NCERT Solutions Class 12 Chemistry Chapter 1: The Solid State – Complete Guide
Chapter 1 of Class 12 Chemistry deals with The Solid State, a fundamental topic that explores the structure and properties of solids. This chapter is crucial for both board exams and competitive examinations like JEE and NEET. Let’s explore the key concepts, important formulas, and problem-solving approaches.
Introduction to Solid State
Solids are characterized by definite shape, definite volume, high density, incompressibility, and rigidity. The constituent particles (atoms, molecules, or ions) are held together by strong interparticle forces and have fixed positions, though they can oscillate about their mean positions.
Classification of Solids
Based on Arrangement of Particles
Crystalline Solids:
- Regular and orderly arrangement of constituent particles
- Sharp melting point
- Anisotropic (different properties in different directions)
- True solids
- Examples: NaCl, Diamond, Quartz
Amorphous Solids:
- Irregular arrangement of particles
- Melt over a range of temperatures
- Isotropic (same properties in all directions)
- Pseudo solids or supercooled liquids
- Examples: Glass, Rubber, Plastics
Types of Crystalline Solids
| Type | Constituent Particles | Bonding | Properties | Examples |
|---|---|---|---|---|
| Ionic | Cations & Anions | Electrostatic | High MP, Brittle, Conduct when molten | NaCl, MgO |
| Covalent | Atoms | Covalent bonds | Very high MP, Hard, Poor conductors | Diamond, SiC |
| Molecular | Molecules | Dispersion/Dipole/H-bond | Low MP, Soft, Non-conductors | Ice, I₂ |
| Metallic | Metal atoms | Metallic bond | Variable MP, Malleable, Good conductors | Fe, Cu, Au |
Crystal Lattice and Unit Cell
Crystal Lattice
A three-dimensional arrangement of points representing the positions of constituent particles in a crystal is called a crystal lattice or space lattice. Each point is called a lattice point.
Unit Cell
The smallest repeating unit in a crystal lattice that represents the complete crystal structure is called a unit cell. There are seven crystal systems based on unit cell dimensions.
Types of Unit Cells
- Primitive (Simple): Particles only at corners
- Body-Centered: Particles at corners + one at body center
- Face-Centered: Particles at corners + one at each face center
- End-Centered: Particles at corners + one at two opposite face centers
Number of Atoms in Different Unit Cells
Contribution of Atoms at Different Positions
- Corner atom: 1/8 (shared by 8 unit cells)
- Face-centered atom: 1/2 (shared by 2 unit cells)
- Body-centered atom: 1 (belongs to one unit cell)
- Edge-centered atom: 1/4 (shared by 4 unit cells)
Atoms per Unit Cell
- Simple Cubic (SC): 8 × 1/8 = 1 atom
- Body-Centered Cubic (BCC): (8 × 1/8) + 1 = 2 atoms
- Face-Centered Cubic (FCC): (8 × 1/8) + (6 × 1/2) = 4 atoms
Close Packing Structures
Close Packing in Two Dimensions
- Square Close Packing: Coordination number = 4
- Hexagonal Close Packing: Coordination number = 6
Close Packing in Three Dimensions
- Hexagonal Close Packing (HCP): ABAB… pattern, coordination number = 12
- Cubic Close Packing (CCP/FCC): ABCABC… pattern, coordination number = 12
Packing Efficiency
Packing efficiency = (Volume occupied by atoms / Total volume of unit cell) × 100
Packing Efficiency Values
- Simple Cubic: 52.4%
- Body-Centered Cubic: 68%
- Face-Centered Cubic: 74%
- HCP: 74%
Voids in Close Packing
Tetrahedral Voids
Formed when a sphere of second layer is above the void of first layer. Number of tetrahedral voids = 2 × number of spheres
Octahedral Voids
Formed when triangular voids of first and second layers do not overlap. Number of octahedral voids = number of spheres
Density Calculations
The density of a crystalline solid can be calculated using:
ρ = (Z × M) / (a³ × Nₐ)
Where:
- ρ = Density
- Z = Number of atoms per unit cell
- M = Molar mass
- a = Edge length of unit cell
- Nₐ = Avogadro’s number
Defects in Crystals
Point Defects
Stoichiometric Defects (Intrinsic):
- Vacancy Defect: Missing atoms from lattice sites. Decreases density.
- Interstitial Defect: Extra atoms in interstitial sites. Increases density.
- Schottky Defect: Equal vacancies of cations and anions. Common in ionic compounds with similar cation and anion sizes (NaCl, KCl).
- Frenkel Defect: Smaller ion displaced to interstitial site. Common when there’s large size difference (AgCl, ZnS).
Non-Stoichiometric Defects:
- Metal Excess Defect: Due to anionic vacancies or extra cations in interstitial sites
- Metal Deficiency Defect: Due to cationic vacancies
Impurity Defects
Foreign atoms occupy lattice positions. Example: Doping of Si with As (n-type) or B (p-type) semiconductors.
Important Formulas Summary
- Relation between r and a for SC: a = 2r
- Relation between r and a for BCC: a = 4r/√3
- Relation between r and a for FCC: a = 2√2r
- Density: ρ = ZM/a³Nₐ
Conclusion
The Solid State chapter forms the foundation for understanding material properties and their applications. Focus on understanding the concepts of unit cells, packing efficiency, and defects. Practice numerical problems on density calculations and relationship between atomic radius and edge length. This chapter carries significant weightage in both board exams and competitive examinations.
Key Concepts: The Solid State (Class 12 Chemistry Chapter 1)
The Solid State is an important chapter for CBSE Class 12 and JEE preparation. It covers crystal structures, unit cells, types of solids, defects, and electrical/magnetic properties.
Types of Solids
- Ionic Solids: Held by electrostatic forces between ions. High melting points, brittle, conduct electricity in molten/dissolved state. Example: NaCl, MgO
- Covalent/Network Solids: Atoms bonded by strong covalent bonds. Very high melting points, hard, poor conductors. Example: Diamond, SiO2, graphite (conducts electricity — exceptional)
- Metallic Solids: Metal cations in a sea of delocalised electrons. Good conductors, malleable, ductile. Example: Fe, Cu, Al
- Molecular Solids: Molecules held by van der Waals forces or H-bonds. Low melting points, poor conductors. Examples: Ice (H-bonds), dry ice CO2 (dispersion forces)
Unit Cells and Crystal Systems
A unit cell is the smallest repeating unit of a crystal lattice. Key unit cells:
- Simple Cubic (SC): Atoms at corners only. Atoms per unit cell = 8 × (1/8) = 1. Packing efficiency = 52.4%
- Body-Centred Cubic (BCC): Atoms at corners + 1 at centre. Atoms per cell = 2. Packing efficiency = 68%. Example: Na, K, Fe
- Face-Centred Cubic (FCC)/CCP: Atoms at corners + face centres. Atoms per cell = 4. Packing efficiency = 74%. Example: Cu, Al, Ag, Au
Important Formulas
- Density of unit cell: ρ = (Z × M) / (NA × a3), where Z = atoms per cell, M = molar mass, NA = Avogadro number, a = edge length
- For SC: r = a/2; For BCC: r = (√3/4)a; For FCC: r = (√2/4)a = a/(2√2)
- Packing efficiency: (Volume of atoms in unit cell / Volume of unit cell) × 100
Interstitial Voids
- Tetrahedral voids: Surrounded by 4 atoms. In n atoms closed packing, there are 2n tetrahedral voids.
- Octahedral voids: Surrounded by 6 atoms. In n atoms closed packing, there are n octahedral voids.
- Radius of tetrahedral void = 0.225 × r (sphere radius); Octahedral void = 0.414 × r
Defects in Solids
- Schottky Defect: Cation and anion both missing from lattice sites. Density decreases. Found in ionic crystals with similar cation/anion sizes. Example: NaCl, KBr
- Frenkel Defect: Cation displaced from lattice to interstitial site. No change in density. Found in crystals with large size difference (small cations). Example: ZnS, AgBr, AgI
- Interstitial Defect: Extra atoms in interstitial sites (for non-ionic). Density increases.
- Impurity Defect: Foreign atoms replace host atoms (e.g., adding SrCl2 to NaCl creates cation vacancies)
Electrical Properties
- Conductors: Overlapping valence and conduction bands — electrons flow freely. Example: metals
- Insulators: Large band gap between valence and conduction bands. Example: diamond
- Semiconductors: Small band gap — conductivity increases with temperature. p-type (electron hole) and n-type (extra electron). Example: Si, Ge
Important Board Exam Questions
- Calculate the number of atoms per unit cell for BCC and FCC structures.
- What is the packing efficiency of FCC? How is it calculated?
- What is the difference between Schottky and Frenkel defects?
- A compound has BCC structure. What is its coordination number?
- An element has FCC structure with edge length 400 pm. Calculate the density if its molar mass is 60 g/mol.
- Explain with examples the difference between conductor, semiconductor, and insulator in terms of band theory.
- What are tetrahedral and octahedral voids?
