Chemistry Notes for class 12
Chapter-1 The Solid State
Solids
Solids are the chemical substances which are characterised by define shape and volume,
rigidity, high density, low compressibility. The constituent particles (atoms, molecules or ions)
are closely packed and held together by strong interparticle forces
Types of Solids
The solids are of two types : Crystalline solids and amorphous solids.
Packing Fraction
It is defined as the ratio of the volume of the unit cell that is occupied by the spheres to the volume of the unit cell.
(i) Primitive cubic unit cell Atoms touch each other along edges.
Hence, d = a or r = a / 2
(r = radius of atom and a = edge length)
Therefore, PF = 4 / 3 πr3 / (2r)3 = 0.524 or 52.4%
(ii) Face centred cubic unit cell Atoms touch each other along the face diagonal.
Hence, d = a / √2
or r = √2a / 4
Therefore; PF = 4 * 4 / 3 πr3 / (4r / √2)r3 = 0.74 or 74%
(iii) Body centred cubic unit cell Atoms touch each other along the body diagonal.
Hence, √3a / 2
or r = √3a / 4
Therefore; PF = 2 * 4 / 3 πr3 / (4r / √3)r3 = 0.68 or 68%
Coordination Number
It is defined as the number of particles immediately adjacent to each particle in the crystal
lattice.
[In simple cubic lattice, CN is 6, in body centred lattice, CN is 8 and in face centred cubic
lattice, CN is 12].
High pressure increases CN and high temperature decreases the CN.
Close Packing in Crystals
Two Dimensional Packing of Constituent Particles
(i) Square close packing Space occupied by spheres is 52.4%.
(ii) Hexagonal close packing Space occupied by spheres is 60.4%.Hence. It is more efficient.
Three Dimensional Packing of Constituent Particles
(i) ABAB arrangement gives hexagonal close packing (hcp).
(ii) ABCABC arrangement gives cubic close packing or face centred CUbIC packing (ccp or fcc).
* In both these arrangements 740/0 space is occupied
* Coordination number in hop and ccp arrangement is 12 while in bcc arrangement, it is 8.
* Close packing of atoms in cubic structure = fcc > bcc > sc.
* All noble gases have ccp structure except He (hcp structure).
Void or Space or Holes
Empty or vacant space present bet veen spheres of a unit cell, is called void or space or hole or interstitial void. When particles are closed packed resulting in either cpp or hcp structure, two types of voids are generated:
Tetrahedral voids are holes or voids surrounded by four spheres Present at the corner of a tetrahedron. Coordination number of a tetrahedral void is 4.
Octahedral voids are holes surrounded by six spheres located on a regular tetrahedron.
Coordination number of octahedral void is 6.
[The number of octahedral voids present in a lattice is equal to the number of close packed
particles. The number of tetrahedral voids present in a lattice is twice to the number of close packed particles.]
Density of Unit Cell (d)
Density of unit ce11 = mass of unit cell / volume of unit cell
d = Z * M / a3 = ZM / a3 * NA
(The density of the unit cell is same as the density of the substance.)
where, d = density of unit cell
M = molecular weight
Z = no. of atoms per unit cell
NA = Avogadro number
a = edge length of unit cell.
The Structure of Ionic Crystals
The ionic radius ratios of cation and anion, play a very important role in giving a clue to the nature of the crystal structure of ionic substances.
Chapter-1 The Solid State
Solids
Solids are the chemical substances which are characterised by define shape and volume,
rigidity, high density, low compressibility. The constituent particles (atoms, molecules or ions)
are closely packed and held together by strong interparticle forces
Types of Solids
The solids are of two types : Crystalline solids and amorphous solids.
Type of Crystalline solid
Structure Determination by X-ray Diffraction (Bragg’s Equation)
When a beam of X-rays falls on a crystal plane composed of regularly arranged atoms or ions, the X-rays are diffracted. If the waves are in phase after reflection, the difference in distance travelled by the two rays ti.e., path difference) must be equal to an integral number of Wavelength, nλ for constructive.
Thus, path difference = WY + YZ
= XY sin θ + xy sin θ
= 2 XY sin θ = 2d sin θ
∴ nλ = 2d sin θ
This equation is called Bragg’s equation.
Where, n = 1. 2, 3… (diffraction order)
λ = wavelength of X·rays incident on crystal
d = distance between atomic planes
θ = angle at which interference occurs.
Unit Cell
The smallest geometrical portion of the crystal lattice which can be used as repetitive unit to build up the whole crystal is called unit cell.
Types of Unit Cell
(i) Simple or primitive Unit cell In which the particles are present at the corners only.
(ii) Face centred unit cell In which the particles are present at the corners as well as at the centre of each of six faces
(iii) Body centred unit cell In which the particles are present at the corners as well as at the centre of the unit cell.
(iv) End centred unit cell In which the particles are present at the corners and at the centre of two opposite faces.
Number of Particles Per Unit Cell
Seven Crystal Systems
There are about 230 crystal forms, which have been grouped into 14 types of space lattices, called Bravais Lattices, on the basis of their symmetry and seven different crystal systems on the basis of interfacial angles and axes.
Seven Crystal Systems
It is defined as the ratio of the volume of the unit cell that is occupied by the spheres to the volume of the unit cell.
(i) Primitive cubic unit cell Atoms touch each other along edges.
Hence, d = a or r = a / 2
(r = radius of atom and a = edge length)
Therefore, PF = 4 / 3 πr3 / (2r)3 = 0.524 or 52.4%
(ii) Face centred cubic unit cell Atoms touch each other along the face diagonal.
Hence, d = a / √2
or r = √2a / 4
Therefore; PF = 4 * 4 / 3 πr3 / (4r / √2)r3 = 0.74 or 74%
(iii) Body centred cubic unit cell Atoms touch each other along the body diagonal.
Hence, √3a / 2
or r = √3a / 4
Therefore; PF = 2 * 4 / 3 πr3 / (4r / √3)r3 = 0.68 or 68%
Coordination Number
It is defined as the number of particles immediately adjacent to each particle in the crystal
lattice.
[In simple cubic lattice, CN is 6, in body centred lattice, CN is 8 and in face centred cubic
lattice, CN is 12].
High pressure increases CN and high temperature decreases the CN.
Close Packing in Crystals
Two Dimensional Packing of Constituent Particles
(i) Square close packing Space occupied by spheres is 52.4%.
(ii) Hexagonal close packing Space occupied by spheres is 60.4%.Hence. It is more efficient.
Three Dimensional Packing of Constituent Particles
(i) ABAB arrangement gives hexagonal close packing (hcp).
(ii) ABCABC arrangement gives cubic close packing or face centred CUbIC packing (ccp or fcc).
* In both these arrangements 740/0 space is occupied
* Coordination number in hop and ccp arrangement is 12 while in bcc arrangement, it is 8.
* Close packing of atoms in cubic structure = fcc > bcc > sc.
* All noble gases have ccp structure except He (hcp structure).
Void or Space or Holes
Empty or vacant space present bet veen spheres of a unit cell, is called void or space or hole or interstitial void. When particles are closed packed resulting in either cpp or hcp structure, two types of voids are generated:
Tetrahedral voids are holes or voids surrounded by four spheres Present at the corner of a tetrahedron. Coordination number of a tetrahedral void is 4.
Coordination number of octahedral void is 6.
[The number of octahedral voids present in a lattice is equal to the number of close packed
particles. The number of tetrahedral voids present in a lattice is twice to the number of close packed particles.]
Density of Unit Cell (d)
Density of unit ce11 = mass of unit cell / volume of unit cell
d = Z * M / a3 = ZM / a3 * NA
(The density of the unit cell is same as the density of the substance.)
where, d = density of unit cell
M = molecular weight
Z = no. of atoms per unit cell
NA = Avogadro number
a = edge length of unit cell.
The Structure of Ionic Crystals
The ionic radius ratios of cation and anion, play a very important role in giving a clue to the nature of the crystal structure of ionic substances.
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