerals, and humic acids was studied. The adsorption processes were controlled by flow microcalorimetry to determine the molar adsorption enthalpies of surfactant accumulation on clay and silicate surfaces. The evaluation of adsorption results for cationic surfactants has shown different mechanisms for solids having permanent (kaolinite, illite, montmorillonite) and pH-dependent surface charges (silica gels and powders). The adsorption mechanism for surfactants on silica surfaces with pH-dependent charges has been explained in terms of the development of charges on the surfaces and their interaction with... 

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. 7.21 Differential molar adsorption enthalpies of single p-xylene and m-xylene as a function of filling in NaY and BaY zeolites at 423 K...

Similarly, one may define the molar integral enthalpy of adsorption, SJt as... 

They are defined in complete analogy to the integral molar energy. The difference between the energy and the enthalpy of adsorption is usually small. If we treat the free gas as being ideal, the difference is AadU = AadHm1 + RT. At 25°C RT is only 2.4 kJ/mol. For this reason we do not need to worry too much about whether a heat of adsorption is the adsorption enthalpy or the internal adsorption energy, if we only want to estimate is. 

Molar Standard Enthalpies of Adsorption (Al /, idsj) and Stretching Frequency Shifts [Av(CO)] of CO Adsorbed on Various d, tf, and d10 Metal Ions... 

Fig. 41. CO stretching frequency shift vs molar standard enthalpies of adsorption for CO adsorbed on various d, d, and d10 metal ions (from data reported in refs. 17, 68, 635, 636, and 638).

Here, AH(A-B) is the partial molar net adsorption enthalpy associated with the transformation of 1 mol of the pure metal A in its standard state into the state of zero coverage on the surface of the electrode material B, ASVjbr is the difference in the vibrational entropies in the above states, n is the number of electrons involved in the electrode process, F the Faraday constant, and Am the surface of 1 mol of A as a mono layer on the electrode metal B [70]. For the calculation of the thermodynamic functions in (12), a number of models were used in [70] and calculations were performed for Ni-, Cu-, Pd-, Ag-, Pt-, and Au-electrodes and the micro components Hg, Tl, Pb, Bi, and Po, confirming the decisive influence of the choice of the electrode material on the deposition potential. For Pd and Pt, particularly large, positive values of E5o% were calculated, larger than the standard electrode potentials tabulated for these elements. This makes these electrode materials the prime choice for practical applications. An application of the same model to the superheavy elements still needs to be done, but one can anticipate that the preference for Pd and Pt will persist. The latter are metals in which, due to the formation of the metallic bond, almost or completely filled d orbitals are broken up, such that these metals tend in an extreme way towards the formation of intermetallic compounds with sp-metals. The perspective is to make use of the Pd or Pt in form of a tape on which the tracer activities are electrodeposited and the deposition zone is subsequently stepped between pairs of Si detectors for a-spectroscopy and SF measurements. 

For the calculation of the net adsorption enthalpies of transactinides on metal surfaces the partial molar enthalpies of solution and the enthalpy of displacement are required. These values can be obtained using the semi-empirical Miedema model [66-70] and the Volume-Vacancy or Surface-Vacancy model [32,70,71]. Data for these calculations are given in [34,72,73]. 

Typically the experiment with a transactinoid element lasts days or even weeks, and results in a single experimental value of the adsorption constant. The only possibility to obtain an estimate of the adsorption enthalpy based on such a result is to calculate the entropy change from the first principles [4] and substitute it into Eq. 5.7. The values of Aa( sS are calculated from the formulae of statistical mechanics for the particular model of the adsorbed state. The evaluation starts with the partition function of single molecule qm and with the molar partition function Z to calculate the absolute molar entropy from the general equation ... 

A hybrid QCM/calorimetry device, Masscal, has been developed recently [199]. This technique combines the mass measurement change upon gas adsorption with the accompanying isothermal heat flow that allows a molar binding enthalpy to be determined. Various thin film chemical and biochemical systems have been studied, such as the hydration isotherms and associated hydration enthalpies determined for the immobihzed enzyme lysozyme [200]. 

Yq surface tension of the pure solvent r = r F2 total adsorption 5 relative oscillation amplitude AHj molar standard enthalpy of transfer Anp density difference Sjj dilational elasticity dilational viscosity rig shear viscosity relative area change X=k/xn dimensionless rate constant interfacial chemical potential n = Yq-y surface tension co, co2 partial molar areas in - 27if circular frequency... 

FIGURE 2.71 Dependence of partial molar (a) enthalpy and (b) entropy of adsorption of water against surface coverage of anatase and rutile of different specific surface area. (Adapted from J. Chem. Thermodynamics, 39, Navrotsky, A., Calorimetry of nanoparticles, surfaces, interfaces, thin films, and multilayers, 2-9, 2007, Copyright 2007, with permission from Elsevier.)... 

Here, AH(A — B) is the partial molar net adsorption enthalpy associated with the transformation of 1 mol of the pure metal A in its standard state into the state of zero... 

There is an advantage in using the constant surface pressure standard state since it yields molar properties (enthalpies and entropies of adsorption) analogous to those associated with phase changes evaluated from the Clapeyron equation [80]. The use of the standard state with constant surface concentration provides differential quantities for the enthalpy and entropy changes which are not directly comparable with those calculated using the methods of statistical thermodynamics. The values of AS calculated by these two standard states differ only by the gas constant, B, and are readily interconverted. 

Industrial adsorption processes normally are cyclic processes in which adsorption and desorption steps of the sorbent material alterate periodically. Often the desorption or regeneration step is cmcial and essentially determine the period and the energetic efficiency of the cycle [1.2, 1.14-1.16]. An important quantity to characterize the desorption process is the (molar) enthalpy (AH ) needed to desorb the leading component either of product or waste - of a gas mixture from the sorbent. In Table 1.2 some examples of desorption processes and their industrial applications together with typical values of the molar desorption enthalpy are given. Summarizing it can be stated that in reversible physidesorption processes molar enthalpies of about (10-50) kJ/mol are needed whereas in irreversible chemisorption processes (70-200) kJ/mol are necessary for desorption. ... 

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