Adsorption is a process that occurs when a gas or liquid solute accumulates on the surface of a solid or a liquid (adsorbent), forming a film of molecules or atoms (the adsorbate). In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances In Chemistry and Surface science, an adsorbate is a substance adhered to a surface (the adsorbent It is different from absorption, in which a substance diffuses into a liquid or solid to form a solution. Absorption, in Chemistry, is a physical or chemical Phenomenon or a process in which Atoms Molecules, or Ions enter some The term sorption encompasses both processes, while desorption is the reverse process. Sorption refers to the action of both absorption and Adsorption taking place simultaneously Desorption is a Phenomenon whereby a substance is released from or through a surface

Adsorption is present in many natural physical, biological, and chemical systems, and is widely used in industrial applications such as activated charcoal, synthetic resins, and water purification. Adsorption, ion exchange, and chromatography are sorption processes in which certain adsorbates are selectively transferred from the fluid phase to the surface of insoluble, rigid particles suspended in a vessel or packed in a column. Ion exchange is an exchange of Ions between two Electrolytes or between an electrolyte Solution and a complex. Chromatography (from Greek χρώμα chroma, color and γραφειν"graphein" to write is the collective term for a family of Laboratory

## Isotherms

Adsorption is usually described through isotherms, that is, the amount of adsorbate on the adsorbent as a function of its pressure (if gas) or concentration (if liquid) at constant temperature. The quantity adsorbed is nearly always normalized by the mass of the adsorbent to allow comparison of different materials.

The first mathematical fit to an isotherm was published by Freundlich and Küster (1894) and is a purely empirical formula for gaseous adsorbates,

$\frac{x}{m}=kP^{\frac{1}{n}}$

where x is the quantity adsorbed, m is the mass of the adsorbent, P is the pressure of adsorbate and k and n are empirical constants for each adsorbent-adsorbate pair at a given temperature. The function has an asymptotic maximum as pressure increases without bound. As the temperature increases, the constants k and n change to reflect the empirical observation that the quantity adsorbed rises more slowly and higher pressures are required to saturate the surface.

### Langmuir

In 1916, Irving Langmuir published a new model isotherm for gases adsorbed on solids, which retained his name. The Langmuir equation or Langmuir isotherm or Langmuir adsorption equation relates the coverage or Adsorption of molecules on a solid surface to Gas Irving Langmuir ( January 31, 1881 in Brooklyn New York – August 16, 1957 in Woods Hole Massachusetts) was an It is a semi-empirical isotherm derived from a proposed kinetic mechanism. It is based on four assumptions:

1. The surface of the adsorbent is uniform, that is, all the adsorption sites are equivalent.
2. Adsorbed molecules do not interact.
3. All adsorption occurs through the same mechanism.

These four assumptions are seldom all true: there are always imperfections on the surface, adsorbed molecules are not necessarily inert, and the mechanism is clearly not the same for the very first molecules to adsorb as for the last. The fourth condition is the most troublesome, as frequently more molecules will adsorb on the monolayer; this problem is addressed by the BET isotherm for relatively flat (non-microporous) surfaces. A microporous material is a material containing pores with diameters less than 2 nm The Langmuir isotherm is nonetheless the first choice for most models of adsorption, and has many applications in surface kinetics (usually called Langmuir-Hinshelwood kinetics) and thermodynamics. By reactions on surfaces it is understood reactions in which at least one of the steps of the Reaction mechanism is the Adsorption of one or more reactants

Langmuir suggested that adsorption takes place through this mechanism: A(g) + S AS, where A is a gas molecule and S is an adsorption site.

The direct and inverse rate constants are k and k-1. If we define surface coverage, θ, as the fraction of the adsorption sites occupied, in the equilibrium we have

$K=\frac{k}{k_{-1}}=\frac{\theta}{(1-\theta)P}$ or $\theta=\frac{KP}{1+KP}.$

Where P is the partial pressure (gas) or the molar concentration of the solution (liquid)

For very low pressures $\theta\approx KP$ and for high pressures $\theta\approx1$

θ is difficult to measure experimentally; usually, the adsorbate is a gas and the quantity adsorbed is given in moles, grams, or gas volumes at standard temperature and pressure (STP) per gram of adsorbent. In Physical sciences standard conditions for temperature and pressure are Standard sets of conditions for experimental measurements to allow comparisons to be made If we call vmon the STP volume of adsorbate required to form a monolayer on the adsorbent (per gram of adsorbent), $\theta = \frac{v}{v_\mathrm{mon}}$ and we obtain an expression for a straight line:

$\frac{1}{v}=\frac{1}{Kv_\mathrm{mon}}\frac{1}{P}+\frac{1}{v_\mathrm{mon}}.$

Through its slope and y-intercept we can obtain vmon and K, which are constants for each adsorbent/adsorbate pair at a given temperature. vmon is related to the number of adsorption sites through the ideal gas law. The ideal gas law is the Equation of state of a hypothetical Ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834 If we assume that the number of sites is just the whole area of the solid divided into the cross section of the adsorbate molecules, we can easily calculate the surface area of the adsorbent. The surface area of an adsorbent depends on its structure; the more pores it has, the greater the area, which has a big influence on reactions on surfaces. By reactions on surfaces it is understood reactions in which at least one of the steps of the Reaction mechanism is the Adsorption of one or more reactants

If more than one gas adsorbs on the surface, we define θE as the fraction of empty sites and we have

$\theta_E=\frac{1}{\displaystyle 1+\sum_{i=1}^n K_iP_i}$

and

$\theta_j=\frac{K_jP_j}{\displaystyle 1+\sum_{i=1}^n K_iP_i}$

where i is each one of the gases that adsorb.

### BET

Often molecules do form multilayers, that is, some are adsorbed on already adsorbed molecules and the Langmuir isotherm is not valid. In 1938 Stephan Brunauer, Paul Emmett, and Edward Teller developed a model isotherm that takes that possibility into account. Edward Teller (original Hungarian name Teller Ede) (January 15 1908 &ndash September 9 2003 was a Hungarian -American theoretical Physicist Their theory is called BET Theory, after the initials in their last names. They modified Langmuir's mechanism as follows:

A(g) + S AS
A(g) + AS A2S
A(g) + A2S A3S and so on
Langmuir isotherm (red) and BET isotherm (green)

The derivation of the formula is more complicated than Langmuir's (see links for complete derivation). We obtain:

$\frac{x}{v(1-x)}=\frac{1}{v_\mathrm{mon}c}+\frac{x(c-1)}{v_\mathrm{mon}c}.$

x is the pressure divided by the vapor pressure for the adsorbate at that temperature (usually denoted P / P0), v is the STP volume of adsorbed adsorbate, vmon is the STP volume of the amount of adsorbate required to form a monolayer and c is the equilibrium constant K we used in Langmuir isotherm multiplied by the vapor pressure of the adsorbate. Vapor pressure (also known as equilibrium vapor pressure or saturation vapor pressure) is the Pressure of a Vapor in equilibrium The key assumption used in deriving the BET equation that the successive heats of adsorption for all layers except the first are equal to the heat of condensation of the adsorbate.

The Langmuir isotherm is usually better for chemisorption and the BET isotherm works better for physisorption for non-microporous surfaces.

Adsorption constants are equilibrium constants, therefore they obey van 't Hoff's equation:

$\left( \frac{\partial \ln K}{\partial \frac{1}{T}} \right)_\theta=-\frac{\Delta H}{R}.$

As can be seen in the formula, the variation of K must be isosteric, that is, at constant coverage. Jacobus Henricus van 't Hoff ( August 30, 1852 &ndash March 1, 1911) was a Dutch physical and organic chemist If we start from the BET isotherm and assume that the entropy change is the same for liquefaction and adsorption we obtain ΔHads = ΔHliqRTlnc, that is to say, adsorption is more exothermic than liquefaction.

### Characteristics and general requirements

Activated carbon is used as an adsorbent

Adsorbents are used usually in the form of spherical pellets, rods, moldings, or monoliths with hydrodynamic diameters between 0. 5 and 10 mm. They must have high abrasion resistance, high thermal stability and small pore diameters, which results in higher exposed surface area and hence high surface capacity for adsorption. The adsorbents must also have a distinct pore structure which enables fast transport of the gaseous vapors.

Most industrial adsorbents fall into one of three classes:

• Oxygen-containing compounds – Are typically hydrophilic and polar, including materials such as silica gel and zeolites. Silica gel is a granular porous form of Silica made synthetically from Sodium silicate. Zeolites (Greek zein, "to boil" lithos, "a stone" are hydrated Aluminosilicate Minerals and have a micro-porous structure
• Carbon-based compounds – Are typically hydrophobic and non-polar, including materials such as activated carbon and graphite.
• Polymer-based compounds - Are polar or non-polar functional groups in a porous polymer matrix.

### Silica gel

Main article: silica gel

Silica gel is a chemically inert, nontoxic, polar and dimensionally stable (< 400 °C) amorphous form of SiO2. Silica gel is a granular porous form of Silica made synthetically from Sodium silicate. It is prepared by the reaction between sodium silicate and sulfuric acid, which is followed by a series of after-treatment processes such as aging, pickling, etc. These after treatment methods results in various pore size distributions.

Silica is used for drying of process air (e. g. oxygen, natural gas) and adsorption of heavy (polar) hydrocarbons from natural gas.

### Zeolites

Main article: zeolite

Zeolites are natural or synthetic crystalline aluminosilicates which have a repeating pore network and release water at high temperature. Zeolites (Greek zein, "to boil" lithos, "a stone" are hydrated Aluminosilicate Minerals and have a micro-porous structure Zeolites are polar in nature.

They are manufactured by hydrothermal synthesis of sodium aluminosilicate or another silica source in an autoclave followed by ion exchange with certain cations (Na+, Li+, Ca2+, K+, NH4+). The channel diameter of zeolite cages usually ranges from 2 to 9 Å (200 to 900 pm). An ångström or angstrom (symbol Å) (ˈɔːŋstrəm Swedish: ˈɔ̀ŋstrœm is an internationally recognized non- SI unit of length equal A picometre ( American spelling: picometer, symbol pm) is a unit of Length in the Metric system, equal to one trillionth The ion exchange process is followed by drying of the crystals, which can be pelletized with a binder to form macroporous pellets.

Zeolites are applied in drying of process air, CO2 removal from natural gas, CO removal from reforming gas, air separation, catalytic cracking, and catalytic synthesis and reforming.

Non-polar (siliceous) zeolites are synthesized from aluminum-free silica sources or by dealumination of aluminum-containing zeolites. The dealumination process is done by treating the zeolite with steam at elevated temperatures, typically greater than 500 °C (1000 °F). This high temperature heat treatment breaks the aluminum-oxygen bonds and the aluminum atom is expelled from the zeolite framework.

### Activated carbon

Main article: activated carbon

Activated carbon is a highly porous, amorphous solid consisting of microcrystallites with a graphite lattice, usually prepared in small pellets or a powder. Activated carbon, also called activated charcoal or activated coal, is a form of Carbon that has been processed to make it extremely porous and thus to It is non-polar and cheap. One of its main drawbacks is that it is combustible.

Activated carbon nitrogen isotherm showing a marked microporous type I behavior

Activated carbon can be manufactured from carbonaceous material, including coal (bituminous, subbituminous, and lignite), peat, wood, or nutshells (i. e. , coconut). The manufacturing process consists of two phases, carbonization and activation. The carbonization process includes drying and then heating to separate by-products, including tars and other hydrocarbons, from the raw material, as well as to drive off any gases generated. The carbonization process is completed by heating the material at 400–600 °C in an oxygen-deficient atmosphere that cannot support combustion.

The carbonized particles are “activated” by exposing them to an oxidizing agent, usually steam or carbon dioxide at high temperature. This agent burns off the pore blocking structures created during the carbonization phase and so, they develop a porous, three-dimensional graphite lattice structure. The size of the pores developed during activation is a function of the time that they treated in this stage. Longer exposure times result in larger pore sizes. The most popular aqueous phase carbons are bituminous based because of their hardness, abrasion resistance, pore size distribution, and low cost, but their effectiveness needs to be tested in each application to determine the optimal product.

Activated carbon is used for adsorption of organic substances and non-polar adsorbates and it is also usually used for waste gas (and waste water) treatment. It is the most widely used adsorbent. Its usefulness derives mainly from its large micropore and mesopore volumes and the resulting high surface area.

Portal site mediated adsorption is a model for site-selective activated gas adsorption in metallic catalytic systems which contain a variety of different adsorption sites. In such systems, low-coordination "edge and corner" defect-like sites can exhibit significantly lower adsorption enthalpies than high-coordination (basal plane) sites. As a result, these sites can serve as "portals" for very rapid adsorption to the rest of the surface. The phenomena relies on the common "spillover" effect, where certain adsorbed species exhibit high mobility on some surfaces. The model explains seemingly inconsistent observations of gas adsorption thermodynamics and kinetics in catalytic systems where surfaces can exist in a range of coordination structures, and it has been successfully applied to bimetallic catalytic systems where synergistic activity is observed.

The original model was developed by King and co-workers (Narayan et al. 1998 and VanderWiel et al. 1999) to describe hydrogen adsorption on silica-supported silver-ruthenium and copper-ruthenium bimetallic catalysts. The same group applied the model to CO hydrogenation (Fischer-Tropsch synthesis). Zupanc et al. (2002) subsequently confirmed the same model on magnesia-supported cesium-ruthenium bimetallic catalysts.