##### Document Text Contents

Page 1

1

CHEMISTRY

By

Pri

nce

Sir

Reconstruct Your Chemistry With Prince Sir

THE SOLID STATE

THEORY SHEET

Page 2

2

CHEMISTRY

Reconstruct Your Chemistry With Prince Sir

By

Pri

nce

Sir

SOLID STATE

General characterishics of solid states

The following are the characteristic propeties of the solid state

1. They hare definite mass, volume and shape.

2. Intermolecular distance are short.

3. Intermolecular forces are strong.

4. Their constituent particles (atoms/molecules/ions) have fixed positions and can only oscillate

about their mean position .

5. They are incompressible and rigid.

Such solids which hare difinite volume and structure and do not lose their shapes are called true solids

eg. NaCl,KCl, sugar, Fe, Ag, Cu etc.

Whereas solids which lose shapes on long standing and flows under its own weight and get distorted

are called pseudo solids super cooled liquids. e.g. glass.

Ordered arrangement :

In solids there is ordered arrangement of the particles of the solid (atoms/molecules/ions).

This ordered arrangement is of two types

1. Long range order, and 2. Short range order.

“Long range order”

In long range order there is a regular pattem of arrangement of particle which represents itself

periodically over the entire solid.

“Short range order :”

In short range order the regular arrangement is periodically repeated over short distances only. On the

basis of the nature of the order, solids can be classified as crystalline solids and amorphous solids.

Crystalline solids - In such solids there is a definite arrangement of particles throughout the

entire there dimentional network of a crystal. These solids thus have ‘long range order’. This three

dimentional arrangement of particle is called crystal lattice (or) space laltice eg. NaCl, KCl, Sugar,

quartz etc.

Amorphous solids - In such solids, particles do not have definite arrangement and thus are

‘short range order’ i.e. portions of regular arrangement are scaltered and in between them

arrangement is disordered. eg. glass

Page 24

24

CHEMISTRY

Reconstruct Your Chemistry With Prince Sir

By

Pri

nce

Sir

Q.12 In a cubic crystal of CsCl (density = 3.97 gm/cm3) the eight corners are occupied by Cl– ions with Cs+

ions at the centre. Calculate the distance between the neighbouring Cs+ and Cl– ions.

Q.13 KF has NaCl structure. What is the distance between K+and F– in KF if density of KF is 2.48 gm/cm3.

Q.14 The composition of a sample of wustite is Fe0.93O1.0. What percentage of iron is present in the form of

Fe(III)?

Q.15 BaTiO3 crystallizes in the prevoskite structure. This structure may be described as a cubic lattice with

barium ions occupying the corner of the unit cell, oxide ions occupying the face-centers and titanium ion

occupying the center of the unit cell.

(a) If titanium is described as occupying holes in BaO lattice, what type of holes does it occupy?

(b) What fraction of this type hole does it occupy?

Q.16 Rbl crystallizes in bcc structure in which each Rb+ is surrounded by eight iodide ions each of radius

2.17 Å. Find the length of one side of RbI unit cell.

Q.17 If NaCl is dopped with 10–3 mol % SrCl2, what is the numbers of cation vacancies?

Q.18 Find the size of largest sphere that will fit in octahedral void in an ideal FCC crystal as a function of

atomic radius 'r'. The insertion of this sphere into void does not distort the FCC lattice. Calculate the

packing fraction of FCC lattice when all the octahedral voids are filled by this sphere.

Q.19 A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.

(a) What is the empirical formula of the compound?

(b) What is the co-ordination number of the Mn ion?

(c) Calculate the edge length of the unit cell, if the radius of Mn ion is 0.65 Å and that of F– ion is 1.36 Å.

Q.20 NaH crystallizes in the same structure as that of NaCl. The edge length of the cubic unit cell of NaH is

4.88 Å.

(a) Calculate the ionic radius of H–, provided the ionic radius of Na+ is 0.95 Å.

(b) Calculate the density of NaH.

Q.21 Metallic gold crystallises in fcc lattice. The length of the cubic unit cell is a = 4.07 Å.

(a) What is the closest distance between gold atoms.

(b) How many “nearest neighbours” does each gold atom have at the distance calculated in (a).

(c) What is the density of gold?

(d) Prove that the packing fraction of gold is 0.74.

Q.22 Ice crystallizes in a hexagonal lattice. At the low temperature at which the structure

was determined, the lattice constants were a = 4.53 Å, and b = 7.60 Å(see figure).

How many molecules are contained in a given unit cell? [density (ice) = 0.92 gm/cm3)]

Page 25

25

CHEMISTRY

By

Pri

nce

Sir

Reconstruct Your Chemistry With Prince Sir

Q.23 Using the data given below, find the type of cubic lattice to which the crystal belongs.

Fe V Pd

a in pm 286 301 388

in gm cm–3 7.86 5.96 12.16

Q.24 Potassium crystallizes in a body-centered cubic lattice with edge length, a = 5.2 Å.

(a) What is the distance between nearest neighbours?

(b) What is the distance between next-nearest neighbours?

(c) How many nearest neighbours does each K atom have?

(d) How many next-nearest neighbours does each K atom have?

(e) What is the calculated density of crystalline potassium?

Q.25 Prove that void space in fluorite structure per unit volume of unit cell is 0.243.

Q.26 A compound formed by elements X & Y, Crystallizes in a cubic structure, where X is at the corners of

the cube and Y is at six face centers. What is the formula of the compound? If side length is 5Å, estimate

the density of the solid assuming atomic weight of X and Y as 60 and 90 respectively.

Q.27 The metal nickel crystallizes in a face centred cubic structure. Its density is 8.9 gm/cm3. Calculate

(a) the length of the edge of the unit cell.

(b) the radius of the nickel atom. [Atomic weight of Ni = 58.89]

Q.28 The olivine series of minerals consists of crystals in which Fe and Mg ions may substitute for each other

causing substitutional impurity defect without changing the volume of the unit cell. In olivine series of

minerals, oxide ion exist as FCC with Si4+ occupying

4

1

th of octahedral voids and divalent ions occupying

4

1

th of tetrahedral voids. The density of forsterite (magnesium silicate) is 3.21 g/cc and that of fayalite

(ferrous silicate )is 4.34 g/cc. Find the formula of forsterite and fayalite minerals and the percentage of

fayalite in an olivine with a density of 3.88 g/cc.

Q.29 The mineral hawleyite, one form of CdS, crystallizes in one of the cubic lattices, with edge length 5.87Å.

The density of hawleyite is 4.63 g cm–3.

(i) In which cubic lattice does hawleyite crystallize?

(ii) Find the Schottky defect in g cm–3.

Q.30 A strong current of trivalent gaseous boron passed through a germanium crystal decreases the density of

the crystal due to part replacement of germanium by boron and due to interstitial vacancies created by

missing Ge atoms. In one such experiment, one gram of germanium is taken and the boron atoms are

found to be 150 ppm by weight, when the density of the Ge crystal decreases by 4%. Calculate the

percentage of missing vacancies due to germanium, which are filled up by boron atoms.

Atomic wt. Ge = 72.6, B = 11

Page 48

48

CHEMISTRY

Reconstruct Your Chemistry With Prince Sir

By

Pri

nce

Sir

Page 49

49

CHEMISTRY

By

Pri

nce

Sir

Reconstruct Your Chemistry With Prince Sir

1

CHEMISTRY

By

Pri

nce

Sir

Reconstruct Your Chemistry With Prince Sir

THE SOLID STATE

THEORY SHEET

Page 2

2

CHEMISTRY

Reconstruct Your Chemistry With Prince Sir

By

Pri

nce

Sir

SOLID STATE

General characterishics of solid states

The following are the characteristic propeties of the solid state

1. They hare definite mass, volume and shape.

2. Intermolecular distance are short.

3. Intermolecular forces are strong.

4. Their constituent particles (atoms/molecules/ions) have fixed positions and can only oscillate

about their mean position .

5. They are incompressible and rigid.

Such solids which hare difinite volume and structure and do not lose their shapes are called true solids

eg. NaCl,KCl, sugar, Fe, Ag, Cu etc.

Whereas solids which lose shapes on long standing and flows under its own weight and get distorted

are called pseudo solids super cooled liquids. e.g. glass.

Ordered arrangement :

In solids there is ordered arrangement of the particles of the solid (atoms/molecules/ions).

This ordered arrangement is of two types

1. Long range order, and 2. Short range order.

“Long range order”

In long range order there is a regular pattem of arrangement of particle which represents itself

periodically over the entire solid.

“Short range order :”

In short range order the regular arrangement is periodically repeated over short distances only. On the

basis of the nature of the order, solids can be classified as crystalline solids and amorphous solids.

Crystalline solids - In such solids there is a definite arrangement of particles throughout the

entire there dimentional network of a crystal. These solids thus have ‘long range order’. This three

dimentional arrangement of particle is called crystal lattice (or) space laltice eg. NaCl, KCl, Sugar,

quartz etc.

Amorphous solids - In such solids, particles do not have definite arrangement and thus are

‘short range order’ i.e. portions of regular arrangement are scaltered and in between them

arrangement is disordered. eg. glass

Page 24

24

CHEMISTRY

Reconstruct Your Chemistry With Prince Sir

By

Pri

nce

Sir

Q.12 In a cubic crystal of CsCl (density = 3.97 gm/cm3) the eight corners are occupied by Cl– ions with Cs+

ions at the centre. Calculate the distance between the neighbouring Cs+ and Cl– ions.

Q.13 KF has NaCl structure. What is the distance between K+and F– in KF if density of KF is 2.48 gm/cm3.

Q.14 The composition of a sample of wustite is Fe0.93O1.0. What percentage of iron is present in the form of

Fe(III)?

Q.15 BaTiO3 crystallizes in the prevoskite structure. This structure may be described as a cubic lattice with

barium ions occupying the corner of the unit cell, oxide ions occupying the face-centers and titanium ion

occupying the center of the unit cell.

(a) If titanium is described as occupying holes in BaO lattice, what type of holes does it occupy?

(b) What fraction of this type hole does it occupy?

Q.16 Rbl crystallizes in bcc structure in which each Rb+ is surrounded by eight iodide ions each of radius

2.17 Å. Find the length of one side of RbI unit cell.

Q.17 If NaCl is dopped with 10–3 mol % SrCl2, what is the numbers of cation vacancies?

Q.18 Find the size of largest sphere that will fit in octahedral void in an ideal FCC crystal as a function of

atomic radius 'r'. The insertion of this sphere into void does not distort the FCC lattice. Calculate the

packing fraction of FCC lattice when all the octahedral voids are filled by this sphere.

Q.19 A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.

(a) What is the empirical formula of the compound?

(b) What is the co-ordination number of the Mn ion?

(c) Calculate the edge length of the unit cell, if the radius of Mn ion is 0.65 Å and that of F– ion is 1.36 Å.

Q.20 NaH crystallizes in the same structure as that of NaCl. The edge length of the cubic unit cell of NaH is

4.88 Å.

(a) Calculate the ionic radius of H–, provided the ionic radius of Na+ is 0.95 Å.

(b) Calculate the density of NaH.

Q.21 Metallic gold crystallises in fcc lattice. The length of the cubic unit cell is a = 4.07 Å.

(a) What is the closest distance between gold atoms.

(b) How many “nearest neighbours” does each gold atom have at the distance calculated in (a).

(c) What is the density of gold?

(d) Prove that the packing fraction of gold is 0.74.

Q.22 Ice crystallizes in a hexagonal lattice. At the low temperature at which the structure

was determined, the lattice constants were a = 4.53 Å, and b = 7.60 Å(see figure).

How many molecules are contained in a given unit cell? [density (ice) = 0.92 gm/cm3)]

Page 25

25

CHEMISTRY

By

Pri

nce

Sir

Reconstruct Your Chemistry With Prince Sir

Q.23 Using the data given below, find the type of cubic lattice to which the crystal belongs.

Fe V Pd

a in pm 286 301 388

in gm cm–3 7.86 5.96 12.16

Q.24 Potassium crystallizes in a body-centered cubic lattice with edge length, a = 5.2 Å.

(a) What is the distance between nearest neighbours?

(b) What is the distance between next-nearest neighbours?

(c) How many nearest neighbours does each K atom have?

(d) How many next-nearest neighbours does each K atom have?

(e) What is the calculated density of crystalline potassium?

Q.25 Prove that void space in fluorite structure per unit volume of unit cell is 0.243.

Q.26 A compound formed by elements X & Y, Crystallizes in a cubic structure, where X is at the corners of

the cube and Y is at six face centers. What is the formula of the compound? If side length is 5Å, estimate

the density of the solid assuming atomic weight of X and Y as 60 and 90 respectively.

Q.27 The metal nickel crystallizes in a face centred cubic structure. Its density is 8.9 gm/cm3. Calculate

(a) the length of the edge of the unit cell.

(b) the radius of the nickel atom. [Atomic weight of Ni = 58.89]

Q.28 The olivine series of minerals consists of crystals in which Fe and Mg ions may substitute for each other

causing substitutional impurity defect without changing the volume of the unit cell. In olivine series of

minerals, oxide ion exist as FCC with Si4+ occupying

4

1

th of octahedral voids and divalent ions occupying

4

1

th of tetrahedral voids. The density of forsterite (magnesium silicate) is 3.21 g/cc and that of fayalite

(ferrous silicate )is 4.34 g/cc. Find the formula of forsterite and fayalite minerals and the percentage of

fayalite in an olivine with a density of 3.88 g/cc.

Q.29 The mineral hawleyite, one form of CdS, crystallizes in one of the cubic lattices, with edge length 5.87Å.

The density of hawleyite is 4.63 g cm–3.

(i) In which cubic lattice does hawleyite crystallize?

(ii) Find the Schottky defect in g cm–3.

Q.30 A strong current of trivalent gaseous boron passed through a germanium crystal decreases the density of

the crystal due to part replacement of germanium by boron and due to interstitial vacancies created by

missing Ge atoms. In one such experiment, one gram of germanium is taken and the boron atoms are

found to be 150 ppm by weight, when the density of the Ge crystal decreases by 4%. Calculate the

percentage of missing vacancies due to germanium, which are filled up by boron atoms.

Atomic wt. Ge = 72.6, B = 11

Page 48

48

CHEMISTRY

Reconstruct Your Chemistry With Prince Sir

By

Pri

nce

Sir

Page 49

49

CHEMISTRY

By

Pri

nce

Sir

Reconstruct Your Chemistry With Prince Sir