Plotting adsorption data

This equation is very convenient to plot adsorption data empirically in a log r vs log [A] plot (Fig. 4.3)... 

The best utility of the Dubinin-Radushkevich equation lies in the fact that the temperature dependence of such equation is manifested in the adsorption potential A, defined as in eq. (3.2-30), that is if one plots adsorption data of different temperatures as the logarithm of the amount adsorbed versus the square of adsorption potential, all the data should lie on the same curve, which is known as the characteristic curve. The slope of such curve is the inverse of the square of the characteristic energy E = PEq. 

The present discussion is restricted to an introductory demonstration of how, in principle, adsorption data may be employed to determine changes in the solid-gas interfacial free energy. A typical adsorption isotherm (of the physical adsorption type) is shown in Fig. X-1. In this figure, the amount adsorbed per gram of powdered quartz is plotted against P/F, where P is the pressure of the adsorbate vapor and P is the vapor pressure of the pure liquid adsorbate. 

Thus D(r) is given by the slope of the V versus P plot. The same distribution function can be calculated from an analysis of vapor adsorption data showing hysteresis due to capillary condensation (see Section XVII-16). Joyner and co-woikers [38] found that the two methods gave very similar results in the case of charcoal, as illustrated in Fig. XVI-2. See Refs. 36 and 39 for more recent such comparisons. There can be some question as to what the local contact angle is [31,40] an error here would shift the distribution curve. 

The following several sections deal with various theories or models for adsorption. It turns out that not only is the adsorption isotherm the most convenient form in which to obtain and plot experimental data, but it is also the form in which theoretical treatments are most easily developed. One of the first demands of a theory for adsorption then, is that it give an experimentally correct adsorption isotherm. Later, it is shown that this test is insufficient and that a more sensitive test of the various models requires a consideration of how the energy and entropy of adsorption vary with the amount adsorbed. Nowadays, a further expectation is that the model not violate the molecular picture revealed by surface diffraction, microscopy, and spectroscopy data, see Chapter VIII and Section XVIII-2 Steele [8] discusses this picture with particular reference to physical adsorption. 

The equation of state for a solid film is often ic= b - aa (note Section IV-4D). Derive the corresponding adsorption isotherm equation. Plot the data of Problem 11 according to your isotherm equation. 

Adsorption Plots. Isotherm plots are the most common method of presenting adsorption data. An isotherm is a curve of constant temperature the adsorbed water content of the adsorbent is plotted against the water partial pressure in equiHbrium with the adsorbent. An isostere plot shows curves of constant adsorbed water content the vapor pressure in equiHbrium with the adsorbent is plotted against temperature. Figure 13 shows isosteres for the three primary adsorbents described previously. In this case, the dew points for the three adsorbents are plotted at 0.5, 5, and 10 kg... 

The conversion and initial rate in the presence and absence of TCE versus the product of the second order rate constant and the dark adsorption appear in Figure 4a,b. Figure 4a shows considerable scatter in the data, reveahng only broad, general trends between conversion or rate and hydroxyl second order rate constant. However, the plots of enhanced conversion and initial rate vs. the corresponding chlorine second order rate constant multiplied by the dark adsorption data are smoother (Figure 4b). 

Physical adsorption of nitrogen was carried out on an ASAP 2400 Micromeritics apparatus. Before measurements, samples were evacuated overnight at 350 °C at vacuum of 2 Pa. For all samples the same adsorption data table was used. Collected adsorption data were treated by BET-isotherm in the range 0.05 < P/micropore volume and mesopore + external surface, t-plot method, with master isotherm of nonporous alumina (Harkins-Jura) was used, t-plot was linearized in the range of 0.35 < t < 0.6 nm. 

A number of models have been developed for the analysis of the adsorption data, including the most common Langmuir [49] and BET (Brunauer, Emmet, and Teller) [50] equations, and others such as t-plot [51], H-K (Horvath-Kawazoe) [52], and BJH (Barrett, Joyner, and Halenda) [53] methods. The BET model is often the method of choice, and is usually used for the measurement of total surface areas. In contrast, t-plots and the BJH method are best employed to calculate total micropore and mesopore volume, respectively [46], A combination of isothermal adsorption measurements can provide a fairly complete picture of the pore size distribution in sohd catalysts. Mary surface area analyzers and software based on this methodology are commercially available nowadays. 

Plot of adsorption data in a double logarithmic plot. In a Langmuir isotherm the initial slope is unity. A Freundlich isotherm shows in a double log plot a slope of n < 1. Such a Freundlich isotherm is obtained if the adsorbent is heterogeneous (decreasing tendency for adsorption with increasing 6). (Modified from Morel, 1983)... 

Fig. 4.8 compares data on the adsorption of lauric acid (C12) and caprylic acid (Cs) at a hydrophobic surface (mercury) as a function of the total bulk concentration for different pH-values. As is to be expected the molecular species becomes adsorbed at much lower concentrations than the carboxylate anions. The latter cannot penetrate into the adsorption layer without being accompanied by positively charged counterions (Na+). As was shown in Fig. 4.4, the adsorption data of pH = 4 can be plotted in the form of a Frumkin (FFG) equation. Fig. 4.9 compares the adsorption of fatty acids on a hydrophobic model surface (Hg) with that of the adsorption on Y-AI2O3. 

Kurbatov plots (jj ) have often been employed to determine the net metal ion/proton exchange, x> from adsorption data. Although Kurbatov constants are convenient curve-fitting parameters, they are insensitive to the variation of x with pH and adsorption density and should be dispensed with for use in adsorbate partitioning calculations, particularly when high adsorption densities are expected ( 9 ). 

Thus, from adsorption data for one gas, data for other gases on the same adsorbent may be found. Several other methods of plotting the characteristic curve have been proposed1(3). 

When measured adsorption data are plotted against the concentration value of the adsorbate at equilibrium, the resulting graph is called an adsorption isotherm. The mathematical description of isotherms invariably involves adsorption models described by Langmuir, Freundlich, or Brauner, Emmet and Teller (known as the BET-model). Discussion of these models is given in Part 111, as conditions relevant to chemical-subsurface interactions are examined. 

The sorption process generally is studied by plotting the equilibrium concentration of a compound on the adsorbent, as a function of equilibrium concentration in the gas or solution at a given temperature. Adsorption isotherms are graphs obtained by plotting measured adsorption data against the concentration value of the adsorbate. Several mechanisms may be involved in the retention of contaminants on... 

A plot of adsorption data of the left-hand side of this equation versus relative pressure (p/po) allows one to estimate Nsm and Ebex. The magnitude of Ebex is found to give... 

Before leaving the nickel experiments, it may be well to refer to the experiments on hydrogen adsorption variously reported in the literature. As an example, the work of Maxted and Hassid (13) had as its main objective the measurement of the slow activated adsorption of hydrogen on reduced nickel oxide catalysts. It has been proved by the foregoing that the slow adsorption is actually absorption. When plotting their data as isobars, as was done in Fig. 9, the similarity between these isobars and those obtained with sintered nickel films is evident. 

Adsorption data are frequently presented as a plot of the amount of adsorbate taken up per unit weight or area of the adsorbent vs the equilibrium concentration remaining in the gaseous or solution phase (adsorption isotherm) pH, temperature and electrolyte concentration are held constant. Depending upon the purpose of the investigation, the extent of adsorption is expressed either as amount of adsorbate vs. surface area of adsorbent, as fraction adsorbed, or, in some cases, as a distribution coefficient, K. ... 

Plot these data in the form suggested by Equation (75) and evaluate the slope and intercept. If Asp for solid C is known by independent study to be 325 m2 g -1, what is o° for the adsorbate Alternatively, suppose a0 for the adsorbate is known to be 0.25 nm2 on this surface. What value of Asp is consistent with the adsorption data ... 

EXAMPLE 9.3 Analysis of Adsorption Data Using the Langmuir Isotherm. Slope and intercept values for the linearized plots of the data in Figure 9.7 are as follows ... 

Data for calcined samples dioo - XRD (100) interplanar spacing, Sbet - BET specific surface area, V, - total pore volume, Vp - primary mesopore volume, Sex - external surface area, wkjs - primary mesopore diameter. Data for uncalcined samples mreS due - mass percent of residue at 1263 K, mSdir - mass decrease in the temperature range of the surfactant decomposition and desorption of the decomposition products (between about 373 and 623 K). Notes a - no peak on XRD spectrum, d,0o cannot be evaluated, b - no linear region on the Os-plot, which would be suitable for the Vp and Sex evaluation. XRD and adsorption data (except for those for HR-A2 sample) taken from Refs. 24 and 26. Thermogravimetric data for DS-AD taken from Ref. 19. 

The adsorption of cobalt (II) at 1.3 X 10"4M Co(ClCh)2 is shown in Figure 2. in the pH range from 1.7 to 12.0. This form of plot, percent adsorption vs. pH or concentration while useful for demonstrating the dramatic increase in adsorption over a narrow pH or concentration range, is however of limited theoretical value. In Figure 3 the cobalt (II) adsorption data are therefore redrawn as log (adsorption density) vs. pH. The vertical dashed lines in Figures 2 and 3 represent the minimum pH for precipitation of 1.3 X 10"4M Co (II) in the absence of adsorption. The plateau of Figure 3 therefore represents adsorbed and precipitated cobalt. 

The results show that any isotherm can fit the data very well. If we choose the the Freundlich equation, which fits the adsorption data the best, the slope and the intercept of the logX versus logY plot yields the equation,... 

The acidic sites on iron oxides are believed to be FeOH sites (32), much like the well-known SiOH sites on silica. Heats of adsorption on iron oxide of bases of known Cg and Eg, having appreciably different ratios of Cg to Eg ("hardness" or "softness"), allow estimation of the and for the acidic sites of iron oxide. Our initial studies were done by measuring adsorption isotherms at two or more temperatures (Figure 7) and from the temperature coefficient of the equilibrium constant K the enthalpy of adsorption was calculated. In Figure 7 the adsorption data is plotted as a Langmuir isotherm ... 

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