Langmuir plots

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).

The Langmuir plots in the linearized form, p/v = a + bP, are linear at the lowest pressures, over a wider range for the oxides, but reach maxima in both cases. 

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)...

For this reason, we sometimes construct Langmuir plots and find they are not particularly linear, particularly at the right-hand side, which represents higher concentrations. This deviation from... 

The gradient of a Langmuir plot is always positive, since it is clearly impossible for a monolayer to contain a negative amount of material. 

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...

Figure 8. A. Arrhenius plot of the first-order rate constants on LaY % 8580cm x band, Flfi/70 0 3650cm l LaY O 3640cm l band, FJfi/70 % 3550cm l. B. Langmuir plot of the apparent rate constants (k) and the leak rate (R) for sample F55/70 at 850° C...

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. 

Michaelis-Menten kinetic parameters can also be estimated by running a series of steady-state CSTR runs with various flow rates and plotting Cs versus (Cst)/(CSq- Cs). Another approach is to use the Langmuir plot (Csr vs Cs) after calculating the reaction rate at different flow rates. The reaction rate can be calculated from the relationship r = F (CSq - Cs)/V. However, the initial rate approach described in Section 2.2.4 is a better way to estimate the kinetic parameters than this method because steady-state CSTR runs are much more difficult to make than batch runs. 

Evaluate the Michaelis-Menten kinetic parameters by employing (a) the Langmuir plot, (b) the Lineweaver-Burk plot, (c) the Eadie-Hofstee plot, and (d) non-linear regression procedure. 

The and K%p can be estimated by the Lmeweaver-Burk plot or the Langmuir plot of experimental data as explained in Chapter 2. 

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...

If the latter explanation is correct, it follows that the value of As as derived by either BET or Langmuir analysis (In fact, many microporous solids do not give linear BET plots although their Langmuir plots may be linear over an appreciable range of p/p°) cannot be accepted as the true surface area of a microporous adsorbent. On the other hand, if the slope of the isotherm is not too low at higher p/p° and provided that capillary condensation is absent, it should (in principle) be possible to assess the external surface area from the multilayer region. 

Pig. The Langmuir plot. The kinetics of a gaseous reaction on solid surface. 

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...

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