Adsorption isotherms Freundlich

The Freundlich isotherm is a limiting form of the Langmirir isotherm, and is applicable only in the middle ranges of vapor pressures. The general form of the Langmirir isotherm is written as 

At low pressures, bp is much smaller than unity and, therefore, can be neglected in the denominator so that the eqnation becomes. V = VJ p, indicating that the amount adsorbed is proportional to the first power of the pressure. At high pressures. Equation 2.104 becomes V=V so that the amount adsorbed becomes independent of the pressure. It is thus apparent that in the middle ranges of pressure, the amount adsorbed can be represented by a fractional exponent l/n, which will tend to vary between zero and unity, depending upon whether the pressure increases or decreases. This can be expressed by a general form of the adsorption equation. 

This is known as the Freundlich equation, which is followed only at medium pressures. The equation is of greater significance for chemisorption although some physical adsorption have also been explained using this equation. 

For adsorption from solution phase, the equation can be written as 

FIGURE 2.26 Linear Freundlich isotherms of Ni(II)ions on different activated. (Source Goyal, M., Rattan, V.K., and Bansal, R.C., Indian J. Ghent. TechnoL. 6, 305, 1999. With 

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An adsorbed film obeys a modified Amagat equation of state, t(t = qkT (see Eq. ni-107). Show that this corresponds to a Freundlich adsorption isotherm (Eq. XI-12) and comment on the situation. 

The dissolution of passive films, and hence the corrosion rate, is controlled by a chemical activation step. In contrast to the enhancement of the rate of dissolution by OH ions under film-free conditions, the rate of dissolution of the passive film is increased by increasing the ion concentration, and the rate of corrosion in film-forming conditions such as near-neutral solutions follows the empirical Freundlich adsorption isotherm ... 

Langmuir and Freundlich adsorption isotherms for toluene and MEK are shown in Figs. 2... 

The adsorption coefficients (K) were determined using the equation for the Freundlich adsorption isotherm ... 

Figure 15.4(A) shows the effect of the R = Zn2+/Al3+ ratio, which determines the charge density of the LDH layer, on the Freundlich adsorption isotherms. K values are far higher than those measured for smectite or other inorganic matrices. The increase in Kf with the charge density (Kf= 215, 228, 325mg/g, respectively, for R = 4, 3 and 2) is supported by a mechanism of adsorption based on an anion exchange reaction. The desorption isotherms confirm that urease is chemically adsorbed by the LDH surface. The aggregation of the LDH platelets can affect noticeably their adsorption capacity for enzymes and the preparation of LDH adsorbant appears to be a determinant step for the immobilization efficiency. [ZnRAl]-urease hybrid LDH was also prepared by coprecipitation with R = 2, 3 and 4 and Q= urease/ZnRAl from 1 /3 up to 2.5. For Q < 1.0,100 % of the urease is retained by the LDH matrix whatever the R value while for higher Q values an increase in the enzyme/LDH weight ratio leads to a decrease in the percentage of the immobilized amount.

These figures are in approximate agreement with values calculated -with the aid of the Freundlich adsorption isotherm (see p. 134) but no definite conclusions may be drawn from them since the actual area of liquid-liquid interface in all probability was variable being dependent on the amount of emulsifying agent present. More recently the quantity of various soaps required to form a stable emulsion of kerosene in water has been determined by Grifiin (J.A.C.8. XLV. 1648, 1923) for sodium oleate, potassium stearate and potassium palmitate and by der Meulen and Riemann ibid. XLVI. 876, 1924) for sodium ricinoleate. 

Freundlich adsorption isotherm constants for several compounds on several adsorbents/water systems at ambient temperature... 

Cremer and Fliigge have suggested for the derivation of the Ostwald-Freundlich adsorption isotherm (29) that the energy of desorption from a catalyst possessing many kinds of such surface centers is a linear function of the energy E. Thus... 

This is the well-known Freundlich adsorption-isotherm Both a and n are functions of temperature. 

Equation (135) is the well-known Freundlich adsorption isotherm. In a number of instances this isotherm accurately describes experimental data. The interpretation of the Freundlich adsorption isotherm as resulting from exponential nonuniformity of surface is due to Zel dovich 43). 

In the Freundlich adsorption isotherm, the amount adsorbed is proportional to a fractional power of the pressure of the adsorptive. For a particular system, the fractional power and the constant of proportionality are functions of temperature. In terms of coverage the isotherm assumes the form... 

Freundlich adsorption isotherm — The empirical adsorption isotherm 0 = bcn (0 surface coverage, b and n are constant, 0 < n < 1, and c is the solution concentration) was initially proposed by Boedecker in 1895 [i], however it was popularized by -> Freundlich [ii], and today is generally referred to as the Freundlich adsorption isotherm [iii]. 

The variation of adsorption with pressure at a given constant temperature is generally expressed graphically as shown in the figure given above. Each curve is known as adsorption isotherm for a particular temperature. The relation ship between the magnitude of adsorption and pressure can be expressed mathematically by a empirically equation commonly known as Freundlich adsorption isotherm, viz. 

For most surfaces are heterogeneous so that K in Eq. 6.22 will vary with 9 and may be attributed entirely to the variation in the heat of adsorption. Which taken into account reduces to Freundlich adsorption isotherm... 

Freundlich adsorption Isotherm see adsorption Isotherm friction 1.4.3, 1.6.10... 

Molecular or ion-pair adsorption The adsorption of potassium bromate on the surface of barium sulfate appears to involve the simultaneous occupation of adjacent sites on the crystal surface by potassium ions and bromate ions this is called an equivalent adsorption because equal amounts of the two ions are adsorbed. Such adsorptions, and in fact many molecular adsorption processes, follow an empirical equation known as the Freundlich adsorption isotherm ... 

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