Class 12 Chemistry Notes Chapter 1 (Solid State) – Examplar Problems Book

Alright class, let's dive deep into the 'Solid State'. This chapter lays the foundation for understanding the structure and properties of materials around us, which is crucial not just for your board exams but also for various competitive government exams. Pay close attention to the details, especially the types of solids, packing, defects, and related calculations.

Solid State: Detailed Notes for Competitive Exams

1. Introduction:

• Solids are characterized by definite mass, volume, and shape.
• They have strong intermolecular forces and short intermolecular distances.
• Constituent particles (atoms, molecules, or ions) have fixed positions and oscillate about their mean positions.
• They are generally incompressible and rigid.

2. Classification of Solids:

• Amorphous Solids:
  • Irregular arrangement of constituent particles (short-range order only).
  • Isotropic in nature (physical properties are the same in all directions).
  • Melt over a range of temperatures.
  • Considered pseudo-solids or supercooled liquids (e.g., glass, rubber, plastics).
  • Undergo irregular cleavage when cut.
• Crystalline Solids:
  • Orderly arrangement of constituent particles in a definite geometric pattern (long-range order).
  • Anisotropic in nature (physical properties like electrical resistance, refractive index show different values along different directions).
  • Have sharp melting points.
  • True solids.
  • Undergo clean cleavage when cut.

3. Classification of Crystalline Solids (Based on Binding Forces):

4. Crystal Lattices and Unit Cells:

• Crystal Lattice (Space Lattice): A regular three-dimensional arrangement of points in space representing the constituent particles.
• Lattice Points: The positions occupied by the constituent particles in the crystal lattice.
• Unit Cell: The smallest repeating portion of the crystal lattice which, when repeated in different directions, generates the entire lattice.
• Parameters of a Unit Cell: Characterized by six parameters: three edge lengths (a, b, c) and three angles between the edges (α, β, γ).
• Types of Unit Cells:
  • Primitive (Simple) Unit Cell: Particles only at the corners.
  • Centred Unit Cell: Particles at corners and some other positions.
    • Body-Centred (BCC): Particles at corners + one at the body center.
    • Face-Centred (FCC): Particles at corners + one at the center of each face.
    • End-Centred: Particles at corners + one at the center of any two opposite faces.
• Seven Crystal Systems: Based on the unit cell parameters (cubic, tetragonal, orthorhombic, monoclinic, hexagonal, rhombohedral/trigonal, triclinic).
• Bravais Lattices: There are 14 possible three-dimensional lattices, known as Bravais lattices.

5. Number of Atoms in a Unit Cell (Z):

• Contribution of particle at corner = 1/8
• Contribution of particle at face centre = 1/2
• Contribution of particle at body centre = 1
• Contribution of particle at edge centre = 1/4
• Primitive Cubic (PC/SC): Z = 8 (corners) × (1/8) = 1
• Body-Centred Cubic (BCC): Z = [8 (corners) × (1/8)] + [1 (body centre) × 1] = 1 + 1 = 2
• Face-Centred Cubic (FCC): Z = [8 (corners) × (1/8)] + [6 (face centres) × (1/2)] = 1 + 3 = 4

6. Close Packing in Solids:

• Coordination Number (CN): The number of nearest neighbours of a particle.
• 1D Packing: CN = 2
• 2D Packing:
  • Square Close Packing (AAA type): CN = 4. Packing efficiency = 52.4%.
  • Hexagonal Close Packing (ABA type): CN = 6. Packing efficiency = 60.4%. More efficient than square close packing.
• 3D Packing (from 2D layers):
  • AAA type (from Square Close Packed layers): Forms Simple Cubic lattice. CN = 6. Packing efficiency = 52.4%.
  • ABAB type (from Hexagonal Close Packed layers): Forms Hexagonal Close Packed (hcp) structure. CN = 12. Packing efficiency = 74%. Examples: Mg, Zn.
  • ABCABC type (from Hexagonal Close Packed layers): Forms Cubic Close Packed (ccp) or Face-Centred Cubic (fcc) structure. CN = 12. Packing efficiency = 74%. Examples: Cu, Ag, Au.
• Note: BCC is not a close-packed structure (Packing efficiency = 68%, CN = 8).

7. Voids (Interstitial Sites): Empty spaces left between the constituent particles in close-packed structures.

• Tetrahedral Void: Surrounded by 4 spheres. Smaller void.
• Octahedral Void: Surrounded by 6 spheres. Larger void.
• Relationship: If the number of close-packed spheres = N
  • Number of Octahedral Voids = N
  • Number of Tetrahedral Voids = 2N
• Location in FCC/CCP:
  • Octahedral Voids: Body centre (1) + Edge centres (12 × 1/4 = 3). Total = 4. (Equal to Z)
  • Tetrahedral Voids: Located on body diagonals (2 per diagonal). Total = 8. (Equal to 2Z)

8. Packing Efficiency: The percentage of total space filled by the particles.

• Packing Efficiency = (Volume occupied by spheres in the unit cell / Total volume of the unit cell) × 100
• Simple Cubic (SC): 52.4%
• Body-Centred Cubic (BCC): 68%
• Hexagonal Close Packed (hcp) & Cubic Close Packed (ccp/fcc): 74% (Most efficient)

9. Calculations Involving Unit Cell Dimensions:

• Density (ρ) of the unit cell:
  ρ = (Z × M) / (a³ × N<0xE2><0x82><0x90>)
  Where:
  • Z = Number of atoms per unit cell
  • M = Molar mass (g/mol)
  • a = Edge length of the unit cell (usually in cm or pm; 1 pm = 10⁻¹⁰ cm)
  • N<0xE2><0x82><0x90> = Avogadro's number (6.022 × 10²³ mol⁻¹)
• Relationship between edge length (a) and radius (r) of atom:
  • SC: a = 2r
  • FCC: a = 2√2 r (or r = a / (2√2))
  • BCC: √3 a = 4r (or r = (√3 / 4) a)

10. Imperfections in Solids (Crystal Defects): Deviations from the perfectly ordered arrangement.

• Point Defects: Irregularities around a point or an atom.

  • Stoichiometric Defects: Do not disturb the stoichiometry.
    • Vacancy Defect: Lattice site is vacant. Decreases density. (Common in non-ionic solids).
    • Interstitial Defect: Constituent particle occupies an interstitial site. Increases density. (Common in non-ionic solids).
    • Schottky Defect: Equal number of cations and anions are missing from lattice sites to maintain electrical neutrality. Decreases density. Shown by ionic solids with high CN and similar cation/anion sizes (e.g., NaCl, KCl, CsCl, AgBr).
    • Frenkel Defect (Dislocation Defect): Smaller ion (usually cation) is dislocated from its normal site to an interstitial site. Density remains unchanged. Shown by ionic solids with low CN and large difference in ion sizes (e.g., ZnS, AgCl, AgBr, AgI). (Note: AgBr shows both Schottky and Frenkel defects).
  • Non-Stoichiometric Defects: Disturb the stoichiometry.
    • Metal Excess Defect:
      • Due to Anionic Vacancies: Anion missing, electron occupies the site (F-centre) to maintain neutrality. F-centres impart colour (e.g., excess Li in LiCl -> pink, excess Na in NaCl -> yellow, excess K in KCl -> violet/lilac). Solids become paramagnetic.
      • Due to presence of extra cations at interstitial sites: Extra cation occupies interstitial site, electron occupies another interstitial site to maintain neutrality (e.g., ZnO turns yellow on heating).
    • Metal Deficiency Defect: Cation missing, adjacent cation acquires higher charge to maintain neutrality. Occurs in metals showing variable oxidation states (e.g., FeO exists as Fe₀.₉₅O, NiO). Results in p-type semiconduction.
  • Impurity Defects: Foreign atoms present at lattice sites or interstitial sites (e.g., adding SrCl₂ to NaCl creates cation vacancies; solid solutions like brass (Cu+Zn)). Doping of semiconductors.

• Line Defects: Irregularities along rows of lattice points (e.g., edge dislocation, screw dislocation). (Generally beyond Class 12 scope).

11. Electrical Properties:

• Conductors: High conductivity (10⁴ to 10⁷ ohm⁻¹m⁻¹). Metals. Valence band overlaps with conduction band.
• Insulators: Very low conductivity (10⁻²⁰ to 10⁻¹⁰ ohm⁻¹m⁻¹). Large energy gap (Eg) between filled valence band and empty conduction band.
• Semiconductors: Intermediate conductivity (10⁻⁶ to 10⁴ ohm⁻¹m⁻¹). Small energy gap (Eg). Conductivity increases with temperature.
  • Intrinsic Semiconductors: Pure substances (e.g., Si, Ge).
  • Extrinsic Semiconductors (Doping): Adding impurity to increase conductivity.
    • n-type: Doping Group 14 (Si, Ge) with Group 15 element (P, As). Excess electrons are charge carriers.
    • p-type: Doping Group 14 (Si, Ge) with Group 13 element (B, Al). Electron holes are charge carriers.

12. Magnetic Properties: Originates from electron spins and orbital motion.

• Diamagnetic: Weakly repelled by magnetic field. All electrons are paired. (e.g., H₂O, NaCl, C₆H₆).
• Paramagnetic: Weakly attracted by magnetic field. Presence of unpaired electrons. Lose magnetism in absence of field. (e.g., O₂, Cu²⁺, Fe³⁺, Cr³⁺).
• Ferromagnetic: Strongly attracted by magnetic field. Can be permanently magnetized. Metal ions grouped into domains, aligned in presence of field. (e.g., Fe, Co, Ni, Gd, CrO₂).
• Antiferromagnetic: Domains align oppositely, cancelling magnetic moment. (e.g., MnO).
• Ferrimagnetic: Domains align anti-parallelly in unequal numbers. Weakly attracted compared to ferromagnetic. (e.g., Fe₃O₄ (magnetite), ferrites like MgFe₂O₄, ZnFe₂O₄). Lose ferrimagnetism on heating and become paramagnetic.

Multiple Choice Questions (MCQs):

1. Which of the following is an amorphous solid?
   (a) Graphite
   (b) Quartz (SiO₂)
   (c) Silicon Carbide (SiC)
   (d) Fused silica (Glass)

2. In a face-centred cubic (FCC) lattice, the number of atoms per unit cell is:
   (a) 1
   (b) 2
   (c) 4
   (d) 6

3. The coordination number of atoms in a body-centred cubic (BCC) structure is:
   (a) 4
   (b) 6
   (c) 8
   (d) 12

4. Schottky defect in crystals is observed when:
   (a) Density of the crystal increases.
   (b) Unequal number of cations and anions are missing from the lattice.
   (c) An ion leaves its normal site and occupies an interstitial site.
   (d) Equal number of cations and anions are missing from the lattice.

5. Doping silicon with phosphorus results in:
   (a) p-type semiconductor
   (b) n-type semiconductor
   (c) Metal
   (d) Insulator

6. The packing efficiency of a simple cubic (SC) lattice is:
   (a) 68%
   (b) 74%
   (c) 52.4%
   (d) 60.4%

7. Which of the following exhibits both Schottky and Frenkel defects?
   (a) NaCl
   (b) AgBr
   (c) ZnS
   (d) CsCl

8. In a close-packed structure of N spheres, the number of tetrahedral voids is:
   (a) N/2
   (b) N
   (c) 2N
   (d) 4N

9. Which type of crystalline solid is characterized by positive ions immersed in a sea of mobile electrons?
   (a) Ionic
   (b) Covalent
   (c) Metallic
   (d) Molecular

10. ZnO appears yellow on heating due to:
    (a) Frenkel defect
    (b) Schottky defect
    (c) Metal excess defect due to interstitial cations
    (d) Metal deficiency defect

Answers to MCQs:

1. (d) Fused silica (Glass)
2. (c) 4
3. (c) 8
4. (d) Equal number of cations and anions are missing from the lattice.
5. (b) n-type semiconductor
6. (c) 52.4%
7. (b) AgBr
8. (c) 2N
9. (c) Metallic
10. (c) Metal excess defect due to interstitial cations

Make sure you understand the concepts behind each point and MCQ. Go through the NCERT textbook and Exemplar problems thoroughly. Let me know if any specific part needs further clarification!