Adsorption isotherm, definition

The preceding derivation, being based on a definite mechanical picture, is easy to follow intuitively kinetic derivations of an equilibrium relationship suffer from a common disadvantage, namely, that they usually assume more than is necessary. It is quite possible to obtain the Langmuir equation (as well as other adsorption isotherm equations) from examination of the statistical thermodynamics of the two states involved. 

One should realize that adsorption isotherms are purely descriptions of macroscopic data and do not definitively prove a reaction mechanism. Mechanisms must be gleaned from molecular investigations (e.g., the use of spectroscopic techniques). Thus the conformity of experimental adsorption data to a particular isotherm does not indicate that this is a unique description of the experimental data, and that only adsorption is in operation. 

Hollabaugh and Chessick (301) concluded from adsorption studies with water, m-propanol, and w-butyl chloride that the surface of rutile is covered with hydroxyl groups. After evacuation at 450°, a definite chemisorption of water vapor was observed as well as of n-propanol. The adsorption of -butyl chloride was very little influenced by the outgassing temperature of the rutile sample (90 and 450°). A type I adsorption isotherm was observed after outgassing at 450°. Apparently surface esters had formed, forming a hydrocarbonlike surface. No further vapor was physically adsorbed up to high relative pressures. 

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. 

It is convenient to divide the extent of adsorption into three categories submonolayer, monolayer, and multilayer. We discuss them in this order. The thermodynamics of adsorption may be developed around experimental isotherms or around calorimetric data. We begin with the definition of adsorption isotherms and how they are determined experimentally (Section 9.2). 

When the crystal surface contains sites of different adsorption energies the adsorbate will condense area by area. According to Predali and Cases89) the adsorption isotherm will be steplike in relation to condensation of molecules on areas i, and each step i is compared with sites having the same energy 0 j. Developing the isotherm with condensation on inhomogenous surfaces they start with the definition of the fraction of sites a and /S on which condensation occurs between undersaturation Afi and dAft. When all the... 

In conclusion, definite information on the density of adsorbed interlayer water cannot be derived from the bulk density measurements. However, such measurements supplement adsorption isotherm data, and both will be helpful in the interpretation of x-ray structure analysis of the configuration of water molecules and exchange cations in the interlayer space. 

Adsorption isotherms, 178-190 Freundlich, 179 Langmuir, 183 S-type, 178-179 L-type, 178-179 C-type, 178-179 H-type, 178-179 Aerobic decomposition, 323 Alkalinity, 82—91 Definition, 88 Types of alkalinity, 82 Aluminosilicate clays, 102 Aluminum cation, 103, 160 Acidity, 160 Complexation, 160 Polymeric aluminum, 160 Exchangeable, 160,162 Hydrolysis, 69, 75 Solubility, 71 Soluble complexes, 69 Aluminum hydroxide, 78-80 Solubility, 78 pH effect, 79... 

Both the basic phosphate and Ca3(P04)2 adsorb definite quantities of Ca(OH)2. These quantities when plotted as functions of the concentrations of Ca(OH)2 have the usual form of adsorption isotherms and therefore give no evidence of the formation of definite compounds, 1 gram of the basic calcium phosphate when in equilibrium with a solution containing 1-099 grams of Ca(OH)2 per litre adsorbs 0-0201 gram of the hydroxide. After 6 months of contact this amount is increased to 0-0243 gram.1... 

The aim of this chapter is simply to introduce a selection of the most appropriate thermodynamic quantities for the processing and interpretation of adsorption isotherm and calorimetric data, which are obtained by the methods described in Chapter 3. We do not consider here the thermodynamic implications of capillary condensation, since these are dealt with in Chapter 7. Special attention is given to the terminology and the definition of certain key thermodynamic quantities, for example, the difference between corresponding molar integral quantities and differential quantities. 

A significant problem in surface complexation models is the definition of adsorption sites, The total number of proton-exchangeable sites can be determined by rapid tritium exchange with the oxide surface (25). Although surface equilibria are usually written in terms of one surface site, e.g. Equations 5, 6, 8, 9, adsorption isotherms for many ions show that the number of molecules adsorbed at maximum surface coverage (fmax) is less than the total number of surface sites. For example, uptake of Se(VI) and Cr(VI) ions on Fe(0H)3(am) at T ax 1/3 and 1/4 the total... 

The phenomenon of adsorption was introduced in sec. 1.1.2. There one can find definitions of elementary notions, including those of adsorbent, adsorbate, adsorptive, desorption, specific surface area, adsorption isotherm (equation) and two-dimensional equation of state. Adsorbed amounts can eonveniently be expressed as moles adsorbed (n ), moles adsorbed per unit area or surface concentration (F = n /A) or, if the adsorption in a monolayer r(max) is known, as... 

In fig. 1.26 the effect of sample pretreatment is illustrated. The original sample is "Cab-0-Sir, a pyrogenic silica. It has a fairly low affinity for water. The isotherm type is between II and III (fig. 1.13). No hysteresis is observed. Stronger outgasslng (fig. (b)), further reduces the affinity for water the curve is now definitely of type II but also shows considerable hysteresis which was attributed to incomplete hydroxylation. In case (c) the surface is made hydro-phobic by methylatlon. The water adsorption isotherm (not shown) remains of type II but as Nj adsorption is not determined by hydrophilic groups, the corresponding Isotherm is of type III. Again, it is hysteresis-free. By application of the theories outlined before, information can be extracted from these isotherms in terms of available areas and enthalpies of adsorption. The authors extended this work with infrared studies. 

The computation of the integral molar entropy of adsorption at any coverage requires knowledge of the adsorption isotherm " = "(p) at a given temperature combined with the calorimetric isotherm Q = Q" (p). We must emphasize the fact that Q is measured by definition under reversible conditions. Therefore, when applying Eq. (48) to experimental data, the quasireversibility of the process must be verified. 

The effect of concentration of suspended adsorbent on sorptive behavior in a seawater matrix was studied by determining adsorption isotherms for DPM and 94, 150, 200,400, and 1000 ppm humic acid. The corresponding values of Kads (Table III) show no definite trend with respect to Increased adsorbent concentration. This is not totally unexpected in view of O Connor and Connolly s observation that systems with low Kads values do not show dramatic changes of Kads with changes in suspended matter concentrations 9). Only systems with high Kads values typically show definite decreases in Kads with increases in adsorbent concentration. 

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