Showing papers on "Freundlich equation published in 1972"

On thermodynamics of adsorption in micropores

Abstract: Adsorption on a nonporous, nonswelling adsorbent and adsorption in micropores represent two limiting cases of physical adsorption which are clearly distinguishable thermodynamically. In the first case, the chemical potential of the adsorbent is independent of the amount of the adsorbed substance; in the second case, it varies with it. The works of Brunauer, which made a whole epoch in the theory of adsorption, belong to the first type of adsorption phenomena; adsorption in micropores, however, is beyond the framework of his investigations. It should be treated in terms of volume filling, and not of layer-by-layer coverage of the surface. In computational methods of the theory in hand, a substantial role is played by the concept of the temperature invariance of free energy of adsorption as a function of the degree of filling. An analysis of this concept is given and the limits of its applicability are assessed. Exact and approximate expressions for the calculation of the basic thermodynamic functions in adsorption in micropores have been obtained. A generalized thermal equation of adsorption, i.e., ψ(θ, p, T) = 0, applicable to the quantitative description of adsorption of molecules sharply differing in electronic structure on microporous adsorbents widely different in nature (active carbons, zeolites, etc.) is considered.

Multilayer adsorption on heterogeneous surfaces

Abstract: Although adsorption forces are usually short range in character, multilayer adsorption also concerns the energetic heterogeneity of the adsorbing surface. In this paper we assume that each energetically homogeneous patch forming the heterogeneous surface follows the Brunauer, Emmett, and Teller (BET) adsorption isotherm, while in the submonolayer range the whole surface follows the Dubinin and Radushkevich (DR) isotherm. By so assuming we are able to obtain the multilayer adsorption isotherm for the whole heterogeneous surface, and to compare BET and DR surface areas.

Adsorption isotherms and equations of state of insoluble vapors at the water-gas interface as studied by gas chromatography

Abstract: : In continuation of previous work on the study of water at interfaces by gas chromatography, the gas-liquid interfacial adsorption isotherms of six insoluble vapors (three n-alkanes and three branched alkanes) have been determined in the range of 4000 sq A /molecule to 500 sq A/ molecule. From these isotherms, isosteric heats of adsorption have been derived, and it has been shown that over the whole concentration range examined the isosteric heat of adsorption is equal to or less than the heat of liquefaction. This points to the fact that water is a low energy surface for hydrocarbons. The free energy of adsorption and the entropy of adsorption at constant surface coverage have been also calculated. Equations of state have been determined. Finally, calculations of thickness of the surface films indicate that the hydrocarbons can be considered to lie flat on the water surface in most cases over the whole concentration range studied. (Author)

The Hydrogen–Oxygen Reaction on Lanthanide Oxides. I. Hydrogen and Oxygen Adsorption on Some Lanthanide Oxides

Abstract: Hydrogen and oxygen adsorption have been measured on neodymium oxide and dysprosium oxide from 77 to 771 °K up to equilibrium pressures of approximately 6 Torr. In addition, hydrogen adsorption measurements have been made on samarium oxide and gadolinium oxide from 77 °K to approximately 100 °K. The adsorption is effectively instantaneous in all cases except for oxygen adsorption on neodymium oxide at 491 and 541 °K. Adsorption appears to be dissociative for all cases studied except for hydrogen adsorption on neodymium oxide at all temperatures and for hydrogen adsorption on dysprosium oxide at high temperatures. For neodymium oxide and dysprosium oxide three types of adsorption are observed in different temperature ranges. At low temperatures, the adsorption is probably physical; at intermediate temperatures, it is either physical, or chemical on isolated double sites; and at high temperatures it is chemical. In general, the Freundlich isotherm gives the highest correlation between calculated and experim...

Hexamethylenetetramine Hydroiodide (HMTA-I) as a Corrosion Inhibitor for Steel in HCI Pickling Solutions

Abstract: The effect of hexamethy lenetetramine. hydroiodide (HMTA-I) as a corrosion inhibitor of steel in aqueous hydrochloric acid solutiOns has been investigated and its behaviourexamined as a function of HCI and inhibitor concentrations.A comparison with the inhibitive efficiency of hexamethylenetetramine (HMTA) shows that HMTA-I iS more efficient than HMTA, espcially at lower acid concentrations.Polarisation mesaurements show that the chemisorption of iodide anions and organic cations increases the overpotential for both hydrogen-ion discharge and metal ionisation.The adsorption oforganic cations, which in the case of HMTA is appreciable only at high HCI concentrations, iS enhanced in the case of HMTA-I by iodide adsorption at anodic areas.The surface coverage in 2M HCl has been calculated and the semi-empirical isotherm of Freundlich has been found to fit the results over the entire range of inhibitor concentration studied (up to 10–2M ).

Kinetics of Adsorption in the Case of the Rectangular Adsorption Isotherm

Abstract: Here, c is the sórbate concentration in the pore volume, expressed in grams per unit pore volume; a is the concentration of the adsórbate bound to the solid skeleton of the particle, expressed in grams per a unit pore volume; D is a constant characterizing the internal diffusion within the adsorbent particle (it is assumed that D is independent of the adsórbate concentration); t is the time coordinate; r is the space coordinate measured from the center of the adsorbent particle; v is the shape factor of the adsorbent particle, its value being 3 for a sphere of the radius R, 2 for an infinite cylinder of the radius R, and 1 for an infinite plate with thickness 2R; eqn. (2) expresses the adsorption isotherm. The statistical moments of the kinetic curves are given by the formula:

Effects of water composition on fluoride removal

Abstract: The effects of water composition as they apply to the design of virgin and regenerated activated alumina and virgin and regenerated bone char defluoridation units were studied. Freundlich isotherm analysis was used to determine the degree of the effect compared to an arbitrary standard. The results showed that ionic strength, divalent metal ions, arsenic, and pH connected to buffering capacity have significant effects. The anions sulfate, nitrate, and chloride showed negligible effect on the removal of fluoride.

Exponential virial expansion for adsorption isotherm

Abstract: A new virial equation for adsorption isotherm is proposed based on the idea of the Starling's exponential virial expansion.

Kinetics of Batch Adsorption on Active Carbon from Aqueous Fuchsine Solution

Abstract: To investigate the kinetic data of batch adsorption of dye-component from its aqueous solution by powdered active carbon, an adsorption isotherm equation of Freundlich was determined at , for the range of concentration between and grams of Fuchsine per liter of solution. Applying the homogeneous diffusion model and the pore diffusion model, adsorption equilibrium and adsorption rate constant are discussed. For the powdered active carbon, the pore diffusion model might be better adapted than the other to the extent of fractional approach of equilibrium E=0.8. The pore diffusivity determined by the model agrees well with the value calculated by Wheeler's method. By experimental runs at , , and , respectively, the activation energy of adsorption of Magenta or Fuchsine by active carbon was determined and suggested as . per gram mole of dye.

Calculation of adsorption equilibrium of binary vapor mixtures for the case of affined isotherms

Abstract: 1. A method was discussed for calculating the values of the integral of the Biggs adsorption equation over the entire range of changes in the adsorption values of the components for the particular case where the condition of the affinity of the adsorption isotherms of binary vapor mixtures at a constant composition of the adsorption phase, and the condition of the additivity of the affinity coefficient of the adsorption solution, are fulfilled. 2. When the indicated conditions are fulfilled the method makes it possible to calculate the adsorption equilibrium of a binary vapor mixture on a solid adsorbent from two individual adsorption isotherms, without making use of the hypothesis of the ideality of adsorption solutions.

Adsorption equilibrium on discretely inhomogeneous surfaces

Abstract: 1. Various types of adsorption equilibrium on surfaces consisting of a limited number of types of adsorption centers were considered, assuming that the equation of the Langmuir adsorption isotherm is fulfilled for each of these types. 2. A method was proposed permitting a determination of the number of types of centers, their relative number, and the corresponding adsorption coefficients according to the experimental adsorption isotherms. The applicability of this method was demonstrated for the example of the adsorption of hydrogen.

Substantiation of the method of an ?ideal adsorption solution? for calculating the adsorption of binary vapor mixtures from the individual isotherms

Abstract: Substantiation was offered for the method of an “ideal adsorption solution,” which was proposed by Myers and Prausnitz to calculate the adsorption equilibrium of binary vapor mixtures with a solid adsorbent from the individual isotherms, for the particular case of adsorption systems for which is fulfilled the condition of an affinity of the adsorption isotherms of the vapor mixtures at a constant composition of the adsorption solution, and the condition of the additivity of the affinity coefficient of such a solution.