Isotherms saturation values

The shape of the Langmuir isotherm is shown schematically in Figure 8.8. The amount of A adsorbed increases as the (gas-phase) concentration cA increases (at a given T), but approaches a limiting ( saturation ) value at sufficiently high cA. 

The fact that Tdhpz on Au is identical to that on Pt at pH 7 is evidence that ri1-N surface-coordinated DHPz is also formed on Au at this same pH. Since (i) the DHPz isotherm on Au at pH 0 is not stepwise unlike those exhibited by compounds attached in multiple orientational states, and (ii) it has already been shown above that hydroquinone, the homoaromatic analogue of DHPz, is not chemisorbed on Au, it can be argued that i -N surface-coordination of DHPz occurs on Au at pH 0 even at coverages below the saturation value. It can be inferred further that the driving forces for protonation and Au-surface-coordination of the N heteroatom are equally competitive in molar acid. 

The adsorption of various aliphatic alcohols from benzene solutions onto silicic acid surfaces has been studied.t The experimental isotherms have an appearance consistent with the Langmuir isotherm. Both the initial slopes of an n/w versus c plot and the saturation value of n/w decrease in the order methanol > ethanol > propanol > butanol. Discuss this order in terms of the molecular structure of the alcohols and the physical significence of the initial slope and the saturation intercept. Which of these two quantities would you expect to be most sensitive to the structure of the adsorbed alcohol molecules Explain. 

The simple formulae we have just derived, although sufficiently accurate for most practical purposes, sometimes fail to represent the facts completely. Examples are known where the adsorption isotherm is linear over a considerable range of concentration in the continuous phase and then bends sharply round at the saturation value. In general, however, the simple formulae are applicable. 

Experimental isotherms from Barrer and Stuart (15) are used as a check on the present theory. Following the liquid filling theory of Dubinin (ll) and other (12, 13, lU), saturation values of for Argon on LiX at the various experimental temperatures are as follows ... 

Experimental isotherms generated by the present authors are also vised as a check on the present theory. Saturation values of... 

With different methods one can recognize different hydrates of phospholipids with different properties. Solved in different organic solvents like benzene, xylene etc. egg yolk phosphatidylcholine adsorbed water in an amount of 13.6 water/mol lipid, independently of the used organic solvent165. Studying adsorption isotherms of water vapor on lipids Elworthy166 has found saturation values at 25 °C ... 

Consider first a flat solid surface in contact with a monocomponent vapour at pressure p. Gas molecules will adsorb, more of them at higher p. The relation between the adsorbed amount and p is the adsorption isotherm, which may obey one of the isotherm equations, discussed in sec. II.1.5f-g. At issue now is what happens if p approaches its saturation value p. Under what conditions will the adsorbed layer gradually thicken, leading to complete wetting, or form separate droplets with between them either a complete or incomplete monolayer or a thin film ... 

The adsorption-desorption isotherms of nitrogen at -196 °C obtained on all the catalysts under investigation were mainly of Type IV of Brunauer s classification [16], exhibiting hysteresis loops closed at P/Po ranging between 0.25 and 0.55. The adsorption data are summarized in Table 1, including BET-C constant, specific surface area(SBEj), total pore volume (Vp), estimated from the saturation values of the adsorption isotherms and average pore radius (r P), assuming cylindrical pore model for which superscript (cp) was used. 

In the simplest case the adsorption isotherm is of the Langmuir type with a steep slope at the initial part and reaching a saturation value at higher amounts of adsorbed solute. The slope of the isotherm corresponds to the distribution coefficient K, discriminating two parts of the isotherm the linear and nonlinear parts. In the linear range K is equal to the Henry constant. For the nonlinear part K becomes... 

The potentiometric titration method possesses some advantages characteristic of potentiometry. The measured e.m.f. values are dependent on the logarithm of the activity (concentration) of the potential-defining ion and this considerably widens the range of concentrations which can be detected. The experimental techniques and routine are rather simple and the obtained results are well reproducible. Owing to the stable activity coefficients of metal cations the measurements can be performed in sufficiently concentrated solutions of the corresponding metal halides. Performing the measurement does not imply any interference in the acid-base processes in the melt studied and the experiment is faster than the isothermal saturation technique discussed above. 

As mentioned in Section 3.7.1.2, there is a considerable scatter of solubility product values obtained in the molten KCl-NaCl eutectic using different methods of solubility determination. This disagreement in the solubility parameters may be explained by differences in the sizes of oxide particles whose solubility is to be determined. The difference in size causes the scatter of the solubility data according to the Ostwald-Freundlich equation and the employment of the isothermal saturation method, which implies the use of commercial powders (often pressed and sintered), leads to values which are considerably lower than those obtained by the potentiometric titration technique where the metal-oxides are formed in situ. Owing to this fact, the regularities connected with the effect of physico-chemical parameters of the oxides or the oxide cations should be derived only from solubility data obtained under the same or similar experimental conditions. However, this does not concern the dissociation constants of the oxides, since homogeneous acid-base equilibria are not sensitive to the properties of the solid phase of... 

In addition to multisite adsorption, many gases and vapors adsorbed by solids do not produce a typical monolayer-type adsorption isotherm (Fig. 9.9a), but rather produce an isotherm indicating multilayer adsorption (Fig. 9.9c). An equation that treats multilayer adsorption is the BET equation, named after developers Brunauer, Emmett, and Teller. Multilayer adsorption is characteristic of physical or van der Waals attraction. It often proceeds with no apparent limit, since multilayer adsorption merges directly into capillary condensation as the vapor pressure of the adsorbate approaches its saturation value. 

The Freundlich isotherm has no definite maximum adsorption or saturation value therefore, when 0 approaches a monolayer, the Freundlich equation necessarily breaks down. For high coverages the exponential distribution function is conveniently replaced by a linear distribution... 

Days between -180...0 d correspond to the isothermal saturation period between the construction and the starting of the heaters. Days between 0... 53 d correspond to the heater adjustment period, which is approximated by a linear increase of the heater temperature to the final value assessed by the measurements. The temperature boundary condition at the rock is of the Robin type < =H(T-T,) with a calibrated value of the heat transfer coefficient H [W/(m K)]. 

We have thus employed the LI and its formalism to obtain two sets of parameters for the adsorption of gelatin, the initial slopes of the isotherms, the "affinities", A, and the saturation values, ag v ich we call the "capacities". In our discussion of the results, we will use the affinity data briefly for a conopari-son of the tendencies of the gelatins to become adsorbed. The capacities will be used for a description of the fully adsorbed state. We will be helped in this by our results on the hydro-dynamic thicknesses, Ar, of the adsorbed layers. The product of the areas occupied per molecule at ag and Ar, assuming mono-layers, yield the volume occupied per molecule in the interphase. 

As for determination of solubility and dissociation parameters it should be noted that this method allows to determine values only if tho potentiometric curve contains the non-saturated solution region. Studies in the wide temperature range are impeded as compared with the isothermal saturation method. 

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