Chemistry Class 12 NCERT Solutions Chapter 1 The Solid State – Important Questions

Introduction

Chemistry is a fundamental subject in the Science stream, and for students pursuing Class 12, the NCERT textbook provides a comprehensive guide to mastering the subject. Chapter 1 of the NCERT Class 12 Chemistry textbook, titled "The Solid State," covers essential concepts that form the foundation for further study in chemistry. This article delves into the important questions from Chapter 1, offering detailed solutions and explanations to help students grasp the fundamental concepts effectively.

Overview of Chapter 1: The Solid State

The solid state is one of the three fundamental states of matter, alongside liquids and gases. This chapter focuses on the structural and physical properties of solids and how they differ from other states of matter. Key topics include:

1. Classification of Solids
2. Crystal Lattices and Unit Cells
3. Types of Solids
4. Properties of Solids
5. Calculation of Density
6. Packing Efficiency

Understanding these concepts is crucial for mastering not only the current chapter but also for preparing for advanced topics in physical chemistry.

1. Classification of Solids

Question 1: Define crystalline and amorphous solids. How do they differ in terms of their arrangement of particles?

Solution:

Crystalline solids are those in which the constituent particles (atoms, ions, or molecules) are arranged in a highly ordered and repeating pattern. This regular arrangement leads to sharp melting points and well-defined geometrical shapes. Examples include table salt (sodium chloride) and diamonds.

Amorphous solids, on the other hand, do not have a long-range order or regular arrangement of particles. The arrangement is more random, similar to that of liquids. Amorphous solids exhibit a range of melting points and do not have a definite shape. Examples include glass and plastics.

Key Differences:

• Arrangement of Particles: Crystalline solids have a regular, repeating arrangement, while amorphous solids have a disordered arrangement.
• Melting Point: Crystalline solids have sharp melting points, whereas amorphous solids have a range of melting points.
• Shape: Crystalline solids exhibit a well-defined shape, while amorphous solids do not.

2. Crystal Lattices and Unit Cells

Question 2: Explain the concept of a crystal lattice and unit cell. What is the significance of the unit cell in crystallography?

Solution:

A crystal lattice is a three-dimensional arrangement of points in space, where each point represents the position of a particle (atom, ion, or molecule) in the crystal. The lattice extends infinitely in all directions, forming the structure of the crystal.

A unit cell is the smallest repeating unit of the crystal lattice that, when repeated in three dimensions, creates the entire lattice. It defines the symmetry and dimensions of the crystal structure. The unit cell is crucial for determining the crystal's properties and can be described by its dimensions (a, b, c) and angles (α, β, γ).

Significance of the Unit Cell:

• Describes Crystal Structure: The unit cell provides a detailed description of the crystal's geometry and symmetry.
• Determines Properties: The arrangement and types of particles within the unit cell influence the physical properties of the crystal.
• Facilitates Calculations: The unit cell allows for calculations of various properties, such as density and packing efficiency.

3. Types of Solids

Question 3: Discuss the different types of solids with examples. How do ionic, covalent, and metallic solids differ from each other?

Solution:

Solids can be classified into several types based on their bonding and properties:

• Ionic Solids: These solids are formed by ionic bonds between positively and negatively charged ions. They have high melting points and are generally soluble in water. Examples include sodium chloride (NaCl) and magnesium oxide (MgO).

• Covalent Solids: Covalent solids are characterized by a network of covalent bonds extending throughout the solid. They have very high melting points and are usually non-conductors. Examples include diamond and silicon carbide (SiC).

• Metallic Solids: Metallic solids consist of a lattice of metal cations surrounded by a 'sea' of delocalized electrons. They are good conductors of heat and electricity, and have high melting points. Examples include iron (Fe) and gold (Au).

Differences:

• Bonding: Ionic solids have ionic bonds, covalent solids have covalent bonds, and metallic solids have metallic bonds.
• Properties: Ionic solids are brittle and have high melting points, covalent solids are hard and have very high melting points, while metallic solids are malleable and good conductors.
• Examples: NaCl (ionic), diamond (covalent), and iron (metallic).

4. Properties of Solids

Question 4: How does the packing efficiency of solids affect their density? Explain with examples.

Solution:

Packing efficiency is a measure of how efficiently the particles are packed within a unit cell of a crystal lattice. It is calculated as the ratio of the volume occupied by the particles to the total volume of the unit cell.

Packing Efficiency Calculation:

For a cubic unit cell: $\text{Packing Efficiency} = \frac{\text{Volume occupied by particles}}{\text{Total volume of unit cell}} \times 100$

Examples:

• Simple Cubic (SC) Cell: Has a packing efficiency of approximately 52%. Each unit cell contains one atom, and the atoms are packed in a simple cubic arrangement.
• Face-Centered Cubic (FCC) Cell: Has a packing efficiency of approximately 74%. Each unit cell contains four atoms, and the atoms are packed in a face-centered cubic arrangement.
• Body-Centered Cubic (BCC) Cell: Has a packing efficiency of approximately 68%. Each unit cell contains two atoms, and the atoms are packed in a body-centered cubic arrangement.

Effect on Density:

Higher packing efficiency means that more of the unit cell's volume is occupied by particles, leading to higher density. Conversely, lower packing efficiency results in lower density.

5. Calculation of Density

Question 5: Derive the formula for the density of a solid from its unit cell parameters.

Solution:

The density ($\rho$) of a solid can be calculated using the formula:

$\rho = \frac{Z \cdot M}{N_A \cdot V_c}$

Where:

• $Z$ = Number of formula units per unit cell
• $M$ = Molar mass of the substance
• $N_A$ = Avogadro's number ($6.022 \times 10^{23}$ mol$^{-1}$)
• $V_c$ = Volume of the unit cell

Steps to Derive the Formula:

1. Calculate the volume of the unit cell ($V_c$). For a cubic unit cell, $V_c = a^3$, where $a$ is the edge length.
2. Determine the number of formula units (Z) per unit cell.
3. Find the molar mass (M) of the substance.
4. Use Avogadro's number to relate the mass of the particles in the unit cell to their density.

Example Calculation:

For a face-centered cubic (FCC) unit cell of copper (Cu):

• $a = 3.6 \, \text{Å}$
• $Z = 4$ (FCC has 4 formula units per unit cell)
• $M = 63.55 \, \text{g/mol}$
• $V_c = a^3$

Convert $a$ to cm: $a = 3.6 \times 10^{-8} \, \text{cm}$.

Calculate $V_c$: $V_c = (3.6 \times 10^{-8})^3 \text{ cm}^3$ $V_c = 4.66 \times 10^{-23} \text{ cm}^3$

Calculate density: $\rho = \frac{4 \times 63.55}{6.022 \times 10^{23} \times 4.66 \times 10^{-23}} \text{ g/cm}^3$ $\rho \approx 8.96 \text{ g/cm}^3$

6. Packing Efficiency

Question 6: What is packing efficiency and how is it calculated for different types of unit cells?

Solution:

Packing efficiency is the fraction of the volume of a unit cell that is occupied by the constituent particles. It is calculated as:

$\text{Packing Efficiency} = \frac{\text{Volume occupied by particles}}{\text{Total volume of unit cell}} \times 100$

Calculation for Different Unit Cells:

• Simple Cubic (SC):

  • Number of atoms per unit cell (Z) = 1
  • Packing efficiency = 52%

• Face-Centered Cubic (FCC):

  • Number of atoms per unit cell (Z) = 4
  • Packing efficiency = 74%

• Body-Centered Cubic (BCC):

  • Number of atoms per unit cell (Z) = 2
  • Packing efficiency = 68%

Example Calculation for FCC:

1. Calculate the volume occupied by the atoms. For FCC, the volume occupied by the atoms is given by:

$\text{Volume occupied by atoms} = Z \times \frac{4}{3} \pi r^3$

2. Calculate the total volume of the unit cell ($V_c$).

3. Substitute into the packing efficiency formula.

Example Calculation:

For FCC with edge length $a$:

• Atomic radius $r$ can be related to $a$ by $a = 2\sqrt{2}r$.
• Volume of the unit cell $V_c = a^3$.

The packing efficiency for FCC is calculated as:

$\text{Packing Efficiency} = \frac{4 \times \frac{4}{3} \pi r^3}{a^3} \times 100$

Using the relation $a = 2\sqrt{2}r$, substitute $a^3$ to find the packing efficiency.

Conclusion

Understanding the concepts from Chapter 1 of the Class 12 NCERT Chemistry textbook is crucial for students to build a strong foundation in the study of solid-state chemistry. The detailed solutions provided here cover important questions related to the classification of solids, crystal lattices, unit cells, types of solids, and calculations involving density and packing efficiency. By mastering these topics, students can better prepare for their exams and develop a deeper understanding of the material properties of solids.