Langmuir adsorption isotherm limitations

Make a plot of Eq. XVII-69 as 6 versus P, and, for comparison, one of a Langmuir adsorption isotherm of same limiting or Henry s law slope. Comment on the comparison. 

Two assumptions essential to obtain Eqs. (82) or (84) are (i) the hetaeron adsorption has an asymptotic limiting value, and (ii) complexes between the eluite and hetaeron form in the mobile phase. The Langmuir adsorption isotherm is used here because it is simple to manipulate mathematically and because most data on the adsorption of detergents used as hetaerons are reported to obey this relationship as determined directly (207, 209) or from analyses of its effect on chromatographic retention ( 4). 

What is the Langmuir adsorption isotherm, and when is it applicable Describe its limitations. 

We can compare the coverage of mobile surface species predicted by Eq. 11.99 with the coverage calculated for immobile species (Langmuir adsorption isotherm) derived in Section 11.5.3. To do this comparison, we take the low-pressure limit of Eq. 11.79, in which the denominator becomes unity. The ratio of the coverages in these two limiting cases is... 

In the limit for g->0, the ideal Langmuir adsorption isotherm is obtained. 

Show that the data fit a Langmuir adsorption isotherm equation and calculate the area occupied by each adsorbed dodecanol molecule at limiting adsorption. 

In the limit of a - 0, the ideal Langmuir adsorption isotherm is obtained. See - Frumkin isotherm, and for the role of surface heterogeneity - Temkin isotherm. Refs. [i] Horanyi G (2002) Specific adsorption. State of art Present knowledge and understanding. In Bard A], Stratmann M, Gileadi M, Urbakh M (eds) Thermodynamics and electrified interfaces. Encyclopedia of electrochemistry, vol. I. Wiley-VCH Verlag, Weinheim, pp 349-382 [ii] Calvo EJ (1986) Fundamentals. The basics of electrode reactions. In Bamford CH, Compton RG (eds) Comprehensive chemical kinetics, vol. 26. Elsevier, Amsterdam, pp 1-78... 

The Langmuir adsorption isotherm (eq. (11.22)) satisfies the limiting conditions described earlier. At low concentrations c a = MA X yields the asymptote... 

II. Let Reaction 4 be the rate-limiting step and assume all other reactions are at equilibrium. Assume that adsorption from the gas phase follows a Langmuir adsorption isotherm. Neglect the reverse of Reaction 4. When performing a site balance, assume the surface is either vacant or covered with adsorbed ethylene and ethyl, i.e., the coverage of atomic hydrogen and adsorbed ethane are negligibly small. 

The Langmuir adsorption isotherm is of limited application since for real surfaces the energy is not the same for aU sites and interactions between adsorbed molecules carmot be ignored. 

The changes in versus [M" ] were fitted to the Langmuir adsorption isotherm [43,46,49]. The Langmuir model is based on the assumptions that adsorption is limited to one monolayer that all surface sites are equivalent and the adsorption to one site is independent of the occupancy condition of the adjacent sites. The com-plexation equilibrium is given by ... 

Although the physical meaning of the Langmuir adsorption isotherm is limited, the experimental data can often be very accurately approximated. Q is the stationary phase concentration, C , is the mobile phase concentration, and a and h are empirical parameters reflecting the maximal adsorption capacity and the equilibrium binding constant. It has to be noted that the Langmuir adsorption... 

Figure 7.2. The classical Langmuir adsorption isotherm (LAI) sketched for two different temperatures (Ti < Ta). The limiting loadings increase with decreasing temperature, i. e. nw (Ta) < nioi,(Ti).

Extending the classical Langmuir adsorption isotherm (7.1) from monolayer to ideal multilayer adsorption and considering the limiting case of infinite many layers, Brunauer, Emmett, and Teller derived in 1938 the AI [7.1-7.5, 7.42]... 

---