Adsorption isotherm Henry

The most simple type, A, is that of a linear increase. It is described by the Henry adsorption isotherm equation ... 

Binding constant (for sensor materials that obey Langmuir adsorption isotherm) or response linearity (for sensor material that obey Henry adsorption isotherm)... 

For example, the concept of Kj, (Eq. (4.9)) corresponds to Henry adsorption isotherm (adsorption is proportional to the equilibrium concentration/pressure of the adsorbate), which can be derived from the adsorption reaction 4.1, whose equilibrium constant defined by Eq. (4.2) depends only on the nature of the adsorbent and the adsorbate, but it is independent of the experimental conditions (over certain limited range). It is well known that in principle Kjy is variable, e.g. the effect of the pH on is demonstrated in Figs. 4.28-4.63. These figures show that the pH is an important but not unique factor affecting the distribution of the adsorbate, e.g. the usually decreases when the concentration of the adsorbate increases at constant pH. However, a few cases of constant over a broad range of concentrations of the adsorbate are also reported in Tables 4.1 and 4.2. 

From Eqs. (2.170) and (2.173) and ideal surface layer and ideal solution bulk the Henry adsorption isotherm is obtained. Thus, K, can be calculated from experimental data... 

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. 

The adsorption free energy and other parameters may be determined, provided that a proper adsorption isotherm is identified and is fitted to experimental data. However, it is usually difficult to unequivocally choose an appropriate isotherm an experimental isotherm may well be fitted to a multitude of theoretical isotherms having several adjustable parameters. If the adsorption isotherm at a very small surface coverage is accessible experimentally, the adsorption free energy can be determined from the limiting slope of the isotherm, as all isotherms reduce to Henry s law when 6 0 ... 

At different types of adsorption isotherms plotted for adsorption of donor particles on oxides (see section 1.5) expressions (1.112) - (1.115) provide the rise in and decrease in with the growth of partial pressure of gas P, the functions themselves being different. Thus, in case of applicability of the Henry isotherm at small P we have the function oi - exp const-P becoming a power function <7s P with the rise in P which is often observed in experiments [154, 155, 169]. 

The simplest adsorption isotherm is that of Henry s law (linear adsorption isotherm),... 

The relationship between r, r2 and has to be specified via the adsorption isotherm. Let us first proceed with the simplest case of the linear Henry regime. 

This expression is analogous to Henry s Law for gas-liquid systems even to the extent that the proportionality constant obeys the van t Hoff equation and Ka = K0e AH/RT where AH is the enthalpy change per mole of adsorbate as it transfers from gaseous to adsorbed phase. At constant temperature, equation 17.1 becomes the simplest form of adsorption isotherm. Unfortunately, few systems are so simple. 

In the limit of low pressure the front end of the adsorption isotherm is approximated by the Henry regime which states that the number of adsorbed molecules per unit volume is proportional to the pressure and to the Henry coefficient, Kh. ... 

For propane, n-pentane and n-hexane the differential heats of adsorption over FER dropped more rapidly, right after 1 molecule was adsorbed per Bronsted acid site. Similar results were obtained with TON. In contrast, with MOR and FAU the drop in the differential heats of adsorption for n-alkanes occurred at lower coverages, indicating that only a certain fraction of the Bronsted acid sites were accessible to the adsorbing alkane probe molecules. With MFI the drop did not occur until 2 molecules of n-alkane were adsorbed per Bronsted acid site, suggesting perhaps a higher stoichiometry of about two n-alkanes per Bronsted acid site. In the cases of i-butane and i-pentane the drop occurred around one alkane per Bronsted acid site. Finally, n-butane adsorption isotherms measured over TON framework type catalysts having three different A1 contents (Si/Al2 = 90, 104, 128) showed Henry coefficients to increase with increase in the A1 content [5], Based... 

The adsorption isotherm —Equation (8) —associated with this surface equation of state is called the Henry law limit, in analogy with the equation that describes the vapor pressure of dilute solutions. The constant m, then, is the adsorption equivalent of the Henry law constant. When adsorption is described by the Henry law limit, the adsorbed state behaves like a two-dimensional ideal gas. 

What is meant by the Henry law limit in the case of an adsorption isotherm ... 

The CB-MC method has been used to simulate the adsorption isotherms of various alkanes in silicalite (170, 171). Using potential parameters that were fitted to obtain good agreement with experimental Henry s law coefficients, Smit and Maesen (170,171) have simulated the adsorption isotherms of straight-chain alkanes in silicalite. Good agreement was obtained for ethane and propane in comparison with the different type-I curves measured experimentally. The overall agreement with experimental isotherms was found to be satisfactory with hexane and heptane, and a kink is seen... 

Nonsymmetrical band spreading may be attributed to nonlinearity of the equilibrium adsorption isotherm (i.e., deviation of isotherm from Henry s Law). This causes the sorbate to move through the column at different rates (rate dependent upon sorbate concentration). 

Which theory is suitable for a certain application The adsorption theory of Henry is applicable at low pressure. This, however, is natural since it can be viewed as the first term in a series of the adsorption function. A widely used adsorption isotherm equation is the BET equation. It usually fits experimental results for 0.05 < P/P0 < 0.35. For very small pressures the fit is not perfect due to the heterogeneity. For higher pressures the potential theory is more suitable at least for flat, homogeneous adsorbents. It often applies to P/Po values from 0.1 to 0.8. Practically for P/Po > 0.35 adsorption is often dominated by the porosity of the material. A more detailed description of adsorption is obtained by computer simulations [382],... 

It is a well-known fact that upon covalent immobilization at the surface, the dissociation constant of the acid-base indicator changes by as much as 3 pK units. This shift clearly illustrates the dramatic effect that the interphase has on the ionization equilibria. It is perhaps the most serious problem with optical sensors that the surface concentration of any species is related to its corresponding bulk activity value through an adsorption isotherm which, with the exception of Henry s law, is a highly nonlinear and variable relationship. It is also known (Davies and Rideal, 1963) that the surface pH is different from the bulk value due to the electrostatic repulsion. 

Figure 30 shows the CTL glow curves for the catalyst pre-adsorbed ethanol or acetone vapor. The catalyst is heated at a rate of 0.5 °C/s in synthetic air. The CTL intensity increases at high temperatures, and the total amount of CTL intensity L depends on the adsorption time At and the gas concentration C during adsorption. We can measure the gas at a very low concentration by measuring the value of L because L is proportional to the product of At and C in a region of low AtC where a Henry-type adsorption isotherm holds. 

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