Adsorption Clausius-Clapeyron equation

Vapor Pressures and Adsorption Isotherms. The key variables affecting the rate of destmction of soHd wastes are temperature, time, and gas—sohd contacting. The effect of temperature on hydrocarbon vaporization rates is readily understood in terms of its effect on Hquid and adsorbed hydrocarbon vapor pressures. For Hquids, the Clausius-Clapeyron equation yields... 

Hint the process of adsorption is a condensation reaction, so we can employ the Clausius-Clapeyron equation (Equation (5.5)) to answer part (1). Be careful, though, because AH for a condensation reaction will be negative.]... 

When the functional form of the correlation is suggested by theory, there is a great deal more confidence that the correlation can be extrapolated into regions of P that have no experimental data, and can be used for other families of compounds other than the training set S. Examples of theory-suggested functional forms include the van der Waals equation of state for gases, the Langmuir isotherm for adsorption and catalysis, and the Clausius-Clapeyron equation for the vapor pressure of liquids. 

Heats of adsorption are usually determined in two ways either by direct calorimetric determination at a chosen temperature, or by calculating the isosteric heats from adsorption isotherms measured at different temperatures and using the Clausius-Clapeyron equation. Thus, isosteric heats of adsorption are calculated from the... 

The techniques described in the foregoing do not easily provide information about the chemisorption bond strength. The Clausius-Clapeyron equation is not applicable in the range of irreversible adsorption. Only by measurements of the desorption rates during the thermal desorption processes at two slightly different temperatures can the activation energy of desorption be estimated. This method has been used by Kubokawa (55). Desorption rates can be calculated from the evolution curves obtained during isothermal desorption as shown, for example, by Czanderna (54). 

Although we shall not be concerned experimentally with measuring heats of adsorption, it is appropriate to comment that Mi for the physical adsorption of a gas is always negative, since the process of adsorption results in a decrease in entropy. The isosteric heat of adsorption (the heat of adsorption at constant coverage 6) can be obtained by application of the Clausius-Clapeyron equation if isotherms are determined at several different temperatures the thermodynamics of adsorption have been fully discussed by Hill. ... 

The heat of adsorption may be calculated from a knowledge of the sorption isotherm at equilibrium by use of the Clausius-Clapeyron equation. 

Now, these calorimetric results allow, in principle, to recalculate adsorption isotherms at other temperatures than 30°C by simple use of the isosteric method derived from the Clausius-Clapeyron equation, for instance in the following form ... 

The objective of this study is to compare the strengfti of adsorptive interaction between adsorbents and thiophene/benzene. Extremely low partial pressures at less than 10 atm would be necessary to meet this objective if isotherms were measured at ambient temperature, because the isotherms at ambient temperature are fairly flat and are difficult to compare. However, it is very difficult to obtain and control such low partial pressures experimentally. Therefore, single component isothoms for benzene and thiophene were measured at 90, 120 and 180 °C using standard gravimetric methods. A Shimadzu TGA-50 automatic recording microbalance was employed. Isosteric heats of adsorption were calculated using the Clausius-Clapeyron equation from isotherms at different temperatures. 

Isosteric heat of adsorption was calculated from the adsorption data collected at different temperatures using Clausius - Clapeyron equation. 

As a useful thermodynamic property, the isosteric heat of adsorption has been generally applied to characterize the adsorbent surface. The isosteric heat of adsorption is evaluated simply by applying the Clausius-Clapeyron equation if one has a good set of adsorption equilibrium ta obtained at several temperatures. 

Summarizing, an attempt has been made to provide a systematic account of the thermodynamic properties of the adsorbed phase. The Gibbs adsorption equation, as an extension of the Clausius-Clapeyron equation, has played a key role in linking experimental isotherm data to the determination of molar or differential entropies and enthalpies. Similarly, calorimetric measurements can be systematically applied to obtain the same type of information. 

The heat of adsorption of ozone on silica gel was calculated for various conditions with the help of the Clausius-Clapeyron equation (Figure 3). In the region of temperature and ozone concentration of most interest, the heat of adsorption is about 5400 cal. per gram-mole of ozone. 

Shekhovtsova and Fomkin [41] developed a discrete site model to describe the adsorption of methane on microporous adsorbents. The model was tested with adsorption on zeoUte NaX and an activated carbon. A sharp decrease in the heats of adsorption was observed at high adsorbed amounts even in the supercritical temperature range. A multilayer adsorption theory was developed by Wang and Hwang [42] to describe the behavior of several adsorbates on activated carbons. The adsorbates employed included several alkanes, hydrogen sulfide, and carbon monoxide. The isosteric heats of adsorption for all gases were determined using the Clausius-Clapeyron equation. 

There is a more or less generalized agreement that the isosteric adsorption heat is strongly affected by the microstructure of the adsorbent, particularly in the case of porous solids. This magnitude is better suited for structural analysis than other thermodynamic quantities. The use of the Clausius—Clapeyron equation to determine the isosteric adsorption heat has several limitations both theoretical and experimental, that are well known. 

In the previous section it was observed that the Langmuir postulates of sites of equal activity and no interaction between occupied and bare sites were responsible for nonagreement with experimental data. It might be surmised that these assumptions correspond to a constant heat of -ad-sm-pt-ion—Indeed.-it-is-p.QssibIe to derive the Langmuir isotherm by assuming that is independent of d. The heat of adsorption can be evaluated from adsorption-equilibrium data. First the Clausius-Clapeyron equation is applied to the two-phase system of gas and adsorbed component on the surface ... 

For the Clausius-Clapeyron equation to be valid the process must be univariant. This means that Eq. (9-10) can be applied only for constant concentration of adsorbate on the surface, that is, constant 6. If adsorption-equilibrium data are available at different temperatures, the slopes of p-vs-T curves at constant 6 may be used with Eq. (9-10) to calculate AH,. Figure 9-2, taken from Beeck, shows such isosteric heats of adsorption as a function of 9 for hydrogen on several metal films. These results are typical of almost all heats-of adsorption in showing a decrease in AH, with increasing surface coverage. 

For the adsorption of a mole of any gaseous molecule onto an inert surface (one that is not changed by the adsorption itself), it can be shown from thermodynamic principles (see Chapter 1) that this vapor-adsorbate phase change is described by the Clausius-Clapeyron equation ... 

Although the heat of adsorption or enthalpy change accompanying adsorption is directly obtained by calorimetry, it can conveniently be evaluated from the adsorption isostere. According to thermodynamics, the relationship between temperature T and pressure P under a state of -(J> phase equilibrium can generally be expressed with the Clausius-Clapeyron equation ... 

When the vapor pressure of a liquid at two different temperatures is known, it is possible to calculate the heat of condensation by means of the Clausius-Clapeyron equation. A similar procedure is employed to calculate the differential heat of adsorption from the isosteres (9 17). 

Heats of snrface reactions are directly obtainable from simple LEED observations. The nsnal application is to measure the enthalpy of adsorption of reversibly bound adsorbates. When the adsorbate produces a characteristic LEED pattern with extra beams, the mere existence of these beams, and not detailed intensity analysis, informs one of the presence of the characteristic adsorbed structure on the surface. At a given temperature there is a pressure at which this surface structure is just maintained, and the rates of evaporation and condensation into the structure are equal. Measurements of this pressure p as a function of absolute temperature T give the isosteric enthalpy of adsorption AH by application of the Clausius-Clapeyron equation for constant coverage... 

The isosteric heats of adsorption have been calculated from isotherms by the use of Clausius-Clapeyron equation. The detailed results 5) show that in all the cases measured physical adsorption is taking place. In this paper the heats given in Table I correspond to half-surface coverage. 

The integral and differential heats of adsorption are determined by measuring the adsorption isotherms for a given system at different temperatures. From the data, the equilibrium pressures necessary to obtain the same coverages at the different temperatures are determined. From the slope of the plots of In = const versus /T, the differential isosteric heats of adsorption for a given coverage are determined by the use of the Clausius-Clapeyron equation ... 

A set of such isotherms is shown in Fig. 9 for the system ethylbenzene/ H-ZSM-5. From such sets, in turn, isosteres were constructed and isosteric heats of adsorption, Qiso, determined via the Clausius-Clapeyron equation. This is illustrated in Fig. 10 using the system ethylbenzene/H-ZSM-5 as an example. 

Values of the enthalpy of adsorption, determined either from the variation of adsorption with temperature (isosteric enthalpy of adsorption) or by direct calorimetric measurements, provide a valuable insight into the mechanism of adsorption. When taken together wifri the data from adsorption isotherms, they provide information which could not be extracted from either set of data alone. Heats of adsorption and other thermodynamic parameters can be obtmned either by direct calorimetric determination, -AH =j n (where ria = adsorbed amount), or by using the Clausius-Clapeyron equation and the data from isosteric measurements. However, the faacX tiiat adsorption is often irreversible in the presence of micropores, fr equently makes estimates of adsorption heats obtained from isosteres very unreliable. 

The value of Q ff is thus defined for a particular coverage Fi. The r.h.s. of Eq. (19) is artalogous to the Clausius-Clapeyron equation and contains a directive for the experimentahst to measure the differential heat of adsorption as a function of coverage [69Traj. The isosteric heat of adsorption is defined very similarly and differs from the differential heat only by kT (about 50 meV at 600 K), = Qjjg. + kT. 

The adsorption isotherms presented in Figure 4 were used for determination of isosteric heat (Qst) of adsorption by extrapolation at different temperatures and for a given coverage according to Clausius-Clapeyron equation (Rouquerol, 1999) ... 

The heats of adsorption, AH, for gases onto a given sohd can, in principle, be measured in a variety of ways and will, in reversible systems, adhere to the Clausius-Clapeyron equation... 

---