NCERT Solutions for Class 12 Chemistry Chapter 1 The Solid State

Q8. How many lattice points are there in one unit cell of each of the following lattice?
(i) Face-centred cubic
(ii) Face-centred tetragonal
(iii) Body-centred

Ans:

(i) There are 14 lattice points in face-centred cubic, 8 from the corners and 6 from the faces.

(ii) There are 14 lattice points in face-centred tetragonal, 8 from the corners and 6 from the faces.

(iii) There are 9 lattice points in body-centred cubic, 1 from the centre and 8 from the corners.

Simple cubic:
In a simple cubic lattice, particles are present only at the corners and they touch each other along the edge.

Let the edge length = a

Radius of each particle = r.
Thus, a = 2r
Volume of spheres = πr³(4/3)
Volume of a cubic unit cell = a ³ = (2r) ³ = 8r ³
We know that the number of particles per unit cell is 1.
Therefore,
Packing efficiency = Volume of one particle/Volume of cubic unit cell = [ πr³(4/3) ] / 8r ³ = 0.524 or 52.4 %

Body-centred cubic:

From ∆FED, we have:
b² = 2a²
b = ( 2a )^1/2
Again, from ∆AFD, we have :
c² = a² + b²
=> c² = a² + 2a²
c² = 3a²
=> c = (3a)^1/2
Let the radius of the atom = r.
Length of the body diagonal, c = 4r
=> (3a)^1/2 = 4r
=> a = 4r/ (3)^1/2
or , r = [ a (3)^1/2 ]/ 4
Volume of the cube, a³ = [4r/ (3)^1/2 ] ³
A BCC lattice has 2 atoms.
So, volume of the occupied cubic lattice = 2πr³(4/3) = πr³( 8/3)
Therefore, packing efficiency = [ πr³( 8/3) ]/ [ { 4r/(3)^1/2 }³ ] = 0.68 or 68%

Face-centred cubic:

Let the edge length of the unit cell = a
let the radius of each sphere = r
Thus, AC = 4r
From the right angled triangle ABC, we have :
AC = ( a² + a² )^1/2 = a(2)^1/2

Therefore, 4r = a(2)^1/2
=> a = 4r/( 2)^1/2
Thus, Volume of unit cell =a³ = { 4r/( 2)^1/2 } ³
a³ = 64r³/2(2)^1/2 = 32r³/ (2)^1/2
No. of unit cell in FCC = 4
Volume of four spheres = 4 × πr³(4/3)

Thus, packing efficiency = [πr³(16/3) ] / [32r³/ (2)^1/2 ] = 0.74 or 74 %

Q9. Silver crystallises in fcc lattice. If edge length of the cell is 4.07 × 10^–8cm and density is 10.5 g cm^–3, calculate the atomic mass of silver.

Ans:

Given:
Edge length, a = 4.077 × 10⁻⁸ cm
Density, d = 10.5 g cm⁻³
The given lattice is of fcc type,
Thus the number of atoms per unit cell, z = 4
We also know that N_A = 6.022 × 10²³ / mol
let M be the atomic mass of silver.
We know, d = zM/a³N_A
=> M = da³N_a / z

= (10.5 x 4.077 × 10⁻⁸ x 6.022 × 10²³ ) / 4 = 107.13 g /mol

Q10. A cubic solid is made of two elements P and Q. Atoms of Q are at the corners of the cube and P at the body-centre. What is the formula of the compound? What are the coordination numbers of P and Q?

Ans:

Given:

Atoms of Q occupy the corners of the cube.
=> Number of Q atoms in a unit cell = 8 x 1/8 = 1
The atom of P occupies the body centre.
=> Number of Q atoms in a unit cell = 1
Therefore, the ratio of the number of P atoms to the number of Q atoms;
X : Y = 1 : 1
Thus, the formula of the compound is PQ
And the coordination number of both the elements is 8.

Q11. Analysis shows that nickel oxide has the formula Ni_0.98O_1.00. What fractions of nickel exist as Ni²⁺ and Ni³⁺ ions?

Ans:

The given formula of nickel oxide is Ni_0.98 O_1.00.
Thus, the ratio of the number of Ni atoms to the number of O atoms is,
Ni : O = 0.98 : 1.00 = 98 : 100
Now,
Total charge on 100 O²⁻ ions = 100 × (−2) = −200
Let the number of Ni²⁺ ions = x.
So, the number of Ni³⁺ ions is 98 − x.
Now,
Total charge on Ni²⁺ ions = x(+2) = +2x
Similarly, total charge on Ni³⁺ ions = (98 − x)(+3) = 294 − 3x
As, the compound is neutral, we can write:
2x + (294 − 3x) + (−200) = 0
⇒ −x + 94 = 0
⇒ x = 94
Therefore, number of Ni²⁺ ions = 94
And, number of Ni³⁺ ions = 98 − 94 = 4
Thus, the fraction of nickel that exists as Ni²⁺ = 94/98 = 0.0959
And, the fraction of nickel that exists as Ni³⁺ = 4/98 = 0.041

Q12. Explain the following with suitable examples:
(a) Ferromagnetism
(b) Paramagnetism
(c) Ferrimagnetism
(d) Antiferromagnetism
(e) 12-16 and 13-15 group compounds.

Ans:

(a) Ferromagnetic:
These substances (ferromagnetic substances) are strongly attracted by magnetic fields. They could be permanently magnetized even when a magnetic field is absent. Few examples of ferromagnetic substances include cobalt, iron, nickel, CrO₂ and gadolinium.
In a solid state, their metal ions come together to form small regions termed domains and each domain behaves like a tiny magnet.
In a magnetized piece of a ferromagnetic substance, these domains are randomly arranged thus, their net magnetic moment becomes zero. However, when it is kept in a magnetic field, the domains orient themselves in the direction of the field. This results in a powerful magnetic effect being produced. This orientation of domains persists even after the field is removed. Hence, the ferromagnetic substance is transformed into a permanent magnet.
Schematic alignment of magnetic moments in ferromagnetic substances:

(b) Paramagnetism :
These substances (paramagnetic substances) are attracted by a magnetic field but after the removal of the field, they lose their magnetism. Examples of paramagnetic substances include Cr³⁺, O₂, Cu²⁺, and Fe³⁺. To undergo paramagnetism, a substance must possess one or more unpaired electrons. These unpaired electrons are pulled by the magnetic field, thus causing paramagnetism.

(c) Antiferromagnetism :
An antiferromagnetic substance has domain structures similar to that of ferromagnetic substances but in the opposite orientation. These oppositely-oriented domains null out each other’s magnetic moments.
Schematic alignment of magnetic moments in antiferromagnetic substances

(d) Ferrimagnetism:
In these substances, the magnetic moments of the domains are oriented in parallel and anti-parallel directions and in unequal numbers. A few examples of ferromagnetic substances include ferrites like MgFe₂O₄ and ZnFe₂O₄, Fe₃O₄ (magnetite), etc.
As compared to ferromagnetic substances these substances are weakly attracted by magnetic fields. Upon heating, they become paramagnetic.

(e) 12-16 and 13-15 group compounds:
The group 12-16 compounds are obtained by combining together group 16 and group 12 elements. Group 13-15 compounds are obtained by combining group 15 and group13 elements. These compounds are prepared to stimulate average valence of four as in Si or Ge. Indium (III) antimonide (IrSb), gallium arsenide (GaAS) and aluminium phosphide (AlP) are some typical compounds of groups 13-15.
GaAs semiconductors provide a very minute response time and they have totally changed the designing of semiconductor devices. A few examples of group 12-16 compounds are zinc sulphide (ZnS), mercury (II) telluride (HgTe), cadmium sulphide (CdS) and cadmium selenide (CdSe). The bonds these compounds have are not perfect covalent. Their bond’s ionic character depends upon the electronegativity of the two species/elements.

Q13. Why are solids rigid?

Ans:

Intermolecular forces of attraction in a solid is really strong, because of this the molecules of solids have fixed positions. Nonetheless, they still can oscillate about their mean positions. This is the reason for solids being rigid.

Q14. Why do solids have a definite volume?

Ans:

Intermolecular forces of attraction in a solid is really strong, because of this the molecules of solids have fixed positions. This makes them very rigid, thus giving them definite volumes.

Q15. Classify the following as amorphous or crystalline solids: Polyurethane, naphthalene, benzoic acid, teflon, potassium nitrate, cellophane, polyvinyl chloride, fibre glass, copper.

Ans:

Crystalline solids:
Naphthalene, potassium nitrate, benzoic acid, and copper
Amorphous solids:
Polyurethane, cellophane, Teflon, fibreglass and polyvinyl chloride.

Q16. For what reason is glass also considered a supercooled liquid?

Ans:

Just like a liquid, glass also flows from top to bottom but very slowly. For this reason, glass is also considered a supercooled liquid.

Q17. Refractive index of a solid is observed to have the same value along all directions. Comment on the nature of this solid. Would it show cleavage property?

Ans:

These solids are isotropic in nature i.e., they have the same value of physical properties in all directions. Thus, they also have the same value of refractive index along with all directions. As the solid is amorphous it will not exhibit cleavage property i.e., it will break into pieces with undefined surfaces when cut.

Q18. Classify the following solids in different categories based on the nature of intermolecular forces operating in them:
Potassium sulphate, tin, benzene, urea, ammonia, water, zinc sulphide, graphite, rubidium, argon, silicon carbide.

Ans:

Potassium sulphate → Ionic solid
Benzene → Molecular (non-polar) solid
Tin → Metallic solid
Urea → Polar molecular solid
Water → Hydrogen bonded molecular solid
Ammonia → Polar molecular solid
Zinc sulphide → Ionic solid
Rubidium → Metallic solid
Graphite → Covalent or network solid
Silicon carbide → Covalent or network solid
Argon → Non-polar molecular solid

Q19. Solid X is a really hard electrical insulator in solid and in a liquid state and it has an extremely high melting point. Identify the type of solid it is.

Ans:

The above qualities are qualities of a covalent or network solid, thus it is a covalent or network solid. The solid could be a diamond.

Q20. Ionic solids do not conduct electricity in the solid state but only in the molten state. Why?

Ans:

The ions of ionic solids are responsible for conducting electricity. In the solid state, however, these ions are not free to move around inside the solid because of the strong electrostatic forces. Hence, ionic solids do not conduct electricity in a solid state. Whereas, in a molten state, the ions are free to move and thus they can conduct electricity.

Q21. What kind of solids are malleable, ductile and electrical conductors?

Ans:

Metallic solids are malleable, ductile and electrical conductors.

Q22. What is the importance of ‘lattice point’?

Ans:

The importance of the lattice point is that every lattice point represents a fundamental particle of a solid which could be an ion, an atom or a molecule.

Q23. What are the parameters that make up a unit cell?

Ans:

A unit cell is made up of the following parameters:
(i) The three dimensions of a unit cell. (the three edges)
(ii) the angles between the edges.

Q24. Differentiate between:
(i) End-centred and face-centred unit cells.
(ii) Monoclinic and hexagonal unit cells.

Ans:

(i)

(ii)

Q25. A cubic unit cell has atoms at its (i) body centre, and (ii) corner, find the amount of atom each unit cell gets after share with its neighbouring unit cells.

Ans:

(i) An atom in the body centre is not shared between unit cells, thus the atom in the body centre only belongs to the unit cell it is in.
(ii) An atom in the corner is shared between 8 adjacent cells. Thus, each cell gets 1/8^th of the atom.

Q26. A molecule is in the square close-packed layer, find its two-dimensional coordination number.

Ans:

A molecule in a square close-packed layer touches four of its neighbours. Thus, its two-dimensional coordination number is 4.

Q27. Find the number of voids in 0.2 moles of a compound forming hexagonal close-packed structure. What number of these are tetrahedral voids?

Ans:

Given:
No. of close-packed particles = 0.2 × 6.022 × 10²³= 1.2044 × 10²³

Thus, no. of octahedral voids = 1.2044 × 10²³

And, no. of tetrahedral voids = 2 × 1.2044 × 10²³ = 2.4088 × 10²³

Thus, total number of voids = 1.2044 × 10²³ + 2.4088 × 10²³ = 3.6132 × 10²³

Q28. A compound is made up of two elements A and B. The atoms of element B form ccp and element A’s atoms take up 1/3rd of the tetrahedral voids. Find the formula of this compound.

Ans:

Given:
Atoms of element B form ccp, thus no. of atoms = n
No. of oct voids = n
No. of td voids = 2n = 2 x n(1/3) = 2n/3
Therefore :
The formula of the compound is A : B
2n/3 : n
2:3 = A₂B₃

Q29. Identify the lattice with the highest packing efficiency (i) hexagonal close-packed (ii) simple cubic or (iii) body-centred lattice.

Ans:

The lattice with the greatest packing efficiency is the hexagonal close-packed lattice with a packing efficiency of 74 %.

Q30. An element with a density of 2.7 × 10³ kg m^-3 has a molar mass of 2.7 × 10^-2 kg / mol and it makes a cubic unit cell with an edge length of 405 pm. What kind of cubic unit cell does it have?

Ans:

Given,
Density ,d = 2.7 × 10³ kg m^-3
Molar mass, M = 2.7 × 10^-2 kg /mol
Edge length, a = 405 pm = 405 × 10^-12 m = 4.05 × 10^-10 m
We know,
Avogadro’s number, N_A = 6.022 × 10²³ mol^-1
We also know that d = ( Z x M)/(a³ x N_A)
=> Z = (d x N_A x a³)/M = 3.99 ∼4
This means that the cell is a face centered cubic.

Q31. When solids are heated what kind of defects can arise in it? Find physical property affected by it and the way it is affected.

Ans:

Heating solids produce vacancy defects in the crystal. This means that when the heat is applied to the solid, some ions or atoms leave their lattice site totally, making those sites empty. Thereby, decreasing the solid’s density.

Q32. Identify the type of stoichiometric defect present in :

(i) AgBr

(ii) ZnS

Ans:

(i) Frenkel and Schottky defects are present in AgBr.
(ii) ZnS contains Frenkel defect.

Q33. If NaCl is doped with 10^–3 mol % of SrCl₂, what is the concentration of cation vacancies?

Ans:

When a cation of higher valence is put in an ionic solid, it starts replacing cations of lower valency such that the crystal remains electrically neutral. Thereby, creating some vacant sites. For instance, if Sr²⁺ is put in NaCl, each Sr²⁺ ion replaces two Na⁺ ions. Thereby creating one vacant for every Sr⁺ ion introduced.

Q34. Explain using an appropriate example of how ionic solids, with anionic vacancies caused due to the metal excess defect, start developing a colour.

Ans:

Let us take an example of NaCl to explain this when NaCl crystals are heated in a sodium vapor atmosphere, sodium atoms are deposited on the crystal’s surface. This causes the Cl^– ions to leave their lattice sites to form NaCl with the deposited sodium atoms. In this process, the sodium atoms on the surface lose their electrons to form Na⁺ ions and the released electrons move into the crystal to fill in the vacant anionic sites. These electrons absorb energy from the incoming visible light and get excited to a higher energy level. Thereby, imparting a yellow colour to the crystals.

Q35. To convert a group 14 element into an n-type semiconductor a suitable impurity is doped into it. To which group does this impurity belong?

Ans:

This impurity should belong to group 15.

Q36. Which substance would be a better choice to make a permanent magnet, ferromagnetic or ferrimagnetic. Explain your answer.

Ans:  Substances like iron, cobalt, nickel, gadolinium and CrO₂, are known as ferromagnetic substances and make better permanent magnets as they are attracted very strongly by the magnetic field. These substances can also be permanently magnetized. The metal ions of ferromagnetic substances, in solid-state are grouped into small regions, which are known as domains. Each domain act as a tiny magnet. Meanwhile, in a magnetized piece of a ferromagnetic substance, the domains are randomly oriented and so the magnetic moments of the domains get cancelled. Nevertheless, when the substance is placed in a magnetic field, all the domains are oriented in the direction of the magnetic field and produces a strong magnetic effect. The ordering of the domains persists even after the removal of the magnetic field. Thus, the ferromagnetic substance becomes a permanent magnet.

The solid-state exercise solutions are solved by subject experts as per CBSE textbook guidelines. From these solutions, students will be able to understand the general characteristics of solid-state, classification of solids, crystal lattice, unit cell and imperfections in solids. The objective is to help the students regarding the pattern of answering the questions, as per the marking scheme.

Class 12 NCERT Solutions for The Solid State

This was an introduction to Chapter 1 of Chemistry Class 12. Along with NCERT sample questions, one must solve previous year questions and participate in mock tests to practise to perfection.

There are three states of matter. They are – solid, liquid and gas. Some of the properties of solids are:

• Solids have a definite shape, volume and mass
• Distance and force: Intermolecular distance is short whereas intermolecular force is strong
• Solids are rigid and cannot be compressed
• Particles have fixed positions

Solids are further classified into two types: Amorphous and crystalline. Crystalline solids have a definite geometric shape, have long-range order. These solids are isotropic and do not have definite heat of fusion. Examples of crystalline solids are Quartz and sodium chloride. Crystalline solids are also called true solids.

Amorphous word is derived from the Greek word ‘amorphous’ which means no form. In this, the particles are of indefinite shape and have short-range order. An example of amorphous solids is Quartz glass. Amorphous solids are also called supercooled or pseudo solids.

Subtopics for Class 12 Chemistry Chapter 1 – The Solid State

1. General Characteristics of Solid State
2. Amorphous and Crystalline Solids
3. Classification of Crystalline Solids
   1. Molecular Solids
   2. Ionic Solids
   3. Metallic Solids
   4. Covalent or Network Solids
4. Crystal Lattices and Unit Cells
   1. Primitive and Centred Unit Cells
5. Number of Atoms in a Unit Cell
   1. Primitive Cubic Unit Cell
   2. Body-Centred Cubic Unit Cell
   3. Face-Centred Cubic Unit Cell
6. Close-Packed Structures
   1. The formula of a Compound and Number of Voids Filled
7. Packing Efficiency
   1. Packing Efficiency in HCP and CCP Structures
   2. The efficiency of Packing in Body-Centred Cubic Structures
   3. Packing Efficiency in Simple Cubic Lattice
8. Calculations Involving Unit Cell Dimensions
9. Imperfections in Solids
   1. Types of Point Defects
   2. Electrical Properties
   3. Conduction of Electricity in Metals
   4. Conduction of Electricity in Semiconductors
   5. Magnetic Properties

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