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 = kdNθ ……. (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) = kdNθ ……. (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.
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
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.
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:
Body center 1
Face center 1/2
Edge center 1/4
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
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.
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:
(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
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
- 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.
- 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:
(1)Physical Adsorption or Vanderwaals Adsorption:
- 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:
- 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