Langmuir plot, adsorption

Fig. 4J Langmuir plots (a) for propane on 5A zeolite (courtesy Ruthven) (fc) for carbon monoxide on zeolite CaY-54 (courtesy Stone). In (a) the adsorption is expressed in terms of number C of molecules of adsorbate per cavity in (b), as m (stp).

Plots of an amount of material adsorbed versus pressure at a fixed temperature are known as adsorption isotherms. They are generally classified in the five main categories described by Brunauer and his co-workers (4). In Figure 6.2 adsorbate partial pressures (P) are normalized by dividing by the saturation pressure at the temperature in question (P0). Type I is referred to as Langmuir-type adsorption and is characterized by a monotonic approach to a limiting amount of adsorption, which presumably corresponds to formation of a monolayer. This type of behavior is that expected for chemisorption. 

Figure 10.10 Langmuir plot concerning the adsorption of beetroot-juice dye onto a porcelain substrate at 25 °C graph of c x (as y ) against c (as V)...

A Langmuir type adsorption isotherm is given in Fig. 4.2a. As is shown in Fig. 4.2b the evaluation of the equilibrium adsorption constant and of rmax is readily obtained from experimental data by plotting Eq. (4.10a) in the reciprocal form... 

A typical N2 adsorption measurement versus relative pressure over a solid that has both micropores and mesopores first involves essentially a mono-layer coverage of the surface up to point B shown in isotherm IV (lUPAC classification) in Figure 13.1. Up to and near point B the isotherm is similar to a Langmuir isotherm for which equilibrium is established between molecules adsorbing from the gas phase onto the bare surface and molecules desorbing from the adsorbed layer. The volume of adsorbed N2 that covers a monolayer volume, hence the surface area of N2 can then be determined from the slope of the linearized Langmuir plot when P/V is plotted against P ... 

Typical adsorption isotherms that obey Eqs. (5) and (7) are shown in Figs. 2.1 and 2.2, respectively. It should be noted that a linear Langmuir plot can be obtained by plotting l/[nA]s against 1/P where the slope is 1/k and the intercept is l/[ng] as seen after rearrangement of Eq. (7). The adsorption isotherms are utilized primarily to determine the surface area of porous solids and the heats of adsorption. The isotherms yield the amount of gas adsorbed. By multiplying with the area occupied per molecule... 

Figure 8. Langmuir plots for adsorption of methane on coal...

An equation of the form of Eq. (2.32) was given by Langmuir (Carberry, 1976) for the treatment of data from the adsorption of gas on a solid surface. If the Michaelis-Menten equation is applicable, the Langmuir plot will result in a straight line, and the slope will be equal to l/rmax. The intercept will be KM/rmax, as shown in Figure 2.5. 

Langmuir plots for pyridine adsorption from cyclohexane onto Hi-Sil were not entirely straight lines, for half of the molecules were slightly more strongly adsorbed. These adsorbed films were tightly packed the rm values corresponded to 30.2 and 30.7 Kz per pyridine molecule at 50° and 25°, respectively. 

Figure 5.10 Langmuir plots for the adsorption of ammonia on charcoal shown in...

Fig. 16 The adsorbed amount of P-d-glucosidase per gram microgel Ta(js is plotted versus the concentration of free enzyme csoi in solution. The dashed line represents the fit of the experimental data by (2). The arrow marks the amount of entrapped enzyme used for kinetic investigation (620 mg P-D-glucosidase per gram microgel). The inset displays the data as a linear Langmuir plot. The adsorption was conducted at 4°C in 10 mM MOPS buffer solution (pH 7.2) and with a micro-gel concentration of 1 wt%. The immobilized enzymes do not prevent the microgel from shrinking at temperatures above the LCST [23]...

Figure 8. Langmuir plot for 2,4,5-T In accord with the Langmuir model for adsorption equilibrium, a linear trace is obtained for the isotherm for 2,4,5-T when (X) 1 is vlotted vs. (Ceq) 1. Intercept of plot is (Xm) 1, and the slope is (bXm) K...

One of the most significant points that we must consider in scientific studies, not limited to studies on photocatalysis, is distinction between evidence and consistency, as least as far as the author thinks. In other words, it is necessary to recognize every fact to be a necessary condition but not a sufficient condition in a strict scientific sense. For example, the fact that a reaction rate obeys the first-order rate law giving a linear relation in a plot of data as in Fig. 6 is only a necessary condition for a monomolecular reaction in homogeneous phase and also a necessary condition for heterogeneous photocatalytic reaction in diffusion-limited conditions or that in surface-reaction limited conditions with a Henry-type adsorption or a Langmuir-type adsorption in the lower-concentration region. 

As the interaction potential at the mid point of the slitlike pore is the deepest in the pore of w < 0.6 nm and it is not seriously different from the double minima even for w > 0.6 nm, molecular potential for a molecule in the micropore can be approximated by the potential at the mid-point of the slitlike pore. The molecular potential indicates the presence of the inherent micropore of the volume of Wl for each adsorptive. Here the inherent micropore must have sufficiently strong molecular field in comparison with the thermal energy at a measuring temperature. The inherent micropore volume Wl for vapour molecules is almost equal to the micropore volume Wq obtained from N2 adsorption at 77 K (Gurvitch rule) Wl for a supercritical gas which depends on the molecule-surface interaction can be evaluated as the saturated amount of adsorption from the Langmuir plot and Wl is less than Wo in general. 

Here, Wl is the inherent micropore volume and Poq is the saturated vapour pressure of a quasivapourized supercritical gas. The plot of [ln(WL/Wo)] vs. In P leads to both values of Poq of the supercritical gas in the quasivapour state under the micropore field and /3Eq, that is, qst,. =i/e- Thus, this extended DR plot is quite useful to obtain the important information on adsorption of a supercritical gas. This extended DR equation can describe the adsorption isotherm of the supercritical gas using the concepts of Poq and Wl which are experimentally estimated by the Langmuir plot of the adsorption isotherm. Poq and Wl can be related to the intermolecular interaction of supercritical gas in the quasivapourized state and the molecule-pore interaction, respectively. Then, we can define the quasirelative pressure of P/Poq and express the adsorption isotherm of a supercritical gas, as if it was a vapour. 

Many examples of adherence of experimental data representing adsorption of ions at constant pH to Langmuir equation are reported in Tables 4.1 and 4.2. The apparent adsorption capacity (from the plateau level or from the slope of the linearized Langmuir plot, Eq. (5.5) depends on the pH. 

Fig. 8.1. Scatchard (A), Langmuir (B and C) and Sips (D) forms of the Law of Mass Action for antibody-antigen interactions. The abbreviations and the derivation of the equations are given in Section 8.3. Polyclonal sera yield curved lines in A, B and C, whereas the interrupted lines represent homogeneous interaction. In the Scatchard (1949) plot, three of the different populations of antibodies are indicated by dotted lines low afTinity (K is small) at r = 2, intermediate ( average ) affinity, Aoat r = 1 and high affinity at small r. The Langmuir (1918) adsorption isotherm can be graphically presented if the total amount of antibody is known (B) or not (C). In the latter case b represents bound antibody (Abt d) and n/r in eq. 9 is substituted by Abio,ai/Abbo d to obtain ...

Many adsorption experiments on long chain fatty acids and other amphiphiles at the liquid/air interface and the close agreement with the von Szyszkowski equation is logically one proof of the validity of Langmuir s adsorption isotherm for the interpretation of y - log c -plots of typical surfactants in aqueous solutions (cf. Appendix 5D). This evidence is also justification for use of the kinetic adsorption/desorption mechanism based on the Langmuir model for interpreting the kinetics and dynamics of surface active molecules. 

Therefore, a linear Langmuir plot is obtained by plotting 1 /o against 1 /P. Such a plot is shown for the adsorption of oxygen, carbon monoxide, and carbon dioxide on silica in Figure 3.18. 

If of Equation 3 is plotted against c, it is found that decreases hyperbolically with increasing c. On the other hand, Qp obeys the Langmuir-type adsorption formula, expressed by Equation 1. In a monomolecular layer of adsorbed protein, it may be assumed that the total number, N, of adsorptive sites on a material surface is constant, as indicated in Equation 4, and that the adsorbed protein molecules contribute n water-binding sites. 

In 1971 Bourne and coworkers in t-bultylbenzene cracking (already cited ( 56)) over silica-alumina determined the adsorption isotherm of benzene on the same material. A Langmuir plot was non-linear at one end they suggested that this portion of the isotherm indicated that site heterogeneity exists, of... 

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