Freundlich

The FreundUch isotherm by itself is not widely used to describe adsorption in zeoUtes. There are a handful of isotherms, for example, O2 on Type A or X can often be fit to the Freundlich form owing to the small deviations from linearity that occur in the isotherm. This estimator has the mathematical form  

The Freundlich form is often employed along with the Langmuir form and is referred to as the Langmuir—FreundUch equation. That model is the basis of a great many useful modifications including many empirical forms that serve to describe adsorption data quite accurately. 

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Freundlich isotherm The empirical relationship between the amount of a substance adsorbed and the concentration of the solute... 

The Freundlich equation, unlike the Langmuir one, does not become linear at low... 

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. 

H. Freundlich, Colloid and Capillary Chemistry, Methuen, London, 1926. 

If the differential distribution function is exponential in Q (Section XVII-14A), the resulting Q(P, T) is that known as the Freundlich isotherm... 

The Freundlich equation is defective as a model because of the physically unrealistic/((2) consequences of this are that Henry s law is not approached at low P, nor is a limiting adsorption reached at high P. These difficulties can be patched by supposing that... 

Freundlich Isotherm. The isotherms for some systems, notably hydrocarbons on activated carbon, conform more closely to the Freundhch... 

Fig. 19. Adsorption isotherm correlation, showing Freundlich isotherm appHcation.

FreundlicVi-Type Relations A binary Freundlich isotherm, obtained from the ideal adsorbed solution theoiy in loading-explicit closed form [Crittenden et al.. Environ. Sci. TechnoL, 19, 1037 (1985)], is... 

Adsorption This is the most widely used of the physical-chemical treatment processes. It is used primarily for the removal of soluble organics with activated carbon serving as the adsorbent. Most liquid-phase-activated carbon adsorption reactions follow a Freundlich Isotherm [Eq. (25-21)]. 

Now, if the solutes interact with themselves more strongly than they do with the stationary phase, then their presence will increase the interaction of further solute with the stationary phase mixture. This gives an isotherm having the shape shown in Figure 10. This type of isotherm is called a Freundlich isotherm, the expression for... 

Figure 11. Peak Distortion Caused by a Freundlich Type Isotherm...

We wUl now touch upon some of these factors. First, let s look at what we mean by system isotherm. Freundlich liquid phase isotherm studies can be used to establish the adsorptive capacity of activated carbon over a range of different concentrations. Under standard conditions, the adsorptive capacity of activated carbon increases as the concentration increases, until we reach a point of maximum saturation capacity. An example of an isotherm for phenol is shown in Figure 8. 

The Freundlich liquid phase isotherm can be used to determine the effect of solubility on the adsorptive capacity of activated carbon over a range of different concentrations. Phenol is highly soluble due to its polar nature whilst, in comparison, tetrachloroethylene (PCE) has a low solubility due to being non-polar. In the isotherms illustrated, the concentration of phenol is low relative to its solubility limit and consequently, the adsorptive capacity peaks at 18% maximum (see Figure 9). In comparison the concentration of tetrachloroethylene is relatively close to its solubility limit and, accordingly, the adsorptive capacity is exceptionally good. 

Solubility is also affected by particle size, small crystals (<1 pm say) exhibiting a greater solubility than large ones. This relationship is quantified in the Gibbs-Thomson, Ostwald-Freundlich equation (see Mullin, 2001)... 

Freund, m. friend acquaintance, freundlich, a. friendly kind, cheerful, pleasant. Freundschait, /, friendship acquaintance favor friends, kindred. 

The isotherms for the two enantiomers of phenylalanine anilide were measured at 40, 50, 60 and 70 C, and the data fitted to each of the models given in Equations (1-3) [42]. The isotherms obtained by fitting the data to the Langmuir equation were of a quality inferior to the other two. Fittings of the data to the Freundlich and to the bi-Langmuir equations were both good. A comparison of the residuals revealed that the different isotherms of d-PA were best fitted to a bi-Langmuir model, while the... 

However, in the pH range 1-4, the effect of the OH ion predominates to such an extent that corrosion rates are similar in the presence of many other anions at concentrations less than 0.1 M. Since an adsorption process is involved in the mechanism, the corrosion rate in the pH range 1-4 may be represented by the Freundlich equation ... 

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 ... 

The dissolution of passive films is, in the main, controlled by a chemical activation step in contrast to film-free conditions at. Many protective anodic films are oxides and hydroxides whose dissolution depends upon the hydrogen ion concentration, and the rate follows a Freundlich adsorption equation ... 

For many metals and alloys the determination of /p is complex, and its magnitude is governed by many factors such as surface finish, rate of formation, alloying constituents, and the presence of those anions, such as halides, that promote localised breakdown. In many instances the attack on passive films by halide ions shows a temperature and concentration dependence similar to the effect of hydrogen ions, i.e. the rate of film dissolution increases with concentration in accordance with a Freundlich adsorption relationship... 

The corrosion rate of a metal, which depends for its protection on a passive oxide film, may be predicted from a simple empirical adsorption law (Freundlich) ... 

The arbitrary division of behaviour has been made because of the extreme behaviour of some chemicals that initiate small areas of attack on a well-passivated metal surface. The form of attack may manifest itself as stress-corrosion cracking, crevice attack or pitting. At certain temperatures and pressures, minute quantities of certain chemicals can result in this form of attack. Chloride ions, in particular, are responsible for many of the failures observed, and it can be present as an impurity in a large number of raw materials. This has led to the development of metals and alloys that can withstand pitting and crevice corrosion, but on the whole these are comparatively expensive. It has become important, therefore, to be able to predict the conditions where more conventional materials may be used. The effect of an increase in concentration on pitting corrosion follows a similar relationship to the Freundlich equation where... 

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