langmuir isotherm

Langmuir Adsorption Isotherm 

In 1916 Langmuir proposed his theory which said that adsorption of a gas on the surface of a solid to be made up of elementary sites each of which could absorb one gas molecule.
It is assumed that all the adsorption sites are equivalent and the ability of the gas molecule to get bound to any one site is independent of whether the neighboring sites are occupied or not.
It is further assumed that a dynamic equilibrium exists between the adsorbed molecule and the free molecule.
If A is the gas molecule and M is the surface site then,

Where “Ka” and “Kd” are the rate constants for adsorption and desorption, respectively.

The rate of adsorption is proportional to the pressure of A, viz, PA and number of vacant sites on the surface, viz, N(1-θ)  where N is the total number of sites and θis the fraction of surface sites occupied by the gas molecules, i.e.

θ =  Number of adsorptions sites occupied / Number of adsorptions sites are available

Thus the rate of adsorption = kapAN(1- θ)                  ……. (1)

The rate of desorption is proportional to the number or adsorbed molecules, Nθ .

Thus the rate of desorption = kd                              ……. (2)

Since at equilibrium, the rate of adsorption is equal to the Rate of desorption, we can write from equation (1) and (2)

KapAN(1-θ) = kd                                             ……. (3)

Or,       KpA(1-θ) = θ                                                      ……. (4)

where,  K = ka / Kd

Equation (4), may thus be written as

(1-θ) / θ = 1 / KpA                                               ……. (5)

Or,      (1 / θ) – 1 = 1 / KpA                                             ……. (6)

 (1 / θ) = (1 / KpA ) + 1 = (1 + KpA) / KpA           ……. (7)


Hence,   θ = KpA/ (1 + KpA )                                         ……. (8)

Equation (8) is called the “Langmuir adsorption isotherm”.

The following five assumptions are involved in derivation of the Langmuir adsorption isotherm:

1.    1. The absorbed gas behaves ideally in the vapour phase.

2.    2. Only a monolayer is formed by the adsorbed gas.

3.    3. The surface of the solid is homogeneous so that each binding site has the same affinity for the gas molecules.

4.    4. There is no lateral interaction between the adsorbate molecules.

5.    5. The adsorbed gas molecules are localized, i.e. they do not move around on the surface.

            The first assumption holds at low pressure, the second assumption breaks down when the pressure of the gas is increased. The third assumption is not strictly true because the real surfaces are quite heterogeneous so that affinity for gas molecule is different at different sites. Crystal imperfections and cracks lead to the creation of different sites on the surface. The fourth and fifth assumptions, too, are not strictly valid.

What are the 7 types of Crystals

7-types of crystals: 

On the basis of axial length in x,y, z-direction, and interfacial angles between them,unit cell can be classified into seven types which are called Seven Crystal System.

7- Crystal Habits
Axial Length
Interfacial Angles
a = b = c        
α = β = γ = 90˚
a = b c        
α = β = γ =90˚
a ≠ b ≠ c        
α = β = γ =90˚
a ≠ b ≠ c        
α = γ =90˚ ,  β 90˚
a ≠ b ≠ c        
α β γ 90˚
a = b ≠ c        
α = β = 90 ˚ , γ =120˚
a = b = c        
α = β = γ 90˚

Where a,b,c is the length of x,y and z-axis respectively.

α,β,γ  is the interfacial angle between x-axis and y-axis, y-axis and z-axis, z-axis and x-axis respectively.


Most symmetric crystal -Cubic Crystal
Most unsymmetric crystal -Triclinic Crystal
To remember this crystal system we have derived a formula and i.e. 
            CUTE OUR MOTHER


What is unit cell? 

The smallest part of the complete space lattice which on repetition again and again in all the possible direction results in the formation of crystal lattice/space lattice is called a unit cell. 

Contribution of a lattice point at a particular position:

location             Contribution
Body center       1
Face center        1/2
Edge center       1/4
Corner               1/8

Classification of the unit cell?

On the basis of the location of the lattice point within the unit cell, there may be two types of unit cells.

1st classification of unit cell

1.Primitive unit cell

In this type of unit cell lattice points are present only at corners.
For example SCC(Simple Cubic Unit Cell)
Lattice points at the corner
Coordination number(Z)=8*1/8=1

2.Non-Primitive unit cell

In this type of unit cell lattice points are present not only at corners but also at some other specific position. For example,
(a)BCC(Body center cubic unit cell)
Coordination number(Z)=Lattice point at corner+Lattice point at the body
(b)FCC(Face center cubic unit cell)
Coordination number(Z)=Lattice point at all corner+lattice point at each face
Where the coordination number(Z)is the total number of particles or atoms or lattice points per unit cell.

2nd classification of unit cell:

On the basis of axial length in x,y, z-direction, and interfacial angles unit cell can be classified into 7 types which are called seven crystal system or seven crystal habits and these are Cubic, Tetragonal, Orthorhombic(Rhombic), Monoclinic, Triclinic, Hexagonal, Rhombohedral.

For brief understanding about the above seven crystals, follow the link below:


What is metal carbonyls? 
Carbon monoxide is undoubtedly one of the most important and most widely studied ligand in organometallic chemistry. Almost all of the transition metals from metal carbonyls (the complex containing only CO as ligands)and these homoleptic carbonyls are useful precursors for other organometallic compounds.
Though carbon monoxide is not considered as a very strong lewis base, yet it forms a strong bond to the metals in their complexes.
In most of the metal carbonyls, the metals are always in low oxidation state, most often in the oxidation state of zero but sometimes -1 or +1, and these carbonyls are often quite stable with respect to dissociation, substitution or oxidation.CO may bond to a single metal or it may act as a bridge between two or more metals. The number of CO ligands considered to the metal is generally in accordance with the 18-electron rule and this rule is followed by 99% of the metal carbonyls.
Classification of Metal Carbonyls: 

1.Classification on the basis of ligands:

Metal carbonyls can be classified into two categories:

(i)Homoleptic carbonyl complexes: The complex in which the metal is bound to only CO as ligands are known as homoleptic carbonyl complexes.for example, Ni(CO)4, Cr(CO)6,Fe(CO)5,Co2(CO)8,Mn2(CO)10,Fe3(CO)12,Ir4(CO)12 etc.

(ii)Heteroleptic carbonyl complexes: The complexes in which a metal is bound to CO as well as other ligands such as PR3,PPh3,PF3,NO.RNC etc.For example, Ni(CO)3PPh3,Mo(CO)3(PF3)3,Cr(CO)3(NO)2 etc.

2.Classification on the basis of a number of metal atoms and the structures of Metal Carbonyls:

(i)Mononuclear Metal Carbonyls: These carbonyls contain only one metallic atom and these carbonyls do not contain any bridging CO ligand.For example Ni(CO)4,Cr(CO)6,Fe(CO)5 etc.

(ii)Polynuclear Metal Carbonyls: Polynuclear carbonyls contain only one or two metal atoms and these are classified as 

(a)Homonuclear Metal Carbonyls: These contain metal atoms of only one element.For example Fe2(CO)9,Mn2(CO)10,Co2(CO)8,Fe3(CO)12,Co4(CO)12,Rh4(CO)12,Ir4(CO)12 etc.
(b)Heteronuclear Metal Carbonyls: These carbonyls contain metals of different elements.For example,MnCo(CO)4
The polynuclear metal carbonyls are also classified as:
(a)Non-bridged Metal Carbonyls: These carbonyls contain terminal CO ligand and M-M bonds.For example,Co2(CO)8 (In solution),Mn2(CO)10,Ir4(CO)12 etc.
(b)Bridged Metal Carbonyls: These carbonyls contain bridged as well as terminal CO ligands and M-M bonds.For example,Fe2(CO)9,Co2(CO)8 (in solid state),Fe3(CO)12 etc.

Bio Inorganic Chemistry

        Bioinorganic chemistry is a field that examines the role of metals in biology. It is the gateway of inorganic chemistry and biochemistry i.e, it describes the mutual relationship between these two sub-disciplines, with the focus upon the function of inorganic substances in living systems, including the transport, speciation and eventually, mineralization of inorganic materials, and including the use of inorganics in medicinal therapy and diagnosis. These substances can be metal ions, composite ions, coordination compounds, or inorganic molecules.
Or,  Bio-inorganic chemistry is a multi-disciplinary field that draws on expertise in biochemistry, chemistry, crystallography, genetics, medicine, microbiology together with the effective application of advanced physical methods. 

Types of Adsorption

Different types of Adsorption

Adsorption may be  classified into flowing types i.e. 
(a) On the basis of concentration
(b)On the basis of nature of force existing between adsorbate and adsorbent molecule

(a)On the basis of concentration 

On the basis of concentration of adsorbate, molecule adsorption can be of following two types
(1)Positive Adsorption
(2)Negative Adsorption

(1)Positive Adsorption:

  • If the concentration of adsorbate is more on the surface as compared to its concentration in the bulk then it is called positive adsorption.
  • For example, when a concentrated solution of KCL is shaken with blood charcoal, it shows positive adsorption.

(2)Negative Adsorption: 

  • If the concentration of adsorbate is less than its concentration in the bulk then it is called negative adsorption.
  • For example, when a dilute solution of KCL is shaken with blood charcoal, it shows positive adsorption.

(b)On the basis of nature of force existing between adsorbate and adsorbent molecule:

On the basis of nature of force existing between adsorbate and adsorbent molecule adsorption again of following two types i.e.
(1)Physical Adsorption or Vanderwaals Adsorption
(2)Chemical Adsorption or Activated adsorption

(1)Physical Adsorption or Vanderwaals Adsorption:

If the physical or Vander Waals’ force of attraction hold the adsorbate molecule to the surface of the adsorbent, it is termed as physical adsorption(physisorption). Since physical forces involve Vander walls’ forces it is,
  • Reversible
  • Involves physical forces
  • Appreciable only at low temperature below the boiling point of adsorbate
  • Not very specific
  • Cause multilayer adsorption
  • Generally has geat of adsorption less than 10 KCal/mol.
  • Due to the formation of multilayers, physical adsorption decreases after sometimes.

(2)Chemical Adsorption or Activated Adsorption:

If the chemical forces hold the adsorbate molecule to the surface of the adsorbent, it is termed as chemical adsorption(chemisorption). Since activated chemisorbent involves a high degree of specificity like chemical forces, the chemisorption is 
  • Irreversible
  • Involves transfer of electrons between gas and solid
  • Appreciable at high temperature 
  • Maybe rapid as well as slow
  • May involve activation energy in the adsorption process
  • Highly specific
  • Leads almost to monolayer
  • Generally has the heat of adsorption greater than about 20 KCal/mol